Non-unified compact residual-distribution methods for scalar advection–diffusion Problems

Singh, Vishal, Chizari, Hossain ORCID: https://orcid.org/0000-0002-6630-1880 and Ismail, Farzad 2018. Non-unified compact residual-distribution methods for scalar advection–diffusion Problems. Journal of Scientific Computing 76 (3) , pp. 1521-1546. 10.1007/s10915-018-0674-1

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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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Engineering
Publisher:	Springer Verlag
ISSN:	0885-7474
Date of Acceptance:	14 February 2018
Last Modified:	05 Nov 2022 02:42
URI:	https://orca.cardiff.ac.uk/id/eprint/135210

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