Preconditioners for the Steady Incompressible Navier-Stokes Problem
نویسندگان
چکیده
In this paper we discuss preconditioners for the incompressible Navier-Stokes equations. In combination with Krylov subspace methods, they give a fast convergence for the solution of the Navier -Stokes equations. With the help of numerical experiments, we report some new findings regarding the convergence of these preconditioners. Besides that, a renumbering scheme for direct solvers and ILU preconditioners is introduced that improves the convergence of the solvers. We compare Bi-CGSTAB and a newly developed Krylov subspace method IDR(s) preconditioned with ILU. Both 2D and 3D experiments are used to measure the performance of the preconditioners.
منابع مشابه
Numerical Solution Techniques for the Steady Incompressible Navier-Stokes Problem
In this paper we discuss some recently published preconditioners for the incompressible Navier-Stokes equations. In combination with Krylov subspace methods, they give a fast convergence for the solution of the Navier -Stokes equations. With the help of numerical experiments, we report some new findings regarding the convergence of these preconditioners. Besides that, a renumbering scheme for d...
متن کاملAugmented Lagrangian Preconditioners for the Incompressible Navier-Stokes Equations
SUMMARY We study different variants of the augmented Lagrangian-based block triangular preconditioner introduced by the first two authors in [SIAM J. The preconditioners are used to accelerate the convergence of the Generalized Minimal Residual (GMRES) method applied to various finite element and MAC discretizations of the Oseen problem in two and three space dimensions. Both steady and unstead...
متن کاملA Comparative Study of Block Preconditioners for Incompressible Flow Problems
Problem statement: We consider the numerical solvers for the linearized Navier-Stokes problem. Both the Stokes problem and Oseen problems are considered. Approach: We used the Mark and Cell (MAC) discretization method to discretize the Navier-Stokes equations. We used preconditioned Krylov subspace methods to solve the resulting linear systems. Results: Numerical experimental results are perfor...
متن کاملAnalysis of Augmented Lagrangian-Based Preconditioners for the Steady Incompressible Navier-Stokes Equations
We analyze a class of modified augmented Lagrangian-based preconditioners for both stable and stabilized finite element discretizations of the steady incompressible Navier–Stokes equations. We study the eigenvalues of the preconditioned matrices obtained from Picard linearization, and we devise a simple and effective method for the choice of the augmentation parameter γ based on Fourier analysi...
متن کاملBlock Preconditioners for the Incompressible Stokes Problem
This paper discusses the solution of the Stokes problem using block preconditioned iterative methods. Block preconditioners are based on the block factorization of the discretized problem. We focus on two specific types: SIMPLE-type preconditioners and the LSC preconditioner. Both methods use scaling to improve their performance. We test convergence of GCR in combination with these precondition...
متن کامل