Linearizing convection terms in the Navier-Stokes equations Original Research Article

Standard approaches to dealing with the convection term in the Navier-Stokes equation involve either nonlinear Newton methods or Picard linearization. This paper focuses on Picard linearizations. Picard updates to the Navier-Stokes convection terms are accepted to be of the form (ūN − 1 · ▽)ūN. Current literature either ignores the possibility of, or recommends against, the (ūN · ▽)ūN − 1 form. Why? Although this form is attractive due to its symmetry within a Finite Element discretization, it is not merely recommended against, it is wholly incorrect! This paper offers evidence to this effect in the form of analysis, numerical experiment and rationale.