Krylov single-step implicit integration factor WENO methods for advection-diffusion-reaction equations

详细信息    查看全文

• 作者：Tian Jiang ^{jtian29@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Yong-Tao Zhang ; ^{yzhang10@nd.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Advection&ndash ; diffusion&ndash ; reaction equations ; Single-step methods ; Implicit integration factor methods ; Krylov subspace approximation ; Weighted essentially non-oscillatory schemes
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：15 April 2016
• 年：2016
• 卷：311
• 期：Complete
• 页码：22-44
• 全文大小：2725 K

文摘

Implicit integration factor (IIF) methods were developed in the literature for solving time-dependent stiff partial differential equations (PDEs). Recently, IIF methods were combined with weighted essentially non-oscillatory (WENO) schemes in Jiang and Zhang (2013) [19] to efficiently solve stiff nonlinear advection–diffusion–reaction equations. The methods can be designed for arbitrary order of accuracy. The stiffness of the system is resolved well and the methods are stable by using time step sizes which are just determined by the non-stiff hyperbolic part of the system. To efficiently calculate large matrix exponentials, Krylov subspace approximation is directly applied to the implicit integration factor (IIF) methods. So far, the IIF methods developed in the literature are multistep methods. In this paper, we develop Krylov single-step IIF-WENO methods for solving stiff advection–diffusion–reaction equations. The methods are designed carefully to avoid generating positive exponentials in the matrix exponentials, which is necessary for the stability of the schemes. We analyze the stability and truncation errors of the single-step IIF schemes. Numerical examples of both scalar equations and systems are shown to demonstrate the accuracy, efficiency and robustness of the new methods.