Part II Implementation - FEniCS Project

22 Lessons Learnt in Mixed Language ProgrammingBy Kent-Andre Mardal, Anders Logg, and Ola Skavhaug 209III Applications 21123 Finite Elements for Incompressible FluidsBy Andy R. Terrel, L. Ridgway Scott, Matthew G. Knepley, Robert C. Kirby andGarth N. Wells 21324 Benchmarking Finite Element Methods for Navier–StokesBy Kristian Valen-Sendstad, Anders Logg and Kent-Andre Mardal 21525 Image-Based Computational HemodynamicsBy Luca Antiga 21726 Simulating the Hemodynamics of the Circle of WillisBy Kristian Valen-Sendstad, Kent-Andre Mardal and Anders Logg 21927 Cerebrospinal Fluid FlowBy Susanne Hentschel, Svein Linge, Emil Alf Løvgren and Kent-Andre Mardal 22127.1 Medical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 22127.2 Mathematical Description . . . . . . . . . . . . . . . . . . . . . . . . 22327.3 Numerical Experiments . . . . . . . . . . . . . . . . . . . . . . . . . 22327.3.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . 22327.3.2 Example 1. Simulation of a Pulse in the SAS. . . . . . . . . . 23027.3.3 Example 2. Simplified Boundary Conditions. . . . . . . . . . 23427.3.4 Example 3. Cord Shape and Position. . . . . . . . . . . . . . 23527.3.5 Example 4. Cord with Syrinx. . . . . . . . . . . . . . . . . . . 23628 Turbulent Flow and Fluid–Structure Interaction with UnicornBy Johan Hoffman, Johan Jansson, Niclas Jansson, Claes Johnson and MurtazoNazarov 23928.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23928.2 Continuum models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24028.3 Mathematical framework . . . . . . . . . . . . . . . . . . . . . . . . 24128.4 Computational method . . . . . . . . . . . . . . . . . . . . . . . . . . 24128.5 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 24128.6 Geometry modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24228.7 Fluid-structure interaction . . . . . . . . . . . . . . . . . . . . . . . . 24228.8 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24228.8.1 Turbulent flow separation . . . . . . . . . . . . . . . . . . . . 24228.8.2 Flight aerodynamics . . . . . . . . . . . . . . . . . . . . . . . 24228.8.3 Vehicle aerodynamics . . . . . . . . . . . . . . . . . . . . . . . 24228.8.4 Biomedical flow . . . . . . . . . . . . . . . . . . . . . . . . . . 24213