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二维显式有限差分方法的求解共有四种方法:等步长(空间步长,即划分单元大小)节点法、等步长单元法、不等步长节点法和不等步长单元法。本文从理论上推导了这四种方法的求解差分方程,以钢板冷却过程为对象,分别计算了钢板的温度变化,并将结果与有限元结果进行了对比。结果表明,等步长节点法较其它三种方法计算时间短、计算结果精度更高,在涉及温度场计算的场合时可优先考虑采用。
There are four methods to solve the two-dimensional explicit finite difference method: step-by-step (spatial step size, that is, division of cell size) node method, equal-step cell method, unequal step node method and unequal step- In this paper, the differential equations of the four methods are deduced theoretically. The change of the temperature of the steel plate is calculated with the steel plate cooling process. The results are compared with the finite element results. The results show that the method of equal-step nodal method has shorter calculation time than the other three methods, and the accuracy of the calculation results is higher. When calculating the temperature field, it can be used preferentially.