Decoupled multiscale numerical approach for reactive transport in marine sediment column

In this work, we consider biotic and abiotic reactive transport processes through marine sediment vertical profiles. The mathematical model is described by a multicomponent transport and formation of dissolved and solid sediment components with coupled nonlinear reaction terms. We present an efficient decoupled multiscale algorithm based on the implicit-explicit time approximation schemes, operator -splitting techniques, and multiscale finite element method. We start with a finite volume approximation by space on the fully resolved grid (fine grid). We present an implicit-explicit scheme (ImEx) for time approximation to construct the efficient numerical algorithm and localize the coupled nonlinear reaction part. The explicit time approximation is constructed for the slow, non -reactive transport subproblem. The nonlinear reaction part uses the implicit approximation. To overcome a more significant time step restriction induced by an explicit approximation of the diffusive part, we combine Operator Splitting with an implicit-explicit scheme for the non -reactive transport part (OS-ImEx). To reduce the size of the non -reactive transport system, we propose a multiscale lower -dimensional model for the non -reactive transport in marine sediment column. By combining the multiscale method with the Operator splitting scheme and implicit-explicit approximation for the non -reactive part, we obtain an efficient decoupled approach that localizes the nonlinear coupled reaction part and performs a faster solution of the non -reactive transport part. Numerical results are presented for one-dimensional and two-dimensional test problems to study the accuracy and efficiency of the proposed decoupled multiscale approach.