计算双螺杆挤出机流体流动的共形区域变换

双螺杆挤出机机筒内部的流体流动区域截面是随时间变化的复杂三连通区域，采取共形映射方法将这样的三连通区域映射成不随时间变化的圆界区域，进一步将流动区域变成一个不随时间变化的柱形区域，可大幅简化双螺杆挤出机流体流动问题的计算。选择以外边界为圆周、内边界为随时间旋转的两个椭圆周的平面区域上的热传导问题为研究对象，用本文方法进行计算并比较了精确解和数值解，计算结果表明两解的绝对误差较小。本文方法可用于双螺杆挤出机流体流动问题的计算，并简化了计算过程。
Abstract：The main result in this paper is an important method for simplifying computation of fluid flow in a twin screw extruder. The sections of fluid flow area inside the extruder are complex time-dependent three-connected regions. In this paper, conformal mappings are used to map the three-connected regions into time-independent regions with circular boundaries and, in addition, the flow area is mapped into a cylindrical time-independent area. As a result, computation of the fluid flow is greatly simplified. As an example, a heat conduction problem for a region with a circular boundary as the outer boundary and two elliptical boundaries rotating over time as the inner boundaries was solved numerically using our the mapping method. The exact solution and the numerical solution were compared. The numerical results show that our method is feasible and can be used to compute problems relating to the fluid flow in a twin screw extruder.