A second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin scheme for the Kerr-Debye model

作者：Huang, Juntao; Shu, Chi-Wang^*

来源：Mathematical Models and Methods in Applied Sciences, 2017, 27(3): 549-579.

DOI：10.1142/S0218202517500099

• Discontinuous Galerkin
• positivity-preserving
• asymptotic-preserving
• stiff systems
• Runge-Kutta methods
• implicit-explicit
• Kerr-Debye model

In this paper, we develop a second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin (DG) scheme for the Kerr-Debye model. By using the approach first introduced by Zhang and Shu in [Q. Zhang and C.-W. Shu, Error estimates to smooth solutions of Runge-Kutta discontinuous Galerkin methods for scalar conservation laws, SIAM J. Numer. Anal. 42 (2004) 641-666.] with an energy estimate and Taylor expansion, the asymptotic- preserving property of the semi-discrete DG methods is proved rigorously. In addition, we propose a class of unconditional positivity-preserving implicit-explicit (IMEX) Runge-Kutta methods for the system of ordinary differential equations arising from the semi-discretization of the Kerr-Debye model. The new IMEX Runge-Kutta methods are based on the modification of the strong-stability-preserving (SSP) implicit Runge-Kutta method and have second-order accuracy. The numerical results validate our analysis.

• 出版日期2017-3
• 单位清华大学