浸入边界法及其应用

浸入边界法主要用于模拟存在复杂外形结构的流场的运动情况和处理各种动边界问题,目前已广泛应用于计算流体力学领域.浸入边界法既是数学建模方法又是数值离散方法,它将物体边界与流体的相互作用通过在流体运动方程中加体积力项来体现,并在数值计算中采用简单的笛卡尔网格,避免了按照物体边界形状生成贴体网格时所遇到的各种问题.浸入边界法分为连续力法和离散力法:连续力法主要用于处理弹性边界问题,它的力源项满足特定的力学关系式;离散力法主要用于处理固体界面问题,它的力源项由边界条件推导得到.着重阐述了浸入边界法的基本原理和数学构造,对目前已有的几种不同的浸入边界法做了简单地介绍,并给出了一些应用实例,最后提出了浸入边界法未来的发展方向.

Immersed Boundary Method and Its Application

The immersed boundary method is a general technique for modeling flow flied with complex geometries and fluid structure interaction and now it is applied in various aspects of fluid dynamics.This immersed boundary method is both a mathematical formulation and a numerical scheme.In immersed boundary method,the structure immersed in fluid is considered as a kind of momentum forcing in Navier-Stokes equations rather than a real body,which avoids the problem of generating a body conformal grid.The immersed boundary methods are split up in continuous forcing and discrete forcing approach.The continuous forcing approaches,which forcing source satisfy a certain kind of mechanical relation,are mainly used in elastic boundary problem;however,the discrete forcing approaches,which forcing source are derived from the boundary conditions,are primarily used in solid boundary problem.An overview and comments on the immersed boundary method were presented.First the basic theory and mathematical construction of immersed boundary were described in detail,then briefly several kinds of immersed methods were introduced,after that some applications on different areas were given,finally the future investigation on the immersed boundary were recommended.