Robust Monolithic Solvers for the Stokes--Darcy Problem with the Darcy Equation in Primal Form

Augmented Interface Systems for the Darcy - Stokes 2 Problem 3

In this paper we study interface equations associated to the Darcy-Stokes problem 8 using the classical Steklov-Poincaré approach and a new one called augmented. We compare 9 these two families of methods and characterize at the discrete level suitable preconditioners 10 with additive and multiplicative structures. Finally, we present some numerical results to as11 sess their behavior in presen...

Partitioned Penalty Methods for the Evolutionary Stokes-darcy-transport Problem

There has been a surge of work on models for coupling surface-water with groundwater flows which is at its core the Stokes-Darcy problem, as well as methods for uncoupling the problem into subdomain, subphysics solves. The resulting (Stokes-Darcy) fluid velocity is important because the flow transports contaminants. The numerical analysis and algorithm development for the evolutionary transport...

Augmented Interface Systems for the Darcy-Stokes Problem

Long time stability of four methods for splitting the evolutionary Stokes-Darcy problem into Stokes and Darcy subproblems

A . This report analyzes the long time stability of four methods for non-iterative, sub-physics, uncoupling for the evolutionary Stokes-Darcy problem. The four methods uncouple each time step into separate Stokes and Darcy solves using ideas from splitting methods. Three methods uncouple sequentially while one is a parallel uncoupling method. We prove long time stability of four splitting based...

A Robust Finite Element Method for Darcy-Stokes Flow

Finite element methods for a family of systems of singular perturbation problems of a saddle point structure are discussed. The system is approximately a linear Stokes problem when the perturbation parameter is large, while it degenerates to a mixed formulation of Poisson’s equation as the perturbation parameter tends to zero. It is established, basically by numerical experiments, that most of ...