Orthogonal spline collocation methods for the stream function-vorticity formulation of the Navier–Stokes equations

2008 ◽  
Vol 24 (2) ◽  
pp. 449-464 ◽  
Author(s):  
Graeme Fairweather ◽  
Heping Ma ◽  
Weiwei Sun
Keyword(s):  
Stream Function ◽  
Stokes Equations ◽  
Collocation Methods ◽  
Navier Stokes ◽  
Spline Collocation ◽  
Navier Stokes Equations ◽  
Orthogonal Spline Collocation

scholarly journals Numerical Simulation of Slip effect on Lid-Driven Cavity Flow Problem for High Reynolds Number: Vorticity – Stream Function Approach

2021 ◽  
Vol 8 (3) ◽  
pp. 418-424
Author(s):  
Syed Fazuruddin ◽  
Seelam Sreekanth ◽  
G. Sankara Sekhar Raju
Keyword(s):  
Reynolds Number ◽  
Stream Function ◽  
Stokes Equations ◽  
Cavity Flow ◽  
Partial Slip ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Slip Conditions ◽  
Driven Cavity Flow

Incompressible 2-D Navier-stokes equations for various values of Reynolds number with and without partial slip conditions are studied numerically. The Lid-Driven cavity (LDC) with uniform driven lid problem is employed with vorticity - Stream function (VSF) approach. The uniform mesh grid is used in finite difference approximation for solving the governing Navier-stokes equations and developed MATLAB code. The numerical method is validated with benchmark results. The present work is focused on the analysis of lid driven cavity flow of incompressible fluid with partial slip conditions (imposed on side walls of the cavity). The fluid flow patterns are studied with wide range of Reynolds number and slip parameters.

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.

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