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SUMMARY:Multi-Moment ADER-Taylor Methods for Systems of Conservation Laws 
 with Source Terms in One Dimension - Matthew Norman\,   (Oak Ridge Nationa
 l Laboratory)
DTSTART:20120926T112500Z
DTEND:20120926T115000Z
UID:TALK40140@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:A new integration method combining the ADER time discretizatio
 n with a multi-moment finite-volume framework is introduced. ADER runtime 
 is reduced by performing only one Cauchy-Kowalewski (C-K) procedure per ce
 ll per time step\, and by using the Differential Transform Method for high
 -order derivatives. Three methods are implemented: (1) single-moment WENO 
 [WENO]\, (2) two-moment Hermite WENO [HWENO]\, and (3) entirely local mult
 i-moment [MM-Loc]. MM-Loc evolves all moments\, sharing the locality of Ga
 lerkin methods yet with a constant time step during p -refinement. \n\nFiv
 e experiments validate the methods: (1) linear advection\, (2) Burger's eq
 uation shock\, (3) transient shallow-water (SW) \, (4) steady-state SW sim
 ulation\, and (5) SW shock. WENO and HWENO methods showed expected polynom
 ial h -refinement convergence and successfully limited oscillations for sh
 ock experiments. MM-Loc showed expected polynomial h -refinement and expon
 ential p -refinement convergence for linear advection and showed sub-expon
 ential (yet super-polynomial) convergence with p -refinement in the SW cas
 e. \n\nHWENO accuracy was generally equal to or better than a five-moment 
 MM-Loc scheme. MM-Loc was less accurate than RKDG at lower refinements\, b
 ut with greater h - and p -convergence\, RKDG accuracy is eventually surpa
 ssed. The ADER time integrator of MM-Loc also proved more accurate with p 
 -refinement at a CFL of unity than a semi-discrete RK analog of MM-Loc. Be
 ing faster in serial and requiring less frequent inter-node communication 
 than Galerkin methods\, the ADER-based MM-Loc and HWENO schemes can be spa
 tially refined and have the same runtime\, making them a competitive optio
 n for further investigation.\n
LOCATION:Seminar Room 1\, Newton Institute
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