A stabilized weighted interior penalty method for thermal convection model in heterogeneous porous media

Yuanyuan Hou, Qianqian Ding, Xiaoming He and Yanping Lin

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 246, issue C, 137-153

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.

Keywords: Thermal convection; Heterogeneous porous media; Stabilized method; Symmetric weighted interior penalty method (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:246:y:2026:i:c:p:137-153

DOI: 10.1016/j.matcom.2026.01.016

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