螺槽区域上偏微分方程模型的几何变换算法

A geometric transformation algorithm for PDE models on a screw channel domain

根据螺槽是一族螺线的集合特点,先建立螺旋直角坐标系,并证明了等截面螺槽区域在螺旋直角坐标系下为柱体区域;再利用数值保角变换,将柱体区域变为长方体区域,使得此类求解区域上的偏微分方程(PDE)模型在区域几何变换后易于数值求解;最后对一个矩形螺槽上的三维Poisson方程边值问题进行了数值计算。结果表明,此算法有效且易用,为研究单螺杆挤出机中三维流体流动提供了易用可行的基础数值方法。

Based on the characteristic that a screw channel is a set of spiral lines,a spiral rectangular coordinate system has been established,and it has been shown that a screw channel domain with uniform section can be converted to a cylindrical domain in this spiral rectangular coordinate system.The cylindrical domain can subsequently be transformed to a cuboid domain by numerical conformal mapping.Partial differential equation（ PDE） models of such a domain can then be numerically solved much more easily after this transformation.As an example,a boundary value problem for a 3-D Poisson equation on a screw channel domain with a rectangular section has been solved numerically,and the numerical results demonstrate that the algorithm is effective and easy to use.The algorithm offers a feasible and easy-to-use basic numerical method for the study of 3-D fluid flow in a single screw extruder.