%0 Journal Article
	%A Yoichi Hikino and  Mutsuto Kawahara
	%D 2010
	%J International Journal of Physical and Mathematical Sciences
	%B World Academy of Science, Engineering and Technology
	%I Open Science Index 47, 2010
	%T A Shape Optimization Method in Viscous Flow Using Acoustic Velocity and Four-step Explicit Scheme
	%U https://publications.waset.org/pdf/12218
	%V 47
	%X 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.
	%P 1416 - 1421