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Boussinesq Algorithm for Enclosed Buoyant Convection in Two Dimensions.



Ronald G. Rehm, Hai C. Tang, Howard R. Baum, James S. Sims, Daniel M. Corley


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.
NIST Interagency/Internal Report (NISTIR) - 4540
Report Number


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


Rehm, R. , Tang, H. , Baum, H. , Sims, J. and Corley, D. (1991), Boussinesq Algorithm for Enclosed Buoyant Convection in Two Dimensions., NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed July 15, 2024)


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Created March 1, 1991, Updated June 2, 2021