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Exponential finite difference scheme for transport equations with discontinuous coefficients in porous media. (English) Zbl 07332892
Summary: In this paper, we propose a novel exponential difference scheme for solving non-linear problems arising in variably saturated flow with discontinuous absolute permeability. First, we derive the discretization for a linear convection-diffusion-reaction problem with discontinuous coefficients. Positivity preserving property, stability and convergence of the scheme are studied. Then, the method is implemented to the transport equation and Richards’ equation. Various numerical experiments on graded and uniform meshes are presented and discussed.
##### MSC:
 76M20 Finite difference methods applied to problems in fluid mechanics 76S05 Flows in porous media; filtration; seepage 76R99 Diffusion and convection 76V05 Reaction effects in flows 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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