A finite element, Navier-Stokes study of the confined, laminar flow over a downstream facing step
Abstract
The two-dimensional, confined, laminar flow over a downstream facing step was studied using a finite element, Navier-Stokes equation solver. The weak form of the stationary, incompressible Navier-Stokes equations in primitive varible form was obtained using the conventional Galerkin technique for mixed problems. Biquadratic Lagrange interpolating polynomials were used to construct the basis functions that generated the finite-dimensional subspace containing the approximate solutions to the velocity field, while the pressure was represented by a discontinuous, piecewise-linear approximation. This particular combination of solution subspaces was previously shown in a mathematically rigorous fashion to yield stable, consistent solutions to the Navier-Stokes equations. The results of the computations were benchmarked against the experimental data of others who utilized alternative, unconventional formulations. With the proper choice of basis functions, a conventional Galerkin scheme can yield results that are in as good and in many cases better agreement with the available experimental data than those of unconventional schemes that rely upon an infusion of artificial dissipation to enhance their numerical stability.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- 1984
- Bibcode:
- 1984PhDT........22T
- Keywords:
-
- Backward Facing Steps;
- Finite Element Method;
- Laminar Flow;
- Navier-Stokes Equation;
- Two Dimensional Flow;
- Algorithms;
- Computational Fluid Dynamics;
- Flow Velocity;
- Galerkin Method;
- Incompressible Flow;
- Fluid Mechanics and Heat Transfer