Nested Cartesian Grid Method in Incompressible and Viscous Fluid Flow

• Main Authors: Ke-Wei, 詹可薇
• Other Authors: Yih-Ferng Peng
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/40404856933328484710

碩士 === 國立暨南國際大學 === 土木工程學系 === 97 === In this paper, the local grid refinement is focused by using a nested grid technique. The nested Cartesian grid method is developed for simulating unsteady, viscous, incompressible flows with complex immersed boundaries. A finite volume method based on a second-order accurate central-difference scheme is used in conjunction with a two-step fractional-step procedure. The key aspects that need to be considered in developing such a nested grid solver are imposition of interface conditions on the nested-block boundaries and accurate discretization of the governing equation in cells that are with block-interface as a control surface. A new interpolation procedure is presented which allows systematic development of a spatial discretization scheme that preserves the spatial accuracy of the underlying solver. As a result, high efficiency and accuracy nested grid method is developed. The present nested grid method has been tested by four numerical examples to examine its performance in the two dimensional problems. The numerical examples include a lid-driven cavity flow problem, flow past a circular cylinder symmetrically installed in a Channel, flow past an ellipse with angle of attack, and flow past two circular cylinders with different diameters. For the numerical simulations of flow past bluff body problems, we used an Immersed Boundary (IB) method where the solid object is represented by a distributed body force in the Navier–Stokes equations. The main advantage of IB method is that the simulations can be performed on a regular Cartesian grid and thus applied with the present nested Cartesian grid method without difficulty. From the numerical experiments, the ability of the solver to simulate flows with complicated immersed boundaries is demonstrated and the nested grid approach can be efficiently combined with fractional-step algorithm to speed up the numerical solutions was also founded.