| Author | J. Bazilevs |
|---|---|
| Title | Comparison of Equal and Mixed-Order Stabilized FEM Formulation for Incompressible Fluid Flow |
| Year | 2001 |
| School | Rensselear Polytechnic Institute |
| Abstract | There exist a variety of finite element formulations for solving incompressible fluid flow. Considered here are : 1. A fully implicit, equal-order, stabilized FEM solved as a monolithic system using a Generalized-* time integrator. Stabilization in this case is achieved by adding SUPG and GLS type terms as well as conservation restoring ones to the Galerkin formulation of Incompressible Navier Stokes Equations. 2. A semi-implicit, equal-order, FEM solved with a projection method. Here an operator splitting technique is used to uncouple velocity from pressure as well as a conventional Laplacian matrix is employed in the pressure solve to introduce a velocity-pressure pair stabilization. 3. A semi-implicit, mixed-order, FEM solved with a projection method. Here a velocity-pressure pair stabilization is accomplished via selecting test functions for velocity and pressure fields from different (compatible) spaces. 4. An implicit, equal-order, FEM solved with a projection method using a Generalized Alpha time integrator on the momentum solve. Here a velocity-pressure pair stabilization is accomplished via an introduction of a conventional Laplacian matrix. Each algorithm choice engenders accuracy and efficiency trade-offs, these are demonstrated on a set of numerical examples. In this document all 4 formulations with their respective time-stepping algorithms are presented with the special emphasis on projection schemes. Their stronger and weaker features are demonstrated on a variety of steady and unsteady flows. |