中文摘要：

该文探讨了间断有限元法（Discontinuous Galerkin Method）在对流与传热问题中的应用,给出了该方法的详细求解过程,并应用其求解了线性、非线性和变系数导热问题以及对流传热问题。讨论了数值通量中的参数对计算效率和收敛性的影响,并给出了合理的参数取值范围。在非线性和变系数导热问题的计算中,为了提高计算效率,还引进了同伦迭代方法。计算结果表明间断有限元法可以有效地应用于求解对流传热问题,并且通过与同伦分析方法相结合,还可以高效地求解许多非线性对流传热问题。由于对流传热问题广泛存在于水动力学中,故此文的研究结果可以为这些问题的求解提供一定的借鉴作用。

英文摘要：

In this paper,the applications of Discontinuous Galerkin Method（DG） in problems of convection and heat transfer were discussed.The solution procedures were given in detail and illustrated by three heat conduction problems,i.e.linear,nonlinear,variable coefficient,respectively,and one convective heat transfer problem.The effects of the stabilization constants on the convergence and computational efficiency were investigated.The valid ranges of these parameters were also given.For the nonlinear and variable coefficient problems,a newly developed technique,namely the Homotopy Analysis Method（HAM） was introduced to provide an iterative scheme.Computational results show that convective heat transfer equations can be solved by the DG method.Combined with the HAM,nonlinear and variable coefficient equations can also be solved efficiently.Convective heat transfer is widely occurred in hydrodynamics,thus we hope that the studies in this paper might be helpful in solving these problems using the DG method.