Geodesic
The space discretization of the one-dimensional barotropic quasi-gas dynamic system of equations and the energy balance equation
Matematičeskoe modelirovanie, Tome 24 (2012) no. 10, pp. 51-64.

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For the barotropic quasi-gas dynamic system of equations, the law of non-increasing total energy is valid. But even in the spatially one-dimensional case, for its standard discretizations the validity of this law cannot be provided since there appear mesh disbalance terms. We propose a new conservative symmetric in space discretization of this system, for which the energy balance equation of the proper form is derived and non-increasing of the total energy is guaranteed (that takes place even in the presence of the potential mass force). Important elements of the method are non-standard space average of the density depending on the state function and discretization of the derivative of this function. The results are valid for any non-uniform mesh. As an important special case, the results are valid for a regularized (quasi-gas dynamic) system of shallow water equations in the general case of non-flat bottom; moreover, here the non-standard discretizations become standard ones but the method is still new. It is the well-balanced in a sense.
Keywords: gas dynamics, shallow water equations, space discretization, energy balance law.
Mots-clés : quasi-gasdynamic system of equations 
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A. A. Zlotnik. The space discretization of the one-dimensional barotropic quasi-gas dynamic system of equations and the energy balance equation. Matematičeskoe modelirovanie, Tome 24 (2012) no. 10, pp. 51-64. http://geodesic.mathdoc.fr/item/MM_2012_24_10_a4/

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