Seminár z kvalitatívnej teórie diferenciálnych rovníc - Hana Mizerová (5.12.2024)

vo štvrtok 5.12.2024 o 14:00 hod. v miestnosti M 223

---

Prednášajúci: Hana Mizerová  

Názov prednášky: Dissipative weak solutions in numerical analysis of compressible Euler equations

Termín: 5.12.2024, 14:00 hod., M 223

Abstrakt:
Numerical simulation of fluid dynamics plays an important role in a wide range of modern industrial and real life applications, such as vehicle engineering, engines design, aerospace or weather forecast. In the past decades, great effort was put in the development of efficient and accurate numerical methods. Based on our approach to numerical analysis of nonlinear equations of fluid dynamics in the spirit of the Lax Equivalence Principle (stability + consistency = convergence), dissipative weak solutions may be seen as a universal closure of stable and consistent approximations. Numerical solution of the complete compressible Euler equations stated in the conservative variables lacks uniform bounds to control the integrability of the convective terms in the discrete energy inequality. To solve this problem, we study convergence of these approximations in terms of the conservative-entropy variables. Combining the concept of dissipative weak solutions, the set-valued version of the Strong law of large numbers and Komlós theorem on strong convergence of empirical averages of integrable functions, we obtain several results on convergence of the Monte Carlo method applied to the isentropic Euler equations with uncertain initial data.

These results are based on a joint work with E. Feireisl, M. Lukáčová, B. She, and C. Yu.

 

 

 

---