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CATEGORIES:Laboratory for Scientific Computing
SUMMARY:A high order cell centred Lagrangian Godunov schem
e for cylindrical geometry - Dr Andy Barlow (AWE)
DTSTART;TZID=Europe/London:20120228T123000
DTEND;TZID=Europe/London:20120228T140000
UID:TALK36631AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/36631
DESCRIPTION:Most Lagrangian hydrocodes have been written withi
n the framework of a staggered grid. These have pr
oved extremely useful\, but they share some defect
s such as mesh imprinting\, failure to maintain sy
mmetry\, and some fail to conserve total energy. I
t is also possible to take a cell-centred approach
\, as is common with Eulerian hydrocodes\, which m
akes full conservation straightforward. The fluxes
across interfaces can be derived from Riemann sol
vers\, which have proved very robust in the Euleri
an context\, and avoid the need for such measures
as artificial viscosity and subzonal pressures. Th
e outstanding issue seems to be the development of
a good method for moving the mesh along with the
flow. However\, significant progress has recently
been made in solving this problem. Most Lagrangian
Godunov schemes either define the nodal velocitie
s as averages of adjacent cell centred velocities
or edge velocities (from the Riemann solver)\, or
introduce a special nodal Riemann solver [1]. We p
ropose here to derive the mesh motion by surroundi
ng each cell vertex with a control volume to which
the conservation laws are applied. We describe th
is as a dual grid. A first order version of this s
cheme was presented in [2]. This talk presents the
extension of this first order scheme to second or
der and cylindrical geometry. An assessment is als
o made of the performance of the second order meth
od in both plane and cylindrical geometry by compa
rison against results obtained with a staggered gr
id compatible finite element code [3]. Two differe
nt approaches are also considered for moving the n
odes based on the dual grid approach\, a method wh
ich reconstructs nodal velocities at the start of
every time step and a second which carries the nod
al velocities as an additional variable.\n\nRefere
nces\n\n1. P.-H. Maire\, A high-order cell-centere
d Lagrangian scheme for two-dimensional compressib
le fluid flows on unstructured mesh\, Journal of C
omputational Physics\, 228 (7)\, 2391-2425(2009).\
n\n2. A. J. Barlow\, P. L. Roe\, A cell centred La
grangian Godunov scheme for shock hydrodynamics\,
Comput. Fluids\, 46\, 133-136\, (2011).\n\n3. A. J
. Barlow\, 'A compatible finite element multi-mate
rial ALE hydrodynamics algorithm.'\, Int. J. Numer
. Meth. Fluids 2008\; 56:953-964.
LOCATION:Seminar Room B\, Rutherford Building\, Cavendish L
aboratory
CONTACT:Dr Nikolaos Nikiforakis
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