用区域变换计算单螺杆挤出机流动区域上的三维泊松方程数值解法

单螺杆挤出机流体流动区域是一个复杂的区域，其截面为双连通区域，且计算求解此流动区域上的泊松方程是用高效的投影算法求解单螺杆挤出机流体流动问题的核心步骤。利用共形映射将此不规则的双连通区域转化为同心圆环，进一步将复杂的求解区域变为规则的圆环柱体区域，可以大大简化问题的计算，并适用于计算包含漏流层的单螺杆挤出机流体流动问题。以截面内边界曲线为椭圆的单螺杆挤出机为例进行了泊松方程的求解计算，将求得的解与精确解进行了对比，结果表明此方法简单有效。

Using area transformation to solve the 3D Poisson equation in the flow area of a single screw extruder

The fluid flow area in a single screw extruder is complex,and its cross section is a bi-connected area.When using an efficient projection algorithm to solve problems of fluid flow in a single screw extruder,the key is to understand the Poisson equation in this area.In this paper,conformal mapping is used to transform an irregular biconnected area into a concentric ring,and the complicated solution area is then transformed into a regular circular cylinder region.This method can greatly reduce computation for this problem and be applied to problems of fluid flow in a single screw extruder with a leakage layer.As an example,a boundary value problem of a Poisson equation has been solved numerically in the fluid flow area of a single screw extruder with an elliptical inner boundary in the cross section,and the numerical solution compared with the exact one.The numerical results shows that this method is simple and effective.