Commenced in January 2007
Paper Count: 31575
A Shape Optimization Method in Viscous Flow Using Acoustic Velocity and Four-step Explicit Scheme
Abstract:The purpose of this study is to derive optimal shapes of a body located in viscous flows by the finite element method using the acoustic velocity and the four-step explicit scheme. The formulation is based on an optimal control theory in which a performance function of the fluid force is introduced. The performance function should be minimized satisfying the state equation. This problem can be transformed into the minimization problem without constraint conditions by using the adjoint equation with adjoint variables corresponding to the state equation. The performance function is defined by the drag and lift forces acting on the body. The weighted gradient method is applied as a minimization technique, the Galerkin finite element method is used as a spatial discretization and the four-step explicit scheme is used as a temporal discretization to solve the state equation and the adjoint equation. As the interpolation, the orthogonal basis bubble function for velocity and the linear function for pressure are employed. In case that the orthogonal basis bubble function is used, the mass matrix can be diagonalized without any artificial centralization. The shape optimization is performed by the presented method.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1078779Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1260
 T.Doyle, M.Gerritsen and G.Iaccarino, Towards sail-shape optimization of a modern clipper ship, Center for Turblence Research, Annual Research Briefs 2002, pp.215-224, 2002.
 A.Jameson, Aerodynamic Design via Control Theory, Journal of Scientific Computing, 3:233-260, 1988.
 A.Jameson and L.Martinelli, Optimum Aerodynamic Design Using the Navier-Stokes Equations, Theoret. Comput. Fluid Dynamics(1998) 10:213-237.
 E.Katamine, H.Azegami, T.Tsubata and S.Itoh, Solution to shape optimization problems of viscous flow fields, International Journal of Computational Fluid Dynamics, Vol. 19, No.1, 45-51, January 2005.
 S.Kim, K.Hosseini, K.Leoviriyakit and A.Jameson, Enhancement of Adjoint Design Methods via Optimization of Adjoint Parameters, AIAA Paper 2005-0448, 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, January 10-13, 2005.
 J.Matsumoto and M.Kawahara, Stable shape identification for fluid-structure interaction problem using MINI element. Journal of Applied Mechanics, JSCE, Vol. 3, 2000.
 J.Matsumoto, A Relationship between Stabilized FEM and Bubble Function Element Stabilization Method with Orthogonal Basis for Incompressible Flows, Journal of Applied Mechanics, JSCE, Vol. 8 August 2005.
 S.Nakajima and M.Kawahara, Shape optimization of a body in compressible inviscid flows, Comp.Meth.Appl.Meth.Engrg., Vol.197.pp.4521- 4530, 2008.
 O.Pironneau, On optimal Design in Fluid Mechanics, J.Fluidmech, Vol. 64, PART 1, 1974, 64(1):97-110.
 H.Yagi and M.Kawahara, Shape Optimization of a Body Located in Incompressible Viscous Flow Using Adjoint Method, in Proc.ECCOMAS2004.