Finite Element Analysis of Incompressible Viscous Flows by the Penalty Function Formulation

SUMMARY The spurious pressures and ostensibly acceptable velocities which sometimes result from certain FEM approximate solutions of the incompressible Navier-Stokes equations are explained in detail. The concept of pressure modes, physical and spurious, pure and impure, is introduced and their effects on discretized solutions is analysed, in the context of both mixed interpolation and penalty approaches. Pressure filtering schemes, which are capable of recovering useful pressures from otherwise polluted numerical results, are developed for two particular elements in two-dimensions and one element in three-dimensions. The automatic pressure filter associated with the penalty method is also explained. Implications regarding the effect of spurious pressure modes on accuracy and ultimate convergence with mesh refinement are discussed and a list of unanswered questions presented. Sufficient numerical examples are discussed to corroborate the theory presented herein.

The cause and cure (!) of the spurious pressures generated by certain fem solutions of the incompressible Navier‐Stokes equations: Part 2

A comparison of various mixed-interpolation finite elements in the velocity-pressure formulation of the Navier-Stokes equations☆

Natural convection in a differentially heated square cavity with a horizontal partition plate on the hot wall

A finite-element procedure is presented for the calculation of two-dimensional, viscous, incompressible flows of a recirculating nature. As in finite-difference procedures, velocity and pressure are uncoupled and the equations are solved one after the other. Velocity fields are determined by first calculating intermediate velocity values based on an estimated pressure distribution and then obtaining appropriate corrections to satisfy the continuity equation. Illustrative examples involving flow in the entrance region between parallel plates, lid-driven cavity flow, and flow around an obstacle demonstrate the accuracy and capabilities of the proposed technique.

Finite-element solution of the incompressible navier-stokes equations

Primitive variables versus stream function finite element solutions of the Navier-Stokes equations

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Primitive variables versus stream function finite element solutions of the Navier-Stokes equations

Primitive variables versus stream function finite element solutions of the Navier-Stokes equations