**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

Tuesday, June 6, 2023 1:00 PM EDT

For Zoom Link please contact ddelreyfernandez@uwaterloo.ca

Professor Mária Lukácová-Medvidová, Professor for Numerical Mathematics, University of Mainz

Dissipative solutions of compressible fluid flows

In this talk I present an overview of our recent results on generalized solutions, the so-called dissipative solutions, of compressible fluid flows. I will concentrate on the inviscid flows, the Euler equations, and mention also the relevant results obtained for viscous compressible flows, governed by the compressible Navier-Stokes equations.

The existence of dissipative solutions will be shown by the convergence analysis of a suitable, invariant-domain preserving finite volume scheme. In the case that the strong solution to the above equations exists, the dissipative solutions coincide with the strong solution on its lifespan. In this case we can also apply the relative entropy to derive rigorous error estimates between numerical solutions and the exact strong solution.

If the strong solution does not exist we apply a new tool, the so-called K-convergence, and show the strong convergence of the empirical means of numerical solutions to a dissipative solution. The latter is the expected value of the dissipative measure-valued solutions and satisfies a weak formulation of the Euler equations modulo the Reynolds stress tensor. We will discuss a relation of the dissipative solutions to the Kolmogorov hypothesis and turbulence.

The present research has been partially supported by TRR 146 Multiscale simulation methods for soft matter systems, TRR 165 Waves to Weather funded by the German Science Foundation and by the Gutenberg Research College.

Event tags

**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is co-ordinated within the Office of Indigenous Relations.