Improvements of the optimal control method to solve turbulent flows
Abstract
Modifications of the optimal control method are introduced for solving a set of NavierStokes partial differential equations. A Burgers equation is defined for the nonlinear convective term, along with a simplified equation for the mean turbulent velocity field between two parallel planes to account for the turbulent terms. The shear stress is expressed in terms of the mean velocity gradient. A least squares formulation is developed through a choice of a linear operator and a cost function in Hilbert space. The continuous iterative algorithm is detailed, as is the finite element discretization procedure. It is noted that six linear systems of equations are solved at each iteration, with the generalized Galerkin method employed for solving the state equation. Applications are demonstrated in cases of the entrance flow between two parallel plates and turbulent flow between two parallel plates. The optimal control problem is shown to be valid for twodimensional modelling of turbulent flows at high Re.
 Publication:

Numerical Methods in Laminar and Turbulent Flow
 Pub Date:
 1981
 Bibcode:
 1981nmlt.proc..303B
 Keywords:

 Computational Fluid Dynamics;
 NavierStokes Equation;
 Optimal Control;
 Parallel Plates;
 Turbulent Flow;
 Flow Velocity;
 Galerkin Method;
 High Reynolds Number;
 Least Squares Method;
 Operators (Mathematics);
 Shear Stress;
 Two Dimensional Flow;
 Velocity Distribution;
 Fluid Mechanics and Heat Transfer