Commun. Comput. Phys., 8 (2010), pp. 995-1015.


On Exact Conservation for the Euler Equations with Complex Equations of State

J. W. Banks 1*

1 Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA 94551, USA.

Received 9 September 2009; Accepted (in revised version) 10 March 2010
Available online 31 May 2010
doi:10.4208/cicp.090909.100310a

Abstract

Conservative numerical methods are often used for simulations of fluid flows involving shocks and other jumps with the understanding that conservation guarantees reasonable treatment near discontinuities. This is true in that convergent conservative approximations converge to weak solutions and thus have the correct shock locations. However, correct shock location results from any discretization whose violation of conservation approaches zero as the mesh is refined. Here we investigate the case of the Euler equations for a single gas using the Jones-Wilkins-Lee (JWL) equation of state. We show that a quasi-conservative method can lead to physically realistic solutions which are devoid of spurious pressure oscillations. Furthermore, we demonstrate that under certain conditions, a quasi-conservative method can exhibit higher rates of convergence near shocks than a strictly conservative counterpart of the same formal order.

AMS subject classifications: 65N08, 35L60, 35L65, 76N15

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Key words: Euler equations, complex EOS, JWL EOS, Godunov methods.

*Corresponding author.
Email: banks20@llnl.gov (J. W. Banks)
 

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