Universal High Order Subroutine with New Shock Detector for Shock Boundary Layer Interaction

摘要

The goal of this work is to develop a new universal high order subroutine forshock boundary layer interaction. First, an effective shock/discontinuitydetector has been developed.The detector has two steps.The first step is tocheck the ratio of the truncation errors on the coarse and fine grids and thesecond step is to check the local ratio of the left and right slopes. Thecurrently popular shock/discontinuity detectors can detect shock, but mistakehigh frequency waves and critical points as shock and then damp the physicallyimportant high frequency waves.Preliminary results show the newshock/discontinuity detector is very delicate and can detect all shocksincluding strong, weak and oblique shocks or discontinuity in function and thefirst, second, and third order derivatives without artificial constants, butnever mistake high frequency waves and critical points, expansion waves asshock. This will overcome the bottle neck problem with numerical simulation forthe shock-boundary layer interaction, shock-acoustic interaction, imageprocess, porous media flow, multiple phase flow and anywhere the high frequencywaves are important, but discontinuity exists and is mixed with high frequencywaves. After detecting the shock we can then use one side high order scheme forshocks and high order central compact scheme for the rest if the shock isappropriately located. Then a high order universal subroutine for finitedifference method is developed which can be used for any finite difference codefor accurate numerical derivatives.