A High-resolution Spatiotemporal Coupling Ghost Fluid Method for Two-Dimensional Compressible Multimedium Flows with Source Terms

TL;DR

This paper introduces a high-resolution ghost fluid method that accurately models entropy transport and tangential fluxes in 2D compressible multimedium flows with source terms, improving simulation fidelity.

Contribution

It presents a novel spatiotemporal coupling ghost fluid method integrating nonlinear geometrical optics and Lax-Wendroff techniques for better multidimensional flow modeling.

Findings

Enhanced accuracy over traditional methods

Improved robustness in complex flow scenarios

Effective handling of source terms and tangential fluxes

Abstract

While exact and approximate Riemann solvers are widely used, they exhibit two fundamental limitations: 1) Fail to represent continuous entropy transport processes, resulting in thermodynamic incompatibility that limits their applicability to compressible flows. 2) Consider only the effects of normal components at interfaces while neglecting the effects of tangential flux and source term, making them unsuitable for multidimensional problems and cases involving source terms. These limitations persist in Riemann problem-based ghost fluid methods. To address these challenges, we developed a novel spatiotemporal coupling high-resolution ghost fluid method featuring two key advancements: 1) Integration of nonlinear geometrical optics to properly account for thermodynamic entropy evolution. 2) Implementation of the Lax-Wendroff/Cauchy-Kowalevski approach to incorporate tangential fluxes and source term effects. These enhancements have been systematically applied to Riemann problem-based ghost fluid methods. Comprehensive numerical experiments demonstrate significant improvements in simulation accuracy and robustness compared to conventional approaches.