A “box-scheme” for the euler equations

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 developped 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.

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