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Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Upwind schemes for scalar advectiondominated problems in the discrete exterior calculus
 Bothe, Dieter: Transport processes at fluidic interfaces Cham: Springer International Publishing, 2017 (Advances in mathematical fluid mechanics) ISBN: 9783319566016 (Print) ISBN: 9783319566023 (Online) ISBN: 3319566016 pp.145175 

 English 
 Book Article 
 Fraunhofer SCAI () 
Abstract
We present the discrete exterior calculus (DEC) to solve discrete partial differential equations on discrete objects such as cell complexes. To cope with advectiondominated problems, we introduce a novel stabilization technique to the DEC. To this end, we use the fact that the DEC coincides in special situations with known discretization schemes such as finite volumes or finite differences. Thus, we can carry over wellestablished upwind stabilization methods introduced for these classical schemes to the DEC. This leads in particular to a stable discretization of the Liederivative. We present the numerical features of this new discretization technique and study its numerical properties for simple model problems and for advectiondiffusion processes on simple surfaces.