NON-UNIQUENESS OF RAREFACTION SHOCK WAVES: EFFECT OF VISCOSITY AND DISPERSION
Yu. A. Bondarenko, V. N. Sofronov, V. P. Kopyshev, V. V. Khrustalev
VANT. Ser.: Mat. Mod. Fiz. Proc. 2003. Вып.4. С. 3-12.
A study is made for automodel solutions of Riemann problem for substances with non-convex strictly monotonous equation of state, in which rarefaction shock waves arise at unloading. Available data on rarefaction shock waves properties are based on the assumption that any discontinuous solutions of gas-dynamic equations are to be derived from smooth solutions of gas-dynamic equations with viscosity through limiting passage to an infinitesimal coefficient of viscosity. In this paper for smooth non-convex barotropic equations of state properties of rarefaction shock waves are obtained by analytical study for another method of gas-dynamic equations regularization that is for the one using artificial normal dispersion. The parameters of rarefaction shock waves gained with a method of disappearing normal dispersion are proved to differ from those gained with a method of disappearing viscosity. Analytical data are confirmed by one-dimensional gas-dynamic calculations using differential schemes with controlled dissipation and dispersion. The obtained results enable one to conclude that problem of choosing unique and “proper” rarefaction shock wave in gas-dynamic calculations should be solved at a level with physical models choice and depends on main physical processes, which are to be thrown away when writing equations of ideal gas dynamics.
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