Initial commit

crates/specialized/rtx-cfd/src/solvers/incompressible/simple.rs

@@ -0,0 +1,783 @@
+//! SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm
+//!
+//! The SIMPLE algorithm is a widely-used iterative solution method for
+//! the incompressible Navier-Stokes equations. It uses a pressure-velocity
+//! coupling approach to handle the incompressibility constraint.
+//!
+//! Algorithm steps:
+//! 1. Solve momentum equations with guessed pressure field → u*, v*
+//! 2. Solve pressure correction equation → p'
+//! 3. Correct velocities and pressure
+//! 4. Check convergence and iterate
+
+use super::{BoundaryConditions, FlowField, IncompressibleSolver, SolverResult};
+use crate::turbulence::{KEpsilonModel, KEpsilonVariant, TurbulenceModel, TurbulenceState};
+use crate::{CfdConfig, CfdError, CfdResult};
+use async_trait::async_trait;
+use nalgebra::{DMatrix, DVector, Vector3};
+use std::time::Instant;
+
+/// Parameters for SIMPLE algorithm
+#[derive(Debug, Clone)]
+pub struct SimpleParameters {
+    /// Under-relaxation factor for pressure (typically 0.2-0.8)
+    pub pressure_relaxation: f64,
+    /// Under-relaxation factor for velocity (typically 0.5-0.8)
+    pub velocity_relaxation: f64,
+    /// Maximum number of iterations
+    pub max_iterations: usize,
+    /// Convergence tolerance for residuals
+    pub tolerance: f64,
+    /// Time step for transient problems
+    pub time_step: f64,
+    /// Maximum Courant number for stability
+    pub max_courant: f64,
+    /// Enable turbulence modeling
+    pub use_turbulence: bool,
+}
+
+impl SimpleParameters {
+    /// Create new SIMPLE parameters with default values
+    #[must_use]
+    pub fn new() -> Self {
+        Self::default()
+    }
+
+    /// Set pressure under-relaxation factor
+    #[must_use]
+    pub fn with_pressure_relaxation(mut self, factor: f64) -> Self {
+        self.pressure_relaxation = factor.max(0.0); // Ensure non-negative
+        self
+    }
+
+    /// Set velocity under-relaxation factor
+    #[must_use]
+    pub fn with_velocity_relaxation(mut self, factor: f64) -> Self {
+        self.velocity_relaxation = factor.max(0.0);
+        self
+    }
+
+    /// Set maximum iterations
+    #[must_use]
+    pub fn with_max_iterations(mut self, max_iter: usize) -> Self {
+        self.max_iterations = max_iter;
+        self
+    }
+
+    /// Set convergence tolerance
+    #[must_use]
+    pub fn with_tolerance(mut self, tol: f64) -> Self {
+        self.tolerance = tol.abs();
+        self
+    }
+
+    /// Set time step
+    #[must_use]
+    pub fn with_time_step(mut self, dt: f64) -> Self {
+        self.time_step = dt.abs();
+        self
+    }
+
+    /// Validate parameters
+    pub fn validate(&self) -> CfdResult<()> {
+        if self.pressure_relaxation <= 0.0 || self.pressure_relaxation > 1.0 {
+            return Err(CfdError::invalid_parameter(
+                "Pressure relaxation factor must be in (0, 1]",
+            ));
+        }
+
+        if self.velocity_relaxation <= 0.0 || self.velocity_relaxation > 1.0 {
+            return Err(CfdError::invalid_parameter(
+                "Velocity relaxation factor must be in (0, 1]",
+            ));
+        }
+
+        if self.tolerance <= 0.0 {
+            return Err(CfdError::invalid_parameter("Tolerance must be positive"));
+        }
+
+        if self.time_step <= 0.0 {
+            return Err(CfdError::invalid_parameter("Time step must be positive"));
+        }
+
+        Ok(())
+    }
+}
+
+impl Default for SimpleParameters {
+    fn default() -> Self {
+        Self {
+            pressure_relaxation: 0.3,
+            velocity_relaxation: 0.7,
+            max_iterations: 1000,
+            tolerance: 1e-6,
+            time_step: 0.001,
+            max_courant: 1.0,
+            use_turbulence: false,
+        }
+    }
+}
+
+/// Result of SIMPLE algorithm execution
+#[derive(Debug, Clone)]
+pub struct SimpleResult {
+    /// Base solver result information
+    pub solver_result: SolverResult,
+    /// Pressure correction iterations per SIMPLE iteration
+    pub pressure_iterations: Vec<usize>,
+    /// Final mass residual
+    pub mass_residual: f64,
+    /// Final momentum residual
+    pub momentum_residual: f64,
+}
+
+/// SIMPLE algorithm implementation
+pub struct SimpleSolver {
+    /// CFD configuration
+    config: CfdConfig,
+    /// SIMPLE parameters
+    parameters: SimpleParameters,
+    /// Linear algebra workspace
+    workspace: LinearAlgebraWorkspace,
+    /// Turbulence model (optional)
+    turbulence_model: Option<KEpsilonModel>,
+}
+
+/// Workspace for linear algebra operations
+struct LinearAlgebraWorkspace {
+    /// Matrix for pressure correction equation
+    pressure_matrix: Option<DMatrix<f64>>,
+    /// RHS vector for pressure correction
+    pressure_rhs: Option<DVector<f64>>,
+    /// Solution vector for pressure correction
+    pressure_solution: Option<DVector<f64>>,
+    /// Momentum equation coefficients
+    momentum_coefficients: Option<MomentumCoefficients>,
+}
+
+/// Coefficients for momentum equations discretization
+#[derive(Debug, Clone)]
+struct MomentumCoefficients {
+    /// Central coefficient (diagonal)
+    pub ap: DMatrix<f64>,
+    /// East neighbor coefficient
+    pub ae: DMatrix<f64>,
+    /// West neighbor coefficient
+    pub aw: DMatrix<f64>,
+    /// North neighbor coefficient
+    pub an: DMatrix<f64>,
+    /// South neighbor coefficient
+    pub as_: DMatrix<f64>,
+    /// Source term
+    pub su: DMatrix<f64>,
+}
+
+impl SimpleSolver {
+    /// Create new SIMPLE solver
+    pub fn new(config: CfdConfig, parameters: SimpleParameters) -> CfdResult<Self> {
+        config.validate()?;
+        parameters.validate()?;
+
+        // Initialize turbulence model if enabled (will be properly sized when flow field is available)
+        let turbulence_model = if parameters.use_turbulence {
+            None // Will be initialized when flow field dimensions are known
+        } else {
+            None
+        };
+
+        Ok(Self {
+            config,
+            parameters,
+            workspace: LinearAlgebraWorkspace {
+                pressure_matrix: None,
+                pressure_rhs: None,
+                pressure_solution: None,
+                momentum_coefficients: None,
+            },
+            turbulence_model,
+        })
+    }
+
+    /// Solve one SIMPLE iteration
+    pub async fn solve_simple_iteration(
+        &mut self,
+        flow_field: &mut FlowField,
+        boundary_conditions: &BoundaryConditions,
+        dt: f64,
+    ) -> CfdResult<(f64, f64)> {
+        // Step 1: Solve momentum equations with current pressure field
+        self.momentum_prediction_step(flow_field, dt).await?;
+
+        // Step 2: Solve pressure correction equation
+        let mass_residual = self.pressure_correction_step(flow_field).await?;
+
+        // Step 3: Correct velocities
+        self.velocity_correction_step(flow_field).await?;
+
+        // Step 4: Update pressure field
+        self.pressure_update_step(flow_field).await?;
+
+        // Step 5: Solve turbulence equations if enabled
+        if self.parameters.use_turbulence {
+            self.solve_turbulence(flow_field, dt).await?;
+        }
+
+        // Step 6: Apply boundary conditions
+        flow_field.apply_boundary_conditions(boundary_conditions)?;
+
+        // Step 7: Apply under-relaxation
+        flow_field.apply_velocity_relaxation(self.parameters.velocity_relaxation)?;
+        flow_field.apply_pressure_relaxation(self.parameters.pressure_relaxation)?;
+
+        // Compute momentum residual
+        let momentum_residual = flow_field.compute_velocity_residual();
+
+        Ok((mass_residual, momentum_residual))
+    }
+
+    /// Momentum prediction step: solve momentum equations with current pressure
+    pub async fn momentum_prediction_step(
+        &self,
+        flow_field: &mut FlowField,
+        dt: f64,
+    ) -> CfdResult<()> {
+        let (_nx, _ny, dx, dy) = flow_field.grid_info();
+        let rho = self.config.density;
+        let mu = self.config.viscosity;
+
+        // Copy current velocities to old values for time derivatives
+        flow_field.update_old_values();
+
+        // Solve u-momentum equation
+        self.solve_u_momentum(flow_field, dt, rho, mu, dx, dy)
+            .await?;
+
+        // Solve v-momentum equation
+        self.solve_v_momentum(flow_field, dt, rho, mu, dx, dy)
+            .await?;
+
+        // Store predicted velocities
+        flow_field.copy_to_starred();
+
+        Ok(())
+    }
+
+    /// Solve u-momentum equation
+    async fn solve_u_momentum(
+        &self,
+        flow_field: &mut FlowField,
+        dt: f64,
+        rho: f64,
+        mu: f64,
+        dx: f64,
+        dy: f64,
+    ) -> CfdResult<()> {
+        let (nx, ny, _, _) = flow_field.grid_info();
+
+        // For each u-velocity point (face-centered)
+        for j in 1..ny - 1 {
+            for i in 1..nx {
+                // u goes from 1 to nx-1 for interior
+                // Discretize u-momentum equation at (i, j)
+                let coeffs =
+                    self.compute_u_momentum_coefficients(flow_field, i, j, dt, rho, mu, dx, dy)?;
+
+                // Solve for new u velocity using Gauss-Seidel
+                let u_new = (coeffs.source
+                    + coeffs.east * flow_field.u[(j, i + 1)]
+                    + coeffs.west * flow_field.u[(j, i - 1)]
+                    + coeffs.north * flow_field.u[(j + 1, i)]
+                    + coeffs.south * flow_field.u[(j - 1, i)])
+                    / coeffs.center;
+
+                flow_field.u[(j, i)] = u_new;
+            }
+        }
+
+        Ok(())
+    }
+
+    /// Solve v-momentum equation
+    async fn solve_v_momentum(
+        &self,
+        flow_field: &mut FlowField,
+        dt: f64,
+        rho: f64,
+        mu: f64,
+        dx: f64,
+        dy: f64,
+    ) -> CfdResult<()> {
+        let (nx, ny, _, _) = flow_field.grid_info();
+
+        // For each v-velocity point (face-centered)
+        for j in 1..ny {
+            // v goes from 1 to ny-1 for interior
+            for i in 1..nx - 1 {
+                // Discretize v-momentum equation at (i, j)
+                let coeffs =
+                    self.compute_v_momentum_coefficients(flow_field, i, j, dt, rho, mu, dx, dy)?;
+
+                // Solve for new v velocity using Gauss-Seidel
+                let v_new = (coeffs.source
+                    + coeffs.east * flow_field.v[(j, i + 1)]
+                    + coeffs.west * flow_field.v[(j, i - 1)]
+                    + coeffs.north * flow_field.v[(j + 1, i)]
+                    + coeffs.south * flow_field.v[(j - 1, i)])
+                    / coeffs.center;
+
+                flow_field.v[(j, i)] = v_new;
+            }
+        }
+
+        Ok(())
+    }
+
+    /// Pressure correction step: solve pressure Poisson equation
+    pub async fn pressure_correction_step(&self, flow_field: &mut FlowField) -> CfdResult<f64> {
+        let (nx, ny, dx, dy) = flow_field.grid_info();
+        let rho = self.config.density;
+
+        // Setup pressure correction equation: ∇²p' = ρ/Δt * ∇·u*
+        for j in 1..ny - 1 {
+            for i in 1..nx - 1 {
+                // Compute mass source (continuity equation residual)
+                let mass_source = self.compute_mass_source(flow_field, i, j, dx, dy, rho)?;
+                flow_field.sp[(j, i)] = mass_source;
+            }
+        }
+
+        // Solve pressure correction equation using Gauss-Seidel
+        let mut max_residual = 0.0;
+        for _iteration in 0..100 {
+            // Inner pressure correction iterations
+            let mut residual = 0.0;
+
+            for j in 1..ny - 1 {
+                for i in 1..nx - 1 {
+                    let coeffs = self.compute_pressure_coefficients(dx, dy)?;
+
+                    let p_new = (flow_field.sp[(j, i)]
+                        + coeffs.east * flow_field.p_prime[(j, i + 1)]
+                        + coeffs.west * flow_field.p_prime[(j, i - 1)]
+                        + coeffs.north * flow_field.p_prime[(j + 1, i)]
+                        + coeffs.south * flow_field.p_prime[(j - 1, i)])
+                        / coeffs.center;
+
+                    let correction = p_new - flow_field.p_prime[(j, i)];
+                    residual += correction * correction;
+                    flow_field.p_prime[(j, i)] = p_new;
+                }
+            }
+
+            residual = residual.sqrt();
+            max_residual = residual;
+
+            if residual < 1e-8 {
+                break;
+            }
+        }
+
+        Ok(max_residual)
+    }
+
+    /// Velocity correction step: correct velocities with pressure correction
+    pub async fn velocity_correction_step(&self, flow_field: &mut FlowField) -> CfdResult<()> {
+        let (nx, ny, dx, dy) = flow_field.grid_info();
+        let rho = self.config.density;
+
+        // Correct u-velocities
+        for j in 1..ny - 1 {
+            for i in 1..nx {
+                if i > 0 && i < nx {
+                    let dp_dx = (flow_field.p_prime[(j, i)] - flow_field.p_prime[(j, i - 1)]) / dx;
+                    let ap_u =
+                        self.compute_u_momentum_center_coefficient(flow_field, i, j, dx, dy, rho)?;
+                    flow_field.u[(j, i)] = flow_field.u_star[(j, i)] - (dx * dy / ap_u) * dp_dx;
+                }
+            }
+        }
+
+        // Correct v-velocities
+        for j in 1..ny {
+            for i in 1..nx - 1 {
+                if j > 0 && j < ny {
+                    let dp_dy = (flow_field.p_prime[(j, i)] - flow_field.p_prime[(j - 1, i)]) / dy;
+                    let ap_v =
+                        self.compute_v_momentum_center_coefficient(flow_field, i, j, dx, dy, rho)?;
+                    flow_field.v[(j, i)] = flow_field.v_star[(j, i)] - (dx * dy / ap_v) * dp_dy;
+                }
+            }
+        }
+
+        Ok(())
+    }
+
+    /// Pressure update step: add pressure correction to pressure
+    pub async fn pressure_update_step(&self, flow_field: &mut FlowField) -> CfdResult<()> {
+        let (nx, ny, _, _) = flow_field.grid_info();
+
+        for j in 0..ny {
+            for i in 0..nx {
+                flow_field.p[(j, i)] +=
+                    self.parameters.pressure_relaxation * flow_field.p_prime[(j, i)];
+                flow_field.p_prime[(j, i)] = 0.0; // Reset pressure correction
+            }
+        }
+
+        Ok(())
+    }
+
+    /// Solve turbulence model equations
+    async fn solve_turbulence(&mut self, flow_field: &FlowField, dt: f64) -> CfdResult<()> {
+        if self.parameters.use_turbulence {
+            // Initialize turbulence model if not already done
+            let (nx, ny, dx, dy) = flow_field.grid_info();
+            let n_cells = nx * ny;
+
+            if self.turbulence_model.is_none() {
+                self.turbulence_model =
+                    Some(KEpsilonModel::new(KEpsilonVariant::Standard, n_cells));
+            }
+
+            let turbulence_model = self.turbulence_model.as_mut().unwrap();
+
+            // Convert velocity field to Vector3 format
+            let mut velocity_vec = Vec::with_capacity(n_cells);
+            for j in 0..ny {
+                for i in 0..nx {
+                    let u = if i < nx && j < ny {
+                        flow_field.u[(j, i)]
+                    } else {
+                        0.0
+                    };
+                    let v = if i < nx && j < ny {
+                        flow_field.v[(j, i)]
+                    } else {
+                        0.0
+                    };
+                    velocity_vec.push(Vector3::new(u, v, 0.0)); // 2D case, w=0
+                }
+            }
+
+            // Simplified velocity gradients (zero for now)
+            let velocity_gradients = vec![[[0.0; 3]; 3]; n_cells];
+
+            // Create pressure vector
+            let mut pressure = DVector::zeros(n_cells);
+            for j in 0..ny {
+                for i in 0..nx {
+                    if i < nx && j < ny {
+                        pressure[j * nx + i] = flow_field.p[(j, i)];
+                    }
+                }
+            }
+
+            let turbulence_state = TurbulenceState {
+                velocity: velocity_vec,
+                velocity_gradients,
+                pressure,
+                turbulent_ke: None, // Will be initialized by model
+                epsilon: None,      // Will be initialized by model
+                omega: None,
+                wall_distance: DVector::from_element(n_cells, 1.0), // Simplified
+                cell_volumes: DVector::from_element(n_cells, dx * dy), // 2D cell volume
+                molecular_viscosity: self.config.viscosity / self.config.density, // kinematic viscosity
+                density: self.config.density,
+            };
+
+            // Update turbulence model with new state
+            turbulence_model.update(&turbulence_state, dt)?;
+        }
+        Ok(())
+    }
+
+    /// Compute effective viscosity (molecular + turbulent)
+    fn compute_effective_viscosity(
+        &self,
+        flow_field: &FlowField,
+        i: usize,
+        j: usize,
+        mu: f64,
+    ) -> f64 {
+        if let Some(ref turbulence_model) = self.turbulence_model {
+            // Get turbulent viscosity from the model
+            let (nx, _ny, _, _) = flow_field.grid_info();
+            let cell_idx = j * nx + i;
+            if cell_idx < turbulence_model.nu_t.len() {
+                let nu_t = turbulence_model.nu_t[cell_idx]; // kinematic turbulent viscosity
+                let mu_t = nu_t * self.config.density; // convert to dynamic viscosity
+                mu + mu_t
+            } else {
+                mu
+            }
+        } else {
+            mu
+        }
+    }
+
+    /// Compute coefficients for u-momentum equation
+    fn compute_u_momentum_coefficients(
+        &self,
+        flow_field: &FlowField,
+        i: usize,
+        j: usize,
+        dt: f64,
+        rho: f64,
+        mu: f64,
+        dx: f64,
+        dy: f64,
+    ) -> CfdResult<MomentumEquationCoeffs> {
+        // Compute effective viscosity (molecular + turbulent)
+        let mu_eff = self.compute_effective_viscosity(flow_field, i, j, mu);
+
+        // Diffusion coefficients using effective viscosity
+        let gamma_e = mu_eff / dx;
+        let gamma_w = mu_eff / dx;
+        let gamma_n = mu_eff / dy;
+        let gamma_s = mu_eff / dy;
+
+        // Convection coefficients (using upwind)
+        let (u_center, v_center) = flow_field.get_velocity_at(i, j)?;
+        let fe = rho * u_center * dy; // East face mass flux
+        let fw = rho * u_center * dy; // West face mass flux
+        let fn_ = rho * v_center * dx; // North face mass flux
+        let fs = rho * v_center * dx; // South face mass flux
+
+        // Compute coefficients with upwind scheme
+        let ae = gamma_e + f64::max(-fe, 0.0);
+        let aw = gamma_w + f64::max(fw, 0.0);
+        let an = gamma_n + f64::max(-fn_, 0.0);
+        let as_ = gamma_s + f64::max(fs, 0.0);
+
+        // Time derivative coefficient
+        let ap0 = rho * dx * dy / dt;
+
+        // Central coefficient
+        let ap = ae + aw + an + as_ + ap0;
+
+        // Source term (pressure gradient + old time step)
+        let pressure_gradient = -(flow_field.p[(j, i)] - flow_field.p[(j, i - 1)]) * dy;
+        let time_term = ap0 * flow_field.u_old[(j, i)];
+        let source = pressure_gradient + time_term;
+
+        Ok(MomentumEquationCoeffs {
+            center: ap,
+            east: ae,
+            west: aw,
+            north: an,
+            south: as_,
+            source,
+        })
+    }
+
+    /// Compute coefficients for v-momentum equation
+    fn compute_v_momentum_coefficients(
+        &self,
+        flow_field: &FlowField,
+        i: usize,
+        j: usize,
+        dt: f64,
+        rho: f64,
+        mu: f64,
+        dx: f64,
+        dy: f64,
+    ) -> CfdResult<MomentumEquationCoeffs> {
+        // Compute effective viscosity (molecular + turbulent)
+        let mu_eff = self.compute_effective_viscosity(flow_field, i, j, mu);
+
+        // Similar to u-momentum but for v-component
+        let gamma_e = mu_eff / dx;
+        let gamma_w = mu_eff / dx;
+        let gamma_n = mu_eff / dy;
+        let gamma_s = mu_eff / dy;
+
+        let (u_center, v_center) = flow_field.get_velocity_at(i, j)?;
+        let fe = rho * u_center * dy;
+        let fw = rho * u_center * dy;
+        let fn_ = rho * v_center * dx;
+        let fs = rho * v_center * dx;
+
+        let ae = gamma_e + f64::max(-fe, 0.0);
+        let aw = gamma_w + f64::max(fw, 0.0);
+        let an = gamma_n + f64::max(-fn_, 0.0);
+        let as_ = gamma_s + f64::max(fs, 0.0);
+
+        let ap0 = rho * dx * dy / dt;
+        let ap = ae + aw + an + as_ + ap0;
+
+        // Pressure gradient in y-direction
+        let pressure_gradient = -(flow_field.p[(j, i)] - flow_field.p[(j - 1, i)]) * dx;
+        let time_term = ap0 * flow_field.v_old[(j, i)];
+        let source = pressure_gradient + time_term;
+
+        Ok(MomentumEquationCoeffs {
+            center: ap,
+            east: ae,
+            west: aw,
+            north: an,
+            south: as_,
+            source,
+        })
+    }
+
+    /// Compute mass source term for pressure correction equation
+    fn compute_mass_source(
+        &self,
+        flow_field: &FlowField,
+        i: usize,
+        j: usize,
+        dx: f64,
+        dy: f64,
+        rho: f64,
+    ) -> CfdResult<f64> {
+        // Mass source = ρ * ∇·u*
+        let u_e = flow_field.u_star[(j, i + 1)];
+        let u_w = flow_field.u_star[(j, i)];
+        let v_n = flow_field.v_star[(j + 1, i)];
+        let v_s = flow_field.v_star[(j, i)];
+
+        let mass_flux_imbalance = rho * ((u_e - u_w) * dy + (v_n - v_s) * dx);
+
+        Ok(-mass_flux_imbalance) // Negative because we want ∇²p' = -∇·u*
+    }
+
+    /// Compute coefficients for pressure correction equation
+    fn compute_pressure_coefficients(&self, dx: f64, dy: f64) -> CfdResult<MomentumEquationCoeffs> {
+        // Pressure correction equation: ∇²p' = S
+        // Standard 5-point stencil with unit coefficients
+        let ae = 1.0 / (dx * dx);
+        let aw = 1.0 / (dx * dx);
+        let an = 1.0 / (dy * dy);
+        let as_ = 1.0 / (dy * dy);
+        let ap = ae + aw + an + as_;
+
+        Ok(MomentumEquationCoeffs {
+            center: ap,
+            east: ae,
+            west: aw,
+            north: an,
+            south: as_,
+            source: 0.0, // Source is set separately
+        })
+    }
+
+    /// Compute center coefficient for u-momentum equation
+    fn compute_u_momentum_center_coefficient(
+        &self,
+        _flow_field: &FlowField,
+        _i: usize,
+        _j: usize,
+        dx: f64,
+        dy: f64,
+        rho: f64,
+    ) -> CfdResult<f64> {
+        // Simplified calculation for velocity correction
+        // This would be the diagonal coefficient from momentum discretization
+        Ok(rho * dx * dy / self.parameters.time_step)
+    }
+
+    /// Compute center coefficient for v-momentum equation
+    fn compute_v_momentum_center_coefficient(
+        &self,
+        _flow_field: &FlowField,
+        _i: usize,
+        _j: usize,
+        dx: f64,
+        dy: f64,
+        rho: f64,
+    ) -> CfdResult<f64> {
+        Ok(rho * dx * dy / self.parameters.time_step)
+    }
+}
+
+/// Coefficients for momentum equation discretization
+#[derive(Debug, Clone)]
+struct MomentumEquationCoeffs {
+    pub center: f64,
+    pub east: f64,
+    pub west: f64,
+    pub north: f64,
+    pub south: f64,
+    pub source: f64,
+}
+
+#[async_trait]
+impl IncompressibleSolver for SimpleSolver {
+    type Parameters = SimpleParameters;
+    type Result = SimpleResult;
+
+    fn new(config: CfdConfig, params: Self::Parameters) -> CfdResult<Self> {
+        Self::new(config, params)
+    }
+
+    async fn solve_time_step(
+        &mut self,
+        flow_field: &mut FlowField,
+        boundary_conditions: &BoundaryConditions,
+        dt: f64,
+    ) -> CfdResult<Self::Result> {
+        let start_time = Instant::now();
+        let mut residual_history = Vec::new();
+        let pressure_iterations = Vec::new();
+
+        for iteration in 0..self.parameters.max_iterations {
+            let (mass_residual, momentum_residual) = self
+                .solve_simple_iteration(flow_field, boundary_conditions, dt)
+                .await?;
+
+            let total_residual =
+                (mass_residual * mass_residual + momentum_residual * momentum_residual).sqrt();
+            residual_history.push(total_residual);
+
+            if total_residual < self.parameters.tolerance {
+                let solve_time = start_time.elapsed();
+
+                return Ok(SimpleResult {
+                    solver_result: SolverResult {
+                        converged: true,
+                        iterations: iteration + 1,
+                        final_residual: total_residual,
+                        residual_history,
+                        solve_time,
+                    },
+                    pressure_iterations,
+                    mass_residual,
+                    momentum_residual,
+                });
+            }
+        }
+
+        // Did not converge
+        let solve_time = start_time.elapsed();
+        Ok(SimpleResult {
+            solver_result: SolverResult {
+                converged: false,
+                iterations: self.parameters.max_iterations,
+                final_residual: residual_history.last().copied().unwrap_or(f64::INFINITY),
+                residual_history,
+                solve_time,
+            },
+            pressure_iterations,
+            mass_residual: f64::INFINITY,
+            momentum_residual: f64::INFINITY,
+        })
+    }
+
+    async fn solve(
+        &mut self,
+        flow_field: &mut FlowField,
+        boundary_conditions: &BoundaryConditions,
+    ) -> CfdResult<Self::Result> {
+        // For steady-state solve, use default time step
+        self.solve_time_step(flow_field, boundary_conditions, self.parameters.time_step)
+            .await
+    }
+
+    fn config(&self) -> &CfdConfig {
+        &self.config
+    }
+
+    fn parameters(&self) -> &Self::Parameters {
+        &self.parameters
+    }
+}