The equations of hydrodynamics are modified by the inclusion of additional terms which greatly simplify the procedures needed for stepwise numerical solution of the equations in problems involving shocks. The quantitative influence of these terms can be made as small as one wishes by choice of a sufficiently fine mesh for the numerical integrations. A set of difference equations suitable for the numerical work is given, and the condition that must be satisfied to insure their stabilty is derived.
REFERENCES
1.
and
G. I.
Taylor
(Proc. Roy. Soc.
A84
, 371
(1910
)) showed, on the basis of general thermodynamical considerations, that dissipation is necessarily present in shock waves.Later,
R.
Becker
(Zeits. f. Physik
8
, 321
(1922
)) gave a detailed discussion of the effects of heat conduction and viscosity.Recently,
L. H.
Thomas
(J. Chem. Phys.
12
, 449
(1944
)) has investigated these effects further in terms of the kinetic theory of gases.2.
Courant
, Friedrichs
, and Lewy
, Math. Ann.
100
, 32
(1928
). It is in this important paper that these authors first published their discovery of the conditional stability of the difference‐equation integration method for partial differential equations.
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© 1950 The American Institute of Physics.
1950
The American Institute of Physics
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