High-order methods for diffuse-interface models in compressible multi-medium flows: A review

The diffuse interface models, part of the family of the front capturing methods, provide an efficient and robust framework for the simulation of multi-species flows. They allow the integration of additional physical phenomena of increasing complexity while ensuring discrete conservation of mass, momentum, and energy. The main drawback brought by the adoption of these models consists of the interface smearing, increasing with the simulation time, therefore, requiring a counteraction through the introduction of sharpening terms and a careful selection of the discretization level. In recent years, the diffuse interface models have been solved using several numerical frameworks including finite volume, discontinuous Galerkin, and hybrid lattice Boltzmann method, in conjunction with shock and contact wave capturing schemes. The present review aims to present the recent advancements of high-order accuracy schemes with the capability of solving discontinuities without the introduction of numerical instabilities and to put them in perspective for the solution of multi-species flows with the diffuse interface method.(c) 2022 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license.

Automated summary

Diffuse interface models, despite interface smearing issues, provide an efficient and robust framework for simulating multi-species flows. Recent advancements in high-order accuracy schemes have allowed these models to solve discontinuities without introducing numerical instabilities in various numerical frameworks.