Topology optimization of fluid domains: kinetic theory approach Export

@article{citeulike:2918828, abstract = {We consider the problem of optimal design of flow domains for Navier-Stokes flows in order to minimize a given performance functional. We attack the problem using topology optimization techniques, or control in coefficients, which are widely known in structural optimization of elastic solids and structures for their flexibility, generality, yet ease of use, and integration with existing FEM software. We use a simple kinetic model to approximate the Navier-Stokes system. Arguably, we take a rather unconventional path in the kinetic theory, using it only to gain insight about the Navier-Stokes-related system of hydrodynamical equations, which we take as our starting point. Thus all the modifications we make to the kinetic models are ldquohydrodynamicallyrdquo inspired and we seek no particular physical explanation for them; the only requirement for us is the convergence (at least, formal) of the kinetic equations towards the correct hydrodynamical limit. We formally compute the hydrodynamical limit of the proposed kinetic system, and rigorously establish the existence of flow solutions and their continuous dependence on the design parameters. Optimal controls are shown to belong to a special class (0-1 solutions) for a popular power dissipation minimization problem for viscous fluids.}, address = {Center for Aerospace Structures, Department of Aerospace Engineering Sciences, University of Colorado, Boulder, CO 80309-0429, USA}, author = {Evgrafov, A. and Pingen, G. and Maute, K.}, citeulike-article-id = {2918828}, citeulike-linkout-0 = {http://dx.doi.org/10.1002/zamm.200700122}, citeulike-linkout-1 = {http://www3.interscience.wiley.com/cgi-bin/abstract/117908547/ABSTRACT}, day = {12}, doi = {10.1002/zamm.200700122}, issn = {00442267}, journal = {ZAMM}, keywords = {2007, adjoint-method, boundary-treatment, fictitious-domain, fluid-mechanics, immersed-boundary, kinetic-model, navier-stokes, optimisation, porous-materials, topology-optimisation}, month = {February}, number = {2}, pages = {129--141}, posted-at = {2008-06-23 14:26:27}, priority = {5}, title = {Topology optimization of fluid domains: kinetic theory approach}, url = {http://dx.doi.org/10.1002/zamm.200700122}, volume = {88}, year = {2008} }

TY - JOUR ID - citeulike:2918828 L3 - citeulike-article-id:2918828 N2 - We consider the problem of optimal design of flow domains for Navier-Stokes flows in order to minimize a given performance functional. We attack the problem using topology optimization techniques, or control in coefficients, which are widely known in structural optimization of elastic solids and structures for their flexibility, generality, yet ease of use, and integration with existing FEM software. We use a simple kinetic model to approximate the Navier-Stokes system. Arguably, we take a rather unconventional path in the kinetic theory, using it only to gain insight about the Navier-Stokes-related system of hydrodynamical equations, which we take as our starting point. Thus all the modifications we make to the kinetic models are ldquohydrodynamicallyrdquo inspired and we seek no particular physical explanation for them; the only requirement for us is the convergence (at least, formal) of the kinetic equations towards the correct hydrodynamical limit. We formally compute the hydrodynamical limit of the proposed kinetic system, and rigorously establish the existence of flow solutions and their continuous dependence on the design parameters. Optimal controls are shown to belong to a special class (0-1 solutions) for a popular power dissipation minimization problem for viscous fluids. IS - 2 JF - ZAMM SN - 00442267 AD - Center for Aerospace Structures, Department of Aerospace Engineering Sciences, University of Colorado, Boulder, CO 80309-0429, USA EP - 141 TI - Topology optimization of fluid domains: kinetic theory approach VL - 88 SP - 129 KW - 2007 KW - adjoint-method KW - boundary-treatment KW - fictitious-domain KW - fluid-mechanics KW - immersed-boundary KW - kinetic-model KW - navier-stokes KW - optimisation KW - porous-materials KW - topology-optimisation AU - Evgrafov, A AU - Pingen, G AU - Maute, K PY - 2008/02/12/ UR - http://dx.doi.org/10.1002/zamm.200700122 ER -