Fast semi-explicit transient solution of Stokes flows with large time steps using a FIC-time procedure

We present a fast semi- explicit time integration scheme for solving transient Stokes flow problems via standard numerical methods in space using regular and irregular grids, such as unstructured meshes in the finite element method (FEM), or grids containing cells of very different sizes in the finite volume method (FVM). The new semi-explicit time integration scheme, termed EFT12 scheme, extends one of the explicit FIC-Time (EFT) integration methods for parabolic problems derived by the authors in [24] that allow considerable larger time steps than the forward Euler (FE) scheme. The EFT12 scheme also provides a faster convergence to the steady-state solution than using the FE scheme. The advantages of the EFT12 scheme for the fast and accurate solution of transient Stokes flow problems are shown in one- and two- dimensional problems using the FEM and the FVM with regular and irregular grids.