Numerical Approximation of Convection-Diffusion Problems Through the PSI Method and Characteristics Method

Benítez, Marta; Chacón Rebollo, Tomás; Gómez Mármol, María Macarena; Narbona-Reina, Gladys

doi:https://doi.org/10.1007/978-3-642-19665-2_3

Title

Numerical Approximation of Convection-Diffusion Problems Through the PSI Method and Characteristics Method

Author(s)

Benítez, Marta

Chacón Rebollo, Tomás

Gómez Mármol, María Macarena

Narbona-Reina, Gladys

Date

2011-01-01

Citation

Benítez García, M., Chacón Rebollo, T., Gómez Mármol, M., Narbona-Reina, G. (2011). Numerical Approximation of Convection-Diffusion Problems Through the PSI Method and Characteristics Method. In: C. Clavero, J. Gracia, F. Lisbona (eds.) BAIL 2010 - Boundary and Interior Layers, Computational and Asymptotic Methods. Lecture Notes in Computational Science and Engineering, vol 81. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19665-2_3

Abstract

[Abstract]: In this work we present some numerical methods for solving evolutive convection-diffusion problems. In order to obtain a physically admissible solution we search for monotone and accurate methods that are also non-linear due to the Godunov’s theorem. We will center in Fluctuation Splitting methods, [8], in particular in PSI scheme, and characteristic type methods, where a new Lagrangian method is proposed. Finally, a numerical test is presented to assess the performance of the numerical methods described in the present work.

Keywords

Convection-diffusion equation
Characteristics method
Fluctuation spliting schemes
Galerkin discretization

Description

This version of the chapter has been accepted for publication, after peer review and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/978-3-642-19665-2_3