Speeding up decoupled calculations of Navier-Stokes equations by multigrid method.

Splitting up method for the 2D stochastic Navier-Stokes equations

Abstract. In this paper, we deal with the convergence of an iterative scheme for the 2-D stochastic Navier-Stokes Equations on the torus suggested by the LieTrotter product formulas for stochastic differential equations of parabolic type. The stochastic system is split into two problems which are simpler for numerical computations. An estimate of the approximation error is given either with per...

Multigrid Solution of the Navier-Stokes Equations on Triangular Meshes

A new Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite-element Galerkin approximation, which can be shown to be equivalent to a finite-volume approximation for regular equilateral triangular meshes. Integration to steady state is performed using a multistage time-stepping scheme, and conv...

Robust Multigrid Algorithms for the Incompressible Navier-Stokes Equations

Anisotropies occur naturally in CFD where the simulation of small scale physical phenomena, such as boundary layers at high Reynolds numbers, causes the grid to be highly stretched leading to a slow down in convergence of multigrid methods. Several approaches aimed at making multigrid a robust solver have been proposed and analyzed in literature using the scalar diffusion equation. However, the...

Towards Optimal Multigrid Efficiency for the Navier-Stokes Equations

On Kato’s Method for Navier–stokes Equations

We investigate Kato’s method for parabolic equations with a quadratic non-linearity in an abstract form. We extract several properties known from linear systems theory which turn out to be the essential ingredients for the method. We give necessary and sufficient conditions for these conditions and provide new and more general proofs, based on real interpolation. In application to the Navier-St...