Local RBFs Based Collocation Methods for Unsteady Navier-Stokes Equations

2015 ◽  
Vol 7 (4) ◽  
pp. 430-440 ◽  
Author(s):  
Xueying Zhang ◽  
Xin An ◽  
C. S. Chen
Keyword(s):  
Linear Systems ◽  
Numerical Experiments ◽  
Stokes Equations ◽  
Sparse Matrix ◽  
High Accuracy ◽  
Collocation Methods ◽  
Navier Stokes ◽  
Sparse Linear Systems ◽  
Navier Stokes Equations ◽  
Weight Coefficients

AbstractThe local RBFs based collocation methods (LRBFCM) is presented to solve two-dimensional incompressible Navier-Stokes equations. In avoiding the ill-conditioned problem, the weight coefficients of linear combination with respect to the function values and its derivatives can be obtained by solving low-order linear systems within local supporting domain. Then, we reformulate local matrix in the global and sparse matrix. The obtained large sparse linear systems can be directly solved instead of using more complicated iterative method. The numerical experiments have shown that the developed LRBFCM is suitable for solving the incompressible Navier-Stokes equations with high accuracy and efficiency.

Preconditioning Techniques for Nonsymmetric Linear Systems in the Computation of Incompressible Flows

2009 ◽  
Vol 76 (2) ◽  
Author(s):  
Murat Manguoglu ◽  
Ahmed H. Sameh ◽  
Faisal Saied ◽  
Tayfun E. Tezduyar ◽  
Sunil Sathe
Keyword(s):  
Linear Systems ◽  
Krylov Subspace ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Handling Time ◽  
Navier Stokes ◽  
Preconditioning Techniques ◽  
Navier Stokes Equations ◽  
Nonsymmetric Linear Systems ◽  
Steady State Solutions

In this paper we present effective preconditioning techniques for solving the nonsymmetric systems that arise from the discretization of the Navier–Stokes equations. These linear systems are solved using either Krylov subspace methods or the Richardson scheme. We demonstrate the effectiveness of our techniques in handling time-accurate as well as steady-state solutions. We also compare our solvers with those published previously.

scholarly journals An Algorithm for the Navier-Stokes Problem

2006 ◽  
Vol Volume 5, Special Issue TAM... ◽  
Author(s):  
F.Z. Nouri ◽  
K. Amoura
Keyword(s):  
Nonlinear Problem ◽  
Numerical Experiments ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Navier Stokes ◽  
Nous Proposons ◽  
Navier Stokes Equations ◽  
International Audience ◽  
The One ◽  
Work First

International audience This study is a continuation of the one done in [7],[8] and [9] which are based on the work, first derived by Glowinski et al. in [3] and [4] and also Bernardi et al. [1] and [2]. Here, we propose an Algorithm to solve a nonlinear problem rising from fluid mechanics. In [7], we have studied Stokes problem by adapting Glowinski technique. This technique is userful as it decouples the pressure from the velocity during the resolution of the Stokes problem. In this paper, we extend our study to show that this technique can be used in solving a nonlinear problem such as the Navier Stokes equations. Numerical experiments confirm the interest of this discretisation. Cette étude est la continuation des travaux [7],[8] et [9] qui sont basés sur l'étude faite par Glowinski et al. [3] et [4] ainsi que Bernardi et al. (voir [1] et [2]). Ici nous proposons un Algorithme pour résoudre un problème non-linéaire issu de la mécanique des fluides. Dans [7] nous avons étudié le problème de Stokes en adaptant la technique de Glowinski, grace à aquelle, on peut découpler la pression de la vitesse lors de la résolution du problème de Stokes. Dans ce travail, nous étendons notre étude et montrons que cette technique peut être utilisée dans la résolution d'un probème non-linéaire comme les quations de Navier Stokes. Des tests numériques confirment l'intérêt de la discrétisation.

Application of a new class of high accuracy TVD schemes to the Navier-Stokes equations

1985 ◽  
Author(s):  
S. CHAKRAVARTHY ◽  
K.-Y. SZEMA ◽  
U. GOLDBERG ◽  
J. GORSKI ◽  
S. OSHER
Keyword(s):  
Stokes Equations ◽  
High Accuracy ◽  
Navier Stokes ◽  
Tvd Schemes ◽  
Navier Stokes Equations ◽  
New Class

scholarly journals A SPLITTING PRECONDITIONER FOR THE INCOMPRESSIBLE NAVIER–STOKES EQUATIONS

2013 ◽  
Vol 18 (5) ◽  
pp. 612-630 ◽  
Author(s):  
Ze-Jun Hu ◽  
Ting-Zhu Huang ◽  
Ning-Bo Tan
Keyword(s):  
Spectrum Analysis ◽  
Numerical Experiments ◽  
Augmented Lagrangian ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Preconditioned Matrix

In this paper, a splitting preconditioner based on the relaxed dimensional factorization (RDF) preconditioner and the modified augmented Lagrangian (MAL) preconditioner for the incompressible Navier–Stokes equations is presented. The preconditioned matrix is analyzed, and similar results arising from the RDF and the MAL preconditioners are obtained. The corresponding details of the spectrum analysis are given. Finally, we compare the three preconditioners and numerical experiments are implemented by using the IFISS package.

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