Research Topic

Quality Assessment for Large Eddy Simulations - An adjoint based a posteriori error estimator

In numerical simulations of flow problems or other engineering models governed by systems of partial differential equations, mesh adaptivity has become a major feature securing the quality of the solution of a simulation. For modeling turbulent flows with Large Eddy Simulations, locally large solution variations are best resolved by a high concentration of mesh points while in domains with less solution activity fewer mesh points are sufficient.
We equip a common flow solver with a Mesh-Moving-PDE, which is able to  redistribute grid points while keeping the data structure. So called monitor functions measure the importance of certain domains by user defined criteria and support the Mesh-Moving-PDE with the needed information where grid points are mostly desired. These criteria are usually physically motivated like the turbulent kinetic energy.
To compare these physically motivated monitor functions with mathematically motivated ones, we add adjoint-based information. For time averaged quantities of interest, we derived an adjoint-based a posteriori error estimator using a stationary adjoint equation. This new error estimator will help to improve mesh quality and also allows to focus on scalar quantities of interest, like for example drag and lift coefficients. Furthermore, a separation of the discretization and the modeling error is in the focus of our research, which will result in more accurate solutions for turbulent flows.

Key Research Area

Multi-Physics; Fluiddynamics; Numerical Simulations


Matthias Frankenbach


Dolivostraße 15

D-64293 Darmstadt



+49 6151 16 - 24401 or 24402


+49 6151 16 - 24404




frankenbach (at) mathem...

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