Parallel adaptive finite element methods for simulation of turbulent flow, fluid-structure interaction and ultrasonic guided wave propagation in piezoelectric media

NAISS 2024/6-17


NAISS Medium Storage

Principal Investigator:

Johan Hoffman


Kungliga Tekniska högskolan

Start Date:


End Date:


Primary Classification:

10105: Computational Mathematics

Secondary Classification:

20301: Applied Mechanics

Tertiary Classification:

20603: Medical Image Processing



The research objectives of this project is to develop parallel adaptive finite element methods for simulation of turbulent flow, fluid-structure interaction (FSI) and ultrasonic guided wave (UGW) propagation in piezoelectric media. We have pioneered (i) a method for turbulence simulation that avoids explicit parameterization of unresolved turbulent scales [1]; (ii) a monolithic approach to FSI that circumvents the coupling problem by expressing the FSI problem as a unified continuum model [2]. Both (i) and (ii) are imbedded into the underlying methodology of adaptive finite element methods, implemented in the open source FEniCS-HPC framework [3] developed in our research group. Since 2008 SNIC/NAISS has supported our research and the development of open source software on Sweden’s most powerful supercomputing resources. In a projects funded by VR we have developed a clinical pathway for patient-specific simulation of the blood flow in the left ventricle of the human heart [4,5,6], and recently we developed a new method to analyse turbulent flow using a triple decomposition of the velocity gradient tensor [7,8]. We also develop a FEniCS-HPC solver to simulate ultrasonic guided wave propagation through elastic and piezoelectric media. This work is part of the EU-project GENEX [9] that aims to develop a new end-to-end digital framework for optimized manufacturing and maintenance of next generation aircraft structures. Here our task is to run a large number of simulations to generate training data for machine learning algorithms. [1] J. Hoffman et al., Towards a parameter-free method for high Reynolds number turbulent flow simulation based on adaptive finite element approximation, Comput. Meth. Appl. Mech. Engrg., Vol.288, pp.60-74, 2015. [2] J. Hoffman et al., Unified continuum modeling of fluid-structure interaction, Mathematical Models and Methods in Applied Sciences, Vol.21(3), pp.491-513, 2011. [3] J.Hoffman et al., FEniCS-HPC: Coupled Multiphysics in Computational Fluid Dynamics, Jülich Aachen Research Alliance (JARA) High-Performance Computing Symposium, Springer, pp.58—69, 2016. [4] D. Larsson et al., "Patient-Specific Left Ventricular Flow Simulations From Transthoracic Echocardiography : Robustness Evaluation and Validation Against Ultrasound Doppler and Magnetic Resonance Imaging," IEEE Transactions on Medical Imaging, vol. 36, no. 11, s. 2261-2275, 2017. [5] J. H. Spühler et al., "3D Fluid-Structure Interaction Simulation of Aortic Valves Using a Unified Continuum ALE FEM Model," Frontiers in Physiology, vol. 9, 2018. [6] J. Kronborg, F. Svelander, S. Eriksson-Lidbrink, L. Lindström, C. Homs-Pons, D. Lucor, J. Hoffman, Computational analysis of flow structures in turbulent ventricular blood flow associated with mitral valve intervention, Frontiers in Physiology, Vol.752, 2022. [7] J. Kronborg, J. Hoffman, The triple decomposition of the velocity gradient tensor as a standardized real Schur form, Physics of Fluids Vol.35(3), 031703, 2023. [8] J. Hoffman, Energy stability analysis of turbulent incompressible flow based on the triple decomposition of the velocity gradient tensor, Physics of Fluids, 33(8), 2021. [9] GENEX project:, 2022.