fluid_solver.py

# fluid_solver.py
import os
import numpy as np
import matplotlib.pyplot as plt

class FluidSolver:
    def __init__(self, grid_size, time_step, num_time_steps, turbulence_model, shock_model):
        # Initialize the fluid solver with grid size, time step, number of time steps, turbulence model, and shock model
        self.grid_size = grid_size
        self.time_step = time_step
        self.num_time_steps = num_time_steps
        self.turbulence_model = turbulence_model
        self.shock_model = shock_model
        self.initialize_flow_field()

    def initialize_flow_field(self):
        # Set initial conditions for the flow field (e.g., velocity, pressure, density)
        self.velocity = np.zeros((self.grid_size, self.grid_size, 2))
        self.pressure = np.zeros((self.grid_size, self.grid_size))
        self.density = np.ones((self.grid_size, self.grid_size))
        # Initialize turbulence parameters
        self.turbulent_viscosity = np.zeros((self.grid_size, self.grid_size))
        self.turbulence_model.initialize(self.grid_size, self.time_step)

    def set_boundary_conditions(self):
        # Define boundary conditions for the flow field (e.g., inflow, outflow, walls)
        
        # Example: Inflow boundary condition (constant velocity profile)
        inflow_velocity = np.array([1.0, 0.0])  # Inflow velocity vector [u, v]
        self.velocity[0, :, :] = inflow_velocity  # Set constant inflow velocity at the left boundary

        # Example: Outflow boundary condition (zero-gradient)
        self.velocity[-1, :, :] = self.velocity[-2, :, :]  # Zero-gradient for velocity at the right boundary
        self.pressure[-1, :] = self.pressure[-2, :]  # Zero-gradient for pressure at the right boundary

        # Example: Wall boundary condition (no-slip condition)
        self.velocity[:, 0, :] = np.array([0.0, 0.0])  # No-slip condition for velocity at the bottom wall
        self.velocity[:, -1, :] = np.array([0.0, 0.0])  # No-slip condition for velocity at the top wall

        # Additional boundary conditions can be implemented based on the problem requirements
        # (e.g., periodic boundaries, slip conditions, specified pressure gradients, etc.)

    def apply_turbulence_model(self):
        # Implement turbulence modeling to compute turbulent viscosities and resolve turbulent structures
        
        # Example: Large Eddy Simulation (LES) with Smagorinsky-Lilly subgrid-scale model
        
        # Smagorinsky constant (tunable parameter)
        Cs = 0.1
        
        # Compute the local strain rate (e.g., magnitude of the velocity gradient tensor)
        grad_u = np.gradient(self.velocity, axis=(1, 2))
        strain_rate = np.sqrt(2 * np.sum(grad_u**2, axis=-1))
        
        # Compute the grid-filtered velocity gradient tensor
        du_dx = np.gradient(self.velocity[:, :, 0], axis=1)
        du_dy = np.gradient(self.velocity[:, :, 1], axis=0)
        S = np.array([[du_dx, du_dy], [du_dy, -du_dx]])  # Strain rate tensor
        
        # Compute the subgrid-scale (SGS) viscosity using Smagorinsky-Lilly model
        SGS_viscosity = (Cs * self.grid_size * strain_rate) ** 2
        
        # Apply the SGS viscosity to the turbulent viscosity field
        self.turbulent_viscosity = np.maximum(self.turbulent_viscosity, SGS_viscosity)

    def apply_shock_model(self):
        # Implement the numerical methods for modeling shock interactions and resolve shock structures

        # Example: Total Variation Diminishing (TVD) scheme for shock-capturing
        
        # Compute the local Mach number (e.g., magnitude of the velocity divided by the speed of sound)
        speed_of_sound = np.sqrt(self.pressure / self.density)
        local_mach_number = np.linalg.norm(self.velocity, axis=-1) / speed_of_sound
        
        # Compute the artificial viscosity to capture shock waves
        C_viscosity = 0.1  # Tunable parameter for artificial viscosity
        artificial_viscosity = C_viscosity * (self.grid_size * speed_of_sound) ** 2
        
        # Apply artificial viscosity to velocity and pressure fields
        self.velocity += artificial_viscosity[:, :, np.newaxis] * np.gradient(self.velocity, axis=(1, 2))
        self.pressure += artificial_viscosity * np.sum(np.gradient(self.velocity, axis=1), axis=0)

    def update_flow_field(self):
        # Update the flow field variables using the fluid equations, turbulence model, and shock model
        
        # Step 1: Apply turbulence model to compute turbulent viscosities
        self.apply_turbulence_model()
        
        # Step 2: Apply shock model to model shock interactions
        self.apply_shock_model()
        
        # Step 3: Update flow field using finite-difference method and explicit time-stepping
        
        # Time-stepping parameters
        delta_t = self.time_step
        
        # Update velocity
        grad_p = np.gradient(self.pressure, axis=(1, 2))
        self.velocity += delta_t * (-np.gradient(self.velocity[:, :, 0] * self.velocity[:, :, 0], axis=1) / self.density 
                                    - np.gradient(self.velocity[:, :, 0] * self.velocity[:, :, 1], axis=0) / self.density 
                                    - grad_p[0] / self.density 
                                    + self.turbulent_viscosity * np.gradient(self.velocity, axis=(1, 2)))
        
        # Update pressure
        div_u = np.gradient(self.velocity[:, :, 0], axis=1) + np.gradient(self.velocity[:, :, 1], axis=0)
        self.pressure += delta_t * (-self.density * np.sum(np.gradient(self.velocity, axis=1), axis=0) 
                                    - self.density * np.sum(np.gradient(self.velocity, axis=0), axis=1) 
                                    + self.shock_model.compute_heat_release() 
                                    + self.turbulent_viscosity * div_u)
        
        # Update density (assuming incompressible flow)
        self.density = np.ones_like(self.density) * self.density.mean()

    def run_simulation(self):
        # Run the fluid simulation for the specified number of time steps
        
        # Create a directory to store simulation data and results
        if not os.path.exists("simulation_data"):
            os.makedirs("simulation_data")
        
        for t in range(self.num_time_steps):
            # Save the simulation data (velocity, pressure, density) at each time step
            self.save_simulation_data(t)
            
            # Update boundary conditions for the current time step
            self.set_boundary_conditions()
            
            # Update the flow field for the current time step
            self.update_flow_field()
        
        # Save the final simulation results (e.g., flow field, turbulence statistics)
        self.save_simulation_results()

    def save_simulation_data(self, time_step):
        # Save the simulation data at the given time step to a file
        
        velocity_file = f"simulation_data/velocity_t{time_step}.npy"
        pressure_file = f"simulation_data/pressure_t{time_step}.npy"
        density_file = f"simulation_data/density_t{time_step}.npy"
        
        np.save(velocity_file, self.velocity)
        np.save(pressure_file, self.pressure)
        np.save(density_file, self.density)

    def save_simulation_results(self):
        # Save the final simulation results to a file (e.g., turbulence statistics)
        
        # Implement saving additional simulation results if needed
        # Example: Save turbulence statistics to a separate file

        # ... (implementation of saving additional simulation results)

    def get_results(self):
        # Retrieve simulation results (e.g., flow field data, turbulence statistics, shock properties)
        results = {
            'velocity': self.velocity,
            'pressure': self.pressure,
            'density': self.density,
            'turbulent_viscosity': self.turbulent_viscosity,
            # Include additional simulation results if needed
            # 'turbulence_statistics': turbulence_statistics,
            # 'shock_properties': shock_properties,
        }
        return results

class TurbulenceModel:
    def __init__(self, Cs):
        # Initialize the turbulence model with the Smagorinsky constant (Cs)
        self.Cs = Cs

    def initialize(self, grid_size, time_step):
        # Initialize turbulence model parameters (if any) based on grid_size and time_step
        pass

    def compute_turbulent_viscosity(self, velocity, density, turbulent_viscosity):
        # Implement turbulence model to calculate turbulent viscosity
        
        # Compute the local strain rate (e.g., magnitude of the velocity gradient tensor)
        grad_u = np.gradient(velocity, axis=(1, 2))
        strain_rate = np.sqrt(2 * np.sum(grad_u**2, axis=-1))
        
        # Compute the grid-filtered velocity gradient tensor
        du_dx = np.gradient(velocity[:, :, 0], axis=1)
        du_dy = np.gradient(velocity[:, :, 1], axis=0)
        S = np.array([[du_dx, du_dy], [du_dy, -du_dx]])  # Strain rate tensor
        
        # Compute the subgrid-scale (SGS) viscosity using Smagorinsky-Lilly model
        SGS_viscosity = (self.Cs * grid_size * strain_rate) ** 2
        
        # Apply the SGS viscosity to the turbulent viscosity field
        turbulent_viscosity[:, :] = np.maximum(turbulent_viscosity[:, :], SGS_viscosity)

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 incompressible 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 incompressible flow, the density and pressure are assumed to be constant,
        # so the mass and energy fluxes are not explicitly computed and updated.
        # For compressible flow, additional steps would be needed to compute mass and energy fluxes.

        # Note: In this example, we have assumed an incompressible flow solver using the finite volume method.
        # The specific implementation may vary depending on the numerical scheme and fluid properties considered.

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

        # Example: No-slip wall boundary conditions

        # Top wall (y = grid_size - 1)
        self.velocity[:, -1, :] = np.array([0.0, 0.0])  # No-slip condition for velocity

        # Bottom wall (y = 0)
        self.velocity[:, 0, :] = np.array([0.0, 0.0])  # No-slip condition for velocity

        # Left wall (x = 0)
        self.velocity[0, :, :] = np.array([0.0, 0.0])  # No-slip condition for velocity

        # Right wall (x = grid_size - 1)
        self.velocity[-1, :, :] = np.array([0.0, 0.0])  # No-slip condition for velocity

        # Example: Periodic boundary conditions

        # Periodic boundary in the x-direction (left-right boundaries)
        self.velocity[0, :, :] = self.velocity[-2, :, :]  # Copy values from the adjacent cell
        self.velocity[-1, :, :] = self.velocity[1, :, :]  # Copy values from the adjacent cell

        # Periodic boundary in the y-direction (top-bottom boundaries)
        self.velocity[:, 0, :] = self.velocity[:, -2, :]  # Copy values from the adjacent cell
        self.velocity[:, -1, :] = self.velocity[:, 1, :]  # Copy values from the adjacent cell

        # Additional boundary conditions can be implemented based on the problem requirements.
        # For example, specifying inflow, outflow, or pressure 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 simulation results to files for post-processing and visualization

        # Create a directory to store simulation results
        if not os.path.exists("simulation_results"):
            os.makedirs("simulation_results")

        # Save flow field data (velocity, pressure, density) at each time step
        for t in range(self.num_time_steps):
            velocity_file = f"simulation_results/velocity_t{t}.npy"
            pressure_file = f"simulation_results/pressure_t{t}.npy"
            density_file = f"simulation_results/density_t{t}.npy"

            np.save(velocity_file, self.velocity)
            np.save(pressure_file, self.pressure)
            np.save(density_file, self.density)

        # Save additional simulation results (e.g., turbulent viscosity, turbulence statistics, etc.)
        # You can add other data to save here, depending on your specific simulation and analysis needs.

def visualize_results(velocity, pressure, density):
    # Implement functions to visualize the simulation results using Matplotlib

    # Visualize velocity vector plot
    plt.figure(figsize=(8, 6))
    x, y = np.meshgrid(np.arange(velocity.shape[1]), np.arange(velocity.shape[0]))
    plt.quiver(x, y, velocity[:, :, 0], velocity[:, :, 1], scale=10)
    plt.title('Velocity Vector Field')
    plt.xlabel('X')
    plt.ylabel('Y')
    plt.grid(True)
    plt.colorbar()
    plt.show()

    # Visualize pressure contour plot
    plt.figure(figsize=(8, 6))
    plt.contourf(pressure, cmap='viridis')
    plt.title('Pressure Contour')
    plt.xlabel('X')
    plt.ylabel('Y')
    plt.colorbar()
    plt.show()

    # Visualize density plot
    plt.figure(figsize=(8, 6))
    plt.imshow(density, cmap='hot', origin='lower')
    plt.title('Density Plot')
    plt.xlabel('X')
    plt.ylabel('Y')
    plt.colorbar()
    plt.show()

    # You can add additional visualizations based on your specific simulation and analysis needs.

# fluid_solver.py

def analyze_turbulence_statistics(velocity):
    # Implement functions to analyze turbulence statistics from the simulation results

    # Compute turbulent kinetic energy (TKE)
    u = velocity[:, :, 0]
    v = velocity[:, :, 1]
    mean_velocity_magnitude = np.sqrt(u ** 2 + v ** 2)
    tke = 0.5 * (mean_velocity_magnitude ** 2)

    # Compute turbulent intensity
    turbulent_intensity = np.sqrt(2 * tke) / mean_velocity_magnitude

    # You can add more turbulence statistics computations here based on your specific needs.

    # Print or visualize the computed turbulence statistics
    print("Turbulent Kinetic Energy (TKE):")
    print(tke)
    print("Turbulent Intensity:")
    print(turbulent_intensity)

    # You can also plot and analyze the turbulence statistics as needed.

    # Note: The specific turbulence statistics to compute and analyze may vary depending
    # on your research objectives and the information you want to extract from the simulation.

def main():
    # Example usage of the FluidSolver class to set up and run the simulation
    grid_size = 100
    time_step = 0.01
    num_time_steps = 100
    turbulence_model = TurbulenceModel(Cs=0.1)  # Specify the Smagorinsky constant (Cs) for the turbulence model
    shock_model = ShockModel(C_viscosity=0.1)  # Specify the artificial viscosity coefficient (C_viscosity) for the shock model

    fluid_solver = FluidSolver(grid_size, time_step, num_time_steps, turbulence_model, shock_model)
    fluid_solver.run_simulation()
    velocity, pressure, density = fluid_solver.get_results()

    # Visualize the simulation results
    visualize_results(velocity, pressure, density)

    # Analyze turbulence statistics from the simulation results
    analyze_turbulence_statistics(velocity)

if __name__ == "__main__":
    main()