On Exact Conservation for the Euler Equations with Complex Equations of State (Communications in Computational Physics, 2010)
Conservative numerical methods are often used for simulations of fluidflows involving shocks and other jumps with the understanding that conservationguarantees reasonable treatment near discontinuities. This is true in that convergentconservative approximations converge to weak solutions and thus have the correctshock locations. However, correct shock location results from any discretization whoseviolation of conservation approaches zero as the mesh is refined. Here we investigatethe case of the Euler equations for a single gas using the Jones-Wilkins-Lee (JWL) equationof state. We show that a quasi-conservative method can lead to physically realisticsolutions which are devoid of spurious pressure oscillations. Furthermore, we demonstratethat under certain conditions, a quasi-conservative method can exhibit higherrates of convergence near shocks than a strictly conservative counterpart of the sameformal order.