Numerical Simulations

Part of the CRM Series in Mathematical Physics book series (CRM)

Numerical simulations yield complete fields of hemodynamical quantities at multiple phases of the flow cycle, and easily test the effects of the involved physical parameters, especially the most important parameters of influence. However, verification and validation must be performed. Furthermore, the sensitivity of the results to the input parameters must be checked by varying the values of the input data. In some circumstances, the model is calibrated by adjusting the model inputs to the observations. The physics of the problem must be preserved by the chosen modeling and selected simulation technique. The code verification stage uses benchmarks with analytical solutions or “accurate” numerical solutions to check the computational implementation. Computation verification is done by comparing results obtained with various mesh densities. Errors and uncertainties are assessed. Modeling errors are associated with assumptions of the mathematical model derived from the conceptual model of the physical problem (model geometry, flow governing parameter values, material properties, constitutive equations, boundary conditions, etc.). Numerical errors arise from discretization features, convergence degree, computation round-off, modeling hypotheses (such as isotropy), and parameter estimations.


Cellular Automaton Contractile Element Immerse Boundary Method Internal Elastic Lamina Lattice Boltzmann Model 
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© Springer Science+Business Media, LLC 2008

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