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SUMMARY:Adaptive High-order Finite Volume Discretizations on Spherical Thi
 n Shells - Phillip Colella\,   (Lawrence Berkeley National Laboratory)
DTSTART:20120925T103500Z
DTEND:20120925T110000Z
UID:TALK40091@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We present an adaptive\, conservative finite volume approach a
 pplicable to solving hyperbolic PDE's on both 2D surface and 3D thin shell
 s on the sphere. The starting point for this method is the equiangular cub
 ed-sphere mapping\, which maps six rectangular coordinate patches (blocks)
  onto the sphere. The images of these blocks form a disjoint union coverin
 g the sphere\, with the mappings of adjacent blocks being continuous\, but
  not differentiable\, at block boundaries. Our method uses a fourth-order 
 accurate discretization to compute flux averages on faces\, with a higher-
 order least squares-based interpolation to compute stencil operations near
  block boundaries. To suppress oscillations at discontinuities and underre
 solved gradients\, we use a limiter that preserves fourth-order accuracy a
 t smooth extrema\, and a redistribution scheme to preserve positivity wher
 e appropriate for advected scalars. By using both space- and time-adaptive
  mesh refinement\, the solver allocates comp utational effort only where g
 reater accuracy is needed. The resulting method is demonstrated to be four
 th-order accurate for advection and shallow water equation model problems\
 , and robust at solution discontinuities. We will also present an approach
  for the compressible Euler equations on a 3D thin spherical shell. Refine
 ment is performed only in the horizontal directions\, The radial direction
  is treated implicitly (using a fourth-order RK IMEX scheme) to eliminate 
 time step constraints from vertical acoustic waves. \n
LOCATION:Seminar Room 1\, Newton Institute
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