@Article{CiCP-38-1515,
author = {Liu , XinyuanXiong , Tao and Yang , Yang},
title = {A Third Order Bound-Preserving Nodal Discontinuous Galerkin Method for Miscible Displacements in Porous Media},
journal = {Communications in Computational Physics},
year = {2025},
volume = {38},
number = {5},
pages = {1515--1551},
abstract = {<p style="text-align: justify;">In this paper, we develop a provable third order bound-preserving (BP)
 nodal discontinuous Galerkin (DG) method for compressible miscible displacements.
 We consider the problem with a multi-component fluid mixture and physically the volumetric concentration of each component, $c_j(j=1,···,N)$, is between 0 and 1. The main
 idea is to apply a positivity-preserving (PP) method to all $c′_js,$ while enforce $∑_jc_j=1$ simultaneously. First, we treat the time derivative of the pressure as a source and choose
 suitable “consistent” numerical fluxes in the pressure and concentration equations to
 construct a nodal interior penalty DG (IPDG) method to enforce $∑_jc_j =1.$ For PP, we
 represent the cell average of $c_j$ as a weighted summation of Gaussian quadrature point
 values, and transform which to some other specially chosen point values. We prove
 that by taking appropriate parameters in the nodal IPDG method and a suitable time
 stability condition, the cell average can be kept positive, which further implies that the
 cell averages of all components are between 0 and 1. Finally, we apply a polynomial
 scaling limiter to obtain physically relevant numerical approximations without sacrificing accuracy. Numerical experiments are given to demonstrate desired accuracy, BP
 and good performances of our proposed approach.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0046},
url = {http://global-sci.org/intro/article_detail/cicp/24465.html}
}