Efficient Variable-Coefficient Finite-Volume Stokes Solvers

Efficient Variable-coefficient Finite-volume Stokes Solvers

We investigate several robust preconditioners for solving the saddle-point linear systems that arise from spatial discretization of unsteady and steady variable-coefficient Stokes equations on a uniform staggered grid. Building on the success of using the classical projection method as a preconditioner for the coupled velocity-pressure system [B. E. Griffith, J. Comp. Phys., 228 (2009), pp. 756...

Efficient Multigrid Solvers for the Stokes Equations using Finite Elements

Mixed nite element application to solve the Stokes equations using di erent smoothers by mean of multigrid technique has been investigated. Multigrid technique's e ciency for positive de nite linear systems is proved but it is much more challenging in the case of saddle-point problems. The e ciency of a multigrid method is highly dependent on the smoother and the coarse grid solver. A two-dimen...

Efficient Parallel Preconditioning of Compact Finite Volume Solvers

Immersed-boundary methods for general finite-difference and finite-volume Navier-Stokes solvers

We present an immersed-boundary algorithm for incompressible flows with complex boundaries, suitable for Cartesian or curvilinear grid system. The key stages of any immersed-boundary technique are the interpolation of a velocity field given on a mesh onto a general boundary (a line in 2D, a surface in 3D), and the spreading of a force field from the immersed boundary to the neighboring mesh poi...

A simple finite difference method for time-dependent, variable coefficient Stokes flow on irregular domains

We present a simple and efficient variational finite difference method for simulating time-dependent Stokes flow in the presence of irregular free surfaces and moving solid boundaries. The method uses an embedded boundary approach on staggered Cartesian grids, avoiding the need for expensive remeshing operations, and can be applied to flows in both two and three dimensions. It uses fully implic...