%0 Conference Paper %1 gravemeier2002threelevel %A Gravemeier, Volker %A Wall, Wolfgang A. %A Ramm, Ekkehard %B Proceedings of the Fifth World Congress on Computational Mechanics (WCCM V), July 7-12, 2002, Vienna, Austria, Editors: Mang, H.A., Rammerstorfer, F.G., Eberhardsteiner, J., Publisher: Vienna University of Technology, Austria %D 2002 %K ibb from:maltevonscheven inproceedings %T A Three-Level Approach for Incompressible Navier-Stokes %X In this work we present a Three-Level FEM for the numerical simulation of the incompressible Navier- Stokes equations. Based on the variational multiscale method and the residual-free bubble concept we pursued the technique of a Two-Level FEM in our previous work. Level 1 is therein attributed to the solution of the large-scale equation by a standard finite element space. On level 2 we seek an approximation of the elementwise residual-free bubbles with the help of a stabilized finite element method restricted to individual elements. This represents our small-scale solution. The Two-Level FEM aimed at the simulation of laminar flows. Now we want to turn our focus on the numerical simulation of turbulent flows by way of a large eddy simulation and in this work our first respective steps are described. With regard to this objective we extend our basic algorithm paying particular attention to the fulfillment of the continuity equation. Moreover, in lieu of the stabilization term we alternatively propose the inclusion of a subgrid viscosity term henceforth. This term should provide us with the required dissipative effect of the unresolved scales on the small-scale equation. The dynamic calculation of the subgrid viscosity constitutes the third level of our algorithm.

@inproceedings{gravemeier2002threelevel, abstract = {In this work we present a Three-Level FEM for the numerical simulation of the incompressible Navier- Stokes equations. Based on the variational multiscale method and the residual-free bubble concept we pursued the technique of a Two-Level FEM in our previous work. Level 1 is therein attributed to the solution of the large-scale equation by a standard finite element space. On level 2 we seek an approximation of the elementwise residual-free bubbles with the help of a stabilized finite element method restricted to individual elements. This represents our small-scale solution. The Two-Level FEM aimed at the simulation of laminar flows. Now we want to turn our focus on the numerical simulation of turbulent flows by way of a large eddy simulation and in this work our first respective steps are described. With regard to this objective we extend our basic algorithm paying particular attention to the fulfillment of the continuity equation. Moreover, in lieu of the stabilization term we alternatively propose the inclusion of a subgrid viscosity term henceforth. This term should provide us with the required dissipative effect of the unresolved scales on the small-scale equation. The dynamic calculation of the subgrid viscosity constitutes the third level of our algorithm.}, added-at = {2021-03-09T13:40:55.000+0100}, author = {Gravemeier, Volker and Wall, Wolfgang A. and Ramm, Ekkehard}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2b87b4e86df137575f0d137b55abf430d/ibb-publication}, booktitle = {Proceedings of the Fifth World Congress on Computational Mechanics (WCCM V), July 7-12, 2002, Vienna, Austria, Editors: Mang, H.A., Rammerstorfer, F.G., Eberhardsteiner, J., Publisher: Vienna University of Technology, Austria}, interhash = {d0047e4e0d7f31bd55238f80f1bfcce2}, intrahash = {b87b4e86df137575f0d137b55abf430d}, keywords = {ibb from:maltevonscheven inproceedings}, timestamp = {2021-03-09T12:40:55.000+0100}, title = {A Three-Level Approach for Incompressible Navier-Stokes}, year = 2002 }