Numerical Simulation of Three-Dimensional, Shape-Preserving Convective Elements

Abstract

The motions resulting from the sudden release of a fixed amount of buoyancy in an incompressible fluid are simulated. Solutions are allowed to reach a steady state in the finite computed volume by the introduction of a dynamical stretching of the coordinate system. Fully nonlinear, transformed, and finite-differenced Navier-Stokes equations are integrated in time over a three-dimensional grid. It is shown that a steady-state solution to the transformed equations is equivalent to a self-preserving solution in real space. Physically realistic results are presented for a range of Reynolds numbers between 10 and 100. In a strongly diffusive regime the simulation agrees with an existing theoretical solution. Reynolds numbers of order 50 are sufficient to reproduce many of the features of laboratory experiments.