ldc.SpectralSolver

class ldc.SpectralSolver(**kwargs)

Bases: LidDrivenCavitySolver

Pseudospectral solver for lid-driven cavity problem.

Uses explicit time-stepping with artificial compressibility to solve the incompressible Navier-Stokes equations on a Legendre-Gauss-Lobatto grid.

Parameters:

paramsSpectralParameters

Parameters with physics (Re, lid velocity, domain size) and spectral-specific settings (Nx, Ny, CFL, beta_squared, etc.).

Methods

__init__	Initialize spectral solver.
mlflow_end	End MLflow run and log final metrics.
mlflow_log_artifact	Log an artifact (e.g., saved HDF5 file) to MLflow.
mlflow_start	Start MLflow run and log parameters.
save	Save complete solver state to HDF5 file.
solve	Solve the lid-driven cavity problem using iterative stepping.
step	Perform one RK4 pseudo time-step.

Examples using ldc.SpectralSolver

Lid-Driven Cavity Flow - Spectral Chebyshev

Lid-Driven Cavity Flow - Spectral Chebyshev

Parameters

alias of SpectralParameters

mlflow_end()

End MLflow run and log final metrics.

mlflow_log_artifact(filepath: str)

Log an artifact (e.g., saved HDF5 file) to MLflow.

Parameters:

filepathstr

Path to the file to log as artifact.

mlflow_start(experiment_name: str, run_name: str, parent_run_name: str = None)

Start MLflow run and log parameters.

Parameters:

experiment_namestr

Name of the MLflow experiment.

run_namestr

Name of the run within the experiment.

parent_run_namestr, optional

If specified, creates a nested run under a parent with this name. Parent is created if it doesn’t exist, or resumed if it does.

save(filepath)

Save complete solver state to HDF5 file.

Saves params, metrics, time_series, and fields for later analysis.

Parameters:

filepathstr or Path

Output file path (use .h5 extension).

solve(tolerance: float = None, max_iter: int = None)

Solve the lid-driven cavity problem using iterative stepping.

This method implements the common iteration loop with residual calculation. Subclasses implement step() to define one iteration.

Stores results in solver attributes: - self.fields : Fields dataclass with solution fields - self.time_series : TimeSeries dataclass with time series data - self.metrics : Metrics dataclass with solver metrics

Parameters:

tolerancefloat, optional

Convergence tolerance. If None, uses params.tolerance.

max_iterint, optional

Maximum iterations. If None, uses params.max_iterations.

step()

Perform one RK4 pseudo time-step.

PN-PN-2: Updates u, v on full grid and p on inner grid.

Returns:

u, v, pnp.ndarray

Updated velocities (full grid) and pressure (inner grid)