A Modified Characteristic-Wise Weno Reconstruction for Capturing the Contact Discontinuity in Multi-Component Flows

The flux difference splitting (FDS) combined with the characteristic-wise weighted essentially non-oscillatory (WENO) reconstruction in single-component flow simulations is quite attractive and preferred for its better non-oscillatory feature near discontinuities. 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 in multi-component flows, is proposed by modifying the total energy in the process of the WENO reconstruction. For example, in the fifth-order WENO reconstruction, on the 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., \gamma^L_{j+1/2} , which can be directly reconstructed from the transport equation of the mass fraction), and then the characteristic-wise WENO reconstruction process is implemented. Numerical examples including several one- and two-dimensional two-component flows confirm the effectiveness and robustness of the proposed method.