Godunov-type schemes for the pressureless gas dynamics and related models

Garg, NK and Gowda, GDV (2022) Godunov-type schemes for the pressureless gas dynamics and related models. In: Applied Mathematics and Computation, 418 .

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Abstract

We study and develop new first-order Godunov-type schemes for the weakly hyperbolic pressureless gas dynamics equations and augmented Burgers� equations. Each of these systems carries the information of propagation of waves with the same fluid velocity. The goal is achieved by first obtaining an Engquist-Osher (EO) type scheme for the pressureless system and then by enhancing the upwinding information present in the EO-type scheme to construct more accurate Godunov-type schemes. The resulting schemes present a lesser amount of numerical dissipation than existing Jordan decomposition-based Flux Difference Splitting (FDS) schemes recently proposed in N. K. GARG, Numer. Algorithms, 83 (2020) 1091�1121 and are compact and robust. These schemes are tested on a number of numerical examples for one- and two-dimensional pressureless equations of gas dynamics and then to augmented Burgers� equations. © 2021

Item Type:	Journal Article
Publication:	Applied Mathematics and Computation
Publisher:	Elsevier Inc.
Additional Information:	The copyright for this article belongs to Elsevier Inc.
Keywords:	Burger's equations; Delta-shock; First order; Gasdynamic equations; Godunov-type schemes; Pressureless; Shock-capturing; Single point; Single-point shock-capturing; Weakly hyperbolic systems, Gas dynamics
Department/Centre:	Division of Mechanical Sciences > Civil Engineering
Date Deposited:	31 Dec 2021 06:59
Last Modified:	31 Dec 2021 06:59
URI:	http://eprints.iisc.ac.in/id/eprint/70656

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