An incremental-stencil WENO reconstruction for simulation of compressible two-phase flows

Abstract

An incremental-stencil WENO reconstruction method, which uses low-order candidate stencils with incrementally increasing width, is proposed for finitevolume simulation of compressible two-phase flow with the quasi-conservative interface model. While recovering the original 5th-order WENO reconstruction in smooth region of the solution, due to the presence of 2-point candidate stencils, the present method is able to handle closely located discontinuities, which is a typical scenario of shock-interface interaction. Furthermore, a MOOD-type positivity preserving approach is applied to ensure physical meaningful reconstruction. Compared with the hybrid method which switches between with the 5th-order WENO and 2nd-order reconstructions, the present method is free of problem-dependent tunable parameters. A number of numerical examples show that the present method achieves small numerical dissipation and good robustness for simulating two-phase flow problems with strong shock-interface interaction and large density ratio.

Curved surface effect on high-speed droplet impingement

“…In this study, the splitting approach is applied to the governing equations (3.1) so the hyperbolic operator and source terms are then solved separately. A fifth-order incremental stencil weighted essentially non-oscillatory (WENO-IS) scheme is applied for the spatial reconstructions (Wang, Xiang & Hu 2018). A Godunov-type Harten-Lax-van Leer contact (HLLC) approximate Riemann solver (Toro 2013) is utilised to solve the Riemann problem at the cell edges.…”

Simulation of liquid jet primary breakup in a supersonic crossflow under Adaptive Mesh Refinement framework

“…The simulation can continue running with negative pressure in virtue of the p  which comes from the stiffened EOS ( ). Therefore, a positivity preserving process is required, and a MOON-type positivity preserving method [42,43] is adopted. In the reconstruction process, the reconstruction method will be switched to a lower order method when negative density or pp  + is detected.…”

Implementation of weighted essentially non‐oscillatory scheme for unsteady and steady compressible flow in pressure‐based algorithm

“…Many efforts have been performed to develop such methods. Part of these efforts have resulted in the development of a high-order accurate bounded schemes, remarkably the total variation diminishing (TVD), 14,15,23 weighted compact nonlinear scheme, 24 monotone advection upstream splitting method, 25,26 essentially non-oscillatory (ENO) 27 and weighted essentially non-oscillatory (WENO) [28][29][30][31][32][33][34] techniques. Although high-order TVD scheme generally presents oscillation-free shock profiles, it switches to the first-order accuracy at discontinuities to bound the results.…”