An implicit box scheme for subsonic compressible flow with dissipative source term

We investigate the stability and convergence of an implicit box scheme for subsonic flows modelled by scalar conservation laws with dissipative and possibly stiff source terms. The scheme is proposed for solving transient gas flow problems in pipeline networks. Such networks are operated in the subsonic flow region and are characterized by pressure losses due to dissipative friction terms. We verify the properties stated by KruA3/4kov's theorem (KruA3/4kov, Math. USSR-Sb. 10:217-243, 1970) for the approximate solution and prove its convergence to the entropy solution.