带源项的守恒系统时间分裂算法定常解的收敛性研究

Study on convergence to steady state of the time splitting method for conservation laws with source terms

时间分裂算法很难获得带源项的守恒系统的定常解,本文中,考虑使用基本的隐式方法积分线性、二次和三次源项,研究了时间分裂算法不能收敛到数值定常态的原因。采用一个刚性参数的方式预测定常态的误差,刚性参数依赖于特定的源项。当源项是解的线性函数时,不存在定常态误差;当源项是解的非线形函数时,发现定常状态的误差是刚性参数的单调增加函数。定常态误差的分析将推广到标准k epsilon双方程湍流模型计算的情况。

It is well known that the time splitting method has difficulty preserving the steady states of conservation laws with source terms. In this paper we estimate the steady state error in terms of a stiffness parameter R, which denotes the ratio of the advection time scale to source term relaxation time scale. We consider linear, quadratic and cubic source terms integrated essentially with an implicit method. We will study why or when the time splitting method does not allow convergence to a numerical steady state. When the source term is a linear function of the solution, there is no steady state error. The steady error is an increasing function of the stiffness parameter if the source term is nonlinear. If the steady state error is large, the computation can not converge to zero machine. The steady state error analysis will be extended to the case of k-epsilon model for high Reynolds number turbulent flow computations.