No Cover Image

Journal article 378 views 48 downloads

Novel semi-implicit, locally conservative Galerkin (SILCG) methods: Application to blood flow in a systemic circulation / Hayder Hasan; Alberto Coccarelli; Perumal Nithiarasu

Computer Methods in Applied Mechanics and Engineering, Volume: 332, Pages: 217 - 233

Swansea University Authors: Hayder, Hasan, Alberto, Coccarelli, Perumal, Nithiarasu

  • hasan2017v2.pdf

    PDF | Accepted Manuscript

    Released with a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND).

    Download (9.92MB)

Abstract

Three novel, locally conservative Galerkin (LCG) methods in their semi-implicit form are proposed for 1D blood flow modelling in arterial networks. These semi-implicit discretizations are: the second order Taylor expansion (SILCG-TE) method, the streamline upwind Petrov–Galerkin (SILCG-SUPG) procedu...

Full description

Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Published: Elsevier BV 2018
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa37572
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract: Three novel, locally conservative Galerkin (LCG) methods in their semi-implicit form are proposed for 1D blood flow modelling in arterial networks. These semi-implicit discretizations are: the second order Taylor expansion (SILCG-TE) method, the streamline upwind Petrov–Galerkin (SILCG-SUPG) procedure and the forward in time and central in space (SILCG-FTCS) method. In the LCG method, enforcement of the flux continuity condition at the element interfaces allows to solve the discretized system of equations at element level. For problems with a large number of degrees of freedoms, this offers a significant advantage over the standard continuous Galerkin (CG) procedure. The well established fully explicit LCG method is used for assessing the accuracy of the proposed new methods. Results presented in this work demonstrate that the proposed SILCG methods are stable and as accurate as the explicit LCG method. Among the three methods proposed, the SILCG-FTCS method requires considerably lower number of iterations per element, and thus requires lowest amount of CPU time. On the other hand, the SILCG-TE and SILCG-SUPG methods are stable and accurate for larger time step sizes. Although the standard Newton method requires evaluation of both the Jacobian matrix and the residual for every single iteration, which may be expensive for standard implicit solvers, the computed results show that the maximum number of iterations per element for SILCG-TE and SILCG-SUPG is less than unity (less than 0.3 and 0.7 respectively). Also, numerical experiments show that the Jacobian matrix can be calculated only once per time step, allowing to save a significant amount of computational time.
Keywords: Semi-implicit; Locally conservative Galerkin (SILCG) methods; SILCG-TE; SILCG-SUPG and SILCG-FTCS methods; Elastic tubes; Systemic circulation; Arterial flow
Start Page: 217
End Page: 233