scirs2-integrate 0.4.0

//! Reynolds-Averaged Navier-Stokes (RANS) implementation
//!
//! This module provides RANS solvers and turbulence models for
//! time-averaged turbulent flow simulation.

use super::models::{RANSModel as RANSModelTrait, TurbulenceConstants, TurbulenceModel};
use crate::error::IntegrateResult;
use scirs2_core::ndarray::{Array2, Array3};

/// RANS turbulence models
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum RANSModel {
    /// k-ε model
    KEpsilon,
    /// k-ω model  
    KOmega,
    /// k-ω SST model
    KOmegaSST,
    /// Reynolds Stress Model (RSM)
    ReynoldsStress,
}

/// Reynolds-Averaged Navier-Stokes solver
#[derive(Debug, Clone)]
pub struct RANSSolver {
    /// Grid dimensions
    pub nx: usize,
    pub ny: usize,
    /// Turbulence model
    pub turbulence_model: RANSModel,
    /// Solver parameters  
    pub reynolds_number: f64,
    pub relaxation_factor: f64,
    /// Model constants
    pub constants: TurbulenceConstants,
}

/// RANS state variables
#[derive(Debug, Clone)]
pub struct RANSState {
    /// Mean velocity components
    pub mean_velocity: Vec<Array2<f64>>,
    /// Mean pressure
    pub mean_pressure: Array2<f64>,
    /// Turbulent kinetic energy
    pub turbulent_kinetic_energy: Array2<f64>,
    /// Dissipation rate (ε)
    pub dissipation_rate: Array2<f64>,
    /// Specific dissipation rate (ω) - for k-ω models
    pub specific_dissipation_rate: Option<Array2<f64>>,
    /// Grid spacing
    pub dx: f64,
    pub dy: f64,
}

impl RANSSolver {
    /// Create a new RANS solver
    pub fn new(nx: usize, ny: usize, turbulence_model: RANSModel, reynoldsnumber: f64) -> Self {
        Self {
            nx,
            ny,
            turbulence_model,
            reynolds_number: reynoldsnumber,
            relaxation_factor: 0.7,
            constants: TurbulenceConstants::default(),
        }
    }

    /// Solve RANS equations
    pub fn solve_rans(
        &self,
        initial_state: RANSState,
        max_iterations: usize,
        tolerance: f64,
    ) -> IntegrateResult<RANSState> {
        let mut state = initial_state;

        for _iteration in 0..max_iterations {
            let old_residual = self.compute_residual(&state)?;

            // Update turbulence quantities
            state = self.update_turbulence_quantities(&state)?;

            // Update mean flow
            state = self.update_mean_flow(&state)?;

            // Apply boundary conditions
            state = Self::apply_rans_boundary_conditions(state)?;

            // Check convergence
            let new_residual = self.compute_residual(&state)?;
            if (old_residual - new_residual).abs() < tolerance {
                break;
            }
        }

        Ok(state)
    }

    /// Update turbulence quantities based on model type
    fn update_turbulence_quantities(&self, state: &RANSState) -> IntegrateResult<RANSState> {
        match self.turbulence_model {
            RANSModel::KEpsilon => self.update_k_epsilon(state),
            RANSModel::KOmega => self.update_k_omega(state),
            RANSModel::KOmegaSST => self.update_k_omega_sst(state),
            RANSModel::ReynoldsStress => self.update_reynolds_stress(state),
        }
    }

    /// Update k-ε model
    fn update_k_epsilon(&self, state: &RANSState) -> IntegrateResult<RANSState> {
        let mut new_state = state.clone();

        for i in 1..(self.nx - 1) {
            for j in 1..(self.ny - 1) {
                let k = state.turbulent_kinetic_energy[[i, j]].max(1e-10);
                let epsilon = state.dissipation_rate[[i, j]].max(1e-10);

                // Compute turbulent viscosity
                let nu_t = self.constants.c_mu * k * k / epsilon;

                // Production term
                let production = self.compute_production_k_epsilon(state, i, j, nu_t)?;

                // Update k equation
                let dk_dt = production - epsilon;
                new_state.turbulent_kinetic_energy[[i, j]] =
                    (k + self.relaxation_factor * dk_dt).max(1e-10);

                // Update ε equation
                let depsilon_dt = self.constants.c_1 * epsilon / k * production
                    - self.constants.c_2 * epsilon * epsilon / k;
                new_state.dissipation_rate[[i, j]] =
                    (epsilon + self.relaxation_factor * depsilon_dt).max(1e-10);
            }
        }

        Ok(new_state)
    }

    /// Update k-ω model
    fn update_k_omega(&self, state: &RANSState) -> IntegrateResult<RANSState> {
        let mut new_state = state.clone();

        // k-ω model constants
        let beta_star = 0.09;
        let alpha = 5.0 / 9.0;
        let beta = 3.0 / 40.0;

        for i in 1..(self.nx - 1) {
            for j in 1..(self.ny - 1) {
                let k = state.turbulent_kinetic_energy[[i, j]].max(1e-10);
                let omega = state
                    .specific_dissipation_rate
                    .as_ref()
                    .map(|arr| arr[[i, j]])
                    .unwrap_or(state.dissipation_rate[[i, j]] / k)
                    .max(1e-10);

                // Compute turbulent viscosity
                let nu_t = k / omega;

                // Production term
                let production = self.compute_production_k_omega(state, i, j, nu_t)?;

                // Update k equation
                let dk_dt = production - beta_star * k * omega;
                new_state.turbulent_kinetic_energy[[i, j]] =
                    (k + self.relaxation_factor * dk_dt).max(1e-10);

                // Update ω equation
                let domega_dt = alpha * omega / k * production - beta * omega * omega;
                if let Some(ref mut omega_arr) = new_state.specific_dissipation_rate {
                    omega_arr[[i, j]] = (omega + self.relaxation_factor * domega_dt).max(1e-10);
                } else {
                    // Initialize omega array if it doesn't exist
                    new_state.specific_dissipation_rate =
                        Some(Array2::from_elem((self.nx, self.ny), omega));
                }
            }
        }

        Ok(new_state)
    }

    /// Update k-ω SST model
    fn update_k_omega_sst(&self, state: &RANSState) -> IntegrateResult<RANSState> {
        // SST model combines k-ε and k-ω models using blending functions
        let f1 = self.compute_sst_blending_function(state)?;

        let k_omega_state = self.update_k_omega(state)?;
        let k_epsilon_state = self.update_k_epsilon(state)?;

        // Blend the results
        let mut new_state = state.clone();
        for i in 0..self.nx {
            for j in 0..self.ny {
                let blend = f1[[i, j]];

                new_state.turbulent_kinetic_energy[[i, j]] = blend
                    * k_omega_state.turbulent_kinetic_energy[[i, j]]
                    + (1.0 - blend) * k_epsilon_state.turbulent_kinetic_energy[[i, j]];

                new_state.dissipation_rate[[i, j]] = blend * k_omega_state.dissipation_rate[[i, j]]
                    + (1.0 - blend) * k_epsilon_state.dissipation_rate[[i, j]];
            }
        }

        Ok(new_state)
    }

    /// Update Reynolds stress model
    fn update_reynolds_stress(&self, state: &RANSState) -> IntegrateResult<RANSState> {
        // Simplified Reynolds Stress Model
        let mut new_state = state.clone();

        // This would involve solving transport equations for all Reynolds stress components
        // For simplicity, we use an algebraic stress model
        for i in 1..(self.nx - 1) {
            for j in 1..(self.ny - 1) {
                let k = state.turbulent_kinetic_energy[[i, j]].max(1e-10);
                let epsilon = state.dissipation_rate[[i, j]].max(1e-10);

                // Compute strain rate
                let s11 = self.compute_strain_component(state, i, j, 0, 0)?;
                let s12 = self.compute_strain_component(state, i, j, 0, 1)?;
                let s22 = self.compute_strain_component(state, i, j, 1, 1)?;

                // Algebraic stress relations
                let c1 = 1.8;
                let time_scale = k / epsilon;

                // Reynolds stress components
                let tau_11 = (2.0 / 3.0) * k - c1 * time_scale * k * s11;
                let tau_12 = -c1 * time_scale * k * s12;
                let tau_22 = (2.0 / 3.0) * k - c1 * time_scale * k * s22;

                // Store Reynolds stresses (would need to add these fields to RANSState)
                // For now, just update k and ε
                let production = tau_11 * s11 + 2.0 * tau_12 * s12 + tau_22 * s22;

                let dk_dt = production - epsilon;
                new_state.turbulent_kinetic_energy[[i, j]] =
                    (k + self.relaxation_factor * dk_dt).max(1e-10);

                let depsilon_dt = self.constants.c_1 * epsilon / k * production
                    - self.constants.c_2 * epsilon * epsilon / k;
                new_state.dissipation_rate[[i, j]] =
                    (epsilon + self.relaxation_factor * depsilon_dt).max(1e-10);
            }
        }

        Ok(new_state)
    }

    /// Compute production term for k-ε model
    fn compute_production_k_epsilon(
        &self,
        state: &RANSState,
        i: usize,
        j: usize,
        nu_t: f64,
    ) -> IntegrateResult<f64> {
        let s11 = self.compute_strain_component(state, i, j, 0, 0)?;
        let s12 = self.compute_strain_component(state, i, j, 0, 1)?;
        let s22 = self.compute_strain_component(state, i, j, 1, 1)?;

        // Production = 2 * nu_t * S_ij * S_ij
        let production = 2.0 * nu_t * (s11 * s11 + 2.0 * s12 * s12 + s22 * s22);
        Ok(production)
    }

    /// Compute production term for k-ω model
    fn compute_production_k_omega(
        &self,
        state: &RANSState,
        i: usize,
        j: usize,
        nu_t: f64,
    ) -> IntegrateResult<f64> {
        // Similar to k-ε but with different formulation
        self.compute_production_k_epsilon(state, i, j, nu_t)
    }

    /// Compute strain rate component
    fn compute_strain_component(
        &self,
        state: &RANSState,
        i: usize,
        j: usize,
        comp_i: usize,
        comp_j: usize,
    ) -> IntegrateResult<f64> {
        if i == 0 || i >= self.nx - 1 || j == 0 || j >= self.ny - 1 {
            return Ok(0.0);
        }

        let dx = state.dx;
        let dy = state.dy;

        let strain = match (comp_i, comp_j) {
            (0, 0) => {
                // ∂u/∂x
                (state.mean_velocity[0][[i + 1, j]] - state.mean_velocity[0][[i - 1, j]])
                    / (2.0 * dx)
            }
            (1, 1) => {
                // ∂v/∂y
                (state.mean_velocity[1][[i, j + 1]] - state.mean_velocity[1][[i, j - 1]])
                    / (2.0 * dy)
            }
            (0, 1) | (1, 0) => {
                // 0.5 * (∂u/∂y + ∂v/∂x)
                let dudy = (state.mean_velocity[0][[i, j + 1]]
                    - state.mean_velocity[0][[i, j - 1]])
                    / (2.0 * dy);
                let dvdx = (state.mean_velocity[1][[i + 1, j]]
                    - state.mean_velocity[1][[i - 1, j]])
                    / (2.0 * dx);
                0.5 * (dudy + dvdx)
            }
            _ => 0.0,
        };

        Ok(strain)
    }

    /// Compute SST blending function F1
    fn compute_sst_blending_function(&self, state: &RANSState) -> IntegrateResult<Array2<f64>> {
        let mut f1 = Array2::zeros((self.nx, self.ny));

        for i in 1..self.nx - 1 {
            for j in 1..self.ny - 1 {
                let k = state.turbulent_kinetic_energy[[i, j]].max(1e-10);
                let epsilon = state.dissipation_rate[[i, j]].max(1e-10);
                let omega = state
                    .specific_dissipation_rate
                    .as_ref()
                    .map(|arr| arr[[i, j]])
                    .unwrap_or(epsilon / k)
                    .max(1e-10);

                // Wall distance (simplified)
                let y_plus = ((i.min(self.nx - 1 - i) + j.min(self.ny - 1 - j)) as f64).max(1.0);

                // Compute blending function arguments
                let sqrt_k = k.sqrt();
                let arg1_1 = sqrt_k / (0.09 * omega * y_plus);
                let arg1_2 = 500.0 / (self.reynolds_number * y_plus * y_plus * omega);
                let arg1 = arg1_1.min(arg1_2);

                f1[[i, j]] = (-4.0 * arg1).exp().tanh();
            }
        }

        Ok(f1)
    }

    /// Update mean flow quantities
    fn update_mean_flow(&self, state: &RANSState) -> IntegrateResult<RANSState> {
        let mut new_state = state.clone();

        // Update mean velocity using RANS equations
        // This is a simplified implementation - full RANS would involve
        // solving the momentum equations with Reynolds stress terms

        for comp in 0..2 {
            for i in 1..self.nx - 1 {
                for j in 1..self.ny - 1 {
                    let k = state.turbulent_kinetic_energy[[i, j]];
                    let epsilon = state.dissipation_rate[[i, j]].max(1e-10);
                    let nu_t = self.constants.c_mu * k * k / epsilon;

                    // Simplified momentum equation update
                    let viscous_term = self.compute_viscous_term(state, i, j, comp, nu_t)?;
                    let pressure_gradient = self.compute_pressure_gradient(state, i, j, comp)?;

                    let velocity_update =
                        self.relaxation_factor * (viscous_term - pressure_gradient);
                    new_state.mean_velocity[comp][[i, j]] += velocity_update;
                }
            }
        }

        Ok(new_state)
    }

    /// Compute viscous term
    fn compute_viscous_term(
        &self,
        state: &RANSState,
        i: usize,
        j: usize,
        comp: usize,
        nu_t: f64,
    ) -> IntegrateResult<f64> {
        let dx = state.dx;
        let dy = state.dy;
        let nu_total = 1.0 / self.reynolds_number + nu_t; // molecular + turbulent viscosity

        // Second derivatives (Laplacian)
        let d2u_dx2 = (state.mean_velocity[comp][[i + 1, j]]
            - 2.0 * state.mean_velocity[comp][[i, j]]
            + state.mean_velocity[comp][[i - 1, j]])
            / (dx * dx);

        let d2u_dy2 = (state.mean_velocity[comp][[i, j + 1]]
            - 2.0 * state.mean_velocity[comp][[i, j]]
            + state.mean_velocity[comp][[i, j - 1]])
            / (dy * dy);

        Ok(nu_total * (d2u_dx2 + d2u_dy2))
    }

    /// Compute pressure gradient
    fn compute_pressure_gradient(
        &self,
        state: &RANSState,
        i: usize,
        j: usize,
        comp: usize,
    ) -> IntegrateResult<f64> {
        let dx = state.dx;
        let dy = state.dy;

        let gradient = match comp {
            0 => {
                // ∂p/∂x
                (state.mean_pressure[[i + 1, j]] - state.mean_pressure[[i - 1, j]]) / (2.0 * dx)
            }
            1 => {
                // ∂p/∂y
                (state.mean_pressure[[i, j + 1]] - state.mean_pressure[[i, j - 1]]) / (2.0 * dy)
            }
            _ => 0.0,
        };

        Ok(gradient)
    }

    /// Apply RANS boundary conditions
    fn apply_rans_boundary_conditions(mut state: RANSState) -> IntegrateResult<RANSState> {
        let (nx, ny) = state.mean_velocity[0].dim();

        // Wall boundary conditions
        for i in 0..nx {
            // Bottom and top walls
            state.mean_velocity[0][[i, 0]] = 0.0; // u = 0
            state.mean_velocity[1][[i, 0]] = 0.0; // v = 0
            state.mean_velocity[0][[i, ny - 1]] = 0.0;
            state.mean_velocity[1][[i, ny - 1]] = 0.0;

            // Turbulence quantities at walls
            state.turbulent_kinetic_energy[[i, 0]] = 0.0;
            state.turbulent_kinetic_energy[[i, ny - 1]] = 0.0;
            state.dissipation_rate[[i, 0]] = 1e6; // High dissipation at wall
            state.dissipation_rate[[i, ny - 1]] = 1e6;

            if let Some(ref mut omega) = state.specific_dissipation_rate {
                omega[[i, 0]] = 1e6;
                omega[[i, ny - 1]] = 1e6;
            }
        }

        for j in 0..ny {
            // Left and right walls
            state.mean_velocity[0][[0, j]] = 0.0;
            state.mean_velocity[1][[0, j]] = 0.0;
            state.mean_velocity[0][[nx - 1, j]] = 0.0;
            state.mean_velocity[1][[nx - 1, j]] = 0.0;

            state.turbulent_kinetic_energy[[0, j]] = 0.0;
            state.turbulent_kinetic_energy[[nx - 1, j]] = 0.0;
            state.dissipation_rate[[0, j]] = 1e6;
            state.dissipation_rate[[nx - 1, j]] = 1e6;

            if let Some(ref mut omega) = state.specific_dissipation_rate {
                omega[[0, j]] = 1e6;
                omega[[nx - 1, j]] = 1e6;
            }
        }

        Ok(state)
    }

    /// Compute residual for convergence checking
    fn compute_residual(&self, state: &RANSState) -> IntegrateResult<f64> {
        let mut residual = 0.0;

        // Compute residual based on velocity and turbulence quantity changes
        for i in 0..self.nx {
            for j in 0..self.ny {
                residual += state.mean_velocity[0][[i, j]].abs();
                residual += state.mean_velocity[1][[i, j]].abs();
                residual += state.turbulent_kinetic_energy[[i, j]].abs();
                residual += state.dissipation_rate[[i, j]].abs();
            }
        }

        Ok(residual / (self.nx * self.ny) as f64)
    }
}

impl RANSState {
    /// Create new RANS state
    pub fn new(nx: usize, ny: usize, dx: f64, dy: f64) -> Self {
        Self {
            mean_velocity: vec![Array2::zeros((nx, ny)), Array2::zeros((nx, ny))],
            mean_pressure: Array2::zeros((nx, ny)),
            turbulent_kinetic_energy: Array2::from_elem((nx, ny), 1e-6),
            dissipation_rate: Array2::from_elem((nx, ny), 1e-4),
            specific_dissipation_rate: None,
            dx,
            dy,
        }
    }

    /// Initialize with k-ω specific dissipation rate
    pub fn with_omega(mut self) -> Self {
        let (nx, ny) = self.mean_velocity[0].dim();
        self.specific_dissipation_rate = Some(Array2::from_elem((nx, ny), 1e-3));
        self
    }

    /// Set initial conditions for lid-driven cavity
    pub fn lid_driven_cavity(nx: usize, ny: usize, dx: f64, dy: f64, lidvelocity: f64) -> Self {
        let mut state = Self::new(nx, ny, dx, dy);

        // Set lid velocity
        for i in 0..nx {
            state.mean_velocity[0][[i, ny - 1]] = lidvelocity;
        }

        // Initialize turbulence quantities
        let turbulence_intensity = 0.05_f64;
        let k_inlet: f64 = 1.5 * (turbulence_intensity * lidvelocity).powi(2);
        let epsilon_inlet: f64 = 0.09 * k_inlet.powf(1.5_f64) / (0.1 * dx);

        state.turbulent_kinetic_energy.fill(k_inlet);
        state.dissipation_rate.fill(epsilon_inlet);

        state
    }
}

impl TurbulenceModel for RANSSolver {
    fn model_type(&self) -> super::models::TurbulenceModelType {
        match self.turbulence_model {
            RANSModel::KEpsilon => super::models::TurbulenceModelType::KEpsilon,
            RANSModel::KOmega => super::models::TurbulenceModelType::KOmega,
            RANSModel::KOmegaSST => super::models::TurbulenceModelType::KOmegaSST,
            RANSModel::ReynoldsStress => super::models::TurbulenceModelType::ReynoldsStress,
        }
    }

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

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

        match self.turbulence_model {
            RANSModel::KEpsilon => {
                for i in 0..nx {
                    for j in 0..ny {
                        for k_idx in 0..nz {
                            mu_t[[i, j, k_idx]] = self.constants.c_mu * k[[i, j, k_idx]].powi(2)
                                / epsilon_or_omega[[i, j, k_idx]].max(1e-10);
                        }
                    }
                }
            }
            RANSModel::KOmega | RANSModel::KOmegaSST => {
                for i in 0..nx {
                    for j in 0..ny {
                        for k_idx in 0..nz {
                            mu_t[[i, j, k_idx]] =
                                k[[i, j, k_idx]] / epsilon_or_omega[[i, j, k_idx]].max(1e-10);
                        }
                    }
                }
            }
            RANSModel::ReynoldsStress => {
                // For RSM, use k-ε formulation
                for i in 0..nx {
                    for j in 0..ny {
                        for k_idx in 0..nz {
                            mu_t[[i, j, k_idx]] = self.constants.c_mu * k[[i, j, k_idx]].powi(2)
                                / epsilon_or_omega[[i, j, k_idx]].max(1e-10);
                        }
                    }
                }
            }
        }

        Ok(mu_t)
    }

    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>> {
        // Simplified implementation - would need full strain rate computation
        let (nx, ny, nz) = _k.dim();
        Ok(Array3::zeros((nx, ny, nz)))
    }

    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
        for i in 0..nx {
            for j in 0..ny {
                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;
            }
        }

        Ok(())
    }
}

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

    #[test]
    fn test_rans_solver_creation() {
        let solver = RANSSolver::new(10, 10, RANSModel::KEpsilon, 1000.0);
        assert_eq!(solver.nx, 10);
        assert_eq!(solver.turbulence_model, RANSModel::KEpsilon);
        assert_eq!(solver.reynolds_number, 1000.0);
    }

    #[test]
    fn test_rans_state_creation() {
        let state = RANSState::new(8, 8, 0.1, 0.1);
        assert_eq!(state.mean_velocity.len(), 2);
        assert_eq!(state.mean_velocity[0].dim(), (8, 8));
        assert_eq!(state.dx, 0.1);
        assert!(state.specific_dissipation_rate.is_none());
    }

    #[test]
    fn test_rans_state_with_omega() {
        let state = RANSState::new(6, 6, 0.1, 0.1).with_omega();
        assert!(state.specific_dissipation_rate.is_some());
        if let Some(omega) = &state.specific_dissipation_rate {
            assert_eq!(omega.dim(), (6, 6));
        }
    }

    #[test]
    fn test_lid_driven_cavity_initialization() {
        let state = RANSState::lid_driven_cavity(10, 10, 0.1, 0.1, 1.0);

        // Check lid velocity
        assert_eq!(state.mean_velocity[0][[5, 9]], 1.0);
        assert_eq!(state.mean_velocity[0][[0, 0]], 0.0);

        // Check turbulence initialization
        assert!(state.turbulent_kinetic_energy[[5, 5]] > 0.0);
        assert!(state.dissipation_rate[[5, 5]] > 0.0);
    }

    #[test]
    fn test_rans_model_enum() {
        assert_eq!(RANSModel::KEpsilon, RANSModel::KEpsilon);
        assert_ne!(RANSModel::KEpsilon, RANSModel::KOmega);
    }
}