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A “box-scheme” for the Euler equations. (English) Zbl 0626.65088
Nonlinear hyperbolic problems, Proc. Adv. Res. Workshop, St. Etienne/France 1986, Lect. Notes Math. 1270, 82-102 (1987).
[For the entire collection see Zbl 0623.00008.]
For the solution of first order partial differential equations with boundary conditions a box scheme is introduced based on a compact discretization in space and the use of the characteristic directions for the integration in time. The scheme is first developed for a non-linear scalar conservation law. Then it is presented for the equations of gas dynamics in a domain of varying area. Applications to the shock tube and to a steady flow in a nozzle exhibit the major features of the scheme. Preliminary results in two-dimensions seem to indicate that the extension is worthy of interest.

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
76N15 Gas dynamics, general