SODF-SPH方法及其在热传导问题中的应用

SODF-SPH Method and Its Applications in Heat Conduction Problems

在光滑粒子流体动力学(SPH)原理的基础上,通过泰勒级数展开提出了计算函数二阶偏导数的SODF-SPH方法。选用相等的粒子间距和相同的光滑长度对一维热传导问题进行了计算和模拟,与传统SPH方法进行了对比分析,结果表明新方法的精度高、收敛速度快且稳定性好;对二维和三维各种热传导问题进行了计算和模拟,与解析解进行了对比,结果表明新方法得到的计算结果与解析解吻合良好。新方法的计算过程能避免计算核函数导数,致使对核函数的要求降低,可选用更多的核函数且计算量较小,可在工程和数值计算中广泛应用。

Based on the principles of SPH method,a SODF-SPH method to compute second order derivatives was constructed through Taylor series expansion.Equal particle distance and same smoothed length were chosen to compute and simulate 1Dheat conduction problems.After compared with conventional SPH method,results show that the accuracy,convergence rate and stability of the new method are better.To compute and simulate 2Dand 3Dheat conduction problems and compared with analytical solutions,the numerical results are in accord with analytical solutions.The derivatives may avoid calculating differential coefficients of kernel function.Therefore,the demands of kernel function are reduced,more kernel functions may be used and the calculation amounts are decreased.The new method may be widely used in engineering fields and numerical calculations.