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.


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


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