Bound-preserving second-order implicit pressure explicit concentration discontinuous Galerkin methods for compressible miscible displacements

Document Type

Article

Publication Date

12-1-2026

Department

Department of Mathematical Sciences

Abstract

In this paper, we apply discontinuous Galerkin (DG) methods for compressible miscible displacements in porous media. Novel bound-preserving second-order Implicit Pressure Explicit Concentration (IMPEC) time marching schemes are designed for Darcy and Darcy-Forchheimer flows. The core idea involves employing a special implicit discretization for the pressure and velocity equations while using strong-stability-preserving explicit discretization for the concentration equation. Different from previous works, the intermediate stages of the implicit and explicit solvers are placed at different time levels. By doing so, it is possible to keep the second order accuracy of the time integrations for Darcy flow, avoiding the correction stage to compensate for the accuracy after each time step. Though this idea can be applied to Darcy-Forchheimer flows, it may require solving a nonlinear system, leading to extra computational cost. It is necessary to linearize the velocity equation. However, due to the mismatch of the intermediate time levels between the implicit and explicit time integrations, a special linearization is carefully designed, keeping the second order accuracy. In addition, we modify the time integration for the pressure and concentration equations such that the bound-preserving technique can be applied to preserve the physical bounds of the concentrations. The proposed scheme is second order accurate in time, and completely avoids nonlinear solvers and the correction stages in the end. Moreover, the time step size for stability is much larger than previous methods, leading to less computational cost. Finally, numerical experiments are conducted to validate the accuracy of the numerical scheme and demonstrate the efficiency of the proposed method.

Publication Title

Journal of Computational Physics

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