纯无网格并行计算在传热方程数值模拟中的应用

考虑纯无网格并行计算在传热方程数值模拟中的应用. 首先将Taylor展开式保留到三阶导数, 拓展应用纯无网格有限点集法(FPM), 对三维热传导方程进行求解以提高数值精度； 其次引入MPI并行计算技术, 通过循环语句的并行, 采用多个CPU计算以提高计算效率, 得到一种针对三维热传导问题模拟的可靠、 高效性纯网格并行FPM算法. 在数值算例中, 先对不同区域上带不同边值条件的传热问题进行求解, 并与解析解对比, 分析给出算法的计算效率和误差； 然后用给出的并行算法对功能梯度材料中温度随时间演化过程进行模拟预测, 并与其他数值结果做比较, 以验证数值预测的可靠性.

Application of Pure Mesh Free Parallel Computation in Numerical Simulation of Heat Transfer Equation

We considered application of pure mesh free parallel computation innumerical simulation of heat transfer equation. Firstly, we reserved the Taylor expansion to the third derivative, and extended thepure mesh-free finite pointset method (FPM) to solve the three-dimensional heat conduction equation in order to improve the numerical accuracy. Secondly, we introduced massage passing interface (MPI) parallel computing technology to improve the computational efficiency byparallel use of multiple CPUs through cyclic statements, and obtained a reliable and efficient pure grid parallel FPM algorithm for three-dimensionalheat conduction problem. In the numerical example, we first solved the heat transfer problems with different boundary conditions in different regions, compared it with the analytical solutions,and analyzed the calculation efficiency and error of the proposed algorithm. Then we used the parallel algorithm to simulate and predict the temperature evolution process with time in functionally graded materials, and compared it with other numerical results to verify the reliability of the numerical prediction.