Improved Integration Techniques for Fluid Flow Finite Element Formulations.
WEAPONS RESEARCH ESTABLISHMENT SALISBURY (AUSTRALIA)
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Two refinements in the application of numerical integration, alternative sampling points and reduced integration, have been investigated for a Galerkin finite element formulation of a representative flow problem. By sampling the solution at the Gauss points a significant improvement in accuracy is achieved. The accuracy gain is lost if the solution at the Gauss points is extrapolated to the edge of the element. Consideration of a one-dimensional problem suggests that the use of reduced integration is equivalent to fitting the equation residual in the least-squares sense over each element. The employment of reduced integration, rather than exact integration, for incompressible, inviscid flow about a two-dimensional cylinder has produced solutions that are ten times more efficient if quadratic rectangular elements, either Serendipity or Lagrange, are used. The utilization of linear rectangular elements has caused a smaller improvement. The improvements associated with the introduction of reduced integration are independent of grid refinement. The use of reduced integration and triangular elements, with both linear and quadratic shape functions, has produced no significant improvement. The results herein reinforce the previously published conclusion that the quadratic, rectangular, Serendipity element is the most efficient element for flow problems of this type. Author
- Statistics and Probability
- Fluid Mechanics