turbulence_model.py

# turbulence_model.py

import numpy as np

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)