注塑成型Hele-Shaw流动模拟中热对流的异步长求解

Thermal convection calculation with variable time step in Hele-Shaw flow simulation of injection molding

在Hele-Shaw流动数值模拟中,速度是压力的后处理结果。如果是点浇口,则浇口附近速度会随单元尺寸缩小而趋于无穷大,导致能量方程作为一个整体求解时,时间步长必须非常小,否则会产生很大误差;而根据热对流物理意义分步求解,则需追踪当前物质在上一时刻位置,当单元速度很高、逆向搜索需穿透多个单元时,搜索可能会失败。鉴于此,基于分步求解法,研究提出一种变长度子时间步长方法处理对流项,确保搜索路径局限在当前单元内,并采用二分法确定子时间步数量,使算法简洁有效。算例表明,该方法在保证计算精度和求解稳定性的同时,可以明显减少计算时间,提高计算效率。

In Hele-Shaw flow simulation,the directly solved variable is pressure and the velocity is only the post-treating result of pressure.Around the injection gate,the velocity may be very high along with reducing elemental size.This means that when the energy conservation equation is solved as a whole,the time step must be very short,otherwise,the error in the heat convection is unavoidable.The above problem can be overcome by using the operator-splitting method,in which the material at the current computing points needs to be tracked back to its position in the last time-step.However,this may lead to a new difficulty.If the elemental velocity is very high,the tracking needs to pass through a few elements and the reverse tracking may fail.To solve the problem,a new algorithm named sub time step with variable size was suggested to deal with the thermal convection in this paper,in which the sub time step using dichotomy was introduced that bounded the tracking path in a certain element.The new algorithm made the computation more simple and effective.The numerical examples showed that the new method had same accuracy as one using uniform small time step and high solving stability,but calculating time was dramatically reduced.