Project B1 (finished)
Project B1 - Jörn Behrens, Michael Hinze, Armin Iske and Thomas Rung: Goal-oriented adaptive meshing in transient multi-scale flows
Principal investigator: Jörn Behrens
Scientific Background and Motivation
The effort associated to mesh-based, transient industrial and geoscientific computational fluid dynamic approaches is considerable and comprises (a) simulation, (b) post-processing and (c) geometry preparation and meshing [Rung et al. 2009; Läuter et al. 2007]. The man-power required to generate high-quality meshes is perhaps the major contributor to the simulation-cycle's total expenditure. When attention is given to complex transient flows, much of the information required for an appropriate meshing/discretization could be obtained from the simulation result, which is of course not available during the meshing phase. Additionally, many such transient flows exhibit a wide range of relevant and interacting scales, which are locally non-uniformly distributed and need to be resolved. Adaptive, dynamic meshes based on local-grid refinement are a viable approach out of this dilemma. The associated grid-control process requires a careful definition of reliable sensors. The majority of such sensors refer to error-indicators based on local flow gradients [Behrens/Bader, 2009]. Such indicators are state-of-the-art but not particularly suitable in coarse meshes and areas of small spatial variations, where the solution is inherently smooth. Furthermore, diverse small-scale physical processes are often under-resolved and therefore parameterized in realistic applications. In these situations gradient-based refinement criteria are naturally limited in their effectiveness. An even more important aspect is the a priori unclear relation between the local discretization error and the simulation goal - e.g. an accurate drag force prediction, which can significantly deteriorate the predictive performance of the refinement strategy. The related information can be obtained from the use of mathematical optimization techniques, which should thus be utilized within the refinement framework [Manzke/Rung, 2011, Günther/Hinze 2008]. The resulting error/goal-based criteria will refer to both the local order-of-accuracy and the local sensitivities and should support anisotropic refinement. These techniques optimize the mesh topology, but as such do not intend to optimize computational requirements. Therefore, additional measures need to be taken to efficiently utilize current computing architectures comprising hierarchical memory layout, pipelined execution order and GPU computing units. Such methods are so-far rather isotropic tree-based refinement techniques [Bader et al., 2008], and it needs to be evaluated whether anisotropic features could be added. Finally, so-called r-refinement techniques, in which the connectivity of the mesh is not touched, but the nodes are moved according to suitable criteria might be a viable option to combine computational efficiency with anisotropic characteristics. Transient-anisotropic, goal oriented mesh-refinement techniques for industrial and geoscientific flow simulations are a severe challenge and require a joint collaborative research effort.
Aims and Objectives
Existing applications utilizing state-of-the-art mesh refinement techniques in transient industrial and geoscientific research fields are to be selected as test beds for the new developments in mesh adaptation. Several criteria are to be implemented, starting from state-of-the-art gradient-based indicators. New criteria, derived from numerical schemes involved (e.g. the jumps at cell boundaries in flux-based methods, or the spectral coefficients in spectral methods), are to be added along with mathematical methods based on averaging techniques or local residuals. These criteria are then to be included in advanced adjoint based adaptive mesh control strategies. It needs to be evaluated, if simpler error equilibration or Lagrangian error propagation methods are able to compete with the more sophisticated adjoint optimization techniques. After adding anisotropic mesh manipulation in accordance with suitable indicators, computational optimization techniques are to be considered.
PhD Student: Susanne Beckers
Susanne Beckers successfully defended her PhD on 10 May 2017