• Schild Mathematik Ost
Mathematische Strömungsmechanik

Seminarreihe "structure preserving numerical methods for hyperbolic equations" im Oberseminar Mathematische Strömungsmechanik

What is a limit of solutions computed by structure preserving schemes?
Datum: 04.03.2022, 15:00 - 16:00 Uhr
Kategorie: Seminar, Veranstaltung
Vortragende: Maria Lukacova

This talk is part of the seminar series "structure preserving numerical methods for hyperbolic equations", click here for more details 


In this talk we discuss the question of convergence of structure preserving finite volume methods for multidimensional Euler equations of gas dynamics. We show that in general there is only weak ∗ convergence to a generalized, the so-called dissipative weak solution. In the case that the strong solution of the Euler equations exists, the dissipative weak solutions coincide with the strong solution on its life span. In this case finite volume solutions converge strongly to the strong solution. Otherwise, we apply a newly developed concept of K-convergence and prove the strong convergence of the empirical means of finite volume solutions to a dissipative weak solution. The latter is the expected value of a dissipative measure-valued solution and satisfies a weak formulation of the Euler equations modulo the Reynolds defect measure. In the class of dissipative weak solutions there exists a solution that is obtained as a vanishing viscosity limit of the Navier-Stokes system. Theoretical results will be illustrated by a series of numerical simulations.

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