• DOI:10.4208/CICP.090909.100310A
• Corpus ID: 16351728

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

@article{Banks2010OnEC,
  title={On Exact Conservation for the Euler Equations with Complex Equations of State},
  author={Jeffrey W. Banks},
  journal={Communications in Computational Physics},
  year={2010}
}

• J. Banks
• Published 2010
• Mathematics
• Communications in Computational Physics

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 discretizationwhose 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) equa- tion of state. We show that a quasi-conservative method can lead to physically realistic solutions which are devoid of spurious pressure oscillations. Furthermore, we demon- strate 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