Entropy preserving low dissipative shock capturing with wave-characteristic based sensor for high-order methods

Shock capturing procedures are required to stabilise numerical simulations of gas dynamics problems featuring non-isentropic discontinuities. In the present work, particular attention is focused on the expected non-monotonicity of the entropy profile across shock waves. A peculiar physical property which was not considered so far in the evaluation of shock capturing techniques. In the context of high-order spectral difference methods and using most recent discontinuity sensors based on the decay rate of the modes of the amplitude of characteristic waves, results show how the choice of a physical-based procedure (additional viscosity) returns a better description of shocks compared to approaches relying on the direct addition of a Laplacian term in the solved equations. Various canonical compressible flows are simulated, in one-, two-, and three-dimensional setups, to illustrate the performance and flexibility of the proposed approach. It is shown that the addition of a well-calibrated bulk viscosity is capable of smoothing out discontinuities without an excessive damping of vortical structures, preserving also specific compressible flow physics, as the non-monotonic entropy profiles through the shocks.