The Locally Conservative Galerkin (LCG) Method — a Discontinuous Methodology Applied to a Continuous Framework
Year: 2009
Author: Rhodri L. T. Bevan, Raoul vanLoon, Perumal Nithiarasu
Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 3 : pp. 319–340
Abstract
This paper presents a comprehensive overview of the element-wise locally conservative Galerkin (LCG) method. The LCG method was developed to find a method that had the advantages of the discontinuous Galerkin methods, without the large computational and memory requirements. The initial application of the method is discussed, to the simple scalar transient convection-diffusion equation, along with its extension to the Navier-Stokes equations utilising the Characteristic Based Split (CBS) scheme. The element-by-element solution approach removes the standard finite element assembly necessity, with an face flux providing continuity between these elemental subdomains. This face flux provides explicit local conservation and can be determined via a simple small post-processing calculation. The LCG method obtains a unique solution from the elemental contributions through the use of simple averaging. It is shown within this paper that the LCG method provides equivalent solutions to the continuous (global) Galerkin method for both steady state and transient solutions. Several numerical examples are provided to demonstrate the abilities of the LCG method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-AAMM-8372
Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 3 : pp. 319–340
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Explicit local flux conservation element-by-element solution local conservation LCG convection-diffusion CBS artificial compressibility incompressible flow.