One-sided GRP Solver and Numerical Boundary Conditions for compressible fluid flows

TL;DR

This paper introduces a one-sided GRP solver that improves boundary condition treatment in compressible fluid flow simulations, reducing spurious reflections and enhancing numerical stability.

Contribution

It develops a novel one-sided generalized Riemann problem solver that eliminates the need for extrapolation techniques at boundaries in compressible flow computations.

Findings

Significant reduction in spurious wave reflections at boundaries

Improved numerical stability in simulations

Effective handling of nonlinear wave interactions with boundaries

Abstract

In the computation of compressible fluid flows, numerical boundary conditions are always necessary for all physical variables at computational boundaries while just partial physical variables are often prescribed as physical boundary conditions. Certain extrapolation technique or ghost cells are often employed traditionally for this issue but spurious wave reflections often arise to cause numerical instability. In this paper, we associate this issue with the one-sided generalized Riemann problem (GRP) solver motivated by the accelerated piston problem in gas dynamics so that the extrapolation technique can be actually avoided. In fact, the compatibility arguments naturally requires to formulate the one-sided generalized Riemann problem and incorporate it into the numerical procedure of boundary conditions. As far as the interaction of nonlinear waves with physical boundaries, such a one-sided GRP solver shows significant effects, as numerical experiments demonstrate, on avoiding spurious wave reflections at the computational boundaries.