Low-Dissipation Central-Upwind Schemes for Compressible Multifluids

TL;DR

This paper presents second-order low-dissipation central-upwind schemes for simulating compressible multifluids with immiscible components, achieving high resolution near interfaces and extending to fifth-order accuracy with A-WENO methods.

Contribution

The paper develops and extends low-dissipation central-upwind schemes for multifluid systems, incorporating interface tracking and limiter strategies, and achieves higher-order accuracy.

Findings

Effective interface resolution with overcompressive limiter.

Second-order scheme demonstrated on 1D and 2D examples.

Extension to fifth-order accuracy with A-WENO framework.

Abstract

We introduce second-order low-dissipation (LD) path-conservative central-upwind (PCCU) schemes for the one- (1-D) and two-dimensional (2-D) multifluid systems, whose components are assumed to be immiscible and separated by material interfaces. The proposed LD PCCU schemes are derived within the flux globalization based PCCU framework and they employ the LD central-upwind (LDCU) numerical fluxes. These fluxes have been recently proposed in [{\sc A. Kurganov and R. Xin}, J. Sci. Comput., 96 (2023), Paper No. 56] for the single-fluid compressible Euler equations and we rigorously develop their multifluid extensions. In order to achieve higher resolution near the material interfaces, we track their locations and use an overcompressive SBM limiter in their neighborhoods, while utilizing a dissipative generalized minmod limiter in the rest of the computational domain. We first develop a second-order finite-volume LD PCCU scheme and then extend it to the fifth order of accuracy via the finite-difference alternative weighted essentially non-oscillatory (A-WENO) framework. We apply the developed schemes to a number of 1-D and 2-D numerical examples to demonstrate the performance of the new schemes.