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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Multi-Moment ADER-Taylor Methods for Systems of Co
nservation Laws with Source Terms in One Dimension
- Matthew Norman\, (Oak Ridge National Laborato
ry)
DTSTART;TZID=Europe/London:20120926T122500
DTEND;TZID=Europe/London:20120926T125000
UID:TALK40140AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/40140
DESCRIPTION:A new integration method combining the ADER time d
iscretization with a multi-moment finite-volume fr
amework is introduced. ADER runtime is reduced by
performing only one Cauchy-Kowalewski (C-K) proced
ure per cell per time step\, and by using the Diff
erential Transform Method for high-order derivativ
es. Three methods are implemented: (1) single-mome
nt WENO [WENO]\, (2) two-moment Hermite WENO [HWEN
O]\, and (3) entirely local multi-moment [MM-Loc].
MM-Loc evolves all moments\, sharing the locality
of Galerkin methods yet with a constant time step
during p -refinement. \n\nFive experiments valida
te the methods: (1) linear advection\, (2) Burger'
s equation shock\, (3) transient shallow-water (SW
) \, (4) steady-state SW simulation\, and (5) SW s
hock. WENO and HWENO methods showed expected polyn
omial h -refinement convergence and successfully l
imited oscillations for shock experiments. MM-Loc
showed expected polynomial h -refinement and expon
ential p -refinement convergence for linear advect
ion and showed sub-exponential (yet super-polynomi
al) convergence with p -refinement in the SW case.
\n\nHWENO accuracy was generally equal to or bett
er than a five-moment MM-Loc scheme. MM-Loc was le
ss accurate than RKDG at lower refinements\, but w
ith greater h - and p -convergence\, RKDG accuracy
is eventually surpassed. The ADER time integrator
of MM-Loc also proved more accurate with p -refin
ement at a CFL of unity than a semi-discrete RK an
alog of MM-Loc. Being faster in serial and requiri
ng less frequent inter-node communication than Gal
erkin methods\, the ADER-based MM-Loc and HWENO sc
hemes can be spatially refined and have the same r
untime\, making them a competitive option for furt
her investigation.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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