A Comparative Study of Lagrangian Methods Using Axisymmetric and Deforming Blobs
Date
2003
Authors
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Publisher
Department of Mathematics
Abstract
This paper presents results from a head-to-head comparison of two Lagrangian
methods for solutions to the two-dimensional, incompressible convection-diffusion equations. The
first Lagrangian method is an axisymmetric core spreading method using Gaussian basis functions.
The second method uses deforming elliptical Gaussian basis functions. Previous results show that
the first method has second-order spatial accuracy and the second method has fourth-order spatial
accuracy. However, the deforming basis functions require more computational effort per element,
so this paper examines computational performance as well as overall accuracy. The test problem is
the deformation and diffusion of ellipsoidal distribution of scalar with an underlying flow field that
has closed circular streamlines. The test suite includes moderate, high and infinite Peclet number
problems. The results indicate that the performance tradeoff for the sample flow calculation occur
at modest problem sizes, and that the fourth-order method offers distinct advantages as a general
approach for challenging problems.
Description
Keywords
Convection-diffusion, particle methods, computational fluid dynamics, deforming blobs