On Stable Simulation for Compressible Flows with Reduced Artificial Stabilization

초록

The main topic of the present study is a robust numerical scheme for compressible flows with a reduced need for artificial stabilization techniques. Spatial and temporal discretization methods that satisfy an identity between the discrete and analytic operators were considered. Different choices of the energy variable for compressible flows were discussed in terms of stability in case of small molecular viscosity and diffusivity. A method to relax the stiffness of the implicit method resulting from a rapidly varying density field was discussed. Using the test cases of the inviscid vortex and viscous shock, it was shown that using the internal energy provides with improved robustness compared to the total energy, especially when combined with a WENO scheme. Different schemes to define the total energy in a staggered grid were also discussed.

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