Abstract
We study the relative usefulness of static and dynamic boundary conditions as a function of system dimensionality. In one space dimension, dynamic boundaries, with the temperatures and velocities of external mirror-image boundary particles linked directly to temperatures and velocities of interior particles, perform qualitatively better than the simpler static-mirror-image boundary condition with fixed boundary temperatures and velocities. In one space dimension, the Euler-Maclaurin sum formula shows that heat-flux errors with dynamic temperature boundaries vary as h(-4), where h is the range of the smooth-particle weight function w(r<h). Geometric effects (lack of a simple sum formula) frustrate a corresponding exact analysis in higher-dimensional problems. We illustrate all of these ideas here for the two-dimensional Rayleigh-Bénard flow.
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