I denne oppgaven utvikles det en endelig elemente Newton's metode løsningsalgoritme for fluid-strukture vekselvirkning med en arbitrary Lagrangian Eulerian formulering. Denne algoritme implementeres som en softwarepakke FSINewton, som er tilgjenlig online som del av det open source biomedisink rammeverket CBC.Solve.
In this thesis a finite element Newton’s method based solution algorithm was created for fluid-structure interaction using an ALE formulation. This algorithm was implemented as a software package, FSINewton, and made available online via the open source biomedical solver framework, CBC.Solve.
Three test problems were formulated and solved to test the computerimplementation of Newton’s method for FSI; the Analytical, Channel with Flap, and 2D Blood vessel problems. The last two problems were used to show that Newton’s method can solve both easy and difficult FSI problems, while the Analytical problem was used to confirm the correctness of the implementation by obtaining L2 convergence of the finite element solutions to the known analytic solution.
Furthermore, four run-time optimizations to FSINewton were imple-mented, namely Jacobian reuse, Jacobian simplification, Jacobian buffering, and reduced order quadrature. These optimizations were tested using the three test problems. On the basis of the observations made the four optimizations were evaluated, with the Jacobian reuse scheme coming out as the most valuable optimization.
Finally, the FSI fixed point solver of CBC.Solve was compared to theNewton solver of this thesis. Comparable run-times were obtained for both solvers, and an example was given to demonstrate the superior robustness of the Newton’s method solver in the case of fluids and structures with similar densities.