IFEM

Isogeometric analysis is a recently developed computational approach that offers the possibility of integrating finite element analysis (FEA) into conventional NURBS -based CAD design tools. Currently, it is necessary to convert data between CAD and FEA packages to analyse new designs during development, a difficult task since the computational geometric approach for each is different. Isogeometric analysis employs complex NURBS geometry (the basis of most CAD packages) in the FEA application directly. This allows models to be designed, tested and adjusted in one go, using a common data set. Applied Mathematics Department, SINTEF ICT (SAM) and Department of Mathematical Sciences, NTNU (IMF) in close collaboration have been advancing this new technology in the field of offshore wind engineering. This has been achieved through the development of an open source code IFEM (www.ifem.no). The code is written in C++ for modularity and parallelized using the PETSc library to take advantage of the most modern high performance computing facilities. The fluid structure interaction simulations are facilitated through the use of the same basis functions. The development of IFEM started with the NFR-project ICADA which focused on isogeometric modules for solid/structural problems. Within NOWITECH the main focus has been on developing modules for 2D and 3D CFD simulations of flow around wind turbine blades. Currently work on fluid-structure interaction for wind turbines are the focus of the NFR-project FSI-WT. Within NOWITECH, SAM and IMF have contributed to the following 5 modules of IFEM: i). IFEM-GeoModeller for creating geometries. ii). IFEM-Mesher for 3D spline based block structured mesh generation iii). IFEM-CFD2D and iv). IFEM-CFD3D for conducting 2D and 3D computational fluid dynamics simulations respectively v). IFEM-FSI for fluid structure interaction simulations.

A fully coupled isogeometric finite element solver for the incompressible Navier-Stokes includes pressure stabilization for equal order elements and SUPG stabilization for high Reynold number flows. The Navier-Stokes solver is based on either a Chorin projection method (incremental pressure correction) along with the Spalart-Allmaras turbulence model or a coupled formulation and variational multiscale turbulence approach. Common to both methods are the Navier-Stokes equations that are discretized using equal order splines for velocity and pressure. So far linear, quadratic and cubic spline elements have been implemented. The meshes for such simulations are characterized by an aspect ratio of up to 1000-10000 close to the wall resulting in slow convergence rate. To address this issue, efficient preconditioners and linear solvers have been implemented using the open source library PETSc (Portable Extensible Toolkit for Scientific Computation). Traditional computational fluid dynamic codes solve the fluid equations on a fixed (Eulerian) grid but fluid-structure interaction problems usually requires an unsteady moving domain for the fluid part. A classical approach to overcome this difficulty is to consider the so-called Arbitrary Lagrangian-Eulerian (ALE) method where the grid is moved arbitrarily inside the fluid domain, following the movement of the boundary. Furthermore, a fluid-structure interaction problem is not only a two-field (fluid and solid) but a three-field coupling problem (fluid, solid and mesh). These issues are taken into account in the code. Input to the IFEM code is given as a standard XML file while HDF5 is the default output format. However, there are converters to convert the HDF5 format to other formats like VTF and VTK which makes it possible to visualize the results in opensource software like Paraview. Intensive validation work is in progress and the most recent developments are communicated through the www.fsi-wt.no website.