Mathematicians often like to think of maths as objective. Science communicator Hana Ayoob joins us to discuss how the fact that humans do maths means that the ways maths is developed, used, and communicated are not neutral.
Speaker Prof Dr Maria Lukacova will talk about 'Numerical analysis of oscillatory solutions of compressible flows'
Oscillatory solutions of compressible flows arise in many practical situations. An iconic example is the Kelvin-Helmholtz problem, where standard numerical methods yield oscillatory solutions. In such a situation, standard tools of numerical analysis for partial differential equations are not applicable.
We will show that structure-preserving numerical methods converge in general to generalised solutions, the so-called dissipative solutions.
The latter describes the limits of oscillatory sequences. We will concentrate on the inviscid flows, the Euler equations of gas dynamics, and mention also the relevant results obtained for the viscous compressible flows, governed by the Navier-Stokes equations.
We discuss a concept of K-convergence that turns a weak convergence of numerical solutions into the strong convergence of
their empirical means to a dissipative solution. The latter satisfies a weak formulation of the Euler equations modulo the Reynolds turbulent stress. We will also discuss suitable selection criteria to recover well-posedness of the Euler equations of gas dynamics. Theoretical results will be illustrated by a series of numerical simulations.
Your chance to ask Mathematrix DPhil students about the process of applying to PhD programs, including written stages and interviews!
A discussion on how race and ethnicity interact with the concept of merit in academia, based on sections from the book 'Misconceiving Merit' by Blair-Loy and Cech.
