Parallel Algorithms for Nonlinear Diffusion by Using Relaxation Approximation

Fausto Cavalli (), Giovanni Naldi () and Matteo Semplice ()
Additional contact information
Fausto Cavalli: University of Milano, Department of Mathematics
Giovanni Naldi: University of Milano, Department of Mathematics
Matteo Semplice: University of Milano, Department of Mathematics

A chapter in Numerical Mathematics and Advanced Applications, 2006, pp 404-411 from Springer

Abstract: Abstract It has been shown that the equation of diffusion, linear and nonlinear, can be obtained in a suitable scaling limit by a two-velocity model of the Boltzmann equation [7] . Several numerical approximations were introduced in order to discretize the corresponding multiscale hyperbolic systems [8, 1, 4]. In the present work we consider relaxed approximations for multiscale kinetic systems with asymptotic state represented by nonlinear diffusion equations. The schemes are based on a relaxation approximation that permits to reduce the second order diffusion equations to first order semi-linear hyperbolic systems with stiff terms. The numerical passage from the relaxation system to the nonlinear diffusion equation is realized by using semi-implicit time discretization combined with ENO schemes and central differences in space. Finally, parallel algorithms are developed and their performance evaluated. Application to porous media equations in one and two space dimensions are presented.

Keywords: Parallel Algorithm; Hyperbolic System; Porous Media Equation; Nonlinear Diffusion Equation; Relaxation System (search for similar items in EconPapers)
Date: 2006
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-34288-5_35

Ordering information: This item can be ordered from
http://www.springer.com/9783540342885

DOI: 10.1007/978-3-540-34288-5_35

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().