Genuinely Multidimensional Kinetic Scheme For Euler Equations

TL;DR

This paper introduces a novel, genuinely multidimensional, mesh-less kinetic scheme based on the Boltzmann equation for solving Euler's equations, improving shock capturing and flow feature isotropy.

Contribution

It develops a new finite difference framework, GINEUS, that operates in multidimensions using polar coordinates and extends to second order with the 'Arc of Approach' concept.

Findings

Enhanced shock capturing capabilities.

Isotropic flow feature resolution.

Outperforms Kinetic Flux Vector Splitting Method in benchmarks.

Abstract

A new framework based on Boltzmann equation which is genuinely multidimensional and mesh-less is developed for solving Euler's equations. The idea is to use the method of moment of Boltzmann equation to operate in multidimensions using polar coordinates. The aim is to develop a framework which is genuinely multidimensional and can be implemented with different methodologies, no matter whether it is in finite difference, finite volume or finite element form. There is a considerable improvement in capturing shocks and other discontinuities. Also, since the method is multidimensional, the flow features are captured isotropically. The method is further extended to second order using 'Arc of Approach' concept. The framework is developed as a finite difference method (called as GINEUS) and is tested on the benchmark test cases. The results are compared against Kinetic Flux Vector Splitting Method.