Finite Element Methods for Large-Strain Poroelasticity/Chemotaxis Models Simulating the Formation of Myocardial Oedema
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Published:2022-07-27
Issue:3
Volume:92
Page:
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ISSN:0885-7474
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Container-title:Journal of Scientific Computing
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language:en
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Short-container-title:J Sci Comput
Author:
Barnafi N. A.ORCID, Gómez-Vargas B.ORCID, Lourenço W. J., Reis R. F., Rocha B. M.ORCID, Lobosco M., Ruiz-Baier R.ORCID, dos Santos R. WeberORCID
Abstract
AbstractIn this paper we propose a novel coupled poroelasticity-diffusion model for the formation of extracellular oedema and infectious myocarditis valid in large deformations, manifested as an interaction between interstitial flow and the immune-driven dynamics between leukocytes and pathogens. The governing partial differential equations are formulated in terms of skeleton displacement, fluid pressure, Lagrangian porosity, and the concentrations of pathogens and leukocytes. A five-field finite element scheme is proposed for the numerical approximation of the problem, and we provide the stability analysis for a simplified system emanating from linearisation. We also discuss the construction of an adequate, Schur complement based, nested preconditioner. The produced computational tests exemplify the properties of the new model and of the finite element schemes.
Funder
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior Faculty of Science, Monash University Australian Research Council
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,General Engineering,Theoretical Computer Science,Software,Applied Mathematics,Computational Mathematics,Numerical Analysis
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