Dynamical spatially heterogeneous model adaptation in compressible flows

• Applicant: Professor Dr. Jan Giesselmann
• Subject Area: Mathematics
• Term: from 2017 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 368503550

The accurate and reliable numerical simulation of fluid mixtures is an important topic in fluid mechanics. A particular challenging case are mixtures which are not in chemical and thermodynamical equilibrium and in which compressible effects cannot be neglected.There is a large number of mathematical models describing flows of such mixtures.In this project we will focus on models based on hyperbolic conservation laws and hyperbolic relaxation equations.Even within this classes the complexity of models differs greatly. For efficient numerical simulations it is desirable to use complex models only where necessary, while simple models are used on large parts of the computational domain. Thus, the following question arises: Is there a rational way, which may be automated, to decide which model is solved on which part of the computational domain?This project aims at deriving a posteriori error estimators for the modelling error, i.e., the goal is to determine quantities which can be computed from the numerical solution of a simple model and which are upper bounds for the distance between the solution to this simple problem and the solution to a complex problem. The purpose of this modelling error estimator is to drive a model adaptive numerical scheme, i.e., a scheme which itself decides locally which model is to be solved (numerically).For constructing such a numerical scheme coupling strategies for discretisations of different models are required. We will implement different coupling strategies which already exist and investigate whether they are compatible with the modelling error estimator.

• DFG Programme: Research Grants