Multilevel gradient-based methods in aerodynamic shape design

A gradient-based method coupled with a multilevel approach is proposed for shape design in aerodynamics. This method extends an existing multilevel gradient-based formulation to another type of control subspaces, i.e. considering another set of subparametrisations and prolongation operators. More precisely, Bézier control points associated with the property of degree elevation are involved instead of shape grid-points coordinates and polynomial interpolation. The good behaviour of the new formulation is demonstrated on a classical 2D nozzle inverse problem considering an adjoint formulation as well as an approximate gradient associated to a one-shot method

Multilevel Optimization : Application to One-Shot Shape Optimum Design

: Gradient method is applied to the optimal control of a system for which each simulation is expensive. Instead of solving completely the flow equation as a state equation in the shape optimization, we use a "one-shot method" which solves simultaneously the system optimality. It is tested for the problem of shape optimization of a nozzle in a 2D Euler flow. (R'esum'e : tsvp) INRIA Sophia Antipolis,B.P. 93, 06902 Sophia-Antipolis Cedex,France Dipartimento di Ingegneria Aerospaziale,Universit`a degli Studi di Pisa,V. Diotisalvi, 2, 56100 Pisa, Italia Unite de recherche INRIA Sophia-Antipolis 2004 route des Lucioles, BP 93, 06902 SOPHIA-ANTIPOLIS Cedex (France) Telephone : (33) 93 65 77 77 -- Telecopie : (33) 93 65 77 65 Optimisation Multi-niveau : Application `a l'optimisation de formes par une m'ethode "One-Shot" R'esum'e : Nous consid'erons la m'ethode de gradient appliqu'ee au controle optimal d'un syst`eme pour lequel chaque simulation est couteuse. Au lieu de r'esoudre comp..

Transport of species in a bio-reactor for bone tissue engineering

One of the most important issue in tissue engineering is the development of bio-reactors in which the best conditions for cells growth can be created and maintained for the time necessary to produce the tissue. These conditions include homogeneous flow distribution to obtain sufficient transport of nutrients (mainly glucose and oxygen) and efficient removal of catabolites together with low levels of shear stress at the surface of internal scaffolds where the cells are supposed to grow. In this work we simulate numerically the flow and transport of nutrients in a bio-reactor used to produce bone tissues which may then be implanted into patients to repair jaw defects. We characterize the flow distribution and the shear stress distribution at the surface of the scaffold. We solve for the transport of nutrients and we simulate the effect of local nutrients concentration at the surface of the scaffold on the growth rate of cellular tissues. Results of the numerical simulation can be used to improve the design of the bio-reactor and to identify the flow conditions which maximize cell growth

Upwind Stabilization Of Navier-Stokes Solvers

: We present a study of the effect of upwinding on stabilisation of both advective and pressure terms in a family of primitive-variable Navier-Stokes solvers. We consider two MUSCL Schemes, the first one applies to compressible flow, the second one to incompressible flow. We illustrate the fact that both numerical models suffer oscillations if a minimal (but not large) amount of upwinding is not associated with acoustics, while advection can be stabilized by the physical diffusion terms when the mesh Reynolds number is small enough. RESUME : On pr'esente une 'etude de l'effet du d'ecentrage sur la stabilisation des termes advectifs et de pression d'une famille de solveurs de Navier Stokes en variables primitives. On consid`ere deux sch'emas MUSCL, l'un s'appliquant `a des 'ecoulements compressibles, l'autre `a des 'ecoulements incompressibles. On illustre le fait que les deux sch'emas pr'esentent des oscillations si une quantit'e minimale de d'ecentrage n'est pas appliqu'ee aux terme..

Exact-gradient shape optimization of a 2D Euler flow

Programme 6 : calcul scientifique, modelisation et logiciels numeriquesSIGLEAvailable at INIST (FR), Document Supply Service, under shelf-number : 14802 E, issue : a.1991 n.1540 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

A hierarchical approach for shape optimization

Programme 6 : calcul scientifique, modelisation et logiciels numeriquesSIGLEAvailable at INIST (FR), Document Supply Service, under shelf-number : 14802 E, issue : a.1993 n.1868 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Multilevel optimization : application to shape optimum design with a one-shot method

Programme 6 : calcul scientifique, modelisation et logiciels numeriquesAvailable at INIST (FR), Document Supply Service, under shelf-number : 14802 E, issue : a.1993 n.2068 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueSIGLEFRFranc