Geodesic
Mathematical modelling of influence of circuit viscosity of numerical methods on a value of the impulse transferred by shock waves
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 2, pp. 29-36

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The analysis of influence of width of the front of a shock wave to the size of the impulse transferred by a motionless firm surface is provided in this work. The profile of a shock wave has been calculated by the modified method of large particles which allows to carry out calculations of distribution of shock waves without obvious introduction of artificial viscosity. It is shown that the width of the "smeared" front of a shock wave calculated by the modified method of large particles doesn't depend on intensity of the shock wave. The similar picture is observed if in numerical methods for calculation of behavior of shock waves square artificial viscosity is used in an explicit form. For carrying out serial calculations for research of transfer of an impulse of shock waves to a firm motionless wall, in this work the analytical solution for pressure profile in shock transition in case of square artificial viscosity in Euler's variables is received. For a shock wave with a triangular profile it has been shown that the size of the impulse transferred to a firm wall doesn't depend on the width of the shock transition.
Keywords: numerical method; mathematical model; conservation laws; shock waves; Courant's number. 
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     author = {Yu. M. Kovalev and E. E. Pigasov},
     title = {Mathematical modelling of influence of circuit viscosity of numerical methods on a value of the impulse transferred by shock waves},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {29--36},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2016_9_2_a2/}
}
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Yu. M. Kovalev; E. E. Pigasov. Mathematical modelling of influence of circuit viscosity of numerical methods on a value of the impulse transferred by shock waves. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 2, pp. 29-36. http://geodesic.mathdoc.fr/item/VYURU_2016_9_2_a2/