瞬态热传导问题的精细积分数值流形方法研究

摘要

Owing to the unique dual cover systems,i.e.,the mathematical cover system and the physical cover system,the numerical manifold method (NMM) is predominant method in domain discretization.As for the precise time integration method (PTIM),it is of high accuracy,absolutely stable,immune from oscillation and the solution is independent of the time step size.In this paper,the NMM,combined with the PTIM,is developed to study two-dimensional (2D) transient heat conduction problems.Based on the governing equations and associated boundary conditions,the NMM discrete equations for the considered problems are derived using the modified variational principle.The details of the PTIM and also the spatial integration scheme are presented for the solution of the time-dependent system of equations.To validate the proposed method,two typical numerical examples are carefully examined.The simulated results show that the 2D unsteady heat conduction problems can be efficiently and accurately tackled by the present approach.%数值流形方法(NMM)因其特有的双覆盖系统(数学覆盖和物理覆盖)在域离散方面具有独特的优势,而精细时间积分法则具有精度高、无条件稳定、无振荡以及计算结果不依赖于时间步长等特点.发展了用于研究二维瞬态热传导问题的精细积分NMM.结合待求问题的控制方程和边界条件,并基于修正变分原理导出了NMM的总体方程,给出了求解此类时间相依方程的精细时间积分及空间积分策略,选取了两个典型算例对方法的有效性进行了验证,结果表明本文方法可以高效高精度地求解瞬态热传导问题.