For plasmas in the collisionless regime, the absence of bulk viscosity permits multistreaming; if this occurs, fluid codes, which by definition prohibit multistreaming, give unphysical results. It is shown that a fluid code, using an energy propagation equation, will conserve energy, but nevertheless can give totally incorrect results if multistreaming occurs. If a temperature propagation equation is used instead, the system continuously loses energy when multistreaming occurs. This energy nonconservation, which is completely independent of cell size and time step, can be used as an internal test for multistreaming, requiring no data outside the fluid code itself.

1.
K. R.
Chu
,
R.
Clark
,
M.
Lampe
,
P.
Liewer
, and
W.
Manheimer
,
Phys. Rev. Lett.
35
,
94
(
1975
).
2.
P. C.
Liewer
and
N. A.
Krall
,
Phys. Fluids
16
,
1953
(
1973
).
3.
E. Oktay, A. W. DeSilva, P. C. Liewer, Y. G. Chen, H. R. Griem, R. Hess, and N. A. Krall, in Plasma Physics and Controlled Nuclear Fusion Reasearch (International Atomic Energy Agency, Vienna, 1975), Vol. III, p. 365.
4.
J. S.
Clarke
,
H. N.
Fisher
, and
R. J.
Mason
,
Phys. Rev. Lett.
30
,
89
(
1973
).
5.
N. K.
Winsor
and
D. A.
Tidman
,
Phys. Rev. Lett.
31
,
1040
(
1971
).
6.
J.
Dawson
,
Nucl. Fusion Suppl.
3
,
1033
(
1962
).
7.
D. A. Tidman and N. A. Krall, Shock Waves in Collisionless Plasmas (Wiley, New York, 1971), Chap. 7.6.
8.
K.
Papadopoulos
,
R. C.
Davidson
,
J. M.
Dawson
,
I.
Haber
,
D. A.
Hammer
,
N. A.
Krall
, and
R.
Shanny
,
Phys. Fluids
14
,
849
(
1971
).
9.
N. A.
Krall
and
P. C.
Liewer
,
Phys. Rev. A
4
,
2094
(
1971
).
10.
E.
Ott
,
J. B.
McBride
,
J. H.
Orens
, and
J. P.
Boris
,
Phys. Rev. Lett.
28
,
88
(
1972
).
11.
D. W.
Forslund
and
C. R.
Shonk
,
Phys. Rev. Lett.
25
,
281
(
1970
).
12.
M.
Lampe
,
W. M.
Manheimer
,
J. B.
McBride
,
J. H.
Orens
,
K.
Papadopoulos
,
R.
Shanny
, and
R.
Sudan
,
Phys. Fluids
15
,
662
(
1972
).
13.
W.
Manheimer
and
J. P.
Boris
,
Phys. Rev. Lett.
28
,
659
(
1972
).
14.
S. P.
Gary
,
J. Plasma Phys.
4
,
753
(
1970
);
P. C.
Liewer
and
N. A.
Krall
,
Phys. Rev. Lett.
30
,
1242
(
1973
).
15.
D. W.
Forslund
,
J. Geophys. Res.
75
,
17
(
1970
).
16.
W. M. Manheimer, Phys. Fluids (in press).
17.
W.
Horton
,
Phys. Rev. Lett.
28
,
1506
(
1972
).
18.
K. Papadopoulos, R. W. Clark, and C. E. Wagner, in Proceedings of the Third Conference on Solar Wind, edited by C. T. Russell (University of California, Los Angeles, 1974), p. 343.
19.
L. D. Landau and E. Lifshitz, Fluid Mechanics (Addison‐Wesley, Reading, Mass., 1959), p. 894.
20.
A. Jeffrey and T. Taniuti, Nonlinear Wave Propagation with Application to Physics and Magnetohydrodynamics (Academic, New York, 1964).
21.
J.
Von Neumann
and
R. D.
Richtmyer
,
J. Appl. Phys.
21
,
232
(
1952
).
22.
R. D. Richtmyer and K. W. Morton, Difference Methods for Initial Value Problems (Wiley, New York, 1957), Sec. 12, 13.
23.
J. P.
Boris
and
D. L.
Book
,
J. Comput. Phys.
11
,
38
(
1973
).
24.
K.
Papadopoulos
,
C. E.
Wagner
, and
I.
Haber
,
Phys. Rev. Lett.
27
,
986
(
1971
).
25.
D. W.
Forslund
and
C. R.
Shonk
,
Phys. Rev. Lett.
25
,
1699
(
1970
).
26.
D. W.
Forslund
and
J. P.
Freidberg
,
Phys. Rev. Lett.
27
,
1189
(
1971
).
27.
P. H.
Sakanaka
,
Phys. Fluids
14
,
611
(
1971
).
28.
R.
Mason
,
Phys. Fluids
15
,
1082
(
1972
).
29.
W.
Manheimer
and
I.
Haber
,
Phys. Fluids
17
,
706
(
1974
).
30.
J.
Denavit
,
J. Comput. Phys.
9
,
75
(
1972
).
31.
P. C. Liewer, presented at the Seventh Conference on Numerical Simulation of Plasmas, New York City (1975).
This content is only available via PDF.
You do not currently have access to this content.