TY - JOUR
T1 - A High Order Positivity-Preserving Discontinuous Galerkin Remapping Method Based on a Moving Mesh Solver for ALE Simulation of the Compressible Fluid Flow
AU - Gu , Xiaolu
AU - Cheng , Juan
AU - Shu , Chi-Wang
JO - Communications in Computational Physics
VL - 5
SP - 1177
EP - 1214
PY - 2023
DA - 2023/12
SN - 34
DO - http://doi.org/10.4208/cicp.OA-2023-0083
UR - https://global-sci.org/intro/article_detail/cicp/22211.html
KW - Remapping, discontinuous Galerkin method, arbitrary Lagrangian-Eulerian, high order accuracy, multi-resolution WENO limiter, positivity-preserving.
AB - <p style="text-align: justify;">The arbitrary Lagrangian-Eulerian (ALE) method is widely used in the field
of compressible multi-material and multi-phase flow problems. In order to implement the indirect ALE approach for the simulation of compressible flow in the context
of high order discontinuous Galerkin (DG) discretizations, we present a high order
positivity-preserving DG remapping method based on a moving mesh solver in this
paper. This remapping method is based on the ALE-DG method developed by Klingenberg et al. [17, 18] to solve the trivial equation $\frac{∂u}{∂t} = 0$ on a moving mesh, which
is the old mesh before remapping at $t = 0$ and is the new mesh after remapping at $t = T.$ An appropriate selection of the final pseudo-time $T$ can always satisfy the relatively mild smoothness requirement (Lipschitz continuity) on the mesh movement
velocity, which guarantees the high order accuracy of the remapping procedure. We
use a multi-resolution weighted essentially non-oscillatory (WENO) limiter which can
keep the essentially non-oscillatory property near strong discontinuities while maintaining high order accuracy in smooth regions. We further employ an effective linear
scaling limiter to preserve the positivity of the relevant physical variables without sacrificing conservation and the original high order accuracy. Numerical experiments are
provided to illustrate the high order accuracy, essentially non-oscillatory performance
and positivity-preserving of our remapping algorithm. In addition, the performance
of the ALE simulation based on the DG framework with our remapping algorithm is
examined in one- and two-dimensional Euler equations.</p>