HR: 16:20h
AN: NG12D-02 INVITED [PDF]
TI: Using Subdivision Surfaces and Adaptive Surface Simplification Algorithms
for Modeling Chemical Heterogeneities in Geophysical Flows
AU: * Schmalzl, J
EM: joergs@uni-muenster.de
AF: Muenster University, Inst. of Geophysics, Corrensstr. 24, Muenster, 48149
Germany
AU: Loddoch, A
EM: loddoch@uni-muenster.de
AF: Muenster University, Inst. of Geophysics, Corrensstr. 24, Muenster, 48149
Germany
AB:
Convective flows govern much of the dynamics of the Earth. Examples
of such flows are convection in the Earth's mantle, convection in magma
chambers and much of the dynamics of the world oceans. Nowadays these
time-dependent flows are often studied by means of three dimensional (3D)
numerical models which solve the equations for the transport of heat and
momentum alternatingly. These flows are often driven by a temperature
difference. But for many flows there is also an active or passive chemical
component that has to be considered. One characteristics of these flows is
that the chemical diffusivity is very small. Implementing such a chemical
field with a very low diffusivity into a numerical model using a field
approach is difficult due to numerical diffusion introduced by the Eulerian
schemes. Using Lagrangian tracers is also difficult in 3D flow since a
massive amount of tracers is needed.
We therefore have implemented a tracer-mesh method which tracks only the
position of the interface between the two different components. Compared to
a 2D tracer-line the insertion of new 3D surface-elements in highly deformed
regions is however more complex. This is due to the topology of the mesh
which changes because of the adaptive refinement. Luckily the refinement of
polygonal meshes is a very active field of research in computer graphics
and has been termed "Subdivision Surfaces". There is a wealth of different
subdivision schemes with different properties. We applied the Butterfly
scheme and the Loop scheme for the refinement of tracer meshes.
When a density difference is connected to a chemical component it often
acts as a restoring force. In many cases, the governing flow is spatially
heterogenous and the spatial location of the heterogeneities is varying in
time (e.g. the location of an upwelling plume). The restoring force of the
density contrast may result in a situation where a highly deformed, and
therefore highly refined region, returns to a simple geometry. In order to
limit the computational expenses we also need a surface simplification
algorithm which removes excess tracers.
In this talk we want to show how these techniques can be successfully
applied in geophysical fluid dynamics and will give application examples.
DE: 1025 Composition of the mantle
DE: 8124 Earth's interior--composition and state (old 8105)
DE: 8147 Planetary interiors (5430, 5724)
SC: Nonlinear Geophysics [NG]
MN: 2003 Fall Meeting