A low-dissipation and time-accurate method for compressible multi-component flow with variable specific heat ratios

Preventing numerical errors generated by interface-capturing schemes in compressible multi-material flows

“…However, because the temperature does not enter the problem, this issue is inconsequential for the Euler equations; it becomes problematic if the diffusion terms (particularly thermal conduction) are included. Similar temperature errors were observed but not analyzed in detail by Billet and Abgrall [3] and Houim and Kuo [10], who both used a double-flux approach. However, total energy is not conserved, so this method is not considered in the main body, but rather is discussed in Appendix A.…”

“…The primitive variables are reconstructed to prevent pressure oscillations. However, conservation errors are expected for the total energy and, as shown by [10], temperature errors may be generated. If the high-order reconstruction is performed in such a way that temperature equilibrium is maintained when applicable (i.e., for the advection of a material interface), temperature errors are not expected to be generated.…”

Numerical simulations of a shock interacting with successive interfaces using the Discontinuous Galerkin method: the multilayered Richtmyer–Meshkov and Rayleigh–Taylor instabilities

“…The Discontinuous Galerkin method [6][7][8][9][10] is a numerical method for solving partial differential equations which combines the advantages of the finite element and finite volume methods. In contrast with previous RMI studies using finite difference and finite volume methods [20,22,26,28,34], the numerical solution is represented in each computational cell of the domain with high-order polynomial basis functions. The method is therefore high-order accurate and is superconvergent in the cell averages at a rate of 2N + 1 [2,3], where N + 1 is the number of basis function in each cell.…”

“…The canonical RMI, consisting of a single planar shock wave interacting with a single planar interface separating two fluids, has been studied extensively in the past, both experimentally [11,21,29,37] and numerically [20,22,26,31,34]. While some of these studies have considered late-time mixing, most have focused on the early time dynamics.…”

Performance of all-speed AUSM-family schemes for DNS of low Mach number turbulent channel flow

“…This ideal case of WENO is sometimes called the Linear-WENO (LWENO) [28]. In the present study, interpolation with linear optimal coefficients is attempted for fifth-and sixth-order WENO, and these methods are hereafter referred to as LWENO5 and LWENO6.…”