Oscillation-free nodal discontinuous spectral element method for the simulation of compressible multicomponent flows

The nodal discontinuous spectral element method (DSEM) is improved to avoid pressure and velocity oscillations from material interfaces in the solution of multi-component compressible flows. A novel double flux method compatible with the DSEM scheme is developed to account for variations in the specific heats ratio at material interfaces. The double flux method consists of a modified Harten-Lax-van Leer-Contact (HLLC) Riemann solver and an averaging technique to freeze the temperature-dependent specific heats ratio during the solution update to remove oscillations. The double flux model is combined with a conservative method of calculating the convective flux function to avoid unnecessary energy conservation error at shock fronts. Numerical diffusion terms are also introduced for capturing a shock wave, contact discontinuity, and material interface, without inducing oscillations at the material interface. A series of one- and two-dimensional tests are conducted to evaluate the efficacy of the numerical scheme in capturing sharp discontinuities, as well as vortices, without introducing significant conservation error. According to the benchmark results, the new approach maintains the pressure, velocity, and temperature equilibriums across material interfaces. Artificial diffusion is added to the equation in a controlled manner that enables a higher Courant-Friedrichs-Lewy (CFL) number for high polynomial orders. The present scheme's performance is validated by comparing the spatiotemporal evolution of characteristic points in the shock-bubble interaction and Richtmyer-Meshokov's instability problems.