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Methods for Numerical Flow Simulation

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Hemodynamical Flows

Part of the book series: Oberwolfach Seminars ((OWS,volume 37))

Abstract

This chapter introduces into computational methods for the simulation of PDE-based models of laminar hemodynamical flows. We discuss space and time discretization with emphasis on operator-splitting and finite-element Galerkin methods because of their flexibility and rigorous mathematical basis. Special attention is paid to the simulation of pipe flow and the related question of artificial outflow boundary conditions. Further topics are efficient methods for the solution of the resulting algebraic problems, techniques of sensitivity-based error control and mesh adaptation, as well as flow control and model calibration. We concentrate on laminar flows in which all relevant spatial and temporal scales can be resolved and no additional modeling of turbulence effects is required. This covers most of the relevant situations of hemodynamical flows. The numerical solution of the corresponding systems is complicated mainly because of the incompressibility constraint which enforces the use of implicit methods and its essentially parabolic or elliptic character which requires the prescription of boundary conditions along the whole boundary of the computational domain.

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  1. Institute of Applied Mathematics, University of Heidelberg, Im Neuenheier Feld 293/294, D-69120, Heidelberg, Germany

    Rolf Rannacher

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Rannacher, R. (2008). Methods for Numerical Flow Simulation. In: Hemodynamical Flows. Oberwolfach Seminars, vol 37. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7806-6_4

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