A hybrid WENO method with modified ghost fluid method for compressible two-medium flow problems

TL;DR

This paper introduces a simplified hybrid WENO method combined with a modified ghost fluid approach to efficiently and robustly simulate compressible two-medium flows, improving computational simplicity and performance.

Contribution

A novel hybrid WENO method integrated with MGFM that simplifies implementation and enhances efficiency for two-medium flow simulations.

Findings

Effective handling of material interfaces as 'invisible'

High accuracy demonstrated in 1D and 2D tests

Reduced computational complexity and time

Abstract

In this paper, we develop a simplified hybrid weighted essentially non-oscillatory (WENO) method combined with the modified ghost fluid method (MGFM) [28] to simulate the compressible two-medium flow problems. The MGFM can turn the two-medium flow problems into two single-medium cases by defining the ghost fluids status in terms of the predicted the interface status, which makes the material interface "invisible". For the single medium flow case, we adapt between the linear upwind scheme and the WENO scheme automatically by identifying the regions of the extreme points for the reconstruction polynomial as same as the hybrid WENO scheme [50]. Instead of calculating their exact locations, we only need to know the regions of the extreme points based on the zero point existence theorem, which is simpler for implementation and saves computation time. Meanwhile, it still keeps the robustness and has high efficiency. Extensive numerical results for both one and two dimensional two-medium flow problems are performed to demonstrate the good performances of the proposed method.