Hybrid WCNS scheme with new discontinuity detector applied to discontinuous inviscid compressible flows

In order to enable high-precision accurate schemes to robustly capture shock waves and quickly obtain high fidelity simulation results of the flow field in supersonic inviscid compressible flow calculations, which usually contains complex structures such as discontinuities and small-scale vortices, a smoothness measurement algorithms based on combinations of sub-stencil derivatives were studied, and a new discontinuity detector was developed to balance accuracy and robustness, making troubled-cell recognition highly resolved for small-scale vortices. Hybrid WCNS (weighted compact nonlinear scheme) methods were studied, which could solve smooth and discontinuous regions in the flow field using linear and nonlinear weighting schemes respectively, to overcome the difficulty of a single nonlinear scheme in achieving design accuracy in smooth areas. Numerical results show that the hybrid WCNS scheme with new discontinuity detector performs well in simulating one-dimensional and two-dimensional Euler equations, and has higher computational efficiency compared to the original WCNS method that uses local characteristic decomposition in the entire flow field.