Vol. 11, No. 1, 2016

Download this article
Download this article For screen
For printing
Recent Issues
Volume 12, Issue 1
Volume 11, Issue 2
Volume 11, Issue 1
Volume 10, Issue 2
Volume 10, Issue 1
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 1
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 1
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 1
Volume 3, Issue 1
Volume 2, Issue 1
Volume 1, Issue 1
The Journal
Subscriptions
Editorial Board
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
A front-tracking shock-capturing method for two gases

Mehdi Vahab and Gregory H. Miller

Vol. 11 (2016), No. 1, 1–35
Abstract

We present a new high-order front-tracking method for hyperbolic systems of conservation laws for two gases separated by a tracked contact discontinuity, using a combination of a high-order Godunov algorithm and level set methods. Our approach discretizes the moving front and gas domains on a Cartesian grid, with control volumes determined by the intersection of the grid with the front. In cut cells, a combination of conservative and nonconservative finite volume quadratures provide small-cell stability. Global conservation is maintained using redistribution. We demonstrate second-order convergence in smooth flow and first-order convergence in the presence of shocks.

Keywords
sharp interface, front-tracking, finite-volume, multifluids, irregular geometries, Cartesian grids, shock-capturing
Mathematical Subject Classification 2010
Primary: 65D32, 76T99, 35L04
Milestones
Received: 26 December 2013
Revised: 22 April 2015
Accepted: 24 July 2015
Published: 6 November 2015
Authors
Mehdi Vahab
Department of Mathematics
Florida State University
Tallahassee, FL 32306
Gregory H. Miller
Department of Chemical Engineering and Materials Science
University of California, Davis
1 Shields Avenue
Davis, CA 95616
United States