Towards a parameter-free method for high Reynolds number turbulent flow simulation based on adaptive finite element approximation
2015 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 288, 60-74 p.Article in journal (Refereed) Published
We present work towards a parameter-free method for turbulent flow simulation based on adaptive finite element approximation of the Navier-Stokes equations at high Reynolds numbers. In this model, viscous dissipation is assumed to be dominated by turbulent dissipation proportional to the residual of the equations, and skin friction at solid walls is assumed to be negligible compared to inertial effects. The result is a computational model without empirical data, where the only parameter is the local size of the finite element mesh. Under adaptive refinement of the mesh based on a posteriori error estimation, output quantities of interest in the form of functionals of the finite element solution converge to become independent of the mesh resolution, and thus the resulting method has no adjustable parameters. No ad hoc design of the mesh is needed, instead the mesh is optimised based on solution features, in particular no bounder layer mesh is needed. We connect the computational method to the mathematical concept of a dissipative weak solution of the Euler equations, as a model of high Reynolds number turbulent flow, and we highlight a number of benchmark problems for which the method is validated.
Place, publisher, year, edition, pages
Elsevier, 2015. Vol. 288, 60-74 p.
finite element method, adaptive mesh refinement, turbulent
Research subject Applied and Computational Mathematics
IdentifiersURN: urn:nbn:se:kth:diva-143878DOI: 10.1016/j.cma.2014.12.004ISI: 000352081900005ScopusID: 2-s2.0-84920828659OAI: oai:DiVA.org:kth-143878DiVA: diva2:709363
FunderSwedish Foundation for Strategic Research EU, European Research Council, 202984Swedish Research Council, 90032202
QC 201407082014-04-012014-04-012016-08-30Bibliographically approved