https://hal.archives-ouvertes.fr/hal-01517950/document

Isogeometric analysis using T-splines

http://www-2.unipv.it/compmech/publications/2007_9.pdf

Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows

We present a fully-coupled monolithic formulation of the fluid-structure interaction of an incompressible fluid on a moving domain with a nonlinear hyperelastic solid. The arbitrary Lagrangian–Eulerian description is utilized for the fluid subdomain and the Lagrangian description is utilized for the solid subdomain. Particular attention is paid to the derivation of various forms of the conservation equations; the conservation properties of the semi-discrete and fully discretized systems; a unified presentation of the generalized-α time integration method for fluid-structure interaction; and the derivation of the tangent matrix, including the calculation of shape derivatives. A NURBS-based isogeometric analysis methodology is used for the spatial discretization and three numerical examples are presented which demonstrate the good behavior of the methodology.

Isogeometric fluid-structure interaction: theory, algorithms, and computations

A fixed-point fluid–structure interaction (FSI) solver with dynamic relaxation is revisited. New developments and insights gained in recent years motivated us to present an FSI solver with simplicity and robustness in a wide range of applications. Particular emphasis is placed on the calculation of the relaxation parameter by both Aitken’s \({\Delta^{2}}\) method and the method of steepest descent. These methods have shown to be crucial ingredients for efficient FSI simulations.

Fixed-point fluid-structure interaction solvers with dynamic relaxation

We develop finite element data structures for T-splines based on Bezier extraction generalizing our previous work for NURBS. As in traditional finite element analysis, the extracted Bezier elements are defined in terms of a fixed set of polynomial basis functions, the so-called Bernstein basis. The Bezier elements may be processed in the same way as in a standard finite element computer program, utilizing exactly the same data processing arrays. In fact, only the shape function subroutine needs to be modified while all other aspects of a finite element program remain the same. A byproduct of the extraction process is the element extraction operator. This operator localizes the topological and global smoothness information to the element level, and represents a canonical treatment of T-junctions, referred to as ‘hanging nodes’ in finite element analysis and a fundamental feature of T-splines. A detailed example is presented to illustrate the ideas. Copyright © 2011 John Wiley & Sons, Ltd.

Isogeometric finite element data structures based on Bézier extraction of T-splines

Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes

https://www.cs.ox.ac.uk/people/christian.michler/Homepage%20of%20Christian%20Michler/Publications_files/MicHulBruBor04CF.pdf

A monolithic approach to fluid–structure interaction

https://www.ices.utexas.edu/media/reports/2007/0701.pdf

Weak Dirichlet Boundary Conditions for Wall-Bounded Turbulent Flows

The numerical solution of fluid-structure interactions with the customary subiteration method incurs numerous deficiencies. We propose a novel solution method based on the conjugation of subiteration with a Newton-Krylov method, and demonstrate its superiority and beneficial characteristics

Christian Michler

Papers

Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes

A monolithic approach to fluid–structure interaction

Weak Dirichlet Boundary Conditions for Wall-Bounded Turbulent Flows

An interface Newton–Krylov solver for fluid–structure interaction

A discontinuous Galerkin method for the Vlasov-Poisson system