HIGAMod: A Hierarchical IsoGeometric Approach for MODel reduction in curved pipes

- We initiate to explore the combination of isogeometric analysis and HiMod
- Isogeometric analysis is conveniently used for the axial discretization
- An accurate and efficient representation of the centerline is obtained
- An accurate and efficient representation of the solution is obtained as well
- Very promising preliminary numerical results are presented

In computational hemodynamics we typically need to solve incompressible fluids in domains given by curved pipes or network of pipes. To reduce the computational costs, or conversely to improve models based on a pure 1D (axial) modeling, an approach called “Hierarchical Model reduction” (HiMod) was recently proposed. It consists of a diverse numerical approximation of the axial and of the transverse components of the dynamics. The latter are properly approximated by spectral methods with a few degrees of freedom, while classical finite elements were used for the main dynamics to easily fit any morphology. However affine elements for curved geometries are generally inaccurate. In this paper we conduct a preliminary exploration of IsoGeometric Analysis (IGA) applied to the axial discretization. With this approach, the centerline is approximated by Non Uniform Rational B-Splines (NURBS). The same functions are used to represent the axial component of the solution. In this way we obtain an accurate representation of the centerline as well as of the solution with few axial degrees of freedom. This paper provides preliminary promising results of the combination of HiMod with IGA - referred to as HIGAMod approach - to be applied in any field involving computational fluid dynamics in generic pipe-like domains.