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A splitting approach for freezing waves

Flohr, Robin; Rottmann-Matthes, Jens


We present a numerical method which is able to approximate traveling waves (e.g. viscous profiles) in systems with hyperbolic and parabolic parts by a direct long-time forward simulation. A difficulty with long-time simulations of traveling waves is that the solution leaves any bounded computational domain in finite time. To handle this problem one should go into a suitable co-moving frame. Since the velocity of the wave is typically unknown, we use the method of freezing [2], see also [1], which transforms the original partial differential equation (PDE) into a partial differential algebraic equation (PDAE) and calculates a suitable co-moving frame on the fly. The efficient numerical approximation of this freezing PDAE is a challenging problem and we introduce a new numerical discretization, suitable for problems that consist of hyperbolic conservation laws which are (nonlinearly) coupled to parabolic equations. The idea of our scheme is to use the operator splitting approach. The benefit of splitting methods in this context lies in the possibility to solve hyperbolic and parabolic parts with different numerical algorithms. We test our method at the (viscous) Burgers’ equation. ... mehr

Volltext §
DOI: 10.5445/IR/1000062694
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2016
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000062694
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 12 S.
Serie CRC 1173 ; 2016/35
Schlagwörter splitting approach, freezing method, traveling waves, asymptotic behavior, steady states
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