101
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

The mathematical simulation of the liquid transport in a multilayered nonwoven

&
Pages 9-34 | Published online: 14 Oct 2010

References

  • Alt , H.W. and Luckhaus , S. 1983 . Quasilinear Elliptic‐Parabolic Differential Equations . Math. Z. , 183 : 311 – 341 .
  • Barenblatt , G.I. 1952 . On certain non‐stationary motions of liquid and gases in porous media . Prikl. Mat. Mech. , 16 : 67 – 78 .
  • Berger , A.E. , Brezis , H. and Rogers , J. 1979 . A numerical method for solving the problem u t – ?f(μ) = . RAIRO Numer. Anal. , 13 : 297 – 312 .
  • Ciegis , R. 1986 . Accuracy of difference schemes for quasilinear parabolic problems . Lith. Math. J. , 26 : 88 – 93 .
  • Ciegis , Raim. , Ciegis , Rem. and Meilunas , M. 1996 . On one general method for the investigation of difference schemes . Lith. Math. J. , 36 : 281 – 302 .
  • Ciegis , R. , Simkevicius , J. and Wasniewski , J. 1996 . Running finite difference schemes for 3D diffusion problems on parallel computers with distributed memory . Informatica , 7 : 295 – 310 .
  • Demmel , J.W. , Heath , M.T. , van , H.A. and Vorst , der . 1993 . Parallel numerical linear algebra . Acta Numerica , 7 : 111 – 197 .
  • Freeman , T.L. and Phillips , C. 1991 . Parallel Numerical Algorithms , New York, London, Toronto, Sydney, Tokyo, Singapore : Prentice Hall .
  • Geist , A. , Beguelin , A. , Dongarra , J. , Jiang , W. , Manchek , R. and Sunderam , V. 1993 . PVM 3.0 User's Guide and Reference Manual , Tennessee .
  • Gilbert , J. and Schreiber , R. 1991 . Optimal data placement for distributed memory architectures . In Parallel Processing for Scientific Computing, SIAM , Mach : 462 – 471 .
  • Golub , G.H. and Loan , Ch. F. Van . 1991 . Matrix Computations , Baltimore and London : The Johns Hopkins University Press .
  • Gropp , W. , Lusk , E. and Skjellum , A. 1994 . Using MPI: Portable Parallel Programming with the Message‐Passing Interface , Cambridge, Massachusetts, London, England : The MIT Press .
  • Jager , W. and Kacur , J. 1991 . Solution of porous medium type systems by linear approximation schemes . Numer. Math. , 60 : 407 – 427 .
  • Jerome , J.W. and Rose , M. 1982 . Error estimates for the multidimensional two‐phase Stefan problem . Math. Comp. , 39 : 489 – 514 .
  • Johnson , C. , Rannacher , R. and Boman , M. 1995 . Numeric and hydrodynamic stability: toward error control in computational fluid dynamics . SIAM J. Numer. Anal. , 32 : 1058 – 1079 .
  • Johnson , S.L. , Saad , Y. and Schultz , M.H. 1987 . Alternating direction methods on multiprocessors . SIAM J. Sci. Stat. Comput. , 8 : 686 – 700 .
  • Kacur , J. , Handlovicova , A. and Kacurova , M. 1993 . Solution of nonlinear diffusion problems by linear approximation schemes . SIAM J. Numer. Anal. , 30 : 1703 – 1722 .
  • Lions , J.L. 1988 . Quelques Methods de Resolution des Problems aux Limites non Lineaires , Paris : Dunod .
  • Marchouk , G.I. 1988 . Splitting Methods Nauka, Moscow (in Russian)
  • Mehrotra , P. , Saltz , J. and Voigt , R. , eds. 1992 . Unstructured Scientific Computation on Scalable Multiprocessors , MIT Press .
  • Nochetto , R.H. 1986 . A note on the approximation of free boundaries by finite element methods . RAIRO Model. Math. Anal. Numer. , 20 : 355 – 368 .
  • Nochetto , R.H. 1987 . Error estimates for multidimensional singular parabolic problems . Japan J. Appl. Math. , 4 : 111 – 138 .
  • Nochetto , R.H. and Verdi , C. 1988 . Approximation of degenerate parabolic problems using numerical integration . SIAM J. Numer. Anal. , 25 : 784 – 814 .
  • Ortega , J.M. 1988 . Introduction to Parallel and Vector Solution of Linear Systems , New York and London : Plenum Press .
  • Rose , M.E. 1983 . Numerical methods for flows through porous media, I . Math. of Comput. , 40 : 435 – 467 .
  • Rose , M.E. 1980 . Numerical methods for flows through porous media, II . Comput. Math. Appl. , 20 : 99 – 122 .
  • Samarskij , A. 1984 . Theorie der Differenzenverfahren , Leipzig : Geest and Portig .
  • Socolovsky , E.A. 1986 . Difference schemes for degenerate parabolic equations . Math. Comput. , 47 : 411 – 420 .
  • Thomas , J.W. 1995 . Numerical Partial Differential Equations: Finite Difference Methods , 88 – 93 . New York, Berlin, Heidelberg : Springer‐Verlag .
  • White , R.E. 1982 . An enthalpy formulation of the Stefan problem . SIAM J. Numer. Anal. , 19 : 1129 – 1157 .
  • Zlamal , M. 1980 . A finite element solution of the nonlinear heat equation . RAIRO Numer. Anal. , 14 : 203 – 216 .

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.