Abstract
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.
Highlights
A detailed review of the application of different high-order methods on unstructured meshes is presented in Ref. 79. Given this variety of schemes for the solution of multi-species flows and the recent introduction of hybridizations of the classical FV schemes with both the discontinuous Galerkin (DG) and LBM frameworks, this review proposes, without the ambition to cover the totality of the available computational frames, to gather the recent advancements in high-order accuracy schemes on unstructured grids and to put them in perspective for the simulation of multi-species flows with the diffuse interface method
A recent review of the main diffuse interface methods (DIM) models is available in Ref. 27; in this work, we focus on the implementation and adaptations required by these models within different numerical frameworks, emphasizing the challenges and advantages relative to each scheme, and comparing their efficiency and accuracy
The algorithm proposes two or more candidate reconstruction functions, for example, one linear polynomial built with a monotone upstream-centered scheme for conservation law (MUSCL) scheme coupled to the multi-dimensional limiting process (MLP) slope limiter, and one non-polynomial reconstruction obtained with the tangent of hyperbola for interface capturing (THINC) approach with quadratic surface representation and Gaussian quadrature (THINC/QQ)
Summary
Recent research in the area of multiphase and multi-species flows has been successfully applied to a wide range of problems in engineering and sciences, for example, detonation of high energy materials,[1,2] shock–bubble interaction,[3,4] propellant mixing in high-pressure combustors,[5,6] tumor growth modeling,[7] and fluidÀsolid interaction.[8,9]. Applications on irregular grids are becoming, in general, a necessity in industrial applications, especially when complicated geometries are considered and present a number of advantages over structured grids, ranging from the ease of mesh smoothness requirement,[78,79] to the maintenance of load balance in parallel computing.[80,81] A detailed review of the application of different high-order methods on unstructured meshes is presented in Ref. 79 Given this variety of schemes for the solution of multi-species flows and the recent introduction of hybridizations of the classical FV schemes with both the DG and LBM frameworks, this review proposes, without the ambition to cover the totality of the available computational frames, to gather the recent advancements in high-order accuracy schemes on unstructured grids and to put them in perspective for the simulation of multi-species flows with the diffuse interface method. The available to-date applications of DI models in conjunction with sharpening techniques on different numerical frameworks and hybrid schemes are presented
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