@Article{CiCP-36-781,
author = {Gao , ZhenGuo , ShuangWang , Bao-Shan and Gu , Yaguang},
title = {High Order Bound- and Positivity-Preserving Finite Difference Affine-Invariant AWENO Scheme for the Five-Equation Model of Two-Medium Flows},
journal = {Communications in Computational Physics},
year = {2024},
volume = {36},
number = {3},
pages = {781--820},
abstract = {<p style="text-align: justify;">Numerical study on compressible two-medium flows has been a hot issue
in recent decades. In this study, we design quasi-conservative finite difference alternative weighted essentially non-oscillatory (AWENO) schemes up to the ninth order
for the five-equation model with the stiffened gas equation of state. We propose uniformly high-order flux-based bound- and positivity-preserving (BP-P) limiters for the
AWENO schemes while preserving the equilibrium solutions simultaneously. Though
the BP-P limiters are used, the numerical solutions have the tendency to generate oscillations especially near strong shock and/or rarefaction waves, due to the sudden drastic scale transition of the density, pressure, etc. To resolve fine structures and the transition of different scales, the latest affine-invariant WENO (Ai-WENO) interpolation is
adopted and generalized up to the ninth order. In addition, we will systematically derive CFL conditions when the Lax-Friedrichs numerical flux is applied. Moreover, we
show the potential of the BP-P limiters for a variant of the five-equation model, usually suggested in finite volume and discontinuous Galerkin methods. For illustration
purposes, we adopt the AWENO schemes and derive the corresponding CFL conditions. A variety of one- and two-dimensional test problems illustrate the high order of
accuracy, effectiveness, and robustness of the proposed BP-P Ai-AWENO schemes.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0153},
url = {http://global-sci.org/intro/article_detail/cicp/23458.html}
}