The research objectives of this project is to develop parallel adaptive finite element methods for simulation of turbulent flow and fluid-structure interaction (FSI).
The underlying mathematical equations are the fundamental conservation laws of mass, momentum and energy. Simulation of turbulent flow is challenging since the range of turbulent scales requires a level of computational resolution that is beyond the capacity of the methods, software and hardware of today; simulation of FSI is challenging since it represents a multi-physics problem where two (or more) models are coupled.
We have pioneered (i) a method for turbulence simulation that avoids explicit parameterization of unresolved turbulent scales ; (ii) a monolithic approach to FSI that circumvents the coupling problem, by expressing the FSI problem as a unified continuum model . Both (i) and (ii) are imbedded into the underlying methodology of adaptive finite element methods, implemented in the open source FEniCS-HPC framework  that we develop in our research group. In benchmark workshops organized by NASA, Boeing and others, we have proven our technology , and since 2008 SNIC has supported our research and the development of open source software on Sweden’s most powerful supercomputing resources. In an ongoing project funded by the Swedish Research Council we have developed a clinical pathway for patient-specific simulation of the blood flow in the left ventricle of the human heart [5,6].
The objectives for this project are: (i) to investigate fundamental mathematical questions regarding existence of solutions to the mathematical equations that describe turbulent flow (with University College Dublin and Imperial College London); (ii) patient-specific simulation of the blood flow in the left ventricle of the human heart (with Karolinska hospital, Karolinska Institute and CNRS Paris); (iii) fluid-structure interaction of human cells (with Linköping University); and (iv) prototype simulations of piezoelectric material as part of the EU project GENEX which started September 2022.
 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.
 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.
 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.
 Johan Jansson et al., Time-resolved Adaptive Direct FEM Simulation of High-lift Aircraft Configurations, in Numerical Simulation of the Aerodynamics of High-Lift Configurations, pp.67-92, Springer, 2018.
 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.
 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.