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Balancing characteristic schemes on piece-wise constant initial data. Jumping transfer. (Russian. English summary) Zbl 1129.76343

The problem of an accurate calculation of a grid value transfer on Euler nets is still one of the most important problems of the numerical hydrodynamics. The main difficulties are connected with phenomenon display on a simple linear transfer equation with constant coefficients of the form \[ \frac{\partial \varphi}{\partial t} + c \frac{\partial \varphi}{\partial x} = 0, \quad c = const >0. \tag{(1)} \] The approximation of the Eq.(1) by linear homogeneous difference schemes on regular grids the so called phase and amplitude errors are arising . It is shown that balancing characteristic approaches to construction of numerical algorithms for the hyperbolic conservation laws gives an exact solution of the simplest convection transfer problem on a set of piece-wise constant initial functions.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76R50 Diffusion
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