Lie-group theoretic method for analyzing interaction of discontinuous waves in a relaxing gas
The essence of this paper is the calculation of the conditions under which a system of partial differential equations describing the flow of an inviscid relaxing gas possesses Lie point symmetries, the determination of corresponding similarity solutions and the examination of the relationships between the parameters in the solutions. This is used in particular to study the effects of the ratio of specific heats and the ambient density on the similarity variable and the relaxation time in the context of the interaction of a weak discontinuity and a strong shock. This strikes me as a rather novel idea. It is not claimed that the similarity solution represents the real solution, but it does enable one to make the comparison under what might be termed ideal conditions. It is a pity that this idea had to be expressed in the context of a rather complex problem -- even though the flow depends upon only one space variable -- and it would be interesting to see a similar analysis performed on a simpler system for which it would be conveniently possible to make a study of the results obtained by using the similarity solution compared with an exact solution, probably obtained by numerical means.
scientific article; zbMATH DE number 5164773