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SUMMARY:A high order cell centred Lagrangian Godunov scheme for cylindrica
 l geometry - Dr Andy Barlow (AWE)
DTSTART:20120228T123000Z
DTEND:20120228T140000Z
UID:TALK36631@talks.cam.ac.uk
CONTACT:Dr Nikolaos Nikiforakis
DESCRIPTION:Most Lagrangian hydrocodes have been written within the framew
 ork of a staggered grid. These have proved extremely useful\, but they sha
 re some defects such as mesh imprinting\, failure to maintain symmetry\, a
 nd some fail to conserve total energy. It is also possible to take a cell-
 centred approach\, as is common with Eulerian hydrocodes\, which makes ful
 l conservation straightforward. The fluxes across interfaces can be derive
 d from Riemann solvers\, which have proved very robust in the Eulerian con
 text\, and avoid the need for such measures as artificial viscosity and su
 bzonal pressures. The outstanding issue seems to be the development of a g
 ood method for moving the mesh along with the flow. However\, significant 
 progress has recently been made in solving this problem. Most Lagrangian G
 odunov schemes either define the nodal velocities as averages of adjacent 
 cell centred velocities or edge velocities (from the Riemann solver)\, or 
 introduce a special nodal Riemann solver [1]. We propose here to derive th
 e mesh motion by surrounding each cell vertex with a control volume to whi
 ch the conservation laws are applied. We describe this as a dual grid. A f
 irst order version of this scheme was presented in [2]. This talk presents
  the extension of this first order scheme to second order and cylindrical 
 geometry. An assessment is also made of the performance of the second orde
 r method in both plane and cylindrical geometry by comparison against resu
 lts obtained with a staggered grid compatible finite element code [3]. Two
  different approaches are also considered for moving the nodes based on th
 e dual grid approach\, a method which reconstructs nodal velocities at the
  start of every time step and a second which carries the nodal velocities 
 as an additional variable.\n\nReferences\n\n1. P.-H. Maire\, A high-order 
 cell-centered Lagrangian scheme for two-dimensional compressible fluid flo
 ws on unstructured mesh\, Journal of Computational Physics\, 228 (7)\, 239
 1-2425(2009).\n\n2. A. J. Barlow\, P. L. Roe\, A cell centred Lagrangian G
 odunov scheme for shock hydrodynamics\, Comput. Fluids\, 46\, 133-136\, (2
 011).\n\n3. A. J. Barlow\, 'A compatible finite element multi-material ALE
  hydrodynamics algorithm.'\, Int. J. Numer. Meth. Fluids 2008\; 56:953-964
 .
LOCATION:Seminar Room B\, Rutherford Building\, Cavendish Laboratory
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