Compact shock capturing scheme for compressible multiscale flow

Aimed at compressible multiscale flow simulations, a fifth-order high-resolution compact shock capturing scheme, compact-reconstruction weighted essentially non-oscillatory (CRWENO), is studied. Nonlinear weights are used to combine lower-order compact schemes to approximate a higher-order compact scheme. The scheme becomes the fifth-order linear compact scheme in smooth regions, while preserves computational stability across discontinuities. Numerical properties were analyzed for CRWENO and weighted essentially non-oscillatory (WENO) which is widely used these days, as well as the linear schemes that they correspond to, i. e. the fifth-order upwind linear scheme and the fifth-order compact scheme. The impacts of nonlinear weights on dissipation and spectral properties are evaluated. The advancements and drawbacks of linear/nonlinear and compact/explicit schemes in compressible multiscale flow simulations are discussed by performing 1D, 2D and 3D typical numerical tests. It can be concluded that CRWENO scheme can obtain non-oscillatory results near strong discontinuous regions. Its compact characteristic improves the problems of over-dissipation and low resolution exiting in nonlinear schemes and makes it clearly resolve multiscale flow structures. In a word, CRWENO is a proper candidate for compressible multiscale flow simulations. © 2017, Editorial Board of JBUAA. All right reserved.