Mikael Mortensen

Biomedical flows

I have been working from 2012-2016 as an adjunct research scientist at Simula Research Laboratory. Here I had the great honor to be working with the late Prof. Hans Petter Langtangen ([1], [2], [3], [4]), at the Center for Biomedical Computing.

I have contributed quite a bit to the FEniCS project, and the incompressible Navier-Stokes solver Oasis has been developed within the FEniCS framework. The solver has been developed for efficiency, with MPI, and it is written entirely in Python. The Oasis solver is documented in the Computer Physics Communications paper [5], where we show that it may run as fast and accurate as the low-level finite volume C++ solvers OpenFOAM and CDP (Stanford).

The Oasis solver has been used in a range of master theses (see Teaching). For one of my master students, Per Thomas Haga, the thesis led to a journal paper on injecting drugs in the Cerebrospinal fluid (CSF) [6]. The animation on the right shows how an injected drug moves up and down inside the CSF channel. It can also be sen that, due to the very low diffusivity of the scalar drug, we modelled the scalar transport using Lagrangian particle tracking.

I have been working quite a bit together with Kristian Valen-Sendstad at Simula, on different aspects of biomedical flows. Our simulations on intracranial aneurysms [1], actually reached the headlines of Norway's larges newspaper (VG) 1, when we found a correlation between transition to turbulence and the risk of aneurysm rupture (more famously known as stroke). For this work I performed most of the simulations when still at FFI.

Figure 1: Headlines in norwegian newspaper VG, 5/11-2011.

More recently we have been studying transition and mesh sensitivity in the FDA nozzle benchmark. In [7] we use both regular CFD and linear stability analysis to show that care must be taken when designing a CFD benchmark. Transition to turbulence can only come from a seed, or perturbation, and an ideal case like the FDA benchmark should not transtition at all unless some noise is added to the system. Figure 2 is showing an unstable eigenmode in the FDA bechmark, showing that transition should in deed occur at the Reynolds number=3500. Here I have conducted the stability simulations using the dog linear stability analysis software package.

Figure 2: Linear stability analysis of the FDA benchmark. Showing the most unstable eigenmode.


  1. K. Valen-Sendstad, K.-A. Mardal, M. Mortensen, B. A. P. Reif and H. P. Langtangen. Direct Numerical Simulation of Transitional Flow in a Patient-Specific Intracranial Aneurysm, Journal of Biomechanics, 44(16), pp. 2826-2832, doi: 10.1016/j.jbiomech.2011.08.015, 2011, http://www.sciencedirect.com/science/article/pii/S002192901100563X.
  2. M. Mortensen and H. P. Langtangen. High Performance Python for Direct Numerical Simulations of Turbulent Flows, Computer Physics Communications, 203, pp. 53-65, doi: 10.1016/j.cpc.2016.02.005, 2016, http://www.sciencedirect.com/science/article/pii/S0010465516300200.
  3. M. Mortensen, K.-A. Mardal and H. P. Langtangen. Simulation of Transitional Flows, Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book, edited by A. Logg, K.-A. Mardal and G. Wells, Springer, pp. pp. 421-440, 2012.
  4. M. Mortensen, H. P. Langtangen and G. N. Wells. A FEniCS-Based Programming Framework for Modeling Turbulent Flow by the Reynolds-Averaged Navier-Stokes Equations, Advances in Water Resources, 34(9), pp. 1082-1101, doi: 10.1016/j.advwatres.2011.02.013, 2011, http://www.sciencedirect.com/science/article/pii/S030917081100039X.
  5. M. Mortensen and K. Valen-Sendstad. Oasis: a High-Level/High-Performance Open Source Navier-Stokes Solver, Computer Physics Communications, 188, pp. 177-188, doi: 10.1016/j.cpc.2014.10.026, 2015, http://www.sciencedirect.com/science/article/pii/S0010465514003786.
  6. P. T. Haga, G. Pizzichelli, M. Mortensen, M. Kuchta, S. H. Pahlavian, E. Sinibaldi, B. A. Martin and K.-A. Mardal. A Numerical Investigation of Intrathecal Isobaric Drug Dispersion Within the Cervical Subarachnoid Space, PLOS ONE, 12(3), pp. 1-21, doi: 10.1371/journal.pone.0173680, 2017, 10.1371/journal.pone.0173680.
  7. A. Bergersen, M. Mortensen and K. Valen-Sendstad. The FDA Nozzle Benchmark: in Theory There Is No Difference Between Theory and Practice, But in Practice There Is, Accepted for publication in International Journal for Numerical Methods in Biomedical Engineering, 2018.