Adaptive mesh based efficient approximations for Darcy scale precipitation–dissolution models in porous media

Abstract

In this work, we consider the Darcy scale precipitation–dissolution reactive transport 1D and 2D models in a porous medium and provide the adaptive mesh based numerical approximations for solving them efficiently. These models consist of a convection-diffusion-reaction PDE with reactions being described by an ODE having a nonlinear, discontinuous, possibly multi-valued right hand side describing precipitate concentration. The bulk concentration in the aqueous phase develops fronts and the precipitate concentration is described by a free and time-dependent moving boundary. The time adaptive moving mesh strategy, based on equidistribution principle in space and governed by a moving mesh PDE, is utilized and modified in the context of present problem for finite difference set up in 1D and finite element set up in 2D. Moreover, we use a predictor corrector based algorithm to solve the nonlinear precipitation–dissolution models. For equidistribution approach, we choose an adaptive monitor function and smooth it based on a diffusive mechanism. Numerical tests are performed to demonstrate the accuracy and efficiency of the proposed method by examples through finite difference approach for 1D and finite element approach in 2D. The moving mesh refinement accurately resolves the front location of Darcy scale precipitation–dissolution reactive transport model and reduces the computational cost in comparison to numerical simulations using a fixed mesh.