  Buoyancy-induced (Rayleigh-Benard) convection of a fluid between two
horizontal plates is a central paradigm for studying the transition to complex
spatiotemporal dynamics in sustained nonequilibrium systems. To improve the
analysis of experimental data and the quantitative comparison of theory with
experiment, we have developed a three-dimensional finite-difference code that
can integrate the three-dimensional Boussinesq equations (which govern the
evolution of the temperature, velocity, and pressure fields associated with a
convecting flow) efficiently in large box-shaped domains with experimentally
appropriate lateral boundary conditions. We discuss some details of this code
and present two applications, one to the occurrence of quasiperiodic dynamics
with as many as 5 incommensurate frequencies in a moderate-aspect-ratio 10x5
convection cell, and one to the onset of spiral defect chaos in square cells
with aspect ratios varying from Gamma=16 to 56.
