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SUMMARY:Numerical Solution of the Advection Equation on Unstructured Spher
 ical Grids with Logarithmic Reconstruction - Oswald Knoth\,   (Leibniz Ins
 titute for Tropospheric Research\, Leipzig)
DTSTART:20120925T082500Z
DTEND:20120925T085000Z
UID:TALK40094@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:There are numerous approaches for solving hyperbolic different
 ial equations in the context of finite volume methods. One popular approac
 h is the limiter free Local-Double-Logarithmic-Reconstruction (LDLR) of Ar
 tebrant and Schroll. The aim of this work is to construct a three-dimensio
 nal reconstructing function based on the LDLR for solving the advection eq
 uation on unstructured spherical grids. The new method should preserve the
  characteristics of the LDLR. That means in particular a reconstruction wi
 thout use of limiters and with a small stencil of only the nearest neighbo
 rs of a particular cell. Also local extrema should be conserved while the 
 local variation of the reconstruction within one cell should be under cont
 rol. \n\nWe propose an ansatz which works on unstructured polyhedral grids
 . To come up to this\, an ansatz function with one logarithmic expression 
 for each face of the polyghedron is constructed. Required gradients at cel
 l face midpoints are determined by use of the Multi-Point-Flux-Approximati
 on (MPFA) method. Further derivative information are obtained with the hel
 p of special barycentric coordinates. All necessary integrals of the ansat
 z functions can be computed exactly. The spatially discretized equations a
 re combined with explicit Runge-Kutta methods to advance the solution in t
 ime. \n\nThe new advection procedure is numerically evaluated with standar
 d test cases from the literature on different unstructured spherical grids
 .\n\n
LOCATION:Seminar Room 1\, Newton Institute
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