Abstract
Recently a numerical method suitable for dealing with hyperbolic systems of conservation laws also in the presence of source terms, both in stiff and non-stiff case, has been developed (Liotta et al., 1999a, b). Here we use such a scheme for getting numerical solutions of the shock structure problem for the model of a radiating gas described by a variable Eddington factor (Anile et al., 1991, 1992; Kremer and Müller, 1992) in the framework of extended thermodynamics.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alí, G. and Romano, V. 1994. Jump conditions for a radiating relativistic gas. J. Math. Phys., 35, 2878–2901.
Anile, A. M., Nikiforakis, N. and Pidatella, R. M. 1999. Assessment of a high resolution centered scheme for the solution of hydrodynamical semiconductor equations. Preprint.
Anile, A. M., Pennisi, S. and Sammartino, M. 1991. A thermodynamical approach to Eddington factors. J. Math. Phys., 32, 544–550.
Anile, A.M., Pennisi, S. and Sammartino, M. 1992. Covariant radiation hydrodynamics. Ann. Inst. H. Poincaré, 56, 49–74.
R. E. Caflish, R. E., Jin, S. and Russo, G. 1997. Uniformly accurate schemes for hyperbolic systems with relaxation. SIAM J. Num. Analysis, 34, 246–281.
Jeffrey, A. 1976. Quasilinear hyperbolic systems and wave. Pitman, New York.
Jou, D., Casas-Vazquez, J. and Lebon, G. 1993. Extended irreversible thermodynamics. Springer, Berlin.
Kremer, G. M. and Müller, I. 1992. Radiation thermodynamics. J. Math. Phys., 33, 2265–2268.
Leveque, R. J. 1992. Numerical methods for conservation laws. Lectures in Mathematics. Birkhäuser Verlag, Zürich ETH.
Levermore, C. D. 1984. Relating Eddington factors to flux limiters. J. Quant. Spectrosc. Radiat. Transfer, 31, 149–160.
Liotta, S. F., Romano, V. and Russo, G. 1999a. Central schemes for systems of balance laws. International Series of Numerical Mathematics, 130, 651–660.
Liotta, S. F., Romano, V. and Russo, G. 1999b. Central schemes for balance laws of relaxation type. To appear in SIAM J. Numerical Analysis.
Liu, T. P. 1987. Hyperbolic conservation laws with relaxation. Comm. Math. Phys., 108, 153–175.
Mascali, G. and Romano, V. 1997. Maximum entropy principle in relativistic radiation hydrodynamics. Ann. Inst. H. Poincaré, 67, 123–144.
Mihalas, D. and Mihalas, B. W. 1984. Foundations of radiation hydrodynamics. Oxford University Press, New York.
Müller, I. and Ruggeri, T. 1998. Rational extended thermodynamics. Springer, Berlin.
Nessyahu, H. and Tadmor, E. 1990. Non-oscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys., 87, 408–448.
Romano, V. and Alí, G. 1993. Shock Structure for a Radiating Gas. Series on Advances in Mathematics for Applied Sciences, 23, 301–307.
Struchtrup, H. 1997. An extended moment method in radiative transfer: The matrices of mean absorption and scattering coefficients. Ann. of Physics, 257, 111–135.
Toro, E. F. 1997. Riemann solvers and numerical methods for fluid dynamics. Springer, Berlin.
Whitam, G. B. 1974. Linear and nonlinear waves. Wiley, New York.
Zel’dovic, Y. B. and Raizer, Y. P. 1967. Physics of shock wave and high-temperature hydrodynamic phenomena. Academic Press, New York.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Anile, A.M., Romano, V. (2001). Numerical Investigation of Shock Waves in a Radiating Gas Described by a Variable Eddington Factor. In: Straughan, B., Greve, R., Ehrentraut, H., Wang, Y. (eds) Continuum Mechanics and Applications in Geophysics and the Environment. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04439-1_1
Download citation
DOI: https://doi.org/10.1007/978-3-662-04439-1_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07500-1
Online ISBN: 978-3-662-04439-1
eBook Packages: Springer Book Archive