Multigrid for Stokes Equations
نویسنده
چکیده
We discuss a basic iterative method by solving u and p alternatively. Starting from some initial guess u, p, one iteration going from (u, p) to (u, p) is (1) Fix p, solve for u; (2) Fix u, solve for p. When p is fixed, there are two equations for u. We can first solve the momentum equation to get u (the term B p is moved to the right hand side), i.e., Au = f −B p. But unless p is the exact solution, Bu will not satisfy the continuity equation. We may project u to the divergence free space using the projection operator PB . If we do so, it is in the type of projection methods. The projection step is not necessary and the corresponding method includes the popular Uzawa methods.
منابع مشابه
A Nonconforming Multigrid Method for the Stationary Stokes Equations
An optimal-order W-cycle multigrid method for solving the stationary Stokes equations is developed, using PI nonconforming divergence-free finite elements.
متن کاملA multigrid smoother for high Reynolds number ows
The linearized Navier-Stokes equations are solved in 2D using a multigrid method where a semi-implicit Runge-Kutta scheme is the smoother. With this smoother the stiiness of the equations due to the disparate scales in the boundary layer is removed and Reynolds number independent convergence is obtained.
متن کاملA Cascade Algorithm for the Stokes Equations
A variant of multigrid schemes for the Stokes problem is discussed. In particular, we propose and analyse a cascadic version for the Stokes problem. The analysis of the transfer between the grids requires special care in order to establish that the complexity is the same as that for classical multigrid algorithms.
متن کاملTextbook Multigrid Efficiency for the Incompressible Navier-Stokes Equations: High Reynolds Number Wakes and Boundary Layers
Textbook multigrid efficiencies for high Reynolds number simulations based on the incompressible Navier-Stokes equations are attained for a model problem of flow past a finite flat plate. Elements of the Full Approximation Scheme multigrid algorithm, including distributed relaxation, defect correction, and boundary treatment, are presented for the three main physical aspects encountered: enteri...
متن کاملMultigrid analysis for the time dependent Stokes problem
Certain implicit time stepping procedures for the incompressible Stokes or Navier-Stokes equations lead to a singular-perturbed Stokes type problem at each type step. The paper presents a convergence analysis of a geometric multigrid solver for the system of linear algebraic equations resulting from the disretization of the problem using a finite element method. Several smoothing iterative meth...
متن کامل