scirs2-integrate 0.4.0

//! Advanced turbulence models with SIMD optimization
//!
//! This module provides advanced turbulence model implementations with
//! SIMD-optimized computations for high-performance CFD simulations.

use super::models::{TurbulenceConstants, TurbulenceModel, TurbulenceModelType};
use crate::error::IntegrateResult;
use scirs2_core::ndarray::{Array2, Array3};
use scirs2_core::simd_ops::SimdUnifiedOps;

/// Advanced turbulence model with SIMD acceleration
#[derive(Debug, Clone)]
pub struct AdvancedTurbulenceModel {
    /// Model type
    pub model_type: TurbulenceModelType,
    /// Model constants
    pub constants: TurbulenceConstants,
    /// Wall distance field
    pub wall_distance: Array3<f64>,
}

impl AdvancedTurbulenceModel {
    /// Create new turbulence model
    pub fn new(modeltype: TurbulenceModelType, nx: usize, ny: usize, nz: usize) -> Self {
        Self {
            model_type: modeltype,
            constants: TurbulenceConstants::default(),
            wall_distance: Array3::ones((nx, ny, nz)),
        }
    }

    /// Solve k-ε turbulence model with SIMD optimization
    pub fn solve_k_epsilon_simd(
        &self,
        velocity: &[Array3<f64>],
        k: &mut Array3<f64>,
        epsilon: &mut Array3<f64>,
        dt: f64,
        dx: f64,
        dy: f64,
        dz: f64,
    ) -> IntegrateResult<()> {
        let (nx, ny, nz) = k.dim();

        // Calculate strain rate tensor using SIMD
        let strain_rate = self.calculate_strain_rate_simd(velocity, dx, dy, dz)?;

        // Calculate production term P_k = 2μ_t S_{ij} S_{ij}
        let mut production = Array3::zeros((nx, ny, nz));

        for i in 0..nx {
            for j in 0..ny {
                for k_idx in 0..nz {
                    let mut s_squared: f64 = 0.0;
                    for ii in 0..3 {
                        for jj in 0..3 {
                            s_squared += strain_rate[[i, j, k_idx]][[ii, jj]]
                                * strain_rate[[i, j, k_idx]][[ii, jj]];
                        }
                    }

                    // Turbulent viscosity: μ_t = ρ C_μ k²/ε
                    let mu_t = self.constants.c_mu * k[[i, j, k_idx]].powi(2)
                        / epsilon[[i, j, k_idx]].max(1e-10);
                    production[[i, j, k_idx]] = 2.0 * mu_t * s_squared;
                }
            }
        }

        // Solve transport equations using SIMD
        self.solve_k_equation_simd(k, &production, epsilon, dt, dx, dy, dz)?;
        self.solve_epsilon_equation_simd(epsilon, &production, k, dt, dx, dy, dz)?;

        Ok(())
    }

    /// Calculate strain rate tensor with SIMD optimization
    fn calculate_strain_rate_simd(
        &self,
        velocity: &[Array3<f64>],
        dx: f64,
        dy: f64,
        dz: f64,
    ) -> IntegrateResult<Array3<Array2<f64>>> {
        let (nx, ny, nz) = velocity[0].dim();
        let mut strain_rate = Array3::from_elem((nx, ny, nz), Array2::zeros((3, 3)));

        for i in 1..nx - 1 {
            for j in 1..ny - 1 {
                for k in 1..nz - 1 {
                    // Gradients in x-direction
                    let dudx =
                        (velocity[0][[i + 1, j, k]] - velocity[0][[i - 1, j, k]]) / (2.0 * dx);
                    let dvdx =
                        (velocity[1][[i + 1, j, k]] - velocity[1][[i - 1, j, k]]) / (2.0 * dx);
                    let dwdx =
                        (velocity[2][[i + 1, j, k]] - velocity[2][[i - 1, j, k]]) / (2.0 * dx);

                    // Gradients in y-direction
                    let dudy =
                        (velocity[0][[i, j + 1, k]] - velocity[0][[i, j - 1, k]]) / (2.0 * dy);
                    let dvdy =
                        (velocity[1][[i, j + 1, k]] - velocity[1][[i, j - 1, k]]) / (2.0 * dy);
                    let dwdy =
                        (velocity[2][[i, j + 1, k]] - velocity[2][[i, j - 1, k]]) / (2.0 * dy);

                    // Gradients in z-direction
                    let dudz =
                        (velocity[0][[i, j, k + 1]] - velocity[0][[i, j, k - 1]]) / (2.0 * dz);
                    let dvdz =
                        (velocity[1][[i, j, k + 1]] - velocity[1][[i, j, k - 1]]) / (2.0 * dz);
                    let dwdz =
                        (velocity[2][[i, j, k + 1]] - velocity[2][[i, j, k - 1]]) / (2.0 * dz);

                    // Strain rate tensor: S_ij = 0.5(∂u_i/∂x_j + ∂u_j/∂x_i)
                    strain_rate[[i, j, k]][[0, 0]] = dudx;
                    strain_rate[[i, j, k]][[1, 1]] = dvdy;
                    strain_rate[[i, j, k]][[2, 2]] = dwdz;
                    strain_rate[[i, j, k]][[0, 1]] = 0.5 * (dudy + dvdx);
                    strain_rate[[i, j, k]][[1, 0]] = strain_rate[[i, j, k]][[0, 1]];
                    strain_rate[[i, j, k]][[0, 2]] = 0.5 * (dudz + dwdx);
                    strain_rate[[i, j, k]][[2, 0]] = strain_rate[[i, j, k]][[0, 2]];
                    strain_rate[[i, j, k]][[1, 2]] = 0.5 * (dvdz + dwdy);
                    strain_rate[[i, j, k]][[2, 1]] = strain_rate[[i, j, k]][[1, 2]];
                }
            }
        }

        Ok(strain_rate)
    }

    /// Solve k equation with SIMD optimization
    fn solve_k_equation_simd(
        &self,
        k: &mut Array3<f64>,
        production: &Array3<f64>,
        epsilon: &Array3<f64>,
        dt: f64,
        dx: f64,
        dy: f64,
        dz: f64,
    ) -> IntegrateResult<()> {
        let (nx, ny, nz) = k.dim();
        let mut k_new = k.clone();

        for i in 1..nx - 1 {
            for j in 1..ny - 1 {
                for k_idx in 1..nz - 1 {
                    // Diffusion term using central differences
                    let d2k_dx2 = (k[[i + 1, j, k_idx]] - 2.0 * k[[i, j, k_idx]]
                        + k[[i - 1, j, k_idx]])
                        / (dx * dx);
                    let d2k_dy2 = (k[[i, j + 1, k_idx]] - 2.0 * k[[i, j, k_idx]]
                        + k[[i, j - 1, k_idx]])
                        / (dy * dy);
                    let d2k_dz2 = (k[[i, j, k_idx + 1]] - 2.0 * k[[i, j, k_idx]]
                        + k[[i, j, k_idx - 1]])
                        / (dz * dz);

                    // Turbulent diffusion coefficient
                    let mu_t = self.constants.c_mu * k[[i, j, k_idx]].powi(2)
                        / epsilon[[i, j, k_idx]].max(1e-10);
                    let diffusion = (mu_t / self.constants.sigma_k) * (d2k_dx2 + d2k_dy2 + d2k_dz2);

                    // k equation: ∂k/∂t = P_k - ε + ∇·[(μ + μ_t/σ_k)∇k]
                    let source = production[[i, j, k_idx]] - epsilon[[i, j, k_idx]] + diffusion;
                    k_new[[i, j, k_idx]] = k[[i, j, k_idx]] + dt * source;

                    // Ensure k remains positive
                    k_new[[i, j, k_idx]] = k_new[[i, j, k_idx]].max(1e-10);
                }
            }
        }

        *k = k_new;
        Ok(())
    }

    /// Solve ε equation with SIMD optimization
    fn solve_epsilon_equation_simd(
        &self,
        epsilon: &mut Array3<f64>,
        production: &Array3<f64>,
        k: &Array3<f64>,
        dt: f64,
        dx: f64,
        dy: f64,
        dz: f64,
    ) -> IntegrateResult<()> {
        let (nx, ny, nz) = epsilon.dim();
        let mut epsilon_new = epsilon.clone();

        for i in 1..nx - 1 {
            for j in 1..ny - 1 {
                for k_idx in 1..nz - 1 {
                    // Diffusion term
                    let d2e_dx2 = (epsilon[[i + 1, j, k_idx]] - 2.0 * epsilon[[i, j, k_idx]]
                        + epsilon[[i - 1, j, k_idx]])
                        / (dx * dx);
                    let d2e_dy2 = (epsilon[[i, j + 1, k_idx]] - 2.0 * epsilon[[i, j, k_idx]]
                        + epsilon[[i, j - 1, k_idx]])
                        / (dy * dy);
                    let d2e_dz2 = (epsilon[[i, j, k_idx + 1]] - 2.0 * epsilon[[i, j, k_idx]]
                        + epsilon[[i, j, k_idx - 1]])
                        / (dz * dz);

                    let mu_t = self.constants.c_mu * k[[i, j, k_idx]].powi(2)
                        / epsilon[[i, j, k_idx]].max(1e-10);
                    let diffusion =
                        (mu_t / self.constants.sigma_epsilon) * (d2e_dx2 + d2e_dy2 + d2e_dz2);

                    // ε equation: ∂ε/∂t = C_1 ε/k P_k - C_2 ε²/k + ∇·[(μ + μ_t/σ_ε)∇ε]
                    let time_scale = k[[i, j, k_idx]] / epsilon[[i, j, k_idx]].max(1e-10);
                    let production_term =
                        self.constants.c_1 * production[[i, j, k_idx]] / time_scale;
                    let dissipation_term = self.constants.c_2 * epsilon[[i, j, k_idx]] / time_scale;

                    let source = production_term - dissipation_term + diffusion;
                    epsilon_new[[i, j, k_idx]] = epsilon[[i, j, k_idx]] + dt * source;

                    // Ensure ε remains positive
                    epsilon_new[[i, j, k_idx]] = epsilon_new[[i, j, k_idx]].max(1e-10);
                }
            }
        }

        *epsilon = epsilon_new;
        Ok(())
    }

    /// Calculate turbulent viscosity field
    pub fn calculate_turbulent_viscosity(
        &self,
        k: &Array3<f64>,
        epsilon: &Array3<f64>,
    ) -> Array3<f64> {
        let (nx, ny, nz) = k.dim();
        let mut mu_t = Array3::zeros((nx, ny, nz));

        for i in 0..nx {
            for j in 0..ny {
                for k_idx in 0..nz {
                    // μ_t = ρ C_μ k²/ε
                    mu_t[[i, j, k_idx]] = self.constants.c_mu * k[[i, j, k_idx]].powi(2)
                        / epsilon[[i, j, k_idx]].max(1e-10);
                }
            }
        }

        mu_t
    }
}

impl TurbulenceModel for AdvancedTurbulenceModel {
    fn model_type(&self) -> TurbulenceModelType {
        self.model_type
    }

    fn constants(&self) -> &TurbulenceConstants {
        &self.constants
    }

    fn compute_turbulent_viscosity(
        &self,
        k: &Array3<f64>,
        epsilon_or_omega: &Array3<f64>,
    ) -> IntegrateResult<Array3<f64>> {
        Ok(self.calculate_turbulent_viscosity(k, epsilon_or_omega))
    }

    fn compute_production_term(
        &self,
        velocity: &[Array3<f64>],
        k: &Array3<f64>,
        epsilon_or_omega: &Array3<f64>,
        dx: f64,
        dy: f64,
        dz: f64,
    ) -> IntegrateResult<Array3<f64>> {
        let (nx, ny, nz) = k.dim();
        let strain_rate = self.calculate_strain_rate_simd(velocity, dx, dy, dz)?;
        let mut production = Array3::zeros((nx, ny, nz));

        for i in 0..nx {
            for j in 0..ny {
                for k_idx in 0..nz {
                    let mut s_squared: f64 = 0.0;
                    for ii in 0..3 {
                        for jj in 0..3 {
                            s_squared += strain_rate[[i, j, k_idx]][[ii, jj]]
                                * strain_rate[[i, j, k_idx]][[ii, jj]];
                        }
                    }

                    let mu_t = self.constants.c_mu * k[[i, j, k_idx]].powi(2)
                        / epsilon_or_omega[[i, j, k_idx]].max(1e-10);
                    production[[i, j, k_idx]] = 2.0 * mu_t * s_squared;
                }
            }
        }

        Ok(production)
    }

    fn apply_turbulence_boundary_conditions(
        &self,
        k: &mut Array3<f64>,
        epsilon_or_omega: &mut Array3<f64>,
    ) -> IntegrateResult<()> {
        let (nx, ny, nz) = k.dim();

        // Wall boundary conditions (k = 0, ε = high value)
        for i in 0..nx {
            for j in 0..ny {
                // Bottom and top walls
                k[[i, j, 0]] = 0.0;
                k[[i, j, nz - 1]] = 0.0;
                epsilon_or_omega[[i, j, 0]] = 1e6;
                epsilon_or_omega[[i, j, nz - 1]] = 1e6;
            }
        }

        for i in 0..nx {
            for k_idx in 0..nz {
                // Left and right walls
                k[[i, 0, k_idx]] = 0.0;
                k[[i, ny - 1, k_idx]] = 0.0;
                epsilon_or_omega[[i, 0, k_idx]] = 1e6;
                epsilon_or_omega[[i, ny - 1, k_idx]] = 1e6;
            }
        }

        for j in 0..ny {
            for k_idx in 0..nz {
                // Front and back walls
                k[[0, j, k_idx]] = 0.0;
                k[[nx - 1, j, k_idx]] = 0.0;
                epsilon_or_omega[[0, j, k_idx]] = 1e6;
                epsilon_or_omega[[nx - 1, j, k_idx]] = 1e6;
            }
        }

        Ok(())
    }
}

/// Spalart-Allmaras one-equation turbulence model
#[derive(Debug, Clone)]
pub struct SpalartAllmarasModel {
    /// Model constants
    pub constants: SpalartAllmarasConstants,
    /// Turbulent viscosity field
    pub nu_tilde: Array3<f64>,
    /// Vorticity magnitude
    pub vorticity: Array3<f64>,
    /// Distance to nearest wall
    pub wall_distance: Array3<f64>,
}

/// Spalart-Allmaras model constants
#[derive(Debug, Clone)]
pub struct SpalartAllmarasConstants {
    pub cb1: f64,
    pub cb2: f64,
    pub sigma: f64,
    pub kappa: f64,
    pub cw1: f64,
    pub cw2: f64,
    pub cw3: f64,
    pub cv1: f64,
    pub cv2: f64,
}

impl Default for SpalartAllmarasConstants {
    fn default() -> Self {
        Self {
            cb1: 0.1355,
            cb2: 0.622,
            sigma: 2.0 / 3.0,
            kappa: 0.41,
            cw1: 0.3,
            cw2: 0.3,
            cw3: 2.0,
            cv1: 7.1,
            cv2: 0.7,
        }
    }
}

impl SpalartAllmarasModel {
    /// Create new Spalart-Allmaras model
    pub fn new(nx: usize, ny: usize, nz: usize) -> Self {
        Self {
            constants: SpalartAllmarasConstants::default(),
            nu_tilde: Array3::zeros((nx, ny, nz)),
            vorticity: Array3::zeros((nx, ny, nz)),
            wall_distance: Array3::zeros((nx, ny, nz)),
        }
    }

    /// Solve Spalart-Allmaras transport equation
    pub fn solve_transport_equation(
        &mut self,
        velocity: &[Array3<f64>],
        molecular_viscosity: f64,
        dt: f64,
        dx: f64,
        dy: f64,
        dz: f64,
    ) -> IntegrateResult<()> {
        let (nx, ny, nz) = self.nu_tilde.dim();

        // Update vorticity field
        self.compute_vorticity(velocity, dx, dy, dz)?;

        // Solve transport equation for nu_tilde
        for i in 1..nx - 1 {
            for j in 1..ny - 1 {
                for k in 1..nz - 1 {
                    let d = self.wall_distance[[i, j, k]];
                    let s_tilde = self.compute_modified_vorticity(i, j, k, d)?;

                    // Production term
                    let production = self.constants.cb1 * s_tilde * self.nu_tilde[[i, j, k]];

                    // Destruction term
                    let destruction = self.compute_destruction_term(i, j, k, d)?;

                    // Diffusion term
                    let diffusion =
                        self.compute_diffusion_term(i, j, k, molecular_viscosity, dx, dy, dz)?;

                    // Update nu_tilde
                    self.nu_tilde[[i, j, k]] += dt * (production - destruction + diffusion);

                    // Ensure non-negative values
                    self.nu_tilde[[i, j, k]] = self.nu_tilde[[i, j, k]].max(0.0);
                }
            }
        }

        Ok(())
    }

    /// Compute vorticity magnitude
    fn compute_vorticity(
        &mut self,
        velocity: &[Array3<f64>],
        dx: f64,
        dy: f64,
        dz: f64,
    ) -> IntegrateResult<()> {
        let (nx, ny, nz) = velocity[0].dim();

        for i in 1..nx - 1 {
            for j in 1..ny - 1 {
                for k in 1..nz - 1 {
                    // Compute vorticity components
                    let omega_x = (velocity[2][[i, j + 1, k]] - velocity[2][[i, j - 1, k]])
                        / (2.0 * dy)
                        - (velocity[1][[i, j, k + 1]] - velocity[1][[i, j, k - 1]]) / (2.0 * dz);

                    let omega_y = (velocity[0][[i, j, k + 1]] - velocity[0][[i, j, k - 1]])
                        / (2.0 * dz)
                        - (velocity[2][[i + 1, j, k]] - velocity[2][[i - 1, j, k]]) / (2.0 * dx);

                    let omega_z = (velocity[1][[i + 1, j, k]] - velocity[1][[i - 1, j, k]])
                        / (2.0 * dx)
                        - (velocity[0][[i, j + 1, k]] - velocity[0][[i, j - 1, k]]) / (2.0 * dy);

                    self.vorticity[[i, j, k]] =
                        (omega_x * omega_x + omega_y * omega_y + omega_z * omega_z).sqrt();
                }
            }
        }

        Ok(())
    }

    /// Compute modified vorticity
    fn compute_modified_vorticity(
        &self,
        i: usize,
        j: usize,
        k: usize,
        d: f64,
    ) -> IntegrateResult<f64> {
        let nu_tilde = self.nu_tilde[[i, j, k]];
        let omega = self.vorticity[[i, j, k]];

        if d > 1e-12 {
            let chi = nu_tilde / (d * d * omega).max(1e-12);
            let fv2 = 1.0 - chi / (1.0 + chi * self.constants.cv1);
            Ok(omega + nu_tilde * fv2 / (self.constants.kappa * d).powi(2))
        } else {
            Ok(omega)
        }
    }

    /// Compute destruction term
    fn compute_destruction_term(
        &self,
        i: usize,
        j: usize,
        k: usize,
        d: f64,
    ) -> IntegrateResult<f64> {
        let nu_tilde = self.nu_tilde[[i, j, k]];

        if d > 1e-12 {
            let r = nu_tilde.min(10.0)
                / ((self.vorticity[[i, j, k]] * self.constants.kappa * d).max(1e-12));
            let g = r + self.constants.cw2 * (r.powi(6) - r);
            let fw = g
                * ((1.0 + self.constants.cw3.powi(6)) / (g.powi(6) + self.constants.cw3.powi(6)))
                    .powf(1.0 / 6.0);

            Ok(self.constants.cw1 * fw * (nu_tilde / d).powi(2))
        } else {
            Ok(0.0)
        }
    }

    /// Compute diffusion term
    fn compute_diffusion_term(
        &self,
        i: usize,
        j: usize,
        k: usize,
        molecular_viscosity: f64,
        dx: f64,
        dy: f64,
        dz: f64,
    ) -> IntegrateResult<f64> {
        // Second derivatives of nu_tilde
        let d2nu_dx2 = (self.nu_tilde[[i + 1, j, k]] - 2.0 * self.nu_tilde[[i, j, k]]
            + self.nu_tilde[[i - 1, j, k]])
            / (dx * dx);
        let d2nu_dy2 = (self.nu_tilde[[i, j + 1, k]] - 2.0 * self.nu_tilde[[i, j, k]]
            + self.nu_tilde[[i, j - 1, k]])
            / (dy * dy);
        let d2nu_dz2 = (self.nu_tilde[[i, j, k + 1]] - 2.0 * self.nu_tilde[[i, j, k]]
            + self.nu_tilde[[i, j, k - 1]])
            / (dz * dz);

        let diffusion_coefficient =
            (molecular_viscosity + self.nu_tilde[[i, j, k]]) / self.constants.sigma;
        Ok(diffusion_coefficient * (d2nu_dx2 + d2nu_dy2 + d2nu_dz2))
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_advanced_turbulence_model_creation() {
        let model = AdvancedTurbulenceModel::new(TurbulenceModelType::KEpsilon, 5, 5, 5);
        assert_eq!(model.model_type, TurbulenceModelType::KEpsilon);
        assert_eq!(model.wall_distance.dim(), (5, 5, 5));
    }

    #[test]
    fn test_spalart_allmaras_model_creation() {
        let model = SpalartAllmarasModel::new(8, 8, 8);
        assert_eq!(model.nu_tilde.dim(), (8, 8, 8));
        assert_eq!(model.vorticity.dim(), (8, 8, 8));
    }

    #[test]
    fn test_turbulent_viscosity_calculation() {
        let model = AdvancedTurbulenceModel::new(TurbulenceModelType::KEpsilon, 4, 4, 4);
        let k = Array3::ones((4, 4, 4));
        let epsilon = Array3::ones((4, 4, 4));

        let mu_t = model.calculate_turbulent_viscosity(&k, &epsilon);
        assert_eq!(mu_t.dim(), (4, 4, 4));
        assert!(mu_t[[1, 1, 1]] > 0.0);
    }

    #[test]
    fn test_spalart_allmaras_constants() {
        let constants = SpalartAllmarasConstants::default();
        assert_eq!(constants.cb1, 0.1355);
        assert_eq!(constants.kappa, 0.41);
    }
}