| Abstract: |
| The dissipative solutions of the Euler equations can be obtained as a limit of suitable structure-preserving, consistent, and stable numerical schemes. If the strong solution to the above equations exists, the dissipative solutions coincide with the strong solution on its life span. Otherwise, we apply the concept of K-convergence and prove the strong convergence of the empirical means of numerical solutions to a dissipative weak 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 turbulent stress.
In this talk, we will discuss the relationship between numerical approximations of oscillatory solutions and selection criteria, such as the Dafermos criterion, which maximises entropy production, or the optimisation of the energy defect. A series of numerical simulations will illustrate theoretical results. |
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