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PROPOSAL AND ANALYSIS OF A NEW NUMERICAT, METHOD 
FOR THE TREATMENT OF HYDRODYNAMICAL SHOCK PROBLEMS 
Summary 
A. The differential eenieeloats of (compressible, non-viscous, non- 
conductive) hydrodynamics are of a not too complicated type as long as the 
motion is continuous and isentropic. It is knovm, however, that almost all 
hydrodynamical setups cause a development of discontinuities, so-called 
shocks, sooner or later. These shocks almost never remain "straight", and 
as soon as they are "curved" or intersect each other, isentropy ceases. The 
mathematical problem then becomes one of a most unusual and altogether in- 
tractable type: A differential equation in a domain with an unknown, "free", 
boundary along which "supernumerary" boundary conditions hold, and in many 
cases the coefficients of the differential equation will themselves depend on 
the (unknown) boundary. 
A rigorous treatment of such a problem is only possible in a few 
exceptional cases. The direct computational procedures for its treatment 
are very complicated and lengthy. 
B This report suggests a computational treatment which corres- 
ponds to the original differential equations, completely ignoring the possi- 
bility of shocks. Arguments are brought forth to support the view that this 
computational treatment will always produce (arbitrarily) good approximations 
of the rigorous theory which allows for shocks. That is, even when shocks 
are formed, and the motion ceases to be isentropic. 
It is shown that the suggested treatment corresponds to a return 
from the continuum (hydrodynamical) theory to a kinetic (molecular) theory, 
using, however, a very simplified quasi-molecular model. The essential sim- 
