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Báo cáo " AN IMPLICIT SCHEME FOR INCOMPRESSIBLE FLOW COMPUTATION WITH ARTIFICIAL COMPRESSIBILITY METHOD "

To simulate the incompressible flow in complex three-dimensional geometry efficiently and accurately, a solver based on solution of the Navier-Stokes equations in the generalized curvilinear coordinate system was developed. The system of equations in three-dimension are solved simultaneously by the artificial compressibility method. The convective terms are differenced using a flux difference splitting approach. The viscous terms are differenced using second-order accurate central differences. An implicit line relaxation scheme is employed to solve the numerical system of equations. . | VNU. JOURNAL OF SCIENCE Mathematics - Physics. T.XXI N04 - 2005 AN IMPLICIT SCHEME FOR INCOMPRESSIBLE FLOW COMPUTATION WITH ARTIFICIAL COMPRESSIBILITY METHOD Nguyen The Duc Institute of Mechanics Vietnamese Academy of Science and Technology Abstract. To simulate the incompressible flow in complex three-dimensional geometry efficiently and accurately a solver based on solution of the Navier-Stokes equations in the generalized curvilinear coordinate system was developed. The system of equations in three-dimension are solved simultaneously by the artificial compressibility method. The convective terms are differenced using a flux difference splitting approach. The viscous terms are differenced using second-order accurate central differences. An implicit line relaxation scheme is employed to solve the numerical system of equations. The solver was tested for two cases including flow past a circular cylinder and flow around a hemispherical head of a cylindrical object. 1. Introduction Solutions to the incompressible Navier-Stokes equations are of interest in many fields of computational fluid dynamics. The problem of coupling changes in the velocity field with changes in pressure field while satisfying the continuity equation is the main difficulty in obtaining solutions to the incompressible Navier-Stokes. There are some types of method have been developed to solve the equations. The stream-function vorticity formulation of the equation has been used often when only two-dimensional problems are of interest but this has no straightforward extension. Other methods using primitive variables can be classified into two groups. The first group of methods can be classified as pressure-based methods. In these methods the pressure field is solved by combining the momentum and mass continuity equations for form a pressure or pressure-correction equation 1 2 . The second group of methods employs the artificial compressibility formulation. This idea was first introduced by Chorin 3