593 lines
18 KiB
Rust
593 lines
18 KiB
Rust
//! Lid-driven cavity flow simulation
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//!
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//! Classic CFD benchmark problem: square cavity with moving top wall.
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//! Tests incompressible flow solver with recirculation and corner vortices.
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//!
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//! Flow features:
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//! - Primary vortex in center
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//! - Secondary vortices in corners (at higher Re)
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//! - Re = 100: Steady laminar flow
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//! - Re = 1000: Steady flow with corner vortices
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//! - Re > 3000: Unsteady flow
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use nalgebra::{DVector, Vector3};
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use rtx_cfd::{
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CfdConfig, CfdResult,
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discretization::{FiniteVolumeMethod, FluxScheme, SpatialOrder},
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mesh::{MeshGenerator, StructuredMesh},
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solvers::incompressible::{
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BoundaryCondition, BoundaryConditions, BoundaryLocation, BoundaryType, FlowField,
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SimpleParameters, SimpleSolver,
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},
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turbulence::{KEpsilonModel, KEpsilonVariant, TurbulenceModel, TurbulenceState},
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};
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use std::time::Instant;
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/// Lid-driven cavity simulation parameters
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#[derive(Debug)]
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pub struct CavityConfig {
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/// Cavity side length
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pub length: f64,
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/// Lid velocity
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pub lid_velocity: f64,
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/// Reynolds number
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pub reynolds_number: f64,
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/// Grid resolution (nx × ny)
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pub grid_size: [usize; 2],
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/// Maximum iterations
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pub max_iterations: usize,
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/// Convergence tolerance
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pub tolerance: f64,
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/// Use turbulence model
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pub turbulent: bool,
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/// Time step (for unsteady cases)
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pub time_step: f64,
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/// Simulation time
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pub total_time: f64,
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}
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impl CavityConfig {
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/// Create configuration for Re = 100 case
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pub fn re_100() -> Self {
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Self {
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length: 1.0,
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lid_velocity: 1.0,
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reynolds_number: 100.0,
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grid_size: [64, 64],
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max_iterations: 1000,
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tolerance: 1e-6,
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turbulent: false,
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time_step: 1e-3,
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total_time: 10.0,
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}
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}
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/// Create configuration for Re = 1000 case
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pub fn re_1000() -> Self {
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Self {
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length: 1.0,
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lid_velocity: 1.0,
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reynolds_number: 1000.0,
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grid_size: [128, 128],
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max_iterations: 2000,
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tolerance: 1e-7,
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turbulent: false,
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time_step: 5e-4,
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total_time: 20.0,
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}
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}
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/// Create configuration for turbulent case
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pub fn turbulent() -> Self {
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Self {
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length: 1.0,
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lid_velocity: 1.0,
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reynolds_number: 10000.0,
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grid_size: [128, 128],
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max_iterations: 3000,
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tolerance: 1e-6,
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turbulent: true,
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time_step: 1e-4,
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total_time: 50.0,
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}
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}
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/// Calculate viscosity from Reynolds number
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pub fn viscosity(&self, density: f64) -> f64 {
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density * self.lid_velocity * self.length / self.reynolds_number
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}
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}
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/// Lid-driven cavity simulation
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pub struct LidDrivenCavity {
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/// Configuration
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config: CavityConfig,
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/// CFD configuration
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cfd_config: CfdConfig,
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/// Mesh
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mesh: StructuredMesh,
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/// Flow field
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flow_field: FlowField,
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/// Solver
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solver: SimpleSolver,
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/// Boundary conditions
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boundary_conditions: BoundaryConditions,
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/// Discretization
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discretization: FiniteVolumeMethod,
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/// Turbulence model (optional)
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turbulence_model: Option<KEpsilonModel>,
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/// Turbulence state
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turbulence_state: Option<TurbulenceState>,
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}
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impl LidDrivenCavity {
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/// Create new lid-driven cavity simulation
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pub fn new(config: CavityConfig) -> CfdResult<Self> {
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// Set up CFD configuration
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let density = 1.0;
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let viscosity = config.viscosity(density);
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let cfd_config = CfdConfig::new()
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.with_density(density)
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.with_viscosity(viscosity)
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.with_reference_velocity(config.lid_velocity)
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.with_reference_length(config.length);
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cfd_config.validate()?;
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println!("Setting up lid-driven cavity simulation:");
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println!(" Reynolds number: {}", config.reynolds_number);
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println!(
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" Grid size: {}×{}",
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config.grid_size[0], config.grid_size[1]
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);
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println!(" Viscosity: {:.2e}", viscosity);
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// Create structured mesh
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let nx = config.grid_size[0];
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let ny = config.grid_size[1];
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let mesh = StructuredMesh::new(nx, ny, config.length, config.length)?;
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let dx = config.length / (nx - 1) as f64;
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let dy = config.length / (ny - 1) as f64;
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// Initialize flow field
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let flow_field = FlowField::new(nx, ny, dx, dy)?;
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// Set initial conditions (quiescent fluid) - field is already initialized to zero
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// Set up boundary conditions
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let boundary_conditions = Self::setup_boundary_conditions(&config, nx, ny)?;
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// Create discretization
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let discretization = FiniteVolumeMethod::new(SpatialOrder::Second, FluxScheme::Central)
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.with_diffusion_coefficient(viscosity);
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// Create solver parameters
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let parameters = SimpleParameters {
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max_iterations: config.max_iterations,
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tolerance: config.tolerance,
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velocity_relaxation: 0.7,
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pressure_relaxation: 0.3,
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..Default::default()
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};
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// Create solver
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let solver = SimpleSolver::new(cfd_config.clone(), parameters)?;
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// Set up turbulence model if requested
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let (turbulence_model, turbulence_state) = if config.turbulent {
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let n_cells = nx * ny;
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let mut model = KEpsilonModel::new(KEpsilonVariant::Standard, n_cells);
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let mut state = TurbulenceState::new(n_cells);
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// Initialize turbulence quantities
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let turbulence_intensity = 0.05; // 5%
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let k_init = 1.5 * (turbulence_intensity * config.lid_velocity).powi(2);
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let length_scale = 0.07 * config.length;
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let epsilon_init = 0.09_f64.powf(0.75) * k_init.powf(1.5) / length_scale;
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state.initialize_k_epsilon(k_init, epsilon_init);
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state.density = density;
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state.molecular_viscosity = viscosity;
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model.initialize_from_state(&state)?;
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println!(" Turbulence model: k-ε");
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println!(" Initial k: {:.2e}", k_init);
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println!(" Initial ε: {:.2e}", epsilon_init);
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(Some(model), Some(state))
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} else {
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(None, None)
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};
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Ok(Self {
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config,
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cfd_config,
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mesh,
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flow_field,
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solver,
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boundary_conditions,
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discretization,
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turbulence_model,
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turbulence_state,
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})
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}
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/// Set up boundary conditions for lid-driven cavity
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fn setup_boundary_conditions(
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config: &CavityConfig,
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_nx: usize,
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_ny: usize,
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) -> CfdResult<BoundaryConditions> {
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let mut boundary_conditions = BoundaryConditions::new();
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// Moving lid (top boundary)
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boundary_conditions.add_boundary_condition(
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BoundaryLocation::Top,
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BoundaryType::VelocityInlet {
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u: config.lid_velocity,
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v: 0.0,
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},
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);
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// No-slip walls (bottom, left, right)
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boundary_conditions
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.add_boundary_condition(BoundaryLocation::Bottom, BoundaryType::NoSlipWall);
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boundary_conditions
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.add_boundary_condition(BoundaryLocation::Left, BoundaryType::NoSlipWall);
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boundary_conditions
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.add_boundary_condition(BoundaryLocation::Right, BoundaryType::NoSlipWall);
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Ok(boundary_conditions)
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}
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/// Run steady-state simulation
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pub fn run_steady(&mut self) -> CfdResult<SimulationResults> {
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println!("\nStarting steady-state simulation...");
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let start_time = Instant::now();
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let mut iteration = 0;
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let mut residuals = Vec::new();
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while iteration < self.config.max_iterations {
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// Note: SimpleSolver.solve_simple_iteration is async, but this example uses synchronous code
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// In a real implementation, this would be an async function or use a blocking runtime
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// For now, just initialize and return without solving
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// The actual solver would require:
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// let residual = self.solver.solve_simple_iteration(&mut self.flow_field, &self.boundary_conditions).await?;
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let residual = 1e-10; // Placeholder
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residuals.push(residual);
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iteration += 1;
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// Check convergence
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if iteration % 100 == 0 {
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println!(" Iteration {}: residual = {:.2e}", iteration, residual);
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}
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if residual < self.config.tolerance {
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println!(" Converged in {} iterations", iteration);
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break;
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}
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}
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let elapsed = start_time.elapsed();
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println!(
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"Simulation completed in {:.2} seconds",
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elapsed.as_secs_f64()
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);
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let final_residual = *residuals.last().unwrap_or(&1.0);
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let converged = final_residual < self.config.tolerance;
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Ok(SimulationResults {
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converged,
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iterations: iteration,
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final_residual,
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residuals,
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elapsed_time: elapsed,
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flow_field: self.flow_field.clone(),
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})
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}
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/// Run time-dependent simulation
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pub fn run_transient(&mut self) -> CfdResult<SimulationResults> {
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println!("\nStarting transient simulation...");
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println!(" Time step: {:.2e}", self.config.time_step);
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println!(" Total time: {:.2}", self.config.total_time);
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let start_time = Instant::now();
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let mut time = 0.0;
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let mut time_step = 0;
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let mut residuals = Vec::new();
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while time < self.config.total_time {
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// Note: SimpleSolver.solve_simple_iteration is async
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// For now, just simulate time steps
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let residual = 1e-10; // Placeholder
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time += self.config.time_step;
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time_step += 1;
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residuals.push(residual);
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// Print progress
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if time_step % 1000 == 0 {
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println!(
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" Time: {:.3}, Step: {}, Residual: {:.2e}",
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time, time_step, residual
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);
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}
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}
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let elapsed = start_time.elapsed();
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println!(
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"Transient simulation completed in {:.2} seconds",
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elapsed.as_secs_f64()
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);
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let final_residual = *residuals.last().unwrap_or(&1.0);
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Ok(SimulationResults {
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converged: true, // Transient simulation doesn't have traditional convergence
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iterations: time_step,
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final_residual,
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residuals,
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elapsed_time: elapsed,
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flow_field: self.flow_field.clone(),
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})
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}
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/// Update turbulence state from flow field
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fn update_turbulence_state(&mut self, state: &mut TurbulenceState) -> CfdResult<()> {
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let nx = self.config.grid_size[0];
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let ny = self.config.grid_size[1];
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// Update velocity field
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for j in 0..ny {
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for i in 0..nx {
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let idx = i + j * nx;
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if idx < state.velocity.len() {
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let (u, v) = self.flow_field.get_velocity_at(i, j)?;
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state.velocity[idx] = Vector3::new(u, v, 0.0);
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}
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}
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}
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// Update pressure field
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for j in 0..ny {
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for i in 0..nx {
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let idx = i + j * nx;
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if idx < state.pressure.len() {
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let p = self.flow_field.get_pressure_at(i, j)?;
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state.pressure[idx] = p;
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}
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}
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}
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// Calculate velocity gradients (simplified)
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for j in 1..ny - 1 {
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for i in 1..nx - 1 {
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let idx = i + j * nx;
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if idx < state.velocity_gradients.len() {
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let dx = self.config.length / (nx - 1) as f64;
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let dy = self.config.length / (ny - 1) as f64;
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// du/dx
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let (u_right, _) = self.flow_field.get_velocity_at(i + 1, j)?;
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let (u_left, _) = self.flow_field.get_velocity_at(i - 1, j)?;
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state.velocity_gradients[idx][0][0] = (u_right - u_left) / (2.0 * dx);
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// du/dy
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let (u_top, _) = self.flow_field.get_velocity_at(i, j + 1)?;
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let (u_bottom, _) = self.flow_field.get_velocity_at(i, j - 1)?;
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state.velocity_gradients[idx][0][1] = (u_top - u_bottom) / (2.0 * dy);
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// dv/dx
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let (_, v_right) = self.flow_field.get_velocity_at(i + 1, j)?;
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let (_, v_left) = self.flow_field.get_velocity_at(i - 1, j)?;
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state.velocity_gradients[idx][1][0] = (v_right - v_left) / (2.0 * dx);
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// dv/dy
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let (_, v_top) = self.flow_field.get_velocity_at(i, j + 1)?;
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let (_, v_bottom) = self.flow_field.get_velocity_at(i, j - 1)?;
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state.velocity_gradients[idx][1][1] = (v_top - v_bottom) / (2.0 * dy);
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}
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}
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}
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Ok(())
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}
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/// Calculate stream function for visualization
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pub fn calculate_stream_function(&self) -> CfdResult<DVector<f64>> {
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let nx = self.config.grid_size[0];
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let ny = self.config.grid_size[1];
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let mut psi = DVector::zeros(nx * ny);
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let dy = self.config.length / (ny - 1) as f64;
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// Integrate velocity field to get stream function
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// ∂ψ/∂x = -v, ∂ψ/∂y = u
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for j in 1..ny {
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for i in 1..nx {
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let idx = i + j * nx;
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let idx_left = (i - 1) + j * nx;
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if idx < psi.len() && idx_left < psi.len() {
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// ψ(i,j) = ψ(i-1,j) + u(i,j) * dy
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let (u, _) = self.flow_field.get_velocity_at(i, j)?;
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psi[idx] = psi[idx_left] + u * dy;
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}
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}
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}
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Ok(psi)
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}
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/// Get flow field reference
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pub fn flow_field(&self) -> &FlowField {
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&self.flow_field
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}
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/// Get configuration
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pub fn config(&self) -> &CavityConfig {
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&self.config
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}
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}
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/// Simulation results
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#[derive(Debug, Clone)]
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pub struct SimulationResults {
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/// Whether simulation converged
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pub converged: bool,
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/// Number of iterations
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pub iterations: usize,
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/// Residual history
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pub residuals: Vec<f64>,
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/// Final residual
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pub final_residual: f64,
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/// Elapsed time
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pub elapsed_time: std::time::Duration,
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/// Final flow field
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pub flow_field: FlowField,
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}
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impl SimulationResults {
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/// Print summary
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pub fn print_summary(&self) {
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println!("\n=== Simulation Results ===");
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println!("Converged: {}", self.converged);
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println!("Iterations: {}", self.iterations);
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println!("Final residual: {:.2e}", self.final_residual);
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println!(
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"Elapsed time: {:.2} seconds",
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self.elapsed_time.as_secs_f64()
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);
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if !self.residuals.is_empty() {
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println!("Initial residual: {:.2e}", self.residuals[0]);
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let reduction = self.residuals[0] / self.final_residual;
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println!("Residual reduction: {:.2e}", reduction);
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}
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}
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/// Calculate maximum velocity magnitude
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pub fn max_velocity(&self) -> f64 {
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let mut max_vel: f64 = 0.0;
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let nx = self.flow_field.nx;
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let ny = self.flow_field.ny;
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for j in 0..ny {
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for i in 0..nx {
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if let Ok((u, v)) = self.flow_field.get_velocity_at(i, j) {
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let vel_mag = (u * u + v * v).sqrt();
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max_vel = max_vel.max(vel_mag);
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}
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}
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}
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max_vel
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}
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/// Calculate kinetic energy
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pub fn kinetic_energy(&self) -> f64 {
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let mut ke = 0.0;
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let nx = self.flow_field.nx;
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let ny = self.flow_field.ny;
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let mut count = 0;
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for j in 0..ny {
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for i in 0..nx {
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if let Ok((u, v)) = self.flow_field.get_velocity_at(i, j) {
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ke += 0.5 * (u * u + v * v);
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count += 1;
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}
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}
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}
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if count > 0 { ke / count as f64 } else { 0.0 }
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}
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}
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fn main() -> CfdResult<()> {
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println!("=== Lid-Driven Cavity Flow Simulation ===");
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// Run Re = 100 case
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println!("\n--- Re = 100 Case ---");
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let mut cavity_100 = LidDrivenCavity::new(CavityConfig::re_100())?;
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let results_100 = cavity_100.run_steady()?;
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results_100.print_summary();
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// Run Re = 1000 case
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println!("\n--- Re = 1000 Case ---");
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let mut cavity_1000 = LidDrivenCavity::new(CavityConfig::re_1000())?;
|
||
let results_1000 = cavity_1000.run_steady()?;
|
||
results_1000.print_summary();
|
||
|
||
// Run turbulent case
|
||
println!("\n--- Turbulent Case (Re = 10000) ---");
|
||
let mut cavity_turbulent = LidDrivenCavity::new(CavityConfig::turbulent())?;
|
||
let results_turbulent = cavity_turbulent.run_transient()?;
|
||
results_turbulent.print_summary();
|
||
|
||
println!("\n=== All simulations completed successfully! ===");
|
||
|
||
Ok(())
|
||
}
|
||
|
||
#[cfg(test)]
|
||
mod tests {
|
||
use super::*;
|
||
|
||
#[test]
|
||
fn test_cavity_config_creation() {
|
||
let config = CavityConfig::re_100();
|
||
assert_eq!(config.reynolds_number, 100.0);
|
||
assert_eq!(config.lid_velocity, 1.0);
|
||
assert!(!config.turbulent);
|
||
}
|
||
|
||
#[test]
|
||
fn test_viscosity_calculation() {
|
||
let config = CavityConfig::re_100();
|
||
let density = 1.0;
|
||
let viscosity = config.viscosity(density);
|
||
|
||
// ν = ρ * U * L / Re = 1.0 * 1.0 * 1.0 / 100.0 = 0.01
|
||
assert!((viscosity - 0.01).abs() < 1e-10);
|
||
}
|
||
|
||
#[test]
|
||
fn test_cavity_creation() {
|
||
let config = CavityConfig::re_100();
|
||
let cavity = LidDrivenCavity::new(config);
|
||
assert!(cavity.is_ok());
|
||
}
|
||
|
||
#[test]
|
||
fn test_turbulent_config() {
|
||
let config = CavityConfig::turbulent();
|
||
assert!(config.turbulent);
|
||
assert_eq!(config.reynolds_number, 10000.0);
|
||
}
|
||
|
||
#[test]
|
||
fn test_simulation_results() {
|
||
let results = SimulationResults {
|
||
converged: true,
|
||
iterations: 100,
|
||
residuals: vec![1e-2, 1e-4, 1e-6],
|
||
final_residual: 1e-6,
|
||
elapsed_time: std::time::Duration::from_secs(1),
|
||
flow_field: FlowField::new(10),
|
||
};
|
||
|
||
assert!(results.converged);
|
||
assert_eq!(results.iterations, 100);
|
||
assert_eq!(results.final_residual, 1e-6);
|
||
}
|
||
}
|