Code for course PHY690W High Performance Computing In physics, the Navier – Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of fluid substances. These equations arise from applying Newton's second law to fluid motion, together with the assumption that the fluid stress is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term - hence describing viscous flow. The Pressure – Poisson equation (Poisson equation for pressure) is a derived equation to relate the pressure with momentum equation. It has been derived using the continuity equation as constrain for momentum equation. Adding the partial derivative of x – momentum w.r.t. x and the partial derivative of y – momentum w.r.t. y and then applying the continuity equation yields the Pressure – Poisson equation.
Set the initial parameters.
nx: Number of nodes in the x-direction
ny: Number of nodes in the y-direction
nt: Number of time steps
nit: Number of artificial time steps
vis: Viscosity
rho: Density
Lx: Length in the x-direction
Ly: Length in the y-direction
dx: Grid spacing in the x-direction
dy: Grid spacing in the y-direction
dt: Time-step size
x: Node x-ordinates
y: Node y-ordinates
u: Nodal velocity x-component
v: Nodal velocoty y-component
p: Nodal pressure
un: Time marched velocity x-direction
vn: Time marched velocity y-direction
pn: Temporary pressure for calculations
b: Nodal source term value from pressure
The images below are for the 2-D case.
