A new succinct alternative multi-resolution weighted essentially non-oscillatory scheme with a local-adaptive particle capturing technique for simulating compressible multi-fluid flows

In this work, an improved alternative multi-resolution weighted essentially non-oscillatory scheme (called “AWENOZS-s”) is proposed to solve compressible conservation equations, in which new types of local and global smoothness indicators are derived on the nested central stencils hierarchy of WENOZS scheme. To capture the multi-component interface, a local-adaptive particle-laden sharp interface capturing (LAPSIC) technique is designed without the direct solving of advection equation, which is different from the traditional level set or volume of fluid methods. The proposed AWENOZS-s scheme, coupling with some other advanced techniques, is implemented to simulate different compressible multi-component flows. The positivity-preserving (PP) and primitive variables (PV) methods are introduced to preserve positivity and equilibrium of density and pressure. In the numerical results, first, the numerical errors and convergence of the AWENOZS-s are illustrated by solving benchmark problems, and it is compared with the previous WENO-type schemes. Second, the proposed AWENOZS-s with PP is used to simulate the compressible single-component flow with strong shocks and compared with traditional WENO-type results, to demonstrate its merits of less dissipation near discontinuity. Finally, the AWENOZS-s with advanced numerical techniques (LAPSIC, PP, and PV) is further applied to simulate the one-dimensional and two-dimensional compressible multi-component flows, and other reference results are given for comparisons. Several classical and challenging problems accompanied by strongly compressible characteristics are numerically investigated. The advantage of the succinct implementation and less computing cost (reduced about 20%) of the proposed scheme compared with the previous AWENOZS scheme is illustrated. All the numerical results are given to show the well performance and robustness of the present hybrid method for strongly compressible multi-fluid flows.