Dr. Ezra Rozier

Refinement criteria for complex applications - Lagrangian error propagation beyond simple gradient-based refinement indicators

For the resolution of flows in fluid dynamics it has become crucial to use mesh-refinement techniques. Indeed, for instance in many approximations of the Navier-Stokes equation, the interesting parts of the flow will be held in one specific zone of the computational domain. Generally, the computational domain will be too wide and thus it would be costful to have a equally fine mesh everywhere. The whole work for refinement will be to spot those zones depending on different criteria. The final goal will be to find a computationally cheap way to gain a lot of precision in your solution’s approximation.

To that extent the study of the behaviour of the error (creation as well as propagation of the error) is an interesting tool to help choosing an interesting spatial refinement criterion. To achieve an ever better description of the propagation error in cases where the flow’s advection is dominant, it can seem interesting to work in a map that follows the flow (Arbitrary Langrange-Eulerian, ALE).

Therefore the aim of this project will be to build an ALE framework, both theoretical and computational, in which it is possible to study error estimates in the situation of convection dominated convection-diffusion equation. This way it would be possible to build up error estimators and refinement criteria that will be both accurate and computationally cheap.

Advisor: Prof. Dr. Jörn Behrens

Co-Advisor: Prof. Dr. Thomas Rung

10.02.2021

Lothar-Collatz-Seminar (online): "Error estimation for moving mesh Discontinuous-Galerkin scheme for the resolution of convection-dominated flows."

1. Master's Thesis : Galilean-invariant simulations for conservation laws with a speed-density component on a moving mesh (https://github.com/EzRo7511/ArepoJulia)