High spatial order vortex methods and Lagrangian techniques using
deforming basis functions
Louis Rossi
Department of Mathematical Sciences, University of Delaware
Tuesday, May 20, 2003 15:00-16:00,
Room 145, NIST North (820)
Gaithersburg
Tuesday, May 20, 2003 13:00-14:00,
Room 4550
Boulder
Abstract:
Broad classes of numerical schemes known as vortex methods, particle
tracking methods, and smoothed particle hydrodynamics all exhibit the
common theme of approximating solutions to linear and nonlinear
partial differential equations as a linear combination of moving,
localized basis functions. In many ways, these techniques bridge
modeling and computational activities because the evolution equation
for each basis function can be interpreted as a localized model for
the original system. The principal advantage to these methods is that
they are naturally adaptive for problems involving convective
derivatives in that the computational resources are expended only
where the field is nonzero and nowhere else. Examples of problems
with this structure are the vorticity equations for high Reynolds
number flows, the linear convection-diffusion equations and the
evolution of moisture in unsaturated porous media. Particle methods
have been effective in computing localized fields in a variety of
settings such as wakes, mixing layers, jets, plumes and infiltration
fingers. One remaining mathematical issue is finding effective ways
to increase the spatial accuracy of the method. In this talk, I will
discuss one way of boosting the accuracy using a class of deforming
elliptical Gaussian basis functions. I will show that the
conventional wisdom of using the velocity field at the centroid to
convect particles is flawed and that one must include a velocity
curvature correction to achieve the anticipated increase in spatial
accuracy. Deforming elements with the corrected velocity field
realizes two additional orders of accuracy even though the particles
do not follow physical streamlines.
Contact: G. B. McFaddenNote: Visitors from outside NIST must contact
Robin Bickel; (301) 975-3668;
at least 24 hours in advance.
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