By Y. Bazilevs, V. M. Calo, T. J. R. Hughes, G. Scovazzi (auth.), René de Borst, Ekkehard Ramm (eds.)
Many good points within the behaviour of buildings, fabrics and flows are brought on by phenomena that take place at one to a number of scales lower than universal degrees of remark. Multiscale equipment account for this scale dependence: They both derive houses on the point of remark by means of repeated numerical homogenization of extra primary actual homes outlined numerous scales under (upscaling), or they create concurrent schemes the place these components of the area which are of curiosity are computed with the next solution than components which are of much less curiosity or the place the answer is various in basic terms slowly. This paintings is as a result of a sustained German-Dutch cooperation and written by way of the world over best specialists within the box and provides a latest, up to date account of modern advancements in computational multiscale mechanics. either upscaling and concurrent computing methodologies are addressed for quite a number software components in computational strong and fluid mechanics: Scale transitions in fabrics, turbulence in fluid-structure interplay difficulties, multiscale/multilevel optimization, multiscale poromechanics.
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Extra resources for Multiscale Methods in Computational Mechanics: Progress and Accomplishments
Shape functions which seem to be better suited than standard polynomial functions are non-uniform rational B-splines p p Ni (u) = wi · Bi (u) p+1 j =1 wj p · Bj (u) , p (19) where wi is the i-th weight and Bi (u) is the i-th B-spline polynomial of degree p defined by recursion on a series of 2p + 2 knot values uk , see  for an introduction. One feature making NURBS-based FEM especially attractive for multiscale simulations is its high solution quality over the complete scale spectrum. Hence, the subgrid-scale terms can really focus on accounting for physical effects and do not have to account for the shortcomings of the coarse-scale method.
To estimate the potential of the resVMM for turbulent FSI computations, preliminary test simulations of turbulent channel flow at Reτ = 395 on a deformable mesh were performed. 2, (23) Advances in Variational Multiscale Methods for Turbulent Flows 49 Fig. 6. Test case for turbulent channel flow on moving grids. 5 25 + u 20 rVM, ALE rVM rVM, ALE rVM 4 15 3 10 5 2 + rms w 1 0 0 rms u+ rms v+ 1 10 100 y + 0 100 200 300 y+ 400 Fig. 7. Results for turbulent channel flow computations on 323 trilinear elements at Reτ = 395.
D. within the DFG Research Unit 509 “Multiscale Methods in Computational Mechanics”. This support is gratefully acknowledged. Furthermore, the second author is grateful to the DFG for the support via the Emmy Noether program. References 1. B. Pope, Turbulent Flows, Cambridge University Press, 2000. 2. R. Hughes, L. E. Jansen, Large eddy simulation and the variational multiscale method, Computing and Visualization in Science, 3:47–59, 2000. 3. V. Gravemeier, The variational multiscale method for laminar and turbulent flow, Archives of Computational Methods in Engineering – State of the Art Reviews, 13:249–324, 2006.