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; this means that new methods need to be developed, and new software implementations are necessary that take full advantage of the most powerful HPC resources available. Simulation of FSI is challenging since it represents a multi-physics problem where two (or more) models are coupled.
Our methodology is adaptive algorithms that optimize the use massively parallel computing resources, based on a posteriori error estimation. We have pioneered (i) a method for turbulence simulation that avoids explicit parameterization of unresolved turbulent scales ; and (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.
The detailed objectives for this project are: (i) to investigate fundamental mathematical questions regarding existence of solutions to the mathematical equations that describe turbulent flow (collaboration with University College Dublin, Imperial College London, and Princeton University); (ii) to develop new asynchronous adaptive finite element methods to minimize the communication costs in our parallel algorithms; (iii) to benchmark our FSI methods against known solutions and experimental data (collaboration with Kings College London and RWTH Aachen University); (iv) patient-specific simulation of the blood flow in the left ventricle of the human heart (collaboration with Danderyd hospital, KI and CNRS Paris); (v) simulation of vertical axis wind turbines (collaboration with Uppsala University).
 J. Hoffman, J. Jansson, N. Jansson, R. Vilela De Abreu, 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, J. Jansson, M. Stöckli, Unified continuum modeling of fluid-structure interaction, Mathematical Models and Methods in Applied Sciences, Vol.21(3), pp.491-513, 2011.
 J.Hoffman, J.Jansson, N.C.Degirmenci, J.H.Spühler, R.V.De Abreu, N.Jansson, A.Larcher, FEniCS-HPC: Coupled Multiphysics in Computational Fluid Dynamics, Jülich Aachen Research Alliance (JARA) High-Performance Computing Symposium, Springer, pp.58—69, 2016.
 Johan Jansson, Krishnasamy, Ezhilmathi, Massimiliano Leoni, Johan Hoffman, 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.