2025/03/06 by Maurice S. Fabien, Fabien, Maurice S. · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Computational Engineering #Differential Equations and Numerical Methods #FOS: Computer and information sciences #Finance #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.2503.04061
openalex publication_date 2025/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a high-order hybridizable discontinuous Galerkin method for the numerical solution of time-dependent three-phase flow in heterogeneous porous media. The underlying algorithm is a semi-implicit operator splitting approach that relaxes the nonlinearity present in the governing equations. By treating the subsequent equations implicitly, we obtain solution that remain stable for large time steps. The hybridizable discontinuous Galerkin method allows for static condensation, which significantly reduces the total number of degrees of freedom, especially when compared to classical discontinuous Galerkin methods. Several numerical tests are given, for example, we verify analytic convergence rates for the method, as well as examine its robustness in both homogeneous and heterogeneous porous media.