Math @ Duke

Publications [#246953] of JianGuo Liu
Papers Published
 Duraisamy, K; Baeder, JD; Liu, JG, Concepts and Application of TimeLimiters to High Resolution Schemes,
Journal of Scientific Computing, vol. 19 no. 13
(2003),
pp. 139162, ISSN 08857474 [doi]
(last updated on 2018/02/22)
Abstract: A new class of implicit highorder nonoscillatory time integration schemes is introduced in a methodoflines framework. These schemes can be used in conjunction with an appropriate spatial discretization scheme for the numerical solution of time dependent conservation equations. The main concept behind these schemes is that the order of accuracy in time is dropped locally in regions where the time evolution of the solution is not smooth. By doing this, an attempt is made at locally satisfying monotonicity conditions, while maintaining a high order of accuracy in most of the solution domain. When a linear high order time integration scheme is used along with a high order spatial discretization, enforcement of monotonicity imposes severe timestep restrictions. We propose to apply limiters to these timeintegration schemes, thus making them nonlinear. When these new schemes are used with high order spatial discretizations, solutions remain nonoscillatory for much larger timesteps as compared to linear time integration schemes. Numerical results obtained on scalar conservation equations and systems of conservation equations are highly promising.


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