Abstract
We suggest an original scheme and an algorithm for the numerical solution of the Euler equations of gas dynamics. The construction of the scheme is based on the mass, momentum, and energy conservation laws. The flux computation is carried out by summation of elementary fluxes formed by small-amplitude running waves that satisfy the linearized equations of gas dynamics. The scheme contains no artificial regularizers, has second-order accuracy on smooth solutions, and is quasimonotone in a neighborhood of the discontinuities. Examples of one- and two-dimensional computations are given.
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