Accepted Article INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids 0000; 00:1–28 Published online in Wiley Online Library (www.onlinelibrary.wiley.com). DOI: 10.1002/fld.4713 A new flux-limiting approach based kinetic scheme for the Euler equations of gas dynamics Raushan Kumar*, Anoop K. Dass Mechanical Engineering Department, Indian Institute of Technology Guwahati, Guwahati, India SUMMARY This paper proposes a new kinetic-theory-based high resolution scheme for the Euler equations of gas dynamics. The scheme uses the well-known connection that the Euler equations are suitable moments of the collisionless Boltzmann equation of kinetic theory. The collisionless Boltzmann equation is discretized using Sweby’s flux limited method and the moment of this Boltzmann level formulation gives an Euler level scheme. It is demonstrated how conventional limiters and an extremum-preserving limiter can be adapted for use in the scheme to achieve a desired effect. A simple TVD criteria relaxing parameter results in improving the resolution of the discontinuities in a significant way. A 1D scheme is formulated first and an extension to 2D on Cartesian meshes is carried out next. Accuracy analysis suggests that the scheme achieves between first and second order accuracy as is expected for any second order flux-limited method. The simplicity and the explicit form of the conservative numerical fluxes add to the efficiency of the scheme. Several standard 1D and 2D test problems are solved to demonstrate the robustness and accuracy. Copyright c  0000 John Wiley & Sons, Ltd. Received . . . KEY WORDS: Collisionless Boltzmann equation, Compressible Flow, Euler equations, Flux-limiting approach 1. INTRODUCTION Construction of efficient discretization schemes for the Euler equations of gas dynamics is an important activity in computational fluid dynamics (CFD) that has received considerable attention in the past four decades. Numerical conservation, upwinding, positivity, entropy condition satisfaction, etc., are some of the well established properties that a numerical scheme needs to satisfy. Upwinding property has become the main guiding principle for simulating hyperbolic nonlinear equations of gas dynamics. Harten et. al. [1] mention that upwinding principle in the computational algorithms for Euler equations is implemented using generally two techniques, namely, Riemann solvers and Boltzmann equation solvers, and all the flux vector splitting techniques can be viewed as some kind of collisionless Boltzmann type equation solvers. The Euler and Navier-Stokes equations of gas dynamics can be obtained by taking moments of the Boltzmann equation of kinetic theory of gases * Correspondence to: *Raushan Kumar, Mechanical Engineering Department, Indian Institute of Technology Guwahati, Assam-781039, India. Email: raushan.kumar@iitg.ac.in This article has been accepted for publication and undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process, which may lead to differences between this version and the Version of Record. Please cite this article as doi: 10.1002/fld.4713 This article is protected by copyright. All rights reserved.