Hybrid differential transform method/smoothed particle hydrodynamics and DT/finite difference method for transient heat conduction problems

摘要

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.