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For transport modelled by the time-dependent convection-diffusion equation, positivity of numerical concentrations and mass conservation are two important properties numerical solvers should respect. This paper investigates such a solver based on the implicit Euler time-marching and finite volume discretization on quadrilateral meshes. The solver uses mapped \( Q_1 \) bilinear polynomials for approximation of the concentration. A new upwinding technique is adopted to handle convection dominance. Flux correction is devised to ensure nonnegative numerical concentrations. Matlab code modules based on efficient implementation of this solver are incorporated into our package DarcyLite. Numerical experiments are presented to illustrate the performance of the new solver.

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DarcyLite Modules for a Property-Preserving Transport Solver

  • 会议论文

  • 发表日期：

    2025年

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  • Jiangguo Liu,
  • Boyang Yu,
  • Yingli Li

摘要

For transport modelled by the time-dependent convection-diffusion equation, positivity of numerical concentrations and mass conservation are two important properties numerical solvers should respect. This paper investigates such a solver based on the implicit Euler time-marching and finite volume discretization on quadrilateral meshes. The solver uses mapped \( Q_1 \) bilinear polynomials for approximation of the concentration. A new upwinding technique is adopted to handle convection dominance. Flux correction is devised to ensure nonnegative numerical concentrations. Matlab code modules based on efficient implementation of this solver are incorporated into our package DarcyLite. Numerical experiments are presented to illustrate the performance of the new solver.