Abstract In the paper, a hybrid method of differential transform (DT) for time in t direction and smoothed particle hydrodynamics (SPH) for space in x and y directions is proposed to solve transient heat conduction problems. Traditionally, SPH is complicated especially as the number of particles is large. SPH provides a simple way to evaluate differentiations and the DT has high accuracy for numerical solutions. Combining DT and SPH, the method is robust with high accuracy. We have compared the numerical solutions of the present method to the exact solutions of the heat problem for some special cases. The accuracy of the present method is found to be better than that of traditional methods of SPH. Besides, the hybrid method of DT for time direction and finite difference method (FDM) for space in x and y directions is also presented for three examples. In the third example, the DT/SPH method is better than the DT/FD method.

中文翻译：

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瞬态热传导问题的混合微分变换法/光滑粒子流体力学和DT/有限差分法

摘要 本文提出了一种t方向时间微分变换(DT)与x、y方向空间平滑粒子流体力学(SPH)混合方法求解瞬态热传导问题。传统上，SPH 是复杂的，尤其是当粒子数量很大时。SPH 提供了一种评估微分的简单方法，并且 DT 对数值解具有很高的准确性。结合 DT 和 SPH，该方法具有鲁棒性和高精度。我们已经将本方法的数值解与某些特殊情况下热问题的精确解进行了比较。发现本方法的准确性优于传统的SPH方法。除了，还针对三个示例介绍了时间方向的 DT 和空间 x 和 y 方向的有限差分法 (FDM) 的混合方法。在第三个例子中，DT/SPH 方法优于 DT/FD 方法。