کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
522906 | 867880 | 2007 | 29 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Application of implicit–explicit high order Runge–Kutta methods to discontinuous-Galerkin schemes Application of implicit–explicit high order Runge–Kutta methods to discontinuous-Galerkin schemes](/preview/png/522906.png)
Despite the popularity of high-order explicit Runge–Kutta (ERK) methods for integrating semi-discrete systems of equations, ERK methods suffer from severe stability-based time step restrictions for very stiff problems. We implement a discontinuous Galerkin finite element method (DGFEM) along with recently introduced high-order implicit–explicit Runge–Kutta (IMEX-RK) schemes to overcome geometry-induced stiffness in fluid-flow problems. The IMEX algorithms solve the non-stiff portions of the domain using explicit methods, and isolate and solve the more expensive stiff portions using an L-stable, stiffly-accurate explicit, singly diagonally implicit Runge–Kutta method (ESDIRK). Furthermore, we apply adaptive time-step controllers based on the embedded temporal error predictors. We demonstrate in a number of numerical test problems that IMEX methods in conjunction with efficient preconditioning become more efficient than explicit methods for systems exhibiting high levels of grid-induced stiffness.
Journal: Journal of Computational Physics - Volume 225, Issue 2, 10 August 2007, Pages 1753–1781