AbstractThis paper presents results computed using LS‐DYNA's new incompressible flow solver for a differentially heated cavity with an 8:1 aspect ratio at a slightly super‐critical Rayleigh number. Three Galerkin‐based solution methods are applied to the 8:1 thermal cavity on a sequence of four grids. The solution methods include an explicit time‐integration algorithm and two second‐order projection methods—one semi‐implicit and the other fully implicit. A series of ad hoc modifications to the basic Galerkin finite element method are shown to result in degraded solution quality with the most serious effects introduced by row‐sum lumping the mass matrix. The inferior accuracy of a lumped mass matrix relative to a consistent mass matrix is demonstrated with the explicit algorithm which fails to obtain a transient solution on the coarsest grid and exhibits a general trend to under‐predict oscillation amplitudes. The best results are obtained with semi‐implicit and fully implicit second‐order projection methods where the fully implicit method is used in conjunction with a ‘smart’ time integrator. Copyright © 2002 John Wiley & Sons, Ltd.