On the non-linear Maxwell–Cattaneo equation with non-constant diffusivity: Shock and discontinuity waves
A numerical study on a non-linear hyperbolic diffusion equation is proposed. The Hartree hybrid method combining finite difference techniques with the method of characteristics is used in the presence of discontinuities between initial and boundary conditions. The technique proved to be an useful to...
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| Veröffentlicht in: | International journal of heat and mass transfer 2008-10, Vol.51 (21), p.5327-5332 |
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| container_title | International journal of heat and mass transfer |
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| creator | Reverberi, Andrea Pietro Bagnerini, Patrizia Maga, Luigi Bruzzone, Agostino Giacinto |
| description | A numerical study on a non-linear hyperbolic diffusion equation is proposed. The Hartree hybrid method combining finite difference techniques with the method of characteristics is used in the presence of discontinuities between initial and boundary conditions. The technique proved to be an useful tool to overcome oscillation problems and spurious solutions in case of strong non-linearities related to both attractive or repulsive interactions between diffusing species. Two different expressions for the diffusion coefficient are used in order to compare our results with the ones obtained in previous studies relying upon the Laplace transform technique and the MacCormack predictor–corrector method. Finally, an analytic approach based on the singular surface theory is proposed to motivate the numerical results and to clarify some controversial aspects concerning the penetration depth of a diffusive front in the presence of interactions. |
| doi_str_mv | 10.1016/j.ijheatmasstransfer.2008.01.039 |
| format | Article |
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| source | Elsevier ScienceDirect Journals Complete |
| subjects | Boson degeneracy and superfluidity of 4he Condensed matter: structure, mechanical and thermal properties Exact sciences and technology Finite-differences Fundamental areas of phenomenology (including applications) Heat conduction Heat transfer Hyperbolic partial differential equations Non-Fickian diffusion Non-Fourier heat conduction Physics Quantum fluids and solids liquid and solid helium Transport processes, second and other sounds, and thermal counterflow kapitza resistance |
| title | On the non-linear Maxwell–Cattaneo equation with non-constant diffusivity: Shock and discontinuity waves |
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