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An implicit solver for 1D arterial network models / Jason Carson; Raoul Van Loon; Raoul van Loon
International Journal for Numerical Methods in Biomedical Engineering, Volume: 33, Issue: 7
Swansea University Author: Raoul, van Loon
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In this study the one dimensional blood flow equations are solved using a newly proposed enhanced trapezoidal rule method ETM, which is an extension to the simplified trapezoidal rule method STM. At vessel junctions the conservation of mass and conservation of total pressure are held as system const...
|Published in:||International Journal for Numerical Methods in Biomedical Engineering|
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In this study the one dimensional blood flow equations are solved using a newly proposed enhanced trapezoidal rule method ETM, which is an extension to the simplified trapezoidal rule method STM. At vessel junctions the conservation of mass and conservation of total pressure are held as system constraints using Lagrange multipliers that can be physically interpreted as external flow rates. The ETM scheme is compared with published arterial network benchmark problems and a dam break problem. Strengths of the ETM scheme include being simple to implement, intuitive connection to lumped parameter models, and no restrictive stability criteria such as the CFL number. The ETM scheme does not require the use of characteristics at vessel junctions, or for inlet and outlet boundary conditions. The ETM forms an implicit system of equations which requires only one global solve per time step for pressure, followed by flow rate update on the elemental system of equations, thus no iterations are required per time step. Consistent results are found for all benchmark cases and for a 56 vessel arterial network problem it gives very satisfactory solutions at a spatial and time discretisation that results in a maximum CFL of 3, taking 4.44 seconds per cardiac cycle. By increasing the time step and element size to produce a maximum CFL number of 15 the method takes only 0.39 seconds per cardiac cycle with only a small compromise on accuracy.
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