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Novel semi-implicit, locally conservative Galerkin (SILCG) methods: Application to blood flow in a systemic circulation
Computer Methods in Applied Mechanics and Engineering, Volume: 332, Pages: 217 - 233
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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...
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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.
Semi-implicit; Locally conservative Galerkin (SILCG) methods; SILCG-TE; SILCG-SUPG and SILCG-FTCS methods; Elastic tubes; Systemic circulation; Arterial flow
Faculty of Science and Engineering