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Time integration for extended discontinuous Galerkin methods with moving domains
Author(s) -
Kummer Florian,
Müller Björn,
Utz Thomas
Publication year - 2017
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5634
Subject(s) - discontinuous galerkin method , scalar (mathematics) , galerkin method , convergence (economics) , order of accuracy , spacetime , mathematics , mathematical optimization , convection–diffusion equation , burgers' equation , context (archaeology) , space time , partial differential equation , computer science , finite element method , mathematical analysis , method of characteristics , geometry , paleontology , physics , quantum mechanics , chemical engineering , biology , engineering , economics , thermodynamics , economic growth
Summary We study time integration schemes for discontinuous Galerkin discretizations of problems with moving immersed interfaces. Two approaches have been discussed in literature so far: splitting schemes and space‐time methods. Splitting schemes are cheap and easy to implement, but are non‐conservative, inherently limited to low orders of accuracy, and require extremely small time steps. Space‐time methods, on the other hand, are conservative, allow for large time steps, and generalize to arbitrary orders of accuracy. However, these advantages come at the expense of a severe growth the systems to be solved. Within this work, we present a generic strategy that combines the advantages of both concepts by evaluating numerical fluxes in a moving reference frame and by making use of a conservative cell‐agglomeration strategy. We study the performance of this strategy in combination with backward‐difference‐formulas and explicit Runge‐Kutta schemes in the context of the scalar transport equation, the Burgers equation, and the heat equation. Our results indicate that higher order spatial and temporal convergence rates can be achieved without increasing the size of the systems to be solved.