对角隐式龙格库塔法在求解瞬态对流扩散方程中的应用

Application of Diagonally Implicit Runge-Kutta Method for Solving Time-Dependent Convection-Diffusion Equation

开发高效求解瞬态对流扩散方程的方法,其空间离散采用改进的节块展开方法(MNEM),时间离散分别选取2阶和4阶精度的对角隐式龙格库塔(DIRK)方法。数值实验结果表明,程序的计算结果同解析解符合很好;MNEM具有跟踪强烈温度变化的能力;两种时间离散方法的效率与问题以及选取的误差限值相关。

An efficient scheme for solving transient convection-diffusion equation was developed. Modified nodal expansion method （MNEM） was utilized for spatial discretization, while two kinds of diagonally implicit Runge-Kutta （DIRK）. schemes--second-order DIRK and fourth-order DIRK were adopted for time discretization. The numerical results show that the numerical results of TDMNEM code agree with analytical solutions very well. MNEM has good ability in capturing sharp temperature variation. The efficiency of two time discretization methods depend on problem and the error criteria which been selected.