High order compact augmented methods for Stokes equations with different boundary conditions.

This paper is devoted to fourth order compact schemes and fast algorithms for solving stationary Stokes equations with different boundary conditions numerically. One of the main ideas is to decouple the Stokes equations into three Poisson equations for the pressure and the velocity via the pressure Poisson equation (PPE). The augmented strategy is utilized to provide numerical boundary conditions for the pressure. Different velocity boundary conditions require different interpolation strategies for the augmented methods. The augmented variable is solved by the GMRES method. A new simple and efficient preconditioning strategy has also been developed to accelerate the convergence of the GMRES iteration. Numerical examples presented in this paper confirmed the designed convergence order and the efficiency of the new methods. • An augmented fourth-order approach is proposed to solve Stokes equations with various boundary conditions. • A new and efficient preconditioning strategy is developed for solving the Schur complement system in the GMRES iteration. • Non-trivial numerical examples are presented to confirm the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]