A hybridizable discontinuous Galerkin method for the dual-porosity-Stokes problem
Aycil Cesmelioglu, Jeonghun J. Lee, Sander Rhebergen, Dorisa Tabaku
TL;DR
This paper develops and analyzes a hybridizable discontinuous Galerkin method for the dual-porosity-Stokes problem, effectively modeling interactions between macrofracture flow and microfracture flow with proven stability and accuracy.
Contribution
The paper introduces a novel HDG method tailored for the dual-porosity-Stokes problem, including rigorous analysis and validation through numerical experiments.
Findings
The HDG method is strongly conservative and well-posed.
Error estimates depend on problem parameters.
Numerical examples confirm theoretical results.
Abstract
We introduce and analyze a hybridizable discontinuous Galerkin (HDG) method for the dual-porosity-Stokes problem. This coupled problem describes the interaction between free flow in macrofractures/conduits, governed by the Stokes equations, and flow in microfractures/matrix, governed by a dual-porosity model. We prove that the HDG method is strongly conservative, well-posed, and give an a priori error analysis showing dependence on the problem parameters. Our theoretical findings are corroborated by numerical examples
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Advanced Mathematical Modeling in Engineering · Computational Fluid Dynamics and Aerodynamics