PROGRAM SUMMARY
Title of program:
vl2dper
Catalogue identifier:
ADJR
Ref. in CPC:
116(1999)336
Operating system: Unix
Number of lines in distributed program, including test data, etc:
1249
Programming language used: Fortran
Computer: Cray C 90
Nature of physical problem:
Since the seventies, two main types of code are available to simulate
plasma evolution: Particles (Lagrangian) codes or Eulerian codes. The
advantage of particles codes is their capacity to go to high dimensions
(two or three), their inconvenience the difficulty they have to
represent with a good accuracy high velocity particles, and the
numerical noise of the code, due to the too low number of particles
used. Hybrid methods such as the deltaF method [2] or VHS method [3]
mixing particles and phase space representation have a low numerical
noise. Nevertheless, as the v-space behaviour is not far from a
maxwellian, a thermal noise is present. This effect is very important
in acceleration processes as the contribution of a few number of fast
particles present a large part of the total energy. The advantage of
the actual code is very low thermal noise, and its capability to
represent all phase space with the same accuracy. Actually the present
code cannot be generalized to three dimensions at present because of the
limited computer memory available.
The major problems where the Eulerian codes are needed are plasma
acceleration problems, specially relativistic cases, solar wind studies
or all problems where a low numerical noise is important.
Method of solution
The method used in the present code is time splitting to transform the
Vlasov equation into a set of transport equations, and solution of the
transport (in phase space) equation by a Flux Balance Method [1]
(F.B.M.). The four equations we get after the splitting are solved
iteratively by FBM, following a symmetrical scheme to conserve a leap
frog integration in time, method. The fields are calculated once every
time step.
Typical running time
The actual test run takes 15810 sec for 400 time steps (neglecting the
code initialization), for a grip of 64 x 128 x 127 x 127, or 0.299 mu
sec per time step per grid point on a Cray C98 computer.
Unusual features of the program
External libraries used: UNICOS Scientific Library (for FFTs), or
C. Temperton's FFT991 subroutine [4].
References
[1] E. Fijalkow, A Numerical Solution to Vlasov Equation, Comp. Phys.
Commun. 116 (1999) 319.
[2] T. Tajima, F.W. Perkins, Proceedings Sherwood Theory Meeting, Univ.
of Maryland, (1983).
[3] D. Nunn, J. Comp. Phys. 108, 180, (1993).
[4] C. Temperton, J. Comp. Phys. 52, 198, (1983).