- Journal Home
- Volume 38 - 2025
- Volume 37 - 2025
- Volume 36 - 2024
- Volume 35 - 2024
- Volume 34 - 2023
- Volume 33 - 2023
- Volume 32 - 2022
- Volume 31 - 2022
- Volume 30 - 2021
- Volume 29 - 2021
- Volume 28 - 2020
- Volume 27 - 2020
- Volume 26 - 2019
- Volume 25 - 2019
- Volume 24 - 2018
- Volume 23 - 2018
- Volume 22 - 2017
- Volume 21 - 2017
- Volume 20 - 2016
- Volume 19 - 2016
- Volume 18 - 2015
- Volume 17 - 2015
- Volume 16 - 2014
- Volume 15 - 2014
- Volume 14 - 2013
- Volume 13 - 2013
- Volume 12 - 2012
- Volume 11 - 2012
- Volume 10 - 2011
- Volume 9 - 2011
- Volume 8 - 2010
- Volume 7 - 2010
- Volume 6 - 2009
- Volume 5 - 2009
- Volume 4 - 2008
- Volume 3 - 2008
- Volume 2 - 2007
- Volume 1 - 2006
Commun. Comput. Phys., 38 (2025), pp. 1515-1551.
Published online: 2025-09
Cited by
- BibTex
- RIS
- TXT
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.
}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2023-0046}, url = {http://global-sci.org/intro/article_detail/cicp/24465.html} }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.