Abstract
In this work, we develop a family of hybrid algorithms to simulate compressible multi-phase flows by solving the quasi-conservative five-equation model. The general numerical framework utilizes targeted essentially non-oscillatory schemes with adaptive dissipation (TENOA) to boost the resolution of high-frequency waves, whereas the Tangent of Hyperbola for INterface Capturing (THINC) scheme is activated near the shock and contact discontinuities as well as material interfaces to maintain their sharpness, based on a novel indicator. Also, the newly derived THINC reconstruction scheme is both simpler and better at preserving the flow symmetry. The robustness of our numerical approach is further fortified through the adaptation of a modified a posteriori multidimensional optimal order detection (MOOD) technique. Moreover, to mitigate carbuncle phenomenon encountered in two-dimensional simulations, a hybrid Riemann solver is also proposed based on the low Mach modification around shock for the Harten-Lax-van Leer contact (HLLC) approximate Riemann solver. Numerical results of the challenging one- and two-dimensional benchmark cases demonstrate the superiority of the proposed methods regarding oscillation-free, interface-sharpening, low-dissipation and robustness properties.
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