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

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 solution and thus have the correct shock location. However, correct shock location results from any discretization whose violation of con-servation 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 con-vergence near shocks than a strictly conservative counterpart of the same formal order