Further studies on equal-order interpolation for Navier-Stokes
Abstract
The simplest quadrilateral element available for the incompressible Navier-Stokes equations is the mixed interpolation 4-node element with bilinear velocity and (piecewise) constant pressure - donoted herein by 4/1. The next simplest is the 4/4 element, in which (continuous) bilinear approximation is also employed for pressure - i.e., the simplest case of equal-order interpolation. The 4/1 element has been very popular, even though it sometimes generates one spurious pressure mode which is usually filterable. But the 4/1 element generates a poor approximation to (Del P) when distorted elements are employed (via the bilinear isoparamatic technique), which often leads to large errors in velocity; e.g. this element generated wrong answers for vortex shedding on the same mesh for which a higher order element (9/4:) performed well. Although the 4/4 element generates ostensibly useless pressures, the pressure gradient and the velocity field might be much more accurate than those from the 4/1 element, especially when distorted meshes are employed. Based on these observations, the 4/4 element was tested on two problems, for which the 4/1 element failed. The 4/4 element is no panacea, however; the multiple (and generally unknown) spurious pressure modes (pure and impure) associated with equal-order interpolation leads to a generally delicate solution procedure. A viable technique for recovering a useful pressure field from the otherwise polluted pressures is presented.
- Publication:
-
NASA STI/Recon Technical Report N
- Pub Date:
- October 1983
- Bibcode:
- 1983STIN...8413512G
- Keywords:
-
- Finite Element Method;
- Interpolation;
- Navier-Stokes Equation;
- Pressure Gradients;
- Velocity Distribution;
- Vortices;
- Approximation;
- Incompressibility;
- Fluid Mechanics and Heat Transfer