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Multidimensional upwinding. I: The method of transport for solving the Euler equations. (English) Zbl 0932.76050
Summary: We present a new discretization of muldidimensional conservation laws. The idea of transport associated with the solution of a scalar equation is used for the convective part of the compressible Euler equations. Then we derive a multidimensional wave structure to model the acoustic part of this nonlinear system, that allows infinitely many propagation directions in the numerical method. This provides the basic knowledge to construct a numerical method that does not rely on Riemann solvers. A more general definition of the waves, together with the concept of consistency, enables the design of effective multidimensional methods. \(\copyright\) Academic Press.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
Software:
CLAWPACK
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