124
A. G. Aksenov
9.5 Conclusions
The proposed approximate Riemann problem solver yields the qualitatively and also
quantitatively good results despite the assumption for the entropy jump smallness
used in computation of the dimensionless coefficients of the gases. It is shown that
the steady solution with the fine structure (~1 mm) of the strong SW in hydrogen
plasma with Mach number M = 16 is quasi-stationary on the distance ~50 cm during
the time scale ~10
−5 s. To prove this result, it was necessary to introduce the radiation
component of the plasma, and thus, it was necessary to transfer from the ideal gas
low to a general equation of state.
Acknowledgements We are grateful to the referees for their careful reading of the manuscript,
valuable suggestions, and remarks.
References
1. Basko, M.M., Churazov, M.D., Aksenov, A.G.: Prospects of heavy ion fusion in cylindrical
geometry. Laser Part. Beams 20, 411–414 (2002)
2. Anisimov, S.I., Zhakhovski˘ ı, V.V., Inogamov, N.A., Nishihara, K., Petrov, Y.V., Khokhlov,
V.A.: Ablated matter expansion and crater formation under the action of ultrashort laser pulse.
JETP 103, 183–197 (2006)
3. Fortov, V.E., Hoffmann, D.H., Sharkov, B.Y.: Reviews of topical problems: intense ion beams
for generating extreme states of matter. Phys. Uspekhi 51, 109–131 (2008) (in Russian)
4. Bruenn, S.W.: Stellar core collapse—numerical model and in fall epoch. ApSS 58, 771–841
(1985)
5. Pelanti, M., Shyue, K.-M.: A mixture-energy-consistent six-equation two-phase numerical
model for fluids with interfaces, cavitation and evaporation waves. J. Comput. Phys. 259,
331–357 (2014)
6. Zhukov, V.T., Zabrodin, A.V., Feodoritova, O.B.: A method for solving two-dimensional equations of heat-conducting gas dynamics in domains of complex configurations. J. Comput. Math.
Math. Phys. 33, 1240–1250 (1993) (in Russian)
7. Miller, G.H., Puckett, E.G.: A high-order Godunov method for multiple condensed phases. J.
Comput. Phys. 128, 134–164 (1996)
8. Dolence, J.C., Burrows, A., Zhang, W.: Two-dimensional core-collapse supernova models with
multi-dimensional transport. Astrophys. J. 800(10), 1–14 (2015)
9. Aksenov, A.G.: Computation of shock waves in plasma. J. Comput. Math. Math. Phys. 55,
1752–1769 (2015)
10. Vereshchagin, G.V., Aksenov, A.G.: Relativistic Kinetic Theory with Applications in Astrophysics and Cosmology. Cambridge University Press, Cambridge (2017)
11. Aksenov, A.G., Chechetkin, V.M., Tishkin, V.F.: Godunov type method and the Shafranov’s
task for multi-temperature plasma. Math. Models Comput. Simul. 11, 360–373 (2019)
12. Colella, P., Woodward, P.R.: The piecewise parabolic method (PPM) for gas dynamical
simulations. J. Comput. Phys. 54, 174–201 (1984)
13. Aksenov, A.G., Churazov, M.D.: Deuterium targets and the MDMT code. Laser Part. Beams
21, 81–84 (2003)
14. Aksenov, A.G., Chechetkin, V.M.: Supernova explosion mechanism with the neutrinos and the
collapse of the rotation core. Astron. Rep. 62, 834–839 (2018)
A. G. Aksenov
9.5 Conclusions
The proposed approximate Riemann problem solver yields the qualitatively and also
quantitatively good results despite the assumption for the entropy jump smallness
used in computation of the dimensionless coefficients of the gases. It is shown that
the steady solution with the fine structure (~1 mm) of the strong SW in hydrogen
plasma with Mach number M = 16 is quasi-stationary on the distance ~50 cm during
the time scale ~10
−5 s. To prove this result, it was necessary to introduce the radiation
component of the plasma, and thus, it was necessary to transfer from the ideal gas
low to a general equation of state.
Acknowledgements We are grateful to the referees for their careful reading of the manuscript,
valuable suggestions, and remarks.
References
1. Basko, M.M., Churazov, M.D., Aksenov, A.G.: Prospects of heavy ion fusion in cylindrical
geometry. Laser Part. Beams 20, 411–414 (2002)
2. Anisimov, S.I., Zhakhovski˘ ı, V.V., Inogamov, N.A., Nishihara, K., Petrov, Y.V., Khokhlov,
V.A.: Ablated matter expansion and crater formation under the action of ultrashort laser pulse.
JETP 103, 183–197 (2006)
3. Fortov, V.E., Hoffmann, D.H., Sharkov, B.Y.: Reviews of topical problems: intense ion beams
for generating extreme states of matter. Phys. Uspekhi 51, 109–131 (2008) (in Russian)
4. Bruenn, S.W.: Stellar core collapse—numerical model and in fall epoch. ApSS 58, 771–841
(1985)
5. Pelanti, M., Shyue, K.-M.: A mixture-energy-consistent six-equation two-phase numerical
model for fluids with interfaces, cavitation and evaporation waves. J. Comput. Phys. 259,
331–357 (2014)
6. Zhukov, V.T., Zabrodin, A.V., Feodoritova, O.B.: A method for solving two-dimensional equations of heat-conducting gas dynamics in domains of complex configurations. J. Comput. Math.
Math. Phys. 33, 1240–1250 (1993) (in Russian)
7. Miller, G.H., Puckett, E.G.: A high-order Godunov method for multiple condensed phases. J.
Comput. Phys. 128, 134–164 (1996)
8. Dolence, J.C., Burrows, A., Zhang, W.: Two-dimensional core-collapse supernova models with
multi-dimensional transport. Astrophys. J. 800(10), 1–14 (2015)
9. Aksenov, A.G.: Computation of shock waves in plasma. J. Comput. Math. Math. Phys. 55,
1752–1769 (2015)
10. Vereshchagin, G.V., Aksenov, A.G.: Relativistic Kinetic Theory with Applications in Astrophysics and Cosmology. Cambridge University Press, Cambridge (2017)
11. Aksenov, A.G., Chechetkin, V.M., Tishkin, V.F.: Godunov type method and the Shafranov’s
task for multi-temperature plasma. Math. Models Comput. Simul. 11, 360–373 (2019)
12. Colella, P., Woodward, P.R.: The piecewise parabolic method (PPM) for gas dynamical
simulations. J. Comput. Phys. 54, 174–201 (1984)
13. Aksenov, A.G., Churazov, M.D.: Deuterium targets and the MDMT code. Laser Part. Beams
21, 81–84 (2003)
14. Aksenov, A.G., Chechetkin, V.M.: Supernova explosion mechanism with the neutrinos and the
collapse of the rotation core. Astron. Rep. 62, 834–839 (2018)