Greedy recursion parameter selection for one-way spatial integration of hyperbolic equations

TL;DR

This paper introduces a greedy algorithm for automatic selection of recursion parameters in one-way wave equations, improving accuracy and reducing computational cost in hyperbolic system simulations.

Contribution

It develops a greedy parameter selection method for OWNS approaches, enhancing convergence speed and stability over heuristic tuning.

Findings

Greedy algorithm outperforms heuristic parameter choices in convergence.

OWNS-P method shows superior stability and convergence properties.

The approach is applicable to linear hyperbolic systems beyond Navier-Stokes.

Abstract

Solutions to hyperbolic systems comprise waves propagating at finite speeds. When wave propagation is predominantly unidirectional, one-way wave equations can be used to evolve only the right-going solution by removing support for left-going waves. The One-Way Navier-Stokes (OWNS) approach, which was originally developed for systems of first-order hyperbolic equations, constructs one-way approximations to the linearized Navier-Stokes equations using a recursive filter to remove left-going waves. The computational cost scales with the number of recursion parameters, which must be carefully chosen to ensure accuracy and stability of the resulting one-way equation. Previous work has chosen parameters based on heuristic estimates of key eigenvalues, which requires trial-and-error tuning while also yielding slow error convergence. We propose a greedy algorithm for automatic parameter selection, which we show yields faster convergence and a net decrease in computational cost for linear and nonlinear disturbance evolution in boundary-layer flows. We review the OWNS projection (OWNS-P) and recursive (OWNS-R) methods, comparing their convergence properties, and show through our numerical analysis and experiments that OWNS-P yields superior convergence and stability properties. Although we demonstrate the method for Navier-Stokes equations, we perform our analyses on systems of linear first-order hyperbolic equations and emphasize that the greedy algorithm is applicable to such systems.