1,610
Views
20
CrossRef citations to date
0
Altmetric
Original Articles

Numerical solution of hyperbolic heat conduction equation

Pages 11-24 | Received 09 Jan 2008, Published online: 14 Oct 2010

References

  • Čiegis , R. , Dementev , A. and Jankevičiūte , G. 2008 . Numerical analysis of hyperbolic two temperature model . Lith. Math. J., , 48 (1) : 46 – 60 . (doi:10.1007/s10986–008–0005–6)
  • Čiegis , R. , Ilgevičius , A. , Liess , H. , Meilūnas , M. and Suboč , O. 2007 . Numerical simulation of the heat conduction in electrical cables . Math. Model. Anal., , 12 (4) : 425 – 439 . (doi:10.3846/1392–6292.2007.12.425–439)
  • Čiegis , R. , Iliev , O. and Lakdawala , Z. 2007 . On parallel numerical algorithms for simulating industrial filtration problems . Computational Methods in Applied Mathematics, , 7 (2) : 118 – 134 .
  • Čiegis , R. , Papastavrou , A. and Zemitis , A. 2000 . Additive splitting methods for elliptic‐parabolic problems . Annalli del Universiteta di Ferrara, Sez. VII, Sc. Mat., , 46 : 291 – 306 .
  • Čiegis , Raim. , Čiegis , Rem. and Zemitis , A. 1999 . “ Parallel numerical methods for the elliptic‐parabolic problem ” . In Progress in Industrial Mathematics at ECMI98 , Edited by: Arkeryd , L. 206 – 213 . Stuttgart, Leipzig : B.G. Teubner .
  • Glass , D.E. , Ozisik , M.N. , McRae , D.S. and Vick , B. 1985 . On the numerical solution of hyperbolic heat conduction . Numerical Heat Transfer, , 8 : 497 – 504 .
  • Haitian , Y. and Qiang , G. 2003 . A precise time stepping scheme to solve hyperbolic and parabolic heat transfer problems with radiative boundary condition . Heat and Mass Transfer, , 39 (7) : 571 – 577 .
  • Larsson , S. and Thomee , V. 2003 . Partial Differential Equations with Numerical Methods. Texts in Applied Mathematics , Springer .
  • LeVeque , R.J. 1991 . Numerical Methods for Conservation Laws , Birkhäuser Verlag .
  • Manzari , Meh.T. and Manzari , Maj.T. 1999 . On numerical solution of hyperbolic heat conduction . Comm. Numer. Methods in Eng., , 15 : 853 – 866 .
  • Mardal , K.A. , Nilssen , T.K. and Staff , G.A. 2007 . Order‐optimal preconditioners for implicit Runge–Kutta schemes applied to parabolic PDEs . SIAM J. Scient. Comput., , 29 (1) : 361 – 375 .
  • Qiu , T.Q. and Tien , C.L. 1993 . Heat transfer mechanisms during short‐pulse laser heating of metals . ASME J. Heat Transfer, , 115 : 835 – 841 .
  • Samarskii , A.A. 2001 . The theory of difference schemes. , New York–Basel : Marcel Dekker, Inc. .
  • Sarra , S.A. 2003 . Spectral methods with postprocessing for numerical hyperbolic heat transfer . Numer. Heat Transfer, Part A, , 43 (7) : 717 – 730 .
  • Shen , W. and Han , S. 2003 . A numerical solution of two–dimensional hyperbolic heat conduction with non‐linear boundary conditions . Heat and Mass Transfer , 39 (5–6) : 499 – 507 .
  • Starikovičius , V. , Čiegis , R. , Iliev , O. and Lakdawala , Z. 2009 . “ A parallel solver for the 3d simulation of flows through oil filters ” . In Parallel Scientific Computing and Optimization. Advances and Applications. Springer Optimization and Its Applications , Edited by: Čiegis , R. volume 27 , 181 – 192 . Springer .
  • Starikovičius , V. , Čiegis , R. and Jakušev , A. 2006 . Analysis of upwind and high‐resolution schemes for solving convection dominated problems in porous media . Math. Model. Anal., , 11 (4) : 447 – 472 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.