Choice of measure source terms in interface coupling for a model problem in gas dynamics (Q2814442)

Two one-dimensional Euler type equations are considered in two domains separated by a spatial interface located at \(x=0\). The pressures verify two different state relations. The equations are coupled by a Dirac measure concentrated on \(x=0\), considered as a source term. The coupling condition (2.7) relating the discontinuous flux-functions is imposed. A relaxation approach is used for numerical solution, involving the Godunov method and a quasilinear system, whose solution tends to the solution of the initial system when the relaxation parameter is large enough. An approximate Riemann solver is proposed and numerical experiments are performed, in constrained optimization problems related with the source term. The paper is an improvement of the result given in [\textit{A. Ambroso} et al., ESAIM, Math. Model. Numer. Anal. 43, No. 6, 1063--1097 (2009; Zbl 1422.76178)], available on Google, where the source term was zero.