shock_model.py

# shock_model.py
import numpy as np

class ShockModel:
    def __init__(self, C_viscosity):
        # Initialize the ShockModel with the artificial viscosity coefficient (C_viscosity)
        self.C_viscosity = C_viscosity

    def compute_shock_properties(self, velocity, pressure, density):
        # Implement shock-capturing methods to handle shocks in the flow field
        
        # Compute the speed of sound in the flow
        speed_of_sound = np.sqrt(pressure / density)
        
        # Compute the local Mach number (e.g., magnitude of the velocity divided by the speed of sound)
        local_mach_number = np.linalg.norm(velocity, axis=-1) / speed_of_sound
        
        # Compute the artificial viscosity to capture shock waves
        artificial_viscosity = self.C_viscosity * (grid_size * speed_of_sound) ** 2
        
        # Apply the artificial viscosity to the velocity and pressure fields
        velocity += artificial_viscosity[:, :, np.newaxis] * np.gradient(velocity, axis=(1, 2))
        pressure += artificial_viscosity * np.sum(np.gradient(velocity, axis=1), axis=0)

    def compute_fluxes(self):
        # Compute fluxes for the fluid solver (e.g., mass, momentum, energy)

        # Finite volume method for compressible flow

        # Cell face areas (assuming uniform grid spacing in both x and y directions)
        dx = 1.0  # Grid spacing in the x-direction
        dy = 1.0  # Grid spacing in the y-direction
        cell_face_area_x = dy
        cell_face_area_y = dx

        # Compute the convective fluxes (momentum fluxes) for each cell face
        convective_flux_x = self.density * self.velocity[:, :, 0] * cell_face_area_x
        convective_flux_y = self.density * self.velocity[:, :, 1] * cell_face_area_y

        # Compute the diffusive fluxes (viscous fluxes) for each cell face using the turbulent viscosity
        grad_u = np.gradient(self.velocity, axis=(1, 2))
        diffusive_flux_x = -self.turbulent_viscosity * grad_u[0] * cell_face_area_x
        diffusive_flux_y = -self.turbulent_viscosity * grad_u[1] * cell_face_area_y

        # Compute the total fluxes (momentum fluxes) for each cell face
        total_flux_x = convective_flux_x + diffusive_flux_x
        total_flux_y = convective_flux_y + diffusive_flux_y

        # Apply the fluxes to update the flow field variables using the finite volume method
        delta_t = self.time_step
        self.velocity[:, :, 0] += (delta_t / cell_face_area_x) * (np.roll(total_flux_x, -1, axis=1) - total_flux_x)
        self.velocity[:, :, 1] += (delta_t / cell_face_area_y) * (np.roll(total_flux_y, -1, axis=0) - total_flux_y)

        # For compressible flow, the density and pressure are updated based on mass and momentum fluxes.
        # Note: The specific implementation may vary depending on the numerical scheme and fluid properties.

        # Compute the mass fluxes for each cell face
        mass_flux_x = self.density * self.velocity[:, :, 0] * cell_face_area_x
        mass_flux_y = self.density * self.velocity[:, :, 1] * cell_face_area_y

        # Apply the mass fluxes to update the density field
        self.density += (delta_t / cell_face_area_x) * (np.roll(mass_flux_x, -1, axis=1) - mass_flux_x)
        self.density += (delta_t / cell_face_area_y) * (np.roll(mass_flux_y, -1, axis=0) - mass_flux_y)

        # Compute the energy fluxes for each cell face (assuming an energy equation is included in the fluid solver)
        # energy_flux_x = ...
        # energy_flux_y = ...
        # self.energy += (delta_t / cell_face_area_x) * (np.roll(energy_flux_x, -1, axis=1) - energy_flux_x)
        # self.energy += (delta_t / cell_face_area_y) * (np.roll(energy_flux_y, -1, axis=0) - energy_flux_y)

        # Note: In this example, we have only shown the computation and update of mass and momentum fluxes.
        # For compressible flow, additional steps would be needed to compute energy fluxes and update the energy field.

        # ... (additional implementation specific to your compressible flow model)

    def update_boundary_conditions(self):
        # Update boundary conditions for each time step in the simulation

        # Example: Outflow boundary condition (zero-gradient for pressure)

        # Right boundary (outflow)
        self.pressure[-1, :] = self.pressure[-2, :]  # Zero-gradient for pressure

        # Additional boundary conditions can be implemented based on the problem requirements.
        # For example, specifying inflow, wall, or periodic boundary conditions.

        # Note: The specific implementation of boundary conditions may vary depending on
        # the flow problem, numerical method, and simulation domain characteristics.

    def save_results_to_file(self):
        # Save shock model results to files for post-processing and visualization

        # Create a directory to store shock model results
        if not os.path.exists("shock_model_results"):
            os.makedirs("shock_model_results")

        # Save shock model data at each time step
        for t in range(self.num_time_steps):
            # Save shock model data to a file (e.g., shock properties, shock wave profiles, etc.)
            shock_properties_file = f"shock_model_results/shock_properties_t{t}.npy"
            np.save(shock_properties_file, self.shock_properties)

            # You can add other data to save here, depending on your specific shock model and analysis needs.

# You can implement additional methods and properties specific to your shock model as needed.