MULTIVARIANT FINITE-ELEMENTS FOR 3-DIMENSIONAL SIMULATION OF VISCOUS INCOMPRESSIBLE FLOWS

Within multivariant elements, which have restricted degrees of freedom at some nodes, different velocity components have different variations. Shape functions for the multivariant elements Q1+P0 and R2+P0 are developed. With such shape functions the value of a velocity component within a multivariant element is shown to depend upon all the independent components of velocity at the nodes of the element. The use of the Q1P0 element to simulate flows with discontinuous boundary conditions generated disturbance throughout the flow domain, giving erroneous pressure and velocity distributions. The Q1+P0 element restricted the disturbance due to such discontinuities to a small region near the singular points, whereas the R2+P0 element completely eliminated the fluctuations. Flows with discontinuous boundary conditions were simulated with reasonable accuracy by partially relaxing the no-slip condition on the Q1P0 elements near the singular points.