Goal-oriented adaptive meshing in transient multi-scale flows
Objectives and Key Questions
Tropical cyclone prediction is depending on multi-scale phenomena, all influencing the path and the behavior of the cyclone. But it is not obvious which of these parameters influences the quantity of interest most. As brute-force method, the whole computational domain could be refined to resolve simply everything. This method is computational expansive especially for huge areas. Therefore it is desirable to have an adaptive mesh which resolves the areas influencing the quantity of interest.
Thus, the questions are:
- What is the quantity of interest?
- Which regions have to be resolved finer to obtain a better numerical solution of the quantity of interest?
Typical quantities of interest for a tropical cyclone are e.g. the path, the potential and kinetic energy, and the vorticity. Formulating these quantities as goal functionals gives the possibility to deduce an adjoint model which provides us with sensitivities of the cyclone model with respect to the desired quantity of interest. Further more weighted residuals of the solutions of the adjoint model and the primal model deliver a rigorous mathematical error estimator indicating the areas of refinement.
Using this error estimator allows an adaptive mesh which refines and coarsens in terms of sensitivity of the model with regard to the quantity of interest.
which is founded by Forschungs- und Wissenschaftsstiftung Hamburg
Responsible group members
- Susanne Beckers
- Jörn Behrens