On the boundary treatment in spectral methods for hyperbolic systems
Motivated by gas pipeline problems (under slowly varying conditions, without shocks), the authors consider the correct approximation of boundary conditions in spectral methods with Chebyshev collocation and implicit time stepping. Converting a special linear hyperbolic system to characteristic variables, discretizing and taking into account there the outgoing resp. incoming characteristics and converting back to physical variables, they obtain a stable discretization. It turns out that the correct conditions contain the prescribed conditions in linear combination with the collocated differential equations. This approach is used in connection with the schemes of \textit{R. M. Beam} and \textit{R. F. Warming} [ibid. 22, 87-110 (1976; Zbl 0336.76021)] and of \textit{A. Lerat} [C. R. Acad. Sci., Paris, Sér. A 288, 1033-1036 (1979; Zbl 0439.65075)] for nonlinear equations. Computational results are presented for a gas flow problem of industrial relevance. Here the implicit method admits great time steps and gives satisfactory accuracy in less CPU time than an explicit method.
simulation of slow transients in gas transportation networks
scientific article; zbMATH DE number 4018322