Vortex Flows and Related Numerical Methods II
ESAIM: Proceedings,
Vol. 1, 1996, pp. 225-240
Application of Fast Parallel and Sequential Tree Codes to
Computing Three-Dimensional Flows with the Vortex Element
and Boundary Element Methods
G.S. Winckelmans
Mechanical Engineering Dept.
Université Catholique de Louvain
Louvain-la-Neuve, B-1348, Belgium
J.K. Salmon
Center for Advanced Computing Research
California Institute of Technology
Pasadena CA 91125, USA
M.S. Warren
Los Alamos National Laboratories
Los Alamos, NM 87545, USA
A. Leonard
Graduate Aeronautical Laboratories
California Institute of Technology
Pasadena CA 91125, USA
B. Jodoin
Chemical Eng. Dept.
Université de Sherbrooke
Sherbrooke (Qc), Canada
Abstract
A fast parallel oct-tree code originally developed for three-dimensional
N-body gravitational simulations was modified into (1) a fast N-vortex code
for viscous and inviscid vortex flow computations using the regularized
vortex particle method (VEM), and (2) a fast N-panel code for solving
boundary integral equations in potential flow aerodynamics using the
boundary element method (BEM). The core of the fast tree code remains
essentially unchanged between the different application codes: gravitation,
VEM, BEM, etc. Only the modules that actually encode the physical model are
changed. Particular attention is given to controlling the error introduced
by the use of multipole expansions to represent the field produced by
groups of elements, i.e., the tree code error. In particular, the
acceptable error bound for use of any multipole expansion approximation is
a run-time parameter. Program outputs include statistics on the errors for
the field evaluation at all element locations. Problems in VEM and BEM
involving N in the range 104 to over 106 are
computed on parallel supercomputers. Problems with N in the range
103 to 105 are computed on workstations. Performance
results are presented, together with sample computational results. For the
VEM method, a high order particle redistribution scheme has been
incorporated, in an efficient way, into the parallel tree code. It is
applied, if necessary, to ensure that the core overlapping condition
remains satisfied in long time computations. In addition, two different
relaxation schemes have also been incorporated and partially tested. Such
schemes are applied, if necessary, to ensure that the particle
representation of the vorticity field remains a good representation of the
true divergence free vorticity field in long time computations.
Vortex Flows and Related
Numerical Methods II
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