BEM Simulation Of Transient Fluid Flow
Phenomena
Author(s)
J. Ravnik & L. ˇ Skerget
Abstract
In this paper a Boundary Element Method based numerical algorithm is presented
for the simulation of three-dimensional unsteady fluid flow and heat transfer.
Four different time discretization techniques are considered and compared on
a model unsteady heat diffusion problem. Analytical solution of the problem
is used to designate the three point second-order finite different approximation
of the accumulation term of the transport equations as the most accurate. This
choice is incorporated into the flow solver and the developed algorithm is used
to simulate Rayleigh–B´enard convection. Oscillatory and chaotic behaviour of the
flow field and heat transfer are observed. Temperature slices and velocity vectors
are presented. Heat flux is presented in terms of the Nusselt number.
Keywords: Boundary Element Method, Rayleigh–B´enard convection, velocityvorticity
formulation, time discretization.
1 Introduction
The Boundary Element Method (BEM) is a numerical technique that has been
successfully applied for the solution of a wide variety of engineering problems and
natural phenomena. In this paper we are focused on unsteady natural convection
phenomena. A transient simulation is required, which must be able to capture the
oscillatory and chaotic nature of the flow problem.
The paper presents a BEM based laminar viscous flow solver and focuses on the
time discretization. Three implicit finite difference approximations and an explicit
approximation of the accumulation term of the transport equations are compared
against an analytical solution of a model problem. The three point second order
finite difference approximation is then incorporated into the flow solver and used
to obtain an unsteady solution of the Rayleigh–B´enard convection problem.
Keywords
Boundary Element Method, Rayleigh–Bénard, convection, velocityvorticity formulation, time discretization
Related Book
Other papers in this volume
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