Rice, J. G. | Search NASA

NASA NTRS1985

Simplex finite element analysis of viscous incompressible flow with penalty function formulation

Viscous flow calculations are important for the determination of separated flows, recirculating flows, secondary flows and so on. This paper presents a penalty function approach for the finite element analysis of steady incompressible viscous flow. A simplex element is used with linear velocity and constant pressure in contrast to other works which usually employ higher order elements. Simplex elements yield analytical expressions for the element matrices which in turn lead to efficient solutions. Earlier works have partially indicated how constraint and lock-up problems might be avoided for simplex elements. This paper extends the earlier works by indicating the approach in detail and verifying that it is successful for several applications not discussed in the literature so far. Solution times and accuracy considerations are discussed for Couette flow, plane Poiseuille flow, a driven cavity problem, and laminar and turbulent flow over a step.

Allaire, P. E.↗

NASA NTRS1984

Penalty function finite element analysis of steady viscous incompressible flow in rotating coordinates

Finite element methods for incompressible viscous flow in turbomachines have not been presented in the literature previously. This paper develops a penalty function primitive variable method including Coriolis and centrifugal force terms for steady flow in a rotating coordinate system. Simplex elements are used with the result of solution times comparable to equivalent finite different solutions. Example cases considered are Couette flow, Poiseuile flow, flow over a step and flow in a rotating channel. Both laminar and turbulent flows are discussed. The accuracy of computed solutions compares well with theoretical solutions and experimenal measurements.

Rosen, M. C.↗