TY - JOUR

T1 - Control volume-radial basis function solution of 2D driven cavity flow in terms of the velocity vorticity formulation

AU - Bustamante, C. A.

AU - Florez, W. F.

AU - Power, H.

AU - Giraldo, M.

AU - Hill, A. F.

PY - 2011

Y1 - 2011

N2 - The two-dimensional Navier Stokes system of equations for incompressible flows is solved in the velocity vorticity formulation by means of the Control Volume-Radial Basis Function (CV-RBF) method. This method is an improvement to the Control Volume Method (CVM) based on the use of Radial Basis Function (RBF) Hermite interpolation instead of the classical polynomial functions. The main advantages of the CV-RBF method are the approximation order, the meshless nature of the interpolation scheme and the presence of the PDE operator in the interpolation. Besides, the vorticity boundary values are computed in terms of the values of the velocity field at the neighbouring nodal points according to its definition by applying the curl operator to the local velocity interpolation function. Several interpolation strategies are tested for both the velocity and vorticity fields. A Newton type algorithm is implemented to solve the coupled system of non linear equations. As test example, the proposed numerical scheme is used to solve the lid driven cavity flow problem up to Re = 5000, where high Reynolds number solutions are achieved by using a Conservative and Hermitian interpolation for the velocity field.

AB - The two-dimensional Navier Stokes system of equations for incompressible flows is solved in the velocity vorticity formulation by means of the Control Volume-Radial Basis Function (CV-RBF) method. This method is an improvement to the Control Volume Method (CVM) based on the use of Radial Basis Function (RBF) Hermite interpolation instead of the classical polynomial functions. The main advantages of the CV-RBF method are the approximation order, the meshless nature of the interpolation scheme and the presence of the PDE operator in the interpolation. Besides, the vorticity boundary values are computed in terms of the values of the velocity field at the neighbouring nodal points according to its definition by applying the curl operator to the local velocity interpolation function. Several interpolation strategies are tested for both the velocity and vorticity fields. A Newton type algorithm is implemented to solve the coupled system of non linear equations. As test example, the proposed numerical scheme is used to solve the lid driven cavity flow problem up to Re = 5000, where high Reynolds number solutions are achieved by using a Conservative and Hermitian interpolation for the velocity field.

KW - Control Volume Method

KW - Local Hermite interpolation

KW - Radial Basis Function

KW - Velocity vorticity

UR - http://www.scopus.com/inward/record.url?scp=82055199177&partnerID=8YFLogxK

M3 - Artículo

AN - SCOPUS:82055199177

VL - 79

SP - 103

EP - 129

JO - CMES - Computer Modeling in Engineering and Sciences

JF - CMES - Computer Modeling in Engineering and Sciences

SN - 1526-1492

IS - 2

ER -