Vol. 11, No. 1, 2016

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A front-tracking shock-capturing method for two gases

Mehdi Vahab and Gregory H. Miller

Vol. 11 (2016), No. 1, 1–35

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.

sharp interface, front-tracking, finite-volume, multifluids, irregular geometries, Cartesian grids, shock-capturing
Mathematical Subject Classification 2010
Primary: 65D32, 76T99, 35L04
Received: 26 December 2013
Revised: 22 April 2015
Accepted: 24 July 2015
Published: 6 November 2015
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