A Modified Characteristic-Wise WENO Reconstruction for Capturing the Contact Discontinuity in Multi-Component Flows (Communications in Computational Physics, 2025)
The flux difference splitting (FDS) combined with the characteristic-wiseweighted essentially non-oscillatory (WENO) reconstruction in single-component flowsimulations is quite attractive and preferred for its better non-oscillatory feature neardiscontinuities. However, when compressible multi-component flows are simulated,the FDS with the characteristic-wise WENO reconstruction may cause spurious oscillations. In this work, we analyze the reason that the oscillations are generated.A new method, which can effectively suppress this kind of spurious oscillations inmulti-component flows, is proposed by modifying the total energy in the process ofthe WENO reconstruction. For example, in the fifth-order WENO reconstruction, onthe global stencil $S^5=(j−2,j−1,···,j+2)$ used to reconstruct the left-side value $U^L_{ j+1/2},$ the total energy values are first modified by using the reconstructed value of the specific heat ratio (i.e., $γ^L_{j+1/2},$ which can be directly reconstructed from the transportequation of the mass fraction), and then the characteristic-wise WENO reconstructionprocess is implemented. Numerical examples including several one-, two- and three-dimensional multi-component flows confirm the effectiveness and robustness of theproposed method.
Keywords: Contact discontinuity; flux difference splitting method; WENO scheme; characteristic-wise reconstruction; multi-component flow.