Abstract

In this article, we propose and analyze a stabilized weighted interior penalty method for solving the thermal convection problems in heterogeneous porous media. We first transform the thermal convection model into the pressure primal form with homogeneous Neumann boundary condition and develop a symmetric weighted interior penalty method to handle the discontinuous Darcy number and automatically adjust the penalty coefficient corresponding to the varying permeability. Then we recover the velocity by a stabilized method and incorporate it into the energy equation to obtain the temperature. The stability and convergence rates of the numerical solutions are rigorously proved and verified by numerical tests. The numerical experiments also include the testing benchmarks for cavity flow problems featuring discontinuous heterogeneous Darcy numbers, to further validate the effectiveness of the proposed scheme.

Department(s)

Mathematics and Statistics

Publication Status

Full Text Access

Comments

National Natural Science Foundation of China, Grant 12201353

Keywords and Phrases

Heterogeneous porous media; Stabilized method; Symmetric weighted interior penalty method; Thermal convection

International Standard Serial Number (ISSN)

0378-4754

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2026 Elsevier, All rights reserved.

Publication Date

01 Aug 2026

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Mathematics Commons

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