Study On Numerical Calculation Using Implicit Direct-force Projected Immersed Boundary Method

Fluid and solid regions are treated as a whole fluid computational domain in immersed boundary method, the fixed grid is used to discrete the domain. Comparing to the traditional move grid method, it isn’t necessay to update grid, saves much time and overcomes the defects of dynamic grid technology. It possesses great superiority for computing large displacement or large deformation problems. Therefore, this paper studys the structure-flu id coupling based on an implicit direct-force projected immersed boundary method. The force density of solid boundary is derivated by using no-slip condition. The smooth function S was used to transform the force density of solid boundary to the Euler grids and correct the flow velocity. Solving the equations of the structure-fluid coupling based on immersed boundary method is analogy to solving the incompressible navier-stokes equations based on step-by-step projected method.The specific research content is shown in the following:(1) First.it is to construct the three-dimensional mathematical model of implicit direct-force projected immersed boundary method,which is used for solving interaction between structure and fluid.The Navier -Stokes equation was discreted by using finite difference method,Quick formation was used to discret convection item, central difference scheme was used to discret the diffusion item, second-order explicit Adams-Bashforth was used to discret time item.(2) The item of volume force was calculated by using evenly spaced discrete nodes instead of immersed boundary. It is transform the velocity of Euler grids to solid boundary to obtain the calculated velocity of solid boundary by using 8,the smooth function. The force density of solid boundary is derivated by using no-slip condition that the calculated velocity is equal to the physical velocity of solid boundary. The flow velocity was corrected again through transforming the force density of solid boundary to Euler grids.(3) The large sparse linear algebra equations were obtained from discreting three-dimensional pressure poisson equation by suing finite difference method, which can be solved by combining surface iteration method with direct simulation method (using the opening source library UMFPACK method),sparse coefficient matrix is stored by using Eigen data format.(4) The calculated procedure of implicit direct-force projected immersed boundary method was writed by using C++ language. First, A three dimensional mathematical problem which has accurate solution and a channel flow problem were calculated to verify the method’s feasibility and numerical stability. It was used to simulate the effects of input power with different active oscillation of two-dimensional hydrofoil, and simulate flow around a three-dimensional sphere.