PENALTY FINITE ELEMENT METHODS FOR THE SOLUTION OF ADVECTION AND FREE CONVECTION FLOWS.
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The penalty method of Courant is employed in conjunction with the finite element method to solve the nonlinear equations governing advection dominated and free convection flows. The penalty finite element developed herein is a four-node quadrilateral element with bilinear shape functions for velocities and stream function. The element possesses the advantages of the stream function as well as the primitive variable models, and is very effective from computational and accuracy considerations. The effectiveness is illustrated via example problems of two-dimensional advection and free convection flows.
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