Adaptive, multi-level numerical scheme for the solution of the Navier-Stokes equations
A simple error analysis is used within the context of segregated finite element solution scheme to solve incompressible fluid flow. An error indicator is defined based on the difference between a numerical solution on an original mesh and an approximated solution on a related mesh. This error indicator is based on satisfying the steady state momentum equations. The advantages of this error indicator are: simplicity of implementation; ability to show regions of high and/or low error; and as the indicator approaches zero the solution approaches convergence. Two examples are chosen for solution; first, the lid-driven cavity problem is solved, followed by the solution of flow over a backward facing step. The solutions are compared to previously published data for validation purposes. It is shown that this rather simple error estimate, when used as a re-meshing guide, can be very effective in obtaining accurate numerical solutions.
American Society of Mechanical Engineers, Applied Mechanics Division, AMD
Fithen, R. M. & Reddy, J. M. (1992). Adaptive, multi-level numerical scheme for the solution of the Navier-Stokes equations. American Society of Mechanical Engineers, Applied Mechanics Division, AMD Conference Porceedings 157: 275-292.