Simulation and visualization of compressible convection in 2- and 3-D

We describe a fluid flow problem in astrophysics which also has applications in other areas of science and engineering. A study of the convection process of heat and material transfer in the outer layers of stars like the sun has led to an extensive investigation of compressible convection in a layer confined between two plates. This work attempts to reach the highest possible Reynolds number regime. High effective Reynolds numbers are achieved by using the Picccwise-Parabolic Method (PPM) to solve the Euler equations. Attempts to demonstrate the validity of this approach have led to related studies of compressible vortex dynamics and of compressible homogeneous turbulence. Results of simulations of compressible convection in both 2-D and in 3-D will be presented. These flows arc so complicated that they can best be appreciated when high-resolution color images of important flow variables are animated, so that the dynamics can be seen directly. A few snapshots arc presented here, and video movies are available from the authors. Visualization techniques which have been developed in this work, particularly those designed for the 3-D flows, are briefly discussed. The Piece wise-Parabolic Method (PPM) is briefly described. In the context of compressible vortex dynamics, results of the PPM code are compared directly to accurate Navier-Stokes simulations. This comparison indicates that if a viscosity is to be used in such simulations which can be rigorously justified on physical grounds, and if the behavior at a very high Reynolds number is sought, then vastly greater computer resources must be devoted to the problem than are required by the PPM code.