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Novel Semi-Implicit Locally Conservative Galerkin SILCG Solvers: Applications to One Dimensional Human Circulation, Heat Transfer and Ageing Problems / Hayder M. Hasan
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DOI (Published version): 10.23889/Suthesis.48065
In this work, three novel, locally conservative Galerkin methods in their semi-implicit form are developed for one dimensional blood ﬂow and heat transfer modelling in a hu-man arterial network. The study is also extended for predicting aging effects on the cir-culation function with an associated t...
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In this work, three novel, locally conservative Galerkin methods in their semi-implicit form are developed for one dimensional blood ﬂow and heat transfer modelling in a hu-man arterial network. The study is also extended for predicting aging effects on the cir-culation function with an associated thermoregulatory mechanism. These semi-implicit discretizations are the second order Taylor expansion (SILCG-TE) method, the streamline upwind Petrov-Galerkin (SILCG-SUPG) procedure and the backward in time and central in space (SILCG-BTCS) method.In the well established fully explicit locally conservative Galerkin method (LCG), enforcement of the ﬂux continuity condition at the element interfaces allows solving the discretized system of equations at the 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 original explicit LCG method is used for assessing the accuracy of the proposed new methods.First, mass and momentum equations are solved in the whole system of 91 arterial seg-ments by using the proposed techniques. Results demonstrate that the proposed SILCG methods are stable and as accurate as the explicit LCG method. Among the three meth-ods proposed, the SILCG-BTCS method requires considerably lower number of iterations per element, and thus requires the 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 due to the presence of the stabilization terms from Taylor expansion based approach and streamline upwind Petrov-Galerkin method.Second, the three approaches are extended to the heat problem by solving the energy equation and combining with blood ﬂow. Here, the interaction between temperature and ﬂexible vessels is tackled. Again, the outcomes show that the new techniques provide desirable accuracy and stability similar to the ﬂow. As SILCG-BTCS is the simplest and fastest one for ﬂow and the same conclusions are derived for heat transfer. Similarly, SLICG-TE and SILCG-SUPG methods still admit higher time steps.Finally, ageing effect is considered on both ﬂow and heat in a human body. The methods presented previously are adapted by changing the necessary parameters related to ageing. The results obtained conﬁrm the ability of the proposed methods for predicting the changes that occur with age such as the changes in blood pressure, ﬂow and heat transfer. Signiﬁcant consequences of ageing are highlighted.
College of Engineering