第二章定常不可压势流的数值计算Numerical.pptVIP

小 结 本章内容（contents） 定常不可压势流差分方法（FDM of elliptic PDE for steady incompressible potential flow） 定常不可压势流源汇法（Source and sink method for axis-symmetric incompressible flow） 椭圆型偏微分方程数值方法（Numerical method for elliptic PDEs） 本章重点（focus） 椭圆型偏微分方程数值方法（Numerical method for elliptic DEs） * 第二章 定常不可压势流的数值计算Chapter 2 Numerical computation of Steady Incompressible Potential Flow 2.1 定常不可压势流的基本方程 The Basic Equation of Incompressible Potential Flow 当流场无旋时，存在速度势函数 ， 应满足Laplace方程 When the flow is irrotational ,there must be exists the potential function ,and it is satisfies the Laplace Equation . 在直角坐标系中可写成 In Cartesian coordinate ,the Laplace Equation is (2D) (3D) 在柱坐标系中 In cylindrical coordinate ,it is 计算出 ，即可得到 和 After gained ,the velocity and pressure can be obtained as follow 若流场中有源或者汇，则 If there exist a source or sink in the flow ,then The equation becomes 假设流场中源的分布（平面问题）， Assume: the distribution of the source and sink is following the field within a cycle regime 则PDE为 Therefore the PDE is 2.2 由分布的源，汇引起的径向流动计算 The computation of the flow introduced by the distributed source and sink . 无量纲化参数 choose the dimensionless parameters as follows, 无量纲方程 the dimensionless equation becomes 流场区域 Flow field regained is limited as 此方程为二阶线性齐次方程，存在精确解 This eq is a two order linear equation ,it has a accurate solution 对于 则，精确解为 The accurate solution is 对应的方程阶为 The corresponding PDE is 边界条件 R=1 时 B.C R=4 时 速度解 The solution of velocity 下面讨论其数值解The numerical value solution will be discussed as following 一般线性二项齐次常微分方程边值问题： In general case , the 2D liner PDE can be written in to express ， using centeral difference scheme, which has 2 order accuracy. 将方程中 和 用中心差分格式表示（具有二阶精度） 微分方程可化为差分方程： T