| In this paper, we apply a small perturbation theory in the study of Aorto-Coronaric bypass anastomoses configurations. We present a class of modified models of Aorto-Coronaric bypass anastomoses configurations using the optimal control theory. Blood is assumed to be Newtonian fluid, pattern of blood flow is found to fit with the Stokes equations. Consider an idealized, tow-dimensional bypass bridge Configurations. Local shape design is based on a transformation from the original domain to a rectangularone: where f{x,ε) represents the above shape and can be developedas f(x,ε)=f0(x) + εf1(x) + ε2f2(x) +……,being f0(x) the unperturbed shape. Assuming the Stokes equations has a solution v,p,and v = v0 + εv1 + ……, p = p0 + εp1+ ……Using small perturbation techniques we can derive a generalized Stokes equations for vk,pk. At this point we can use optimal control theory to solve the equations for v1, p1 .The control function f1(x) is another unknown for the equations and represents a perturbation in the shape f0(x). To determine f1 (x),we have to choose a cost functional. It is a simplified functional depending on the flow vorticity: J (f1,v1,p1) = . Then we derive aclass of modified models for optimal control by minimizing the cost functional. Next, we analyze uniqueness and existence results and introduce an iterative process. Finally, we extend the approach and results using unsteady Stokes equations.
|
PDF Full Text Request