基于指数变换的对角隐式龙格库塔法求解中子点堆动力学方程

Application of Diagonally Implicit Runge Kutta with Exponential Transformation on Point Kinetic Equations

点堆动力学对于反应堆安全运行有着重要作用,但点堆动力学方程是刚性的,通常使得数值求解所采用的步长很小。本文研究了基于指数变换的对角隐式龙格库塔(DIRK)方法用来求解点堆动力学方程。基于指数变换的DIRK保留了DIRK方法适合求解刚性方程的特点,同时在反应性引入较大的情况下,它比对角隐式库塔方法表现更好。若干算例,如反应性阶跃、线性或者正弦变化等,表明基于指数变换的DIRK方法具有很高的计算精度。

The point kinetics is very important to the safety of the reactor operation.However,these equations are stiff,with very small time step for solution.The diagonally implicit Runge Kutta(DIRK)with exponential transformation is studied for point kinetics.It keeps the advantage of diagonally implicit Runge Kutta method which is suitable for stiff equations and owns the better performance than the diagonally implicit Runge Kutta method when the positive reactivity is inserted.Several cases,such as step,ramp,and sinusoidal reactivity insertion are used to show that this method owns high accuracy.