TY - JOUR
T1 - High Order Bound- and Positivity-Preserving Finite Difference Affine-Invariant AWENO Scheme for the Five-Equation Model of Two-Medium Flows
AU - Gao , Zhen
AU - Guo , Shuang
AU - Wang , Bao-Shan
AU - Gu , Yaguang
JO - Communications in Computational Physics
VL - 3
SP - 781
EP - 820
PY - 2024
DA - 2024/10
SN - 36
DO - http://doi.org/10.4208/cicp.OA-2023-0153
UR - https://global-sci.org/intro/article_detail/cicp/23458.html
KW - Compressible two-medium flow, AWENO scheme, affine-invariant WENO interpolation, bound- and positivity-preserving limiters.
AB - <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>