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http://hdl.handle.net/1942/37559
Title: | Implicit two-derivative deferred correction time discretization for the discontinuous Galerkin method | Authors: | ZEIFANG, Jonas SCHUETZ, Jochen |
Issue Date: | 2022 | Publisher: | Source: | JOURNAL OF COMPUTATIONAL PHYSICS, 464 (Art N° 111353) | Abstract: | In this paper, we use an implicit two-derivative deferred correction time discretization approach and combine it with a spatial discretization of the discontinuous Galerkin spectral element method to solve (non-)linear PDEs. The resulting numerical method is high order accurate in space and time. As the novel scheme handles two time derivatives, the spatial operator for both derivatives has to be defined. This results in an extended system matrix of the scheme. We analyze this matrix regarding possible simplifications and an efficient way to solve the arising (non-)linear system of equations. It is shown how a carefully designed preconditioner and a matrix-free approach allow for an efficient implementation and application of the novel scheme. For both, linear advection and the compressible Euler equations, up to eighth order of accuracy in time is shown. Finally, it is illustrated how the method can be used to approximate solutions to the compressible Navier-Stokes equations. | Keywords: | Multiderivative schemes;Discontinuous;Galerkin spectral element method;Implicit time stepping | Document URI: | http://hdl.handle.net/1942/37559 | ISSN: | 0021-9991 | e-ISSN: | 1090-2716 | DOI: | 10.1016/j.jcp.2022.111353 | ISI #: | WOS:000814746200003 | Rights: | 2022 Elsevier Inc. All rights reserved | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2023 |
Appears in Collections: | Research publications |
Files in This Item:
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1-s2.0-S0021999122004156-main.pdf Restricted Access | Published version | 1.2 MB | Adobe PDF | View/Open Request a copy |
Two-derivative deferred correction time discretization for the discontinuous Galerkin method.pdf | Non Peer-reviewed author version | 1.09 MB | Adobe PDF | View/Open |
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