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Journal of Scientific Computing

Erschienen in:

05.03.2018

Non-unified Compact Residual-Distribution Methods for Scalar Advection–Diffusion Problems

verfasst von: Vishal Singh, Hossain Chizari, Farzad Ismail, Appendix by Rémi Abgrall

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2018

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Abstract

This paper solves the advection–diffusion equation by treating both advection and diffusion residuals in a separate (non-unified) manner. An alternative residual distribution (RD) method combined with the Galerkin method is proposed to solve the advection–diffusion problem. This Flux-Difference RD method maintains a compact-stencil and the whole process of solving advection–diffusion does not require additional equations to be solved. A general mathematical analysis reveals that the new RD method is linearity preserving on arbitrary grids for the steady-state advection–diffusion equation. The numerical results show that the flux difference RD method preserves second-order accuracy on various unstructured grids including highly randomized anisotropic grids on both the linear and nonlinear scalar advection–diffusion cases.

Vorheriger Artikel WSGD-OSC Scheme for Two-Dimensional Distributed Order Fractional Reaction–Diffusion Equation

Nächster Artikel Discontinuous Galerkin Method with Staggered Hybridization for a Class of Nonlinear Stokes Equations

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Titel: Non-unified Compact Residual-Distribution Methods for Scalar Advection–Diffusion Problems
verfasst von: Vishal Singh
Hossain Chizari
Farzad Ismail
Appendix by Rémi Abgrall
Publikationsdatum: 05.03.2018
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2018
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-018-0674-1

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