期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 233, 期 -, 页码 100-131出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2012.07.039
关键词
Energy conservation; Time reversibility; Runge-Kutta method; Additive Runge-Kutta method; Incompressible Navier-Stokes equations; Differential-algebraic equations; Algebraic stability; L stability; Stiffness
Energy-conserving methods have recently gained popularity for the spatial discretization of the incompressible Navier-Stokes equations. In this paper implicit Runge-Kutta methods are investigated which keep this property when integrating in time. Firstly, a number of energy-conserving Runge-Kutta methods based on Gauss, Radau and Lobatto quadrature are constructed. These methods are suitable for convection-dominated problems (such as turbulent flows), because they do not introduce artificial diffusion and are stable for any time step. Secondly, to obtain robust time-integration methods that work also for stiff problems, the energy-conserving methods are extended to a new class of additive Runge-Kutta methods, which combine energy conservation with L-stability. In this class, the Radau IIA/B method has the best properties. Results for a number of test cases on two-stage methods indicate that for pure convection problems the additive Radau IIA/B method is competitive with the Gauss methods. However, for stiff problems, such as convection-dominated flows with thin boundary layers, both the higher order Gauss and Radau IIA/B method suffer from order reduction. Overall, the Gauss methods are the preferred method for energy-conserving time integration of the incompressible Navier-Stokes equations. (C) 2012 Elsevier Inc. All rights reserved.
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