Abstract
A dynamic adaptation method is applied to gas dynamics problems with nonlinear heat conduction. The adaptation function is determined by the condition that the energy equation is quasi-stationary and the grid point distribution is quasi-uniform. The dynamic adaptation method with the adaptation function thus determined and a front-tracking technique are used to solve the model problem of a piston moving in a heat-conducting gas. It is shown that the results significantly depend on the thermal conductivity chosen. The numerical results obtained on a 40-node grid are compared with self-similar solutions to this problem.
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References
Ya. B. Zel’dovich and A. S. Kompaneets, “On the Theory of Heat Transfer with a Temperature-Dependent Heat Conductivity,” in Collected Works Dedicated to Academician A.F. Ioffe on the Occasion of His 70th Birthday (Akad. Nauk SSSR, Moscow, 1950), pp. 61–71 [in Russian].
G. I. Barenblatt and I. M. Vishik, “On the Finite Velocity of Propagation in Unsteady Fluid Flows through Porous,” Prikl. Mat. Mekh. 20, 411–417 (1956).
A. A. Samarskii and I. M. Sobol’, “Examples of Numerical Computation of Heat Waves,” Zh. Vychisl. Mat. Mat. Fiz. 3, 703–719 (1963).
P. P. Volosevich, S. P. Kurdyumov, L. N. Busurina, and V. P. Krus, “Solution of the One-Dimensional Plane Problem of Piston Motion in a Heat-Conducting Gas,” Zh. Vychisl. Mat. Mat. Fiz. 3, 159–169 (1963).
A. A. Samarskii, S. P. Kurdyumov, and P. P. Volosevich, “Traveling Waves in a Medium with Nonlinear Conductivity,” Zh. Vychisl. Mat. Mat. Fiz. 5, 199–217 (1965).
P. P. Volosevich, S. P. Kurdyumov, and E. I. Levanov, “Various Heating Regimes in the Interaction of Intense Radiation Fluxes with Matter,” Prikl. Mekh. Tekh. Fiz., No. 5, 41–48 (1972).
V. P. Korobeinikov, “Propagation of a Strong Spherical Detonation Wave in a Heat-Conducting Gas,” Dokl. Akad. Nauk SSSR 113, 1006–1009 (1954).
P. P. Volosevich and E. I. Levanov, Self-Similar Solutions of Problems in Gas Dynamics and Hear Transfer (MFTI, Moscow, 1997) [in Russian].
R. Marshak, “An Influence of the Radiation on the Behavior of the Shock Waves,” Phys. Fluids, No. 1, 24–29 (1958).
P. V. Breslavskii and V. I. Mazhukin, “Dynamically Adapted Grids for Interacting Discontinuous Solutions,” Zh. Vychisl. Mat. Mat. Fiz. 47, 717–737 (2007) [Comput. Math. Math. Phys. 47, 687–706 (2007)].
P. V. Breslavsky and V. I. Mazhukin, “Simulation of Interacting Discontinuous Solutions on Dynamically Adaptive Grids,” Comput. Methods Appl. Math. 7(2), 103–117 (2007).
A. V. Mazhukin and V. I. Mazhukin, “Dynamic Adaptation for Parabolic Equations,” Zh. Vychisl. Mat. Mat. Fiz. 47, 1911–2034 (2007) [Comput. Math. Math. Phys. 47, 1833–1855 (2007)].
P. V. Breslavskii and V. I. Mazhukin, “Dynamic Adaptation Method in Gas Dynamics Simulations,” Mat. Model. 7(12), 48–78 (1995).
V. I. Mazhukin, A. A. Samarskii, and A. V. Shapranov, “Dynamic Adaptation Method in the Burgers Problem,” Dokl. Akad. Nauk 333, 165–169 (1993).
L. I. Sedov, Similarity and Dimensional Methods in Mechanics (Academic, New York, 1959; Nauka, Moscow, 1987).
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Original Russian Text © P.V. Breslavskii, V.I. Mazhukin, 2008, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2008, Vol. 48, No. 11, pp. 2067–2080.
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Breslavskii, P.V., Mazhukin, V.I. Dynamic adaptation method in gasdynamic simulations with nonlinear heat conduction. Comput. Math. and Math. Phys. 48, 2102–2115 (2008). https://doi.org/10.1134/S0965542508110158
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DOI: https://doi.org/10.1134/S0965542508110158