Dynamic Capillary Effects in the Simulation of Flow and Transport in Porous Media: A New Linearisation Method
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In this thesis mathematical models with and without dynamic capillary effects are developed to model water flow and solute transport through a porous medium. The system of equations are discretised using the finite volume method TPFA in space and the backward Euler method in time. To solve the nonlinear systems appearing at each time step numerically, robust linearisation methods are proposed. These methods do not involve the computation of derivatives. The methods are analysed and have been shown to be linearly convergent and robust. Moreover, the convergence was shown to be independent of mesh size. The influence that the dynamic effects have on flow and transport is studied numerically. Additional numerical experiments were conducted to study the convergence of the linearisation schemes. The numerical results are shown to be in correspondence with the theoretical results.