European Union’s Horizon 2020 research and innovation programme

Marie Sklodowska-Curie grant agreement NO 705402, POROSOS

FAST SOLVERS FOR MULTIPHYSIC PROBLEMS: DARCY-STOKES AND BIOT-STOKES SYSTEMS

We have proposed a monolithic multigrid solver for the coupled porous medium and Stokes flow system. An Uzawa smoother is employed in multigrid, which is a decoupled procedure based on a symmetric Gauss-Seidel smoothing for velocity components and a simple Richardson iteration for the pressure field. Since a realaxation parameter is involved in the Richardson iteration, local Fourier analysis is applied to determine the optimal parameters.

This monolithic approach has been applied for the coupled Stokes flow and deformable porous medium system. Therefore we have a coupled Stokes-Biot system. Either a coupled Vanka smoother or a decoupled Uzawa smoother is used as relaxation method in the multigrid algorithm.

PUBLICATIONS:

Uzawa smoother in multigrid for the coupled porous médium and Stokes flow system. P. Luo, C. Rodrigo, F.J. Gaspar, C.W. Oosterlee. SIAM Journal on Scientific Computing (2017) : LINK

Monolithic multigrid method for the coupled Stokes flow and deformable porous médium system. P. Luo, C. Rodrigo, F .J. Gaspar, C.W. Oosterlee. Journal of Computational Physics LINK