摘要
The local characteristic fields of compressible Euler equations can be decomposedinto linearly degenerate and genuinely nonlinear, respectively. The former isassociated with a contact discontinuity (the slip lines for multi-dimensional cases) andthe latter is associated with shocks and rarefaction waves (Toro, Riemann Solvers andNumerical Methods for Fluid Dynamics, Springer, 2009). The weighted essentiallynon-oscillatory (WENO) scheme can capture shock waves well but its resolution forshort waves still needs to be improved, while one kind of new scheme constructed bythe boundary variation diminishing (BVD) principle with the THINC (Tangent of Hyperbolafor INterface Capturing) reconstruction can resolve the contact discontinuitieswith higher resolution but it may generate spurious numerical phenomena in somespecial cases. Combining the physical characteristics and the advantages of WENOand BVD schemes, this paper proposes a hybrid reconstruction method, in which theclassical WENO scheme is used to discretize the genuinely nonlinear fields and thehigher resolution BVD scheme is used to discretize the linearly degenerate field(s).Numerical experiments show that the hybrid method can preserve high accuracy nearboth contact discontinuities and short waves as the used higher resolution schemewhile effectively avoiding spurious numerical phenomena (such as oscillations andovershoots). Compared with the BVD scheme, the hybrid method also improves computationalefficiency, since it uses a more efficient WENO scheme in genuinely nonlinearfields.
基金
supported by the National Natural Science Foundation of China under Grants Nos.12172364,11872067 and 91852203.
