A Comparative Study of Lagrangian Methods Using Axisymmetric and Deforming Blobs

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 Péclet 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.