The generalized problem of breakup of an arbitrary discontinuity

Abstract The problem of breakup of an arbitrary discontinuity in a gas (the Riemann problem) is generalized to the case when an arbitrary, in general space-variable, distribution of the gas-dynamic parameters is given on both sides of the discontinuity at the initial instant of time (the generalized Riemann problem /1/). The solvability of this, in general non-selfsimilar, model is proved and analytical formulas are found for its solution in a small neighbourhood of the points of discontinuity in the x , t plane, where x is the space coordinate and t is the time. A complete analysis of the selfsimilar Riemann problem was developed by Kochin /2/. The generalized Riemann problem is in general non-selfsimilar and does not admit of a simple analytical solution over the entire x , t plane. However, some analytical solutions may be obtained for this problem. Thus, for a linear initial distribution, analytical formulas were obtained in /1/ for the values of the derivatives of the gas-dynamic parameters along the contact discontinuity for t = 0.