##
Boussinesq Algorithm for Enclosed Buoyant Convection in Two Dimensions.

Boussinesq Algorithm for Enclosed Buoyant Convection in
Two Dimensions.
(2098 K)

Rehm, R. G.; Tang, H. C.; Baum, H. R.; Sims, J. S.;
Corley, D. M.

NISTIR 4540; 39 p. March 1991.

### Available from:

National Technical Information Service

Order number: PB91-178848

### Keywords:

algorithms; Boussinesq flow; computational fluid
dynamics; gravity currents; stratified flow; trench
effect; boussinesq approximation; thermal conductivity

### Abstract:

*
Approximate equations for a Boussinesq model with
viscous dissipation and thermal conduction describing
buoyant convection driven by a heat source in
rectangular enclosure are derived. The
finite-difference algorithm for computing transient
solutions in two dimensions to these equations is
presented. The algorithm allows the enclosure fluid to
be stratified in a direction parallel to the enclosure
walls initially, or for gravity to have an arbitrary
direction relative to the enclosure (but with no initial
stratification). Computational results of transient,
two-dimensional buoyant convection for very high
resolution are presented. The hydrodynamics is directly
based on the time-dependent Navier-Stokes equations; the
model is valid in the Boussinesq approximation. No
turbulence model or other empirical parameters are
introduced. There is no inflow or outflow at
boundaries; this assumption, although rather
restrictive, allows the mathematical problem to be
properly formulated so that no other empiricism is
introduced by specification of the algorithmic boundary
conditions. A finite-difference scheme second-order in
space and first-order in time is used to integrate the
evolution equations, and an elliptic solver is used to
solve the pressure equation. The algorithms have been
verified by comparisons with exact solutions to the
equations in simple, special cases, and predictions of
the overall model when the viscosity and thermal
conductivity are zero have been compared with
experimental results. The use of Lagrangian particle
tracking allows one to visualize the flow patterns.
*