diff --git a/doc/ambit_doc.pdf b/doc/ambit_doc.pdf index 05897228..3b800779 100644 Binary files a/doc/ambit_doc.pdf and b/doc/ambit_doc.pdf differ diff --git a/doc/ambit_doc.tex b/doc/ambit_doc.tex index 2986f3cb..5bb78ba9 100644 --- a/doc/ambit_doc.tex +++ b/doc/ambit_doc.tex @@ -158,7 +158,7 @@ \section{Preface} In the following, a brief description of the supported problem types is given, including the strong and weak form of the underlying equations as well as the discrete assembled systems that are solved.\\ -Examples of input files for the respective problem types can be found in the folder \verb\ambit/testing\. +Examples of input files for the respective problem types can be found in the folder \verb\doc/examples\ (with detailed setup descriptions) or amogst the test cases in the folder \verb\tests\. %\begin{figure}[!htp] %\centering @@ -168,14 +168,16 @@ \section{Preface} \section{Solid mechanics} --- problem type: \verb\solid\\\ +-- Example: \verb\doc/examples/solid\\\ --- solid mechanics are formulated in a Total Lagrangian frame +-- Problem type: \verb\solid\\\ + +-- Solid mechanics are formulated in a Total Lagrangian frame \subsection{Strong form} \subsubsection{Displacement-based} --- primary variable: displacement $\bs{u}$ +-- Primary variable: displacement $\bs{u}$ \begin{alignat}{3} \bs{\nabla}_{0} \cdot \bs{P}(\bs{u},\bs{v}(\bs{u})) + \hat{\bs{b}}_{0} &= \rho_{0} \bs{a}(\bs{u}) \quad &&\text{in} \; \mathit{\Omega}_{0} \times [0, T], \label{eq:divP} \\ \bs{u} &= \hat{\bs{u}} \quad &&\text{on} \; \mathit{\Gamma}_{0}^{\mathrm{D}} \times [0, T], \label{eq:bc_u}\\ @@ -185,7 +187,7 @@ \subsubsection{Displacement-based} \end{alignat} \subsubsection{Incompressible mechanics} --- primary variables: displacement $\bs{u}$ and pressure $p$ +-- Primary variables: displacement $\bs{u}$ and pressure $p$ \begin{alignat}{3} \bs{\nabla}_{0} \cdot \bs{P}(\bs{u},p,\bs{v}(\bs{u})) + \hat{\bs{b}}_{0} &= \rho_{0} \bs{a}(\bs{u}) \quad &&\text{in} \; \mathit{\Omega}_{0} \times [0, T], \label{eq:divP} \\ J(\bs{u})-1 &= 0 \quad &&\text{in} \; \mathit{\Omega}_{0} \times [0, T], \label{eq:J} \\ @@ -200,21 +202,21 @@ \subsubsection{Incompressible mechanics} \subsection{Weak form} \subsubsection{Displacement-based} --- primary variable: displacement $\bs{u}$\\ +-- Primary variable: displacement $\bs{u}$\\ -- Principal of Virtual Work: \begin{align} r(\bs{u};\delta\bs{u}) := \delta \mathcal{W}_{\mathrm{kin}}(\bs{u};\delta\bs{u}) + \delta \mathcal{W}_{\mathrm{int}}(\bs{u};\delta\bs{u}) - \delta \mathcal{W}_{\mathrm{ext}}(\bs{u};\delta\bs{u}) = 0, \quad \forall \; \delta\bs{u}\label{eq:res_u_solid} \end{align} --- kinetic virtual work: +-- Kinetic virtual work: \begin{align} \delta \mathcal{W}_{\mathrm{kin}}(\bs{u};\delta\bs{u}) &= \int\limits_{\Om_{0}} \rho_{0}\,\bs{a}(\bs{u}) \cdot \delta\bs{u} \,\mathrm{d}V \label{eq:deltaWkin} \end{align} --- internal virtual work: +-- Internal virtual work: \begin{align} \delta \mathcal{W}_{\mathrm{int}}(\bs{u};\delta\bs{u}) &= \int\limits_{\Om_{0}} \bs{P}(\bs{u},\bs{v}(\bs{u})) : \bs{\nabla}_{0} \delta\bs{u} \,\mathrm{d}V \label{eq:deltaWint} \end{align} --- external virtual work:\\ +-- External virtual work:\\ \begin{itemize} \item conservative Neumann load: \begin{align} @@ -248,36 +250,47 @@ \subsubsection{Displacement-based} \end{itemize} +-- Discrete linear system +\begin{align} +\left. \bs{\mathsf{K}}_{uu} \right|_{n+1}^{k} \Delta\bs{\mathsf{u}}_{n+1}^{k+1}=-\left. \ROP_{u} \right|_{n+1}^{k} \label{eq:lin_sys_solid} +\end{align} + \subsubsection{Incompressible mechanics: 2-field displacement and pressure variables} --- primary variables: displacement $\bs{u}$ and pressure $p$ +-- Primary variables: displacement $\bs{u}$ and pressure $p$ \begin{align} r_u(\bs{u},p;\delta\bs{u}) &:= \delta \mathcal{W}_{\mathrm{kin}}(\bs{u};\delta\bs{u}) + \delta \mathcal{W}_{\mathrm{int}}(\bs{u},p;\delta\bs{u}) - \delta \mathcal{W}_{\mathrm{ext}}(\bs{u};\delta\bs{u}) = 0, \quad \forall \; \delta\bs{u} \label{eq:res_u_solid_incomp}\\ r_p(\bs{u};\delta p) &:= \delta \mathcal{W}_{\mathrm{pres}}(\bs{u};\delta p) = 0, \quad \forall \; \delta p \end{align} --- kinetic virtual work: (\ref{eq:deltaWkin})\\ --- internal virtual work: +-- Kinetic virtual work: (\ref{eq:deltaWkin})\\ +-- Internal virtual work: \begin{align} \delta \mathcal{W}_{\mathrm{int}}(\bs{u},p;\delta\bs{u}) &= \int\limits_{\Om_{0}} \bs{P}(\bs{u},p,\bs{v}(\bs{u})) : \bs{\nabla}_{0} \delta\bs{u} \,\mathrm{d}V \label{eq:deltaWint_incomp} \end{align} --- pressure virtual work: +-- Pressure virtual work: \begin{align} \delta \mathcal{W}_{\mathrm{pres}}(\bs{u};\delta p) &= \int\limits_{\Om_{0}} (J(\bs{u}) - 1) \,\delta p \,\mathrm{d}V \label{eq:deltaWpres} \end{align} +-- Discrete linear system +\begin{align} +\begin{bmatrix} \bs{\mathsf{K}}_{uu} & \bs{\mathsf{K}}_{up} \\ \\ \bs{\mathsf{K}}_{pu} & \zerom \end{bmatrix}_{n+1}^{k}\begin{bmatrix} \Delta\bs{\mathsf{u}} \\ \\ \Delta\bs{\mathsf{p}} \end{bmatrix}_{n+1}^{k+1}=-\begin{bmatrix} \ROP_{u} \\ \\ \ROP_{p} \end{bmatrix}_{n+1}^{k} \label{eq:lin_sys_solid_incomp} +\end{align} \section{Fluid mechanics} \subsection{Eulerian reference frame} --- problem type: \verb\fluid\\\ +-- Example: \verb\doc/examples/fluid\\\ --- incompressible Navier-Stokes equations in Eulerian reference frame\\ +-- Problem type: \verb\fluid\\\ + +-- Incompressible Navier-Stokes equations in Eulerian reference frame\\ \subsubsection{Strong Form} --- primary variables: velocity $\bs{v}$ and pressure $p$ +-- Primary variables: velocity $\bs{v}$ and pressure $p$ \begin{alignat}{3} \bs{\nabla} \cdot \bs{\sigma}(\bs{v},p) + \hat{\bs{b}} &= \rho\left(\frac{\partial\bs{v}}{\partial t} + (\bs{\nabla}\bs{v})\,\bs{v}\right) \quad &&\text{in} \; \mathit{\Om}_t \times [0, T], \label{eq:divsigma_ns} \\ \bs{\nabla}\cdot \bs{v} &= 0 \quad &&\text{in} \; \mathit{\Om}_t \times [0, T],\label{eq:divv_ns}\\ @@ -292,7 +305,7 @@ \subsubsection{Strong Form} \end{align} \subsubsection{Weak Form} --- primary variables: velocity $\bs{v}$ and pressure $p$\\ +-- Primary variables: velocity $\bs{v}$ and pressure $p$\\ -- Principle of Virtual Power \begin{align} @@ -300,23 +313,23 @@ \subsubsection{Weak Form} r_p(\bs{v};\delta p) &:= \delta \mathcal{P}_{\mathrm{pres}}(\bs{v};\delta p), \quad \forall \; \delta p \label{eq:res_p_fluid} \end{align} --- kinetic virtual power: +-- Kinetic virtual power: \begin{align} \delta \mathcal{P}_{\mathrm{kin}}(\bs{v};\delta\bs{v}) = \int\limits_{\Om_t} \rho\left(\frac{\partial\bs{v}}{\partial t} + (\bs{\nabla}\bs{v})\,\bs{v}\right) \cdot \delta\bs{v} \,\mathrm{d}v \end{align} --- internal virtual power: +-- Internal virtual power: \begin{align} \delta \mathcal{P}_{\mathrm{int}}(\bs{v},p;\delta\bs{v}) = \int\limits_{\Om_t} \bs{\sigma}(\bs{v},p) : \bs{\nabla} \delta\bs{v} \,\mathrm{d}v \end{align} --- pressure virtual power: +-- Pressure virtual power: \begin{align} \delta \mathcal{P}_{\mathrm{pres}}(\bs{v};\delta p) = \int\limits_{\Om_t} (\bs{\nabla}\cdot\bs{v})\,\delta p\,\mathrm{d}v \end{align} --- external virtual power:\\ +-- External virtual power:\\ \begin{itemize} \item conservative Neumann load: \begin{align} @@ -336,53 +349,53 @@ \subsubsection{Stabilization}\label{subsubsec:stab} Streamline-upwind Petrov-Galerkin/pressure-stabilizing Petrov-Galerkin (SUPG/PSPG) methods are implemented, either using the full or a reduced scheme\\ Full scheme according to \cite{tezduyar2000}: \verb\supg_pspg\:\\ --- velocity residual operator (\ref{eq:res_v_fluid}) is augmented with the following terms: +-- Velocity residual operator (\ref{eq:res_v_fluid}) is augmented with the following terms: \begin{align} r_v \leftarrow r_v &+ \frac{1}{\rho}\int\limits_{\Om_t} \tau_{\mathrm{SUPG}}\,(\bs{\nabla}\delta\bs{v})\,\bs{v} \cdot \left[\rho\left(\frac{\partial \bs{v}}{\partial t} + (\bs{\nabla}\bs{v})\,\bs{v}\right) - \bs{\nabla} \cdot \bs{\sigma}(\bs{v},p)\right]\,\mathrm{d}v \\ & + \int\limits_{\Om_t} \tau_{\mathrm{LSIC}}\,\rho\,(\bs{\nabla}\cdot\delta\bs{v})(\bs{\nabla}\cdot\bs{v})\,\mathrm{d}v \end{align} --- pressure residual operator (\ref{eq:res_p_fluid}) is augmented with the following terms: +-- Pressure residual operator (\ref{eq:res_p_fluid}) is augmented with the following terms: \begin{align} r_p \leftarrow r_p &+ \frac{1}{\rho}\int\limits_{\Om_t} \tau_{\mathrm{PSPG}}\,(\bs{\nabla}\delta p) \cdot \left[\rho\left(\frac{\partial \bs{v}}{\partial t} + (\bs{\nabla}\bs{v})\,\bs{v}\right) - \bs{\nabla} \cdot \bs{\sigma}(\bs{v},p)\right]\,\mathrm{d}v \end{align}\\ Reduced scheme (optimized for first-order): \verb\supg_pspg2\:\\ --- velocity residual operator (\ref{eq:res_v_fluid}) is augmented with the following terms: +-- Velocity residual operator (\ref{eq:res_v_fluid}) is augmented with the following terms: \begin{align} r_v \leftarrow r_v &+ \int\limits_{\Om_t} d_1\,((\bs{\nabla}\bs{v})\,\bs{v}) \cdot (\bs{\nabla}\delta\bs{v})\,\bs{v}\,\mathrm{d}v \\ & + \int\limits_{\Om_t} d_2\,(\bs{\nabla}\cdot\bs{v}) (\bs{\nabla}\cdot\delta\bs{v})\,\mathrm{d}v\\ &+ \int\limits_{\Om_t} d_3\,(\bs{\nabla}p) \cdot (\bs{\nabla}\delta\bs{v})\,\bs{v}\,\mathrm{d}v \end{align} --- pressure residual operator (\ref{eq:res_p_fluid}) is augmented with the following terms: +-- Pressure residual operator (\ref{eq:res_p_fluid}) is augmented with the following terms: \begin{align} r_p \leftarrow r_p &+ \frac{1}{\rho}\int\limits_{\Om_t} d_1\,((\bs{\nabla}\bs{v})\,\bs{v}) \cdot (\bs{\nabla}\delta p)\,\mathrm{d}v \\ &+ \frac{1}{\rho}\int\limits_{\Om_t} d_3\,(\bs{\nabla}p) \cdot (\bs{\nabla}\delta p)\,\mathrm{d}v \end{align} --- discrete linear system +-- Discrete linear system \begin{align} \begin{bmatrix} \bs{\mathsf{K}}_{vv} & \bs{\mathsf{K}}_{vp} \\ \\ \bs{\mathsf{K}}_{pv} & \bs{\mathsf{K}}_{pp} \end{bmatrix}_{n+1}^{k}\begin{bmatrix} \Delta\bs{\mathsf{v}} \\ \\ \Delta\bs{\mathsf{p}} \end{bmatrix}_{n+1}^{k+1}=-\begin{bmatrix} \ROP_{v} \\ \\ \ROP_{p} \end{bmatrix}_{n+1}^{k} \label{eq:lin_sys_fluid} \end{align} --- note that $\bs{\mathsf{K}}_{pp}$ is zero for Taylor-Hood elements (without stabilization) +-- Note that $\bs{\mathsf{K}}_{pp}$ is zero for Taylor-Hood elements (without stabilization) \subsection{ALE reference frame} --- problem type: \verb\fluid_ale\\\ +-- Problem type: \verb\fluid_ale\\\ --- incompressible Navier-Stokes equations in Arbitrary Lagrangian Eulerian (ALE) reference frame\\ +-- Incompressible Navier-Stokes equations in Arbitrary Lagrangian Eulerian (ALE) reference frame\\ -- ALE domain problem deformation governed by linear-elastic or nonlinear hyperelastic solid, displacement field $\bs{d}$\\ --- fluid mechanics formulated with respect to the reference frame, using ALE deformation gradient $\bs{F}(\bs{d}) = \bs{I} + \bs{\nabla}_0\bs{d}$ and its determinant, $J(\bs{d})=\det \bs{F}(\bs{d})$\\ +-- Fluid mechanics formulated with respect to the reference frame, using ALE deformation gradient $\bs{F}(\bs{d}) = \bs{I} + \bs{\nabla}_0\bs{d}$ and its determinant, $J(\bs{d})=\det \bs{F}(\bs{d})$\\ \subsubsection{ALE problem} --- displacement-based quasi-static solid\\ +-- Displacement-based quasi-static solid\\ --- primary variable: domain displacement $\bs{d}$\\ +-- Primary variable: domain displacement $\bs{d}$\\ --- strong form: +-- Strong form: \begin{alignat}{3} \bs{\nabla}_{0} \cdot \bs{\sigma}^{\mathrm{G}}(\bs{d}) &= \bs{0} \quad &&\text{in} \; \mathit{\Om}_0, \label{eq:divsigma_ale} \\ \bs{d} &= \hat{\bs{d}} \quad &&\text{on} \; \mathit{\Gm}_0^{\mathrm{D}}, \label{eq:dbc_ale} @@ -399,7 +412,7 @@ \subsubsection{ALE problem} \subsubsection{Strong form} --- primary variables: velocity $\bs{v}$ and pressure $p$ +-- Primary variables: velocity $\bs{v}$ and pressure $p$ \begin{alignat}{3} \bs{\nabla}_{0} \bs{\sigma}(\bs{v},\bs{d},p) : \bs{F}^{-\mathrm{T}} + \hat{\bs{b}} &= \rho\left(\frac{\partial\bs{v}}{\partial t} + (\bs{\nabla}_0\bs{v}\,\bs{F}^{-1})\,\bs{v}\right) \quad &&\text{in} \; \mathit{\Om}_0 \times [0, T], \label{eq:divsigma_ns} \\ \bs{\nabla}_{0}\bs{v} : \bs{F}^{-\mathrm{T}} &= 0 \quad &&\text{in} \; \mathit{\Om}_0 \times [0, T],\label{eq:divv_ns}\\ @@ -415,7 +428,7 @@ \subsubsection{Strong form} \subsubsection{Weak form} --- primary variables: velocity $\bs{v}$, pressure $p$, and domain displacement $\bs{d}$\\ +-- Primary variables: velocity $\bs{v}$, pressure $p$, and domain displacement $\bs{d}$\\ -- Principle of Virtual Power \begin{align} @@ -423,23 +436,23 @@ \subsubsection{Weak form} r_p(\bs{v},\bs{d};\delta p) &:= \delta \mathcal{P}_{\mathrm{pres}}(\bs{v},\bs{d};\delta p), \quad \forall \; \delta p \label{eq:res_p_fluid_ale} \end{align} --- kinetic virtual power: +-- Kinetic virtual power: \begin{align} \delta \mathcal{P}_{\mathrm{kin}}(\bs{v},\bs{d};\delta\bs{v}) = \int\limits_{\Om_0} J \rho\left(\frac{\partial\bs{v}}{\partial t} + (\bs{\nabla}_{0}\bs{v}\,\bs{F}^{-1})\,\bs{v}\right) \cdot \delta\bs{v} \,\mathrm{d}V \end{align} --- internal virtual power: +-- Internal virtual power: \begin{align} \delta \mathcal{P}_{\mathrm{int}}(\bs{v},p,\bs{d};\delta\bs{v}) = \int\limits_{\Om_0} J\bs{\sigma}(\bs{v},p,\bs{d}) : \bs{\nabla}_{0} \delta\bs{v}\,\bs{F}^{-1} \,\mathrm{d}V \end{align} --- pressure virtual power: +-- Pressure virtual power: \begin{align} \delta \mathcal{P}_{\mathrm{pres}}(\bs{v},\bs{d};\delta p) = \int\limits_{\Om_0} J\,\bs{\nabla}_{0}\bs{v} : \bs{F}^{-\mathrm{T}}\delta p\,\mathrm{d}V \end{align} --- external virtual power:\\ +-- External virtual power:\\ \begin{itemize} \item conservative Neumann load: \begin{align} @@ -458,32 +471,32 @@ \subsubsection{Weak form} \subsubsection{Stabilization} ALE forms of stabilization introduced in sec. \ref{subsubsec:stab}\\ \verb\supg_pspg\:\\ --- velocity residual operator (\ref{eq:res_v_fluid_ale}) is augmented with the following terms: +-- Velocity residual operator (\ref{eq:res_v_fluid_ale}) is augmented with the following terms: \begin{align} r_v \leftarrow r_v &+ \frac{1}{\rho}\int\limits_{\Om_0}J\, \tau_{\mathrm{SUPG}}\,(\bs{\nabla}_0\delta\bs{v}\,\bs{F}^{-1})\,\bs{v}\;\cdot \\ & \qquad\quad \cdot\left[\rho\left(\frac{\partial \bs{v}}{\partial t} + (\bs{\nabla}_0\bs{v}\,\bs{F}^{-1})\,(\bs{v}-\bs{w})\right) - \bs{\nabla}_{0} \bs{\sigma}(\bs{v},\bs{d},p) : \bs{F}^{-\mathrm{T}}\right]\,\mathrm{d}V \\ & + \int\limits_{\Om_0}J\, \tau_{\mathrm{LSIC}}\,\rho\,(\bs{\nabla}_{0}\delta\bs{v} : \bs{F}^{-\mathrm{T}})(\bs{\nabla}_{0}\bs{v} : \bs{F}^{-\mathrm{T}})\,\mathrm{d}V \end{align} --- pressure residual operator (\ref{eq:res_p_fluid_ale}) is augmented with the following terms: +-- Pressure residual operator (\ref{eq:res_p_fluid_ale}) is augmented with the following terms: \begin{align} r_p \leftarrow r_p &+ \frac{1}{\rho}\int\limits_{\Om_0}J\, \tau_{\mathrm{PSPG}}\,(\bs{F}^{-\mathrm{T}}\bs{\nabla}_{0}\delta p) \;\cdot \\ & \qquad\quad \cdot \left[\rho\left(\frac{\partial \bs{v}}{\partial t} + (\bs{\nabla}_0\bs{v}\,\bs{F}^{-1})\,(\bs{v}-\bs{w})\right) - \bs{\nabla}_{0} \bs{\sigma}(\bs{v},\bs{d},p) : \bs{F}^{-\mathrm{T}}\right]\,\mathrm{d}V \end{align}\\ \verb\supg_pspg2\:\\ --- velocity residual operator (\ref{eq:res_v_fluid_ale}) is augmented with the following terms: +-- Velocity residual operator (\ref{eq:res_v_fluid_ale}) is augmented with the following terms: \begin{align} r_v \leftarrow r_v &+ \int\limits_{\Om_0} J\,d_1\,((\bs{\nabla}_{0}\bs{v}\,\bs{F}^{-1})\,(\bs{v}-\bs{w})) \cdot (\bs{\nabla}_{0}\delta\bs{v}\,\bs{F}^{-1})\,\bs{v}\,\mathrm{d}V \\ & + \int\limits_{\Om_0} J\,d_2\,(\bs{\nabla}_{0}\bs{v} : \bs{F}^{-\mathrm{T}}) (\bs{\nabla}_{0}\delta\bs{v} : \bs{F}^{-\mathrm{T}})\,\mathrm{d}V\\ &+ \int\limits_{\Om_0} J\,d_3\,(\bs{F}^{-\mathrm{T}}\bs{\nabla}_{0}p) \cdot (\bs{\nabla}_{0}\delta\bs{v}\,\bs{F}^{-1})\,\bs{v}\,\mathrm{d}V \end{align} --- pressure residual operator (\ref{eq:res_p_fluid_ale}) is augmented with the following terms: +-- Pressure residual operator (\ref{eq:res_p_fluid_ale}) is augmented with the following terms: \begin{align} r_p \leftarrow r_p &+ \frac{1}{\rho}\int\limits_{\Om_0} J\,d_1\,((\bs{\nabla}_{0}\bs{v}\,\bs{F}^{-1})\,(\bs{v}-\bs{w})) \cdot (\bs{F}^{-\mathrm{T}}\bs{\nabla}_{0}\delta p)\,\mathrm{d}V \\ &+ \frac{1}{\rho}\int\limits_{\Om_0} J\,d_3\,(\bs{F}^{-\mathrm{T}}\bs{\nabla}_{0}p) \cdot (\bs{F}^{-\mathrm{T}}\bs{\nabla}_{0}\delta p)\,\mathrm{d}V \end{align} --- discrete linear system +-- Discrete linear system \begin{align} \begin{bmatrix} \bs{\mathsf{K}}_{vv} & \bs{\mathsf{K}}_{vp} & \bs{\mathsf{K}}_{vd} \\ \\ \bs{\mathsf{K}}_{pv} & \bs{\mathsf{K}}_{pp} & \bs{\mathsf{K}}_{pd} \\ \\ \bs{\mathsf{K}}_{dv} & \zerom & \bs{\mathsf{K}}_{dd} \end{bmatrix}_{n+1}^{k}\begin{bmatrix} \Delta\bs{\mathsf{v}} \\ \\ \Delta\bs{\mathsf{p}} \\ \\ \Delta\bs{\mathsf{d}} \end{bmatrix}_{n+1}^{k+1}=-\begin{bmatrix} \ROP_{v} \\ \\ \ROP_{p} \\ \\ \ROP_{d} \end{bmatrix}_{n+1}^{k} \label{eq:lin_sys_fluid_ale} \end{align} @@ -493,58 +506,62 @@ \section{Coupling} \subsection{Solid + 0D flow} --- problem type: \verb\solid_flow0d\\\ +-- Example: \verb\doc/examples/solid_flow0d\\\ + +-- Problem type: \verb\solid_flow0d\\\ -- (\ref{eq:res_u_solid}) or (\ref{eq:res_u_solid_incomp}) augmented by following term: \begin{align} r_u \leftarrow r_u + \int\limits_{\Gm_0^{\fS\mhyphen \mathrm{0d}}}\!\mathit{\Lambda}\,J\bs{F}^{-\mathrm{T}}\bs{n}_0\cdot\delta\bs{u}\,\mathrm{d}A \end{align} --- multiplier constraint +-- Multiplier constraint \begin{align} r_{\lambda}(\mathit{\Lambda},\bs{u};\delta\mathit{\Lambda}):= \left(\int\limits_{\Gm_0^{\mathrm{\fS\mhyphen 0d}}}\! J\bs{F}^{-\mathrm{T}}\bs{n}_{0}\cdot\bs{v}(\bs{u})\,\mathrm{d}A - Q^{\mathrm{0d}}(\mathit{\Lambda})\right) \delta\mathit{\Lambda}, \quad \forall \; \delta\mathit{\Lambda} \end{align} --- discrete linear system for displacement-based solid +-- Discrete linear system for displacement-based solid \begin{align} \begin{bmatrix} \bs{\mathsf{K}}_{uu} & \bs{\mathsf{K}}_{u\lmzi} \\ \\ \bs{\mathsf{K}}_{\lmzi u} & \bs{\mathsf{K}}_{\lmzi\lmzi}\end{bmatrix}_{n+1}^{k}\begin{bmatrix} \Delta\bs{\mathsf{u}} \\ \\ \Delta\LMZ \end{bmatrix}_{n+1}^{k+1}=-\begin{bmatrix} \ROP_{u} \\ \\ \ROP_{\lmzi}\end{bmatrix}_{n+1}^{k} \label{eq:lin_sys_solid_0d} \end{align} --- discrete linear system for incompressible solid +-- Discrete linear system for incompressible solid \begin{align} \begin{bmatrix} \bs{\mathsf{K}}_{uu} & \bs{\mathsf{K}}_{up} & \bs{\mathsf{K}}_{u\lmzi} \\ \\ \bs{\mathsf{K}}_{pu} & \zerom & \zerom \\ \\ \bs{\mathsf{K}}_{\lmzi u} & \zerom & \bs{\mathsf{K}}_{\lmzi\lmzi}\end{bmatrix}_{n+1}^{k}\begin{bmatrix} \Delta\bs{\mathsf{u}} \\ \\ \Delta\bs{\mathsf{p}} \\ \\ \Delta\LMZ \end{bmatrix}_{n+1}^{k+1}=-\begin{bmatrix} \ROP_{u} \\ \\ \ROP_{p} \\ \\ \ROP_{\lmzi}\end{bmatrix}_{n+1}^{k} \label{eq:lin_sys_solid_incomp_0d} \end{align} \subsection{Fluid + 0D flow} --- problem type: \verb\fluid_flow0d\\\ +-- Example: \verb\doc/examples/fluid_flow0d\\\ + +-- Problem type: \verb\fluid_flow0d\\\ -- (\ref{eq:res_v_fluid}) augmented by following term: \begin{align} r_v \leftarrow r_v + \int\limits_{\Gm_t^{\fF\mhyphen \mathrm{0d}}}\!\mathit{\Lambda}\,\bs{n}\cdot\delta\bs{v}\,\mathrm{d}a \end{align} --- multiplier constraint +-- Multiplier constraint \begin{align} r_{\lambda}(\mathit{\Lambda},\bs{v};\delta\mathit{\Lambda}):= \left(\int\limits_{\Gm_t^{\mathrm{\fF\mhyphen 0d}}}\! \bs{n}\cdot\bs{v}\,\mathrm{d}a - Q^{\mathrm{0d}}(\mathit{\Lambda})\right) \delta\mathit{\Lambda}, \quad \forall \; \delta\mathit{\Lambda} \end{align} --- discrete linear system +-- Discrete linear system \begin{align} \begin{bmatrix} \bs{\mathsf{K}}_{vv} & \bs{\mathsf{K}}_{vp} & \bs{\mathsf{K}}_{v\lmzi} \\ \\ \bs{\mathsf{K}}_{pv} & \bs{\mathsf{K}}_{pp} & \zerom \\ \\ \bs{\mathsf{K}}_{\lmzi v} & \zerom & \bs{\mathsf{K}}_{\lmzi\lmzi}\end{bmatrix}_{n+1}^{k}\begin{bmatrix} \Delta\bs{\mathsf{v}} \\ \\ \Delta\bs{\mathsf{p}} \\ \\ \Delta\LMZ \end{bmatrix}_{n+1}^{k+1}=-\begin{bmatrix} \ROP_{v} \\ \\ \ROP_{p} \\ \\ \ROP_{\lmzi}\end{bmatrix}_{n+1}^{k} \label{eq:lin_sys_fluid_0d} \end{align} \subsection{ALE fluid + 0D flow} --- problem type: \verb\fluid_ale_flow0d\\\ +-- Problem type: \verb\fluid_ale_flow0d\\\ -- (\ref{eq:res_v_fluid_ale}) augmented by following term: \begin{align} r_v \leftarrow r_v + \int\limits_{\Gm_0^{\fF\mhyphen \mathrm{0d}}}\!\mathit{\Lambda}\,J\bs{F}^{-\mathrm{T}}\bs{n}_{0}\cdot\delta\bs{v}\,\mathrm{d}A \end{align} --- multiplier constraint +-- Multiplier constraint \begin{align} r_{\lambda}(\mathit{\Lambda},\bs{v},\bs{d};\delta\mathit{\Lambda}):= \left(\int\limits_{\Gm_0^{\mathrm{\fF\mhyphen 0d}}}\! J\bs{F}^{-\mathrm{T}}\bs{n}_{0}\cdot(\bs{v}-\bs{w}(\bs{d}))\,\mathrm{d}A - Q^{\mathrm{0d}}(\mathit{\Lambda})\right) \delta\mathit{\Lambda}, \quad \forall \; \delta\mathit{\Lambda} @@ -552,7 +569,7 @@ \subsection{ALE fluid + 0D flow} with $\bs{w}(\bs{d})=\frac{\mathrm{d}\bs{d}}{\mathrm{d}t}$\\ --- discrete linear system +-- Discrete linear system \begin{align} \begin{bmatrix} \bs{\mathsf{K}}_{vv} & \bs{\mathsf{K}}_{vp} & \bs{\mathsf{K}}_{v\lmzi} & \bs{\mathsf{K}}_{vd} \\ \\ \bs{\mathsf{K}}_{pv} & \bs{\mathsf{K}}_{pp} & \zerom & \bs{\mathsf{K}}_{pd} \\ \\ \bs{\mathsf{K}}_{\lmzi v} & \zerom & \bs{\mathsf{K}}_{\lmzi \lmzi} & \bs{\mathsf{K}}_{\lmzi d} \\ \\ \bs{\mathsf{K}}_{dv} & \zerom & \zerom & \bs{\mathsf{K}}_{dd} \end{bmatrix}_{n+1}^{k}\begin{bmatrix} \Delta\bs{\mathsf{v}} \\ \\ \Delta\bs{\mathsf{p}} \\ \\ \Delta\LMZ \\ \\ \Delta\bs{\mathsf{d}} \end{bmatrix}_{n+1}^{k+1}=-\begin{bmatrix} \ROP_{v} \\ \\ \ROP_{p} \\ \\ \ROP_{\lmzi} \\ \\ \ROP_{d}\end{bmatrix}_{n+1}^{k} \label{eq:lin_sys_fluid_ale_0d} \end{align} @@ -560,16 +577,16 @@ \subsection{ALE fluid + 0D flow} \subsection{Fluid-Solid Interaction (FSI)} --- problem type: \verb\fsi\\\ +-- Problem type: \verb\fsi\\\ --- not yet fully implemented! +-- Not yet fully implemented! \subsection{Fluid-Solid Interaction (FSI) + 0D flow} --- problem type: \verb\fsi_flow0d\\\ +-- Problem type: \verb\fsi_flow0d\\\ --- not yet fully implemented! +-- Not yet fully implemented! % %\section{Fluid-reduced-solid-interaction (FrSI)} @@ -726,7 +743,9 @@ \subsection{Fluid-Solid Interaction (FSI) + 0D flow} \section{0D flow: Lumped parameter models} --- problem type: \verb\flow0d\\\ +-- Example: \verb\doc/examples/flow0d\\\ + +-- Problem type: \verb\flow0d\\\ \subsection{``Syspul'' circulation model} diff --git a/doc/examples/flow0d/syspul_plots.png b/doc/examples/flow0d/syspul_plots.png deleted file mode 100644 index e0d9659f..00000000 Binary files a/doc/examples/flow0d/syspul_plots.png and /dev/null differ diff --git a/doc/examples/flow0d/syspul_results.png b/doc/examples/flow0d/syspul_results.png new file mode 100644 index 00000000..3a6ce16a Binary files /dev/null and b/doc/examples/flow0d/syspul_results.png differ diff --git a/doc/examples/flow0d/syspul_setup.png b/doc/examples/flow0d/syspul_setup.png new file mode 100644 index 00000000..f3595a60 Binary files /dev/null and b/doc/examples/flow0d/syspul_setup.png differ diff --git a/doc/examples/fluid/README.md b/doc/examples/fluid/README.md new file mode 100644 index 00000000..805b5379 --- /dev/null +++ b/doc/examples/fluid/README.md @@ -0,0 +1,18 @@ +# README # + +This example shows how to set up 2D fluid flow in a channel around a rigid obstacle, using Taylor-Hood elements. + + +### Instructions ### + +Run the simulation, either in one of the provided Docker containers or using your own FEniCSx/Ambit installation, using the command +``` +mpiexec -n 1 python3 fluid_channel.py +``` +It is fully sufficient to use one core (mpiexec -n 1) for the presented setup. + +Open the results file results_channel_velocity.xdmf and results_channel_pressure.xdmf in Paraview, and visualize the velocity as well as the pressure over time. + +### Solution + +The figure shows the velocity magnitude (top) as well as the pressure (bottom part) at the end of the simulation. diff --git a/doc/examples/fluid/channel_results.png b/doc/examples/fluid/channel_results.png new file mode 100644 index 00000000..0d6e13fb Binary files /dev/null and b/doc/examples/fluid/channel_results.png differ diff --git a/doc/examples/fluid/channel_setup.png b/doc/examples/fluid/channel_setup.png new file mode 100644 index 00000000..6c083b81 Binary files /dev/null and b/doc/examples/fluid/channel_setup.png differ diff --git a/doc/examples/fluid/fluid_channel.py b/doc/examples/fluid/fluid_channel.py new file mode 100644 index 00000000..b14049d8 --- /dev/null +++ b/doc/examples/fluid/fluid_channel.py @@ -0,0 +1,97 @@ +#!/usr/bin/env python3 + +""" +A 2D fluid dynamics problem of incompressible Navier-Stokes channel flow around a rigid cylindrical obstacle. +""" + +import ambit_fe +import numpy as np +from pathlib import Path + + +def main(): + + basepath = str(Path(__file__).parent.absolute()) + + """ + Parameters for input/output + """ + IO_PARAMS = {# problem type 'fluid': incompressible Navier-Stokes flow + 'problem_type' : 'fluid', + # the meshes for the domain and boundary topology are specified separately + 'mesh_domain' : basepath+'/input/channel_domain.xdmf', + 'mesh_boundary' : basepath+'/input/channel_boundary.xdmf', + # at which step frequency to write results (set to 0 in order to not write any output) + 'write_results_every' : 1, + # where to write the output to + 'output_path' : basepath+'/tmp/', + # which results to write + 'results_to_write' : ['velocity','pressure'], + # the 'midfix' for all simulation result file names: will be results__.xdmf/.h5 + 'simname' : 'fluid_channel'} + + """ + Parameters for the linear and nonlinear solution schemes + """ + SOLVER_PARAMS = {'solve_type' : 'direct', + #'direct_solver' : 'superlu_dist', # no idea why, but mumps does not seem to like this system in parallel... + 'tol_res' : [1e-8, 1e-8], + 'tol_inc' : [1e-8, 1e-8]} + + """ + Parameters for the fluid mechanics time integration scheme, plus the global time parameters + """ + TIME_PARAMS = {'maxtime' : 0.5, + 'numstep' : 100, + 'timint' : 'ost', + 'theta_ost' : 1.0} + + """ + Finite element parameters: Taylor-Hood elements with quadratic approximation for the velocity and linear approximation for the pressure + """ + FEM_PARAMS = {# the order of the finite element ansatz functions for the velocity and pressure + 'order_vel' : 2, + 'order_pres' : 1, + # the degree of the quadrature scheme + 'quad_degree' : 5} + + """ + Constitutive parameters for the fluid: let's use parameters of glycerine + """ + MATERIALS = { 'MAT1' : {'newtonian' : {'mu' : 1420.0e-6}, # kPa s + 'inertia' : {'rho' : 1.26e-6}} } # kg/mm^3 + + + """ + Time curves, e.g. any prescribed time-controlled/-varying loads or functions + """ + class time_curves(): + + def tc1(self, t): + + Umax = 1e3 + + t_ramp = 0.3 + + return Umax * 0.5*(1.-np.cos(np.pi*t/t_ramp)) * (t < t_ramp) + Umax * (t >= t_ramp) + + + """ + Boundary conditions: ids: 1: inflow, 2: bottom wall, 3: axial outflow, 4: top wall - 5: obstacle + Wall and obstactle are fixed, in-flow velocity is prescribed, outflow is free ("Neumann zero") + """ + BC_DICT = { 'dirichlet' : [{'id' : [1], 'dir' : 'x', 'curve' : 1}, + {'id' : [2,4,5], 'dir' : 'all', 'val' : 0.}]} + + + # problem setup + problem = ambit_fe.ambit_main.Ambit(IO_PARAMS, TIME_PARAMS, SOLVER_PARAMS, FEM_PARAMS, MATERIALS, BC_DICT, time_curves=time_curves()) + + # solve time-dependent problem + problem.solve_problem() + + + +if __name__ == "__main__": + + main() diff --git a/doc/examples/fluid/input/channel_boundary.xdmf b/doc/examples/fluid/input/channel_boundary.xdmf new file mode 100644 index 00000000..60956bd3 --- 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--git a/doc/examples/fluid_flow0d/README.md b/doc/examples/fluid_flow0d/README.md new file mode 100644 index 00000000..360846c7 --- /dev/null +++ b/doc/examples/fluid_flow0d/README.md @@ -0,0 +1,18 @@ +# README # + +This example demonstrates how to couple 3D fluid flow to a 0D lumped-parameter model. + + +### Instructions ### + +Run the simulation, either in one of the provided Docker containers or using your own FEniCSx/Ambit installation, using the command +``` +mpiexec -n 1 python3 fluid_flow0d_pipe.py +``` +It is fully sufficient to use one core (mpiexec -n 1) for the presented setup. + +Open the results file results_fluid_flow0d_pipe_velocity.xdmf in Paraview, and visualize the velocity over time. + +### Solution + +The figure shows the velocity streamlines and magnitude at the end of the simulation. diff --git a/doc/examples/fluid_flow0d/fluid_flow0d_pipe.py b/doc/examples/fluid_flow0d/fluid_flow0d_pipe.py new file mode 100644 index 00000000..a01f0148 --- /dev/null +++ b/doc/examples/fluid_flow0d/fluid_flow0d_pipe.py @@ -0,0 +1,166 @@ +#!/usr/bin/env python3 + +""" +A fluid mechanics problem of incompressible Navier-Stokes flow through a pipe, which is separated by an internal valve (always closed). A 0D model of two 2-element Windkessels in series +bypasses flow from the one region to the other. The setup is rather academic but should illustrate how 0D models can be used to connect independent fluid regions. +""" + +import ambit_fe +import numpy as np +from pathlib import Path + + +def main(): + + basepath = str(Path(__file__).parent.absolute()) + + + """ + Parameters for input/output + """ + IO_PARAMS = {# problem type 'fluid_flow0d' indicates a coupling of the individual problems 'fluid' and 'flow0d' + 'problem_type' : 'fluid_flow0d', + # For this setup in order to model an internal valve/Dirichlet boundary, we need to duplicate the pressure space at this boundary; otherwise, + # any Dirichlet condition on the velocity inside the domain will not prevent fluid to experience a pressure gradient across that plane, leading + # to unphysical de- and acceleration of fluid infront of and behind the valve. + # This duplicate pressure space can only be achieved using the mixed Dolfinx branch, which is installed in the Ambit devenv Docker container. + # In the future, this functionality is expected to be merged into the main branch of Dolfinx (as it has been announced). + 'USE_MIXED_DOLFINX_BRANCH' : True, + # indicate which domain IDs (specified in 'mesh_domain' file) should be split (creating a submesh) + 'duplicate_mesh_domains': [1,2], + # the meshes for the domain and boundary topology are specified separately + 'mesh_domain' : basepath+'/input/pipe_domain.xdmf', + 'mesh_boundary' : basepath+'/input/pipe_boundary.xdmf', + 'order_fib_input' : 1, + # at which step frequency to write results (set to 0 in order to not write any output) + 'write_results_every' : 1, + # where to write the output to + 'output_path' : basepath+'/tmp/', + # which results to write: here, all 3D fields need to be specified, while the 0D model results are output nevertheless + 'results_to_write' : ['velocity','pressure'], + # the 'midfix' for all simulation result file names: will be results__.xdmf/.h5/.txt + 'simname' : 'fluid_flow0d_pipe'} + + """ + Parameters for the linear and nonlinear solution schemes + """ + SOLVER_PARAMS = {# this specifies which linear solution strategy to use; since this problem has less than 10'000 degrees of freedom, we comfortably can use a direct solver + 'solve_type' : 'direct', + # residual and increment tolerances: first value for the fluid mechanics problem (momentum balance and continuity), second value for the 3D-0D constraint problem + 'tol_res' : [1e-8, 1e-8, 1e-6], + 'tol_inc' : [1e-8, 1e-8, 1e-6], + # subsolver tolerances for the 0D model solver: tolerances for residual and increment + 'subsolver_params' : {'tol_res' : 1e-6, + 'tol_inc' : 1e-6}} + + """ + Parameters for the solid mechanics time integration scheme, plus the global time parameters + """ + TIME_PARAMS_FLUID = {# the maximum simulation time - here 0.2 seconds + 'maxtime' : 0.2, + # the number of time steps which the simulation time is divided into - so here, a time step lasts 0.2/100 s = 0.002 s = 2 ms + 'numstep' : 100, + # the fluid mechanics time integration scheme: we use a One-Step-theta scheme with theta=1, hence a Backward Euler + 'timint' : 'ost', + 'theta_ost' : 1.0} + + """ + Parameters for the 0D model time integration scheme + """ + TIME_PARAMS_FLOW0D = {# the 0D model time integration scheme: we use a One-Step-theta method with theta = 0.5, which corresponds to the trapezoidal rule + 'timint' : 'ost', + 'theta_ost' : 0.5, + # do initial time step using backward scheme (theta=1), to avoid fluctuations for quantities whose d/dt is zero + 'initial_backwardeuler' : True, + # the initial conditions of the 0D ODE model + 'initial_conditions' : {'q_in_0' : 0.0, # initial in-flux + 'q_d_0' : 0.0, # initial distal flux + 'p_d_0' : 0.0, # initial distal pressure + 'q_out_0' : 0.0}} # initial out-flux + + """ + Parameters for the 0D model + """ + MODEL_PARAMS_FLOW0D = {# the type of 0D model: 'CRLinoutlink' refers to two Windkessel models in series (each with compliance C, resistance R, and inertance L), + # connecting an in- to an out-flow (note that the IN-flow into the 0D model is provided by the OUT-flow of the fluid domain) + 'modeltype' : 'CRLinoutlink', + # the parameters of the 0D model + 'parameters' : {'C_in' : 1e3, # in-flow compliance (proximal to fluid out-flow surface) + 'R_in' : 160e-6, # in-flow resistance (proximal to fluid out-flow surface) + 'L_in' : 0.0, # in-flow inertance (proximal to fluid out-flow surface) + 'C_out' : 0.01, # out-flow compliance (proximal to fluid in-flow surface) + 'R_out' : 1e-6, # out-flow resistance (proximal to fluid in-flow surface) + 'L_out' : 0.0}} # out-flow inertance (proximal to fluid in-flow surface) + """ + Finite element parameters + """ + FEM_PARAMS = {# the order of the finite element ansatz functions for the velocity and pressure + 'order_vel' : 1, + 'order_pres' : 1, + # the quadrature degree + 'quad_degree' : 5, + # stabilization scheme: we make use of a reduced scheme ('supg_pspg2') optimized for first-order elements, which does not have + # the inertia term in the strong residual + 'stabilization' : {'scheme' : 'supg_pspg2', # scheme name + 'vscale' : 1e3, # velocity scale + 'dscales' : [1.,1.,1.], # stabilization parameter scales + 'symmetric' : True}} # modification to make the effective stress symmetric + + """ + 3D-0D coupling parameters + """ + COUPLING_PARAMS = {# the surfaces IDs which couple to the 0D world + 'surface_ids' : [[4],[6]], + # the coupling type: 'monolithic_lagrange' here is a more general scheme that enforces equality of 3D and 0D fluxes/volumes via (Lagrange) multipliers, outsourcing the 0D + # solve to a sub-solver in each nonlinear iteration, whereas 'monolithic_direct' would embed the 0D system of equations directly into the monolithic system matrix (which + # would be only available for solid mechanics) + 'coupling_type' : 'monolithic_lagrange', + # for 'monolithic_lagrange', we need the pressures to be the exchanged quantities between 3D and 0D world (being the Lagrange multipliers) + 'coupling_quantity' : ['pressure','pressure'], + # the coupling variables which are enforced between 3D and 0D: can be volume or flux + 'variable_quantity' : ['flux','flux'], + # flux scaling: in the 0D world, flux variables are always positively defined, while an in-flux into the fluid domain is against the unit outward surface normal; + # so, we need to scale in-fluxes by -1 + 'cq_factor' : [1.,-1.]} + + """ + Constitutive parameters for the 3D fluid: we have two separate domains, but assign the same parameters to them + """ + MATERIALS_FLUID = { # newtonian fluids with parameters for blood - kg-mm-s system + 'MAT1' : {'newtonian' : {'mu' : 4.0e-6}, # kPa s + 'inertia' : {'rho' : 1.025e-6}}, # kg/mm^3 + 'MAT2' : {'newtonian' : {'mu' : 4.0e-6}, # kPa s + 'inertia' : {'rho' : 1.025e-6}}} # kg/mm^3 + + + """ + Time curves, e.g. any prescribed time-controlled/-varying loads or functions + """ + class time_curves(): + + def tc1(self, t): + vmax = 1e3 # mm/s + T=0.4 # s + return 0.5*vmax*(1.-np.cos(2.*np.pi*t/T)) + + + """ + Boundary conditions: ids: 1,5: lateral wall - 2: inflow, 5: axial outflow, 6: top outflow, 3: valve + Inflow is prescribed, lateral wall as well as "valve" (inner domain separator plane) are fixed, a stabilized Neumann condition is applied to the outflow. + """ + BC_DICT = { 'dirichlet' : [{'id' : [2], 'dir' : 'z', 'curve' : 1}, # inflow + {'id' : [1,5], 'dir' : 'all', 'val' : 0.}, # lateral wall + {'id' : [3], 'dir' : 'all', 'val' : 0.}], # inner (valve) plane + 'stabilized_neumann' : [{'id' : [4,6,7], 'par1' : 0.205e-6, 'par2' : 1.}] } # par1 should be ~ 0.2*rho + + # Pass parameters to Ambit to set up the problem + problem = ambit_fe.ambit_main.Ambit(IO_PARAMS, [TIME_PARAMS_FLUID, TIME_PARAMS_FLOW0D], SOLVER_PARAMS, FEM_PARAMS, [MATERIALS_FLUID, MODEL_PARAMS_FLOW0D], BC_DICT, time_curves=time_curves(), coupling_params=COUPLING_PARAMS) + + # Call the Ambit solver to solve the problem + problem.solve_problem() + + + +if __name__ == "__main__": + + main() diff --git a/doc/examples/fluid_flow0d/input/pipe_boundary.xdmf b/doc/examples/fluid_flow0d/input/pipe_boundary.xdmf new file mode 100644 index 00000000..6f5fbe38 --- /dev/null +++ b/doc/examples/fluid_flow0d/input/pipe_boundary.xdmf @@ -0,0 +1,9803 @@ + + + + + + 15.0 -3.673940397442e-15 0.0 + 15.0 -3.673940397442e-15 50.0 + 7.5 -12.99038105676 33.333333333333 + 15.0 -3.673940397442e-15 100.0 + 7.5 12.990381056767 66.666666666667 + 14.711779206048 2.9263548302419 0.0 + 13.858192987669 5.7402514854763 0.0 + 12.472044184538 8.333553495294 0.0 + 10.606601717798 10.606601717798 0.0 + 8.3335534952941 12.472044184538 0.0 + 5.7402514854764 13.858192987669 0.0 + 2.926354830242 14.711779206048 0.0 + 3.089450676424e-14 15.0 0.0 + -2.9263548302419 14.711779206048 0.0 + -5.7402514854763 13.858192987669 0.0 + -8.333553495294 12.472044184538 0.0 + -10.606601717798 10.606601717798 0.0 + -12.472044184538 8.3335534952941 0.0 + -13.858192987669 5.7402514854764 0.0 + 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differ diff --git a/doc/examples/solid_flow0d/heart_syspul_results.png b/doc/examples/solid_flow0d/heart_syspul_results.png new file mode 100644 index 00000000..5379f2fa Binary files /dev/null and b/doc/examples/solid_flow0d/heart_syspul_results.png differ diff --git a/doc/examples/solid_flow0d/heart_syspul_setup.png b/doc/examples/solid_flow0d/heart_syspul_setup.png new file mode 100644 index 00000000..3ac6eb6b Binary files /dev/null and b/doc/examples/solid_flow0d/heart_syspul_setup.png differ diff --git a/src/ambit_fe/ale/ale_main.py b/src/ambit_fe/ale/ale_main.py index c5d02e6f..82c83f95 100644 --- a/src/ambit_fe/ale/ale_main.py +++ b/src/ambit_fe/ale/ale_main.py @@ -123,7 +123,7 @@ def __init__(self, io_params, time_params, fem_params, constitutive_models, bc_d self.numdof = self.d.vector.getSize() # initialize ALE time-integration class - self.ti = timeintegration.timeintegration_ale(time_params, fem_params, time_curves, self.t_init, self.comm) + self.ti = timeintegration.timeintegration_ale(time_params, fem_params, time_curves=time_curves, t_init=self.t_init, dim=self.dim, comm=self.comm) # initialize kinematics_constitutive class self.ki = ale_kinematics_constitutive.kinematics(self.dim) diff --git a/src/ambit_fe/boundaryconditions.py b/src/ambit_fe/boundaryconditions.py index 9e60cb97..20ff40b6 100644 --- a/src/ambit_fe/boundaryconditions.py +++ b/src/ambit_fe/boundaryconditions.py @@ -51,7 +51,7 @@ def dirichlet_bcs(self, bcdict, V): if 'curve' in d.keys(): assert('val' not in d.keys()) - load = expression.template_vector() + load = expression.template_vector(dim=self.dim) if d['dir'] == 'all': curve_x, curve_y, curve_z = d['curve'][0], d['curve'][1], d['curve'][2] else: curve_x, curve_y, curve_z = d['curve'], d['curve'], d['curve'] load.val_x, load.val_y, load.val_z = self.ti.timecurves(curve_x)(self.ti.t_init), self.ti.timecurves(curve_y)(self.ti.t_init), self.ti.timecurves(curve_z)(self.ti.t_init) @@ -107,7 +107,7 @@ def dirichlet_vol(self, bcdict, V): if 'curve' in d.keys(): assert('val' not in d.keys()) assert('file' not in d.keys()) - load = expression.template_vector() + load = expression.template_vector(dim=self.dim) if d['dir'] == 'all': curve_x, curve_y, curve_z = d['curve'][0], d['curve'][1], d['curve'][2] else: curve_x, curve_y, curve_z = d['curve'], d['curve'], d['curve'] load.val_x, load.val_y, load.val_z = self.ti.timecurves(curve_x)(self.ti.t_init), self.ti.timecurves(curve_y)(self.ti.t_init), self.ti.timecurves(curve_z)(self.ti.t_init) @@ -162,7 +162,7 @@ def neumann_bcs(self, bcdict, V, V_real, ds_, F=None, funcs_to_update=None, func if 'curve' in n.keys(): assert('val' not in n.keys()) - load = expression.template_vector() + load = expression.template_vector(dim=self.dim) load.val_x, load.val_y, load.val_z = self.ti.timecurves(n['curve'][0])(self.ti.t_init), self.ti.timecurves(n['curve'][1])(self.ti.t_init), self.ti.timecurves(n['curve'][2])(self.ti.t_init) func.interpolate(load.evaluate) funcs_to_update_vec.append({func : [self.ti.timecurves(n['curve'][0]), self.ti.timecurves(n['curve'][1]), self.ti.timecurves(n['curve'][2])]}) @@ -202,7 +202,7 @@ def neumann_bcs(self, bcdict, V, V_real, ds_, F=None, funcs_to_update=None, func if 'curve' in n.keys(): assert('val' not in n.keys()) - load = expression.template_vector() + load = expression.template_vector(dim=self.dim) load.val_x, load.val_y, load.val_z = self.ti.timecurves(n['curve'][0])(self.ti.t_init), self.ti.timecurves(n['curve'][1])(self.ti.t_init), self.ti.timecurves(n['curve'][2])(self.ti.t_init) func.interpolate(load.evaluate) funcs_to_update_vec.append({func : [self.ti.timecurves(n['curve'][0]), self.ti.timecurves(n['curve'][1]), self.ti.timecurves(n['curve'][2])]}) @@ -262,7 +262,7 @@ def neumann_prestress_bcs(self, bcdict, V, V_real, ds_, funcs_to_update=None, fu if 'curve' in n.keys(): assert('val' not in n.keys()) - load = expression.template_vector() + load = expression.template_vector(dim=self.dim) load.val_x, load.val_y, load.val_z = self.ti.timecurves(n['curve'][0])(self.ti.t_init), self.ti.timecurves(n['curve'][1])(self.ti.t_init), self.ti.timecurves(n['curve'][2])(self.ti.t_init) func.interpolate(load.evaluate) funcs_to_update_vec.append({func : [self.ti.timecurves(n['curve'][0]), self.ti.timecurves(n['curve'][1]), self.ti.timecurves(n['curve'][2])]}) @@ -413,7 +413,7 @@ def bodyforce(self, bcdict, V, V_real, dx_, funcs_to_update=None): func, func_dir = fem.Function(V_real), fem.Function(V) # direction needs to be set - driection = expression.template_vector() + driection = expression.template_vector(dim=self.dim) dir_x, dir_y, dir_z = b['dir'][0], b['dir'][1], b['dir'][2] dir_norm = np.sqrt(dir_x**2. + dir_y**2. + dir_z**2.) driection.val_x, driection.val_y, driection.val_z = dir_x/dir_norm, dir_y/dir_norm, dir_z/dir_norm diff --git a/src/ambit_fe/expression.py b/src/ambit_fe/expression.py index ece092e6..b88ad869 100644 --- a/src/ambit_fe/expression.py +++ b/src/ambit_fe/expression.py @@ -20,15 +20,25 @@ def evaluate(self, x): # template vector expression class class template_vector: - def __init__(self): + def __init__(self, dim=3): + + self.dim = dim + self.val_x = 0.0 self.val_y = 0.0 self.val_z = 0.0 def evaluate(self, x): - return ( np.full(x.shape[1], self.val_x), - np.full(x.shape[1], self.val_y), - np.full(x.shape[1], self.val_z) ) + + if self.dim==3: + return ( np.full(x.shape[1], self.val_x), + np.full(x.shape[1], self.val_y), + np.full(x.shape[1], self.val_z) ) + elif self.dim==2: + return ( np.full(x.shape[1], self.val_x), + np.full(x.shape[1], self.val_y) ) + else: + raise ValueError("Unknown dimension, %i" % (self.dim)) # dummy function diff --git a/src/ambit_fe/fluid/fluid_main.py b/src/ambit_fe/fluid/fluid_main.py index 970c0752..ff34e218 100644 --- a/src/ambit_fe/fluid/fluid_main.py +++ b/src/ambit_fe/fluid/fluid_main.py @@ -283,7 +283,7 @@ def __init__(self, io_params, time_params, fem_params, constitutive_models, bc_d self.numdof = self.v.vector.getSize() + self.p.vector.getSize() # initialize fluid time-integration class - self.ti = timeintegration.timeintegration_fluid(time_params, fem_params, time_curves=time_curves, t_init=self.t_init, comm=self.comm) + self.ti = timeintegration.timeintegration_fluid(time_params, fem_params, time_curves=time_curves, t_init=self.t_init, dim=self.dim, comm=self.comm) # get time factors self.timefac_m, self.timefac = self.ti.timefactors() diff --git a/src/ambit_fe/solid/solid_main.py b/src/ambit_fe/solid/solid_main.py index 100fca9f..ae45b02d 100644 --- a/src/ambit_fe/solid/solid_main.py +++ b/src/ambit_fe/solid/solid_main.py @@ -237,7 +237,7 @@ def __init__(self, io_params, time_params, fem_params, constitutive_models, bc_d self.mor_params = mor_params # initialize solid time-integration class - self.ti = timeintegration.timeintegration_solid(time_params, fem_params, time_curves, self.t_init, self.comm) + self.ti = timeintegration.timeintegration_solid(time_params, fem_params, time_curves=time_curves, t_init=self.t_init, dim=self.dim, comm=self.comm) # get time factors self.timefac_m, self.timefac = self.ti.timefactors() diff --git a/src/ambit_fe/timeintegration.py b/src/ambit_fe/timeintegration.py index a5e73332..61e76fe7 100644 --- a/src/ambit_fe/timeintegration.py +++ b/src/ambit_fe/timeintegration.py @@ -18,7 +18,7 @@ class timeintegration(): - def __init__(self, time_params, time_curves=None, t_init=0., comm=None): + def __init__(self, time_params, time_curves=None, t_init=0., dim=3, comm=None): try: self.timint = time_params['timint'] except: self.timint = 'static' @@ -31,6 +31,8 @@ def __init__(self, time_params, time_curves=None, t_init=0., comm=None): self.time_curves = time_curves self.t_init = t_init + self.dim = dim + self.comm = comm # time-dependent functions to update @@ -62,7 +64,7 @@ def print_prestress_step(self, N, t, Nmax, lsp, ni=0, li=0, wt=0): def set_time_funcs(self, t, funcs, funcs_vec): for m in funcs_vec: - load = expression.template_vector() + load = expression.template_vector(dim=self.dim) load.val_x, load.val_y, load.val_z = list(m.values())[0][0](t), list(m.values())[0][1](t), list(m.values())[0][2](t) list(m.keys())[0].interpolate(load.evaluate) list(m.keys())[0].vector.ghostUpdate(addv=PETSc.InsertMode.INSERT, mode=PETSc.ScatterMode.FORWARD) @@ -118,8 +120,8 @@ def timecurves(self, cnum): # Solid mechanics time integration class class timeintegration_solid(timeintegration): - def __init__(self, time_params, fem_params, time_curves=None, t_init=0., comm=None): - timeintegration.__init__(self, time_params, time_curves=time_curves, t_init=t_init, comm=comm) + def __init__(self, time_params, fem_params, time_curves=None, t_init=0., dim=3, comm=None): + timeintegration.__init__(self, time_params, time_curves=time_curves, t_init=t_init, dim=dim, comm=comm) if self.timint == 'genalpha': @@ -303,8 +305,8 @@ def compute_genalpha_params(self, rho_inf): # cf. Chung and Hulbert (1993) # Fluid mechanics time integration class class timeintegration_fluid(timeintegration): - def __init__(self, time_params, fem_params, time_curves=None, t_init=0., comm=None): - timeintegration.__init__(self, time_params, time_curves=time_curves, t_init=t_init, comm=comm) + def __init__(self, time_params, fem_params, time_curves=None, t_init=0., dim=3, comm=None): + timeintegration.__init__(self, time_params, time_curves=time_curves, t_init=t_init, dim=dim, comm=comm) if self.timint == 'ost':