Mikael Mortensen

Direct numerical simulation of transitional flow in a patient-specific intracranial aneurysm

In experiments turbulence has previously been shown to occur in intracranial aneurysms. The effects of turbulence induced oscillatory wall stresses could be of great importance in understanding aneurysm rupture. To investigate the effects of turbulence on blood flow in an intracranial aneurysm, we performed a high resolution computational fluid dynamics (CFD) simulation in a patient specific middle cerebral artery (MCA) aneurysm using a realistic, pulsatile inflow velocity. The flow showed transition to turbulence just after peak systole, before relaminarization occurred during diastole. The turbulent structures greatly affected both the frequency of change of wall shear stress (WSS) direction and WSS magnitude, which reached a maximum value of 41.5Pa. The recorded frequencies were predominantly in the range of 1-500Hz. The current study confirms, through properly resolved CFD simulations that turbulence can occur in intracranial aneurysms.

A FEniCS-based programming framework for modeling turbulent flow by the Reynolds-averaged Navier-Stokes equations

Abstract Finding an appropriate turbulence model for a given flow case usually calls for extensive experimentation with both models and numerical solution methods. This work presents the design and implementation of a flexible, programmable software framework for assisting with numerical experiments in computational turbulence. The framework targets Reynolds-averaged Navier–Stokes models, discretized by finite element methods. The novel implementation makes use of Python and the FEniCS package, the combination of which leads to compact and reusable code, where model- and solver-specific code resemble closely the mathematical formulation of equations and algorithms. The presented ideas and programming techniques are also applicable to other fields that involve systems of nonlinear partial differential equations. We demonstrate the framework in two applications and investigate the impact of various linearizations on the convergence properties of nonlinear solvers for a Reynolds-averaged Navier–Stokes model.

Direct numerical simulations of the double scalar mixing layer. Part I: Passive scalar mixing and dissipation

The double scalar mixing layer (DSML) is a canonical problem for studying the mixing of multiple streams and, with reaction, combustion of the partially premixed type. In a DSML, a third stream consisting of a premixture of the reactants is introduced in between the pure fuel and air streams of the classic twin-feed or binary mixing problem. The well-known presumed probability density function (PDF), such as the β-PDF, can adequately model passive scalar mixing for the binary mixing problem on which state-of-the-art turbulent combustion models such as conditional moment closure and flamelet approaches rely. However, the β-PDF model, now a standard in CFD simulation, cannot describe turbulent mixing involving multiple streams; e.g., the asymmetric three-stream mixing characterizing the DSML. In this paper, direct numerical simulations of the DSML are performed to make available a high-fidelity database for developing more general, fine-scale mixing models required to compute turbulent combustion problems o...

Computational Fluid Dynamics for Engineers: Frontmatter

Computational fluid dynamics (CFD) has become an indispensable tool for many engineers. This book gives an introduction to CFD simulations of turbulence, mixing, reaction, combustion and multiphase flows. The emphasis on understanding the physics of these flows helps the engineer to select appropriate models with which to obtain reliable simulations. Besides presenting the equations involved, the basics and limitations of the models are explained and discussed. The book, combined with tutorials, project and Power-Point lecture notes (all available for download), forms a complete course. The reader is given hands-on experience of drawing, meshing and simulation. The tutorials cover flow and reactions inside a porous catalyst, combustion in turbulent non-premixed flow and multiphase simulation of evaporating sprays. The project deals with the design of an industrial-scale selective catalytic reduction process and allows the reader to explore various design improvements and apply best practice guidelines in the CFD simulations.

Computational Fluid Dynamics for Engineers by Bengt Andersson

Computational fluid dynamics (CFD) has become an indispensable tool for many engineers. This book gives an introduction to CFD simulations of turbulence, mixing, reaction, combustion and multiphase flows. The emphasis on understanding the physics of these flows helps the engineer to select appropriate models with which to obtain reliable simulations. Besides presenting the equations involved, the basics and limitations of the models are explained and discussed. The book, combined with tutorials, project and Power-Point lecture notes (all available for download), forms a complete course. The reader is given hands-on experience of drawing, meshing and simulation. The tutorials cover flow and reactions inside a porous catalyst, combustion in turbulent non-premixed flow and multiphase simulation of evaporating sprays. The project deals with the design of an industrial-scale selective catalytic reduction process and allows the reader to explore various design improvements and apply best practice guidelines in the CFD simulations.

A comparison of finite element schemes for the incompressible Navier–Stokes equations

Numerical algorithms for the computation of fluid flow have been an active area of research for 12062 several decades and still remain an important field to study. As a result, there exists a large literature 12063 on discretization schemes for the incompressible Navier–Stokes equations, and it can be hard to 12064 judge which method works best for any particular problem. Furthermore, since the development of 12065 any particular discretization scheme is often a long process and tied to a specific implementation, 12066 comparisons of different methods are seldom made.

Preconditioners for Saddle Point Systems with Trace Constraints Coupling 2D and 1D Domains

We study preconditioners for a model problem describing the coupling of two elliptic subproblems posed over domains with different topological dimension by a parameter dependent constraint. A pair of parameter robust and efficient preconditioners is proposed and analyzed. Robustness and efficiency of the preconditioners is demonstrated by numerical experiments.

Conditional velocity statistics in the double scalar mixing layer – A mapping closure approach

In this work we use 3D direct numerical simulations (DNS) to investigate the average velocity conditioned on a conserved scalar in a double scalar mixing layer (DSML). The DSML is a canonical multistream flow designed as a model problem for the extensively studied piloted diffusion flames. The conditional mean velocity appears as an unclosed term in advanced Eulerian models of turbulent non-premixed combustion, like the conditional moment closure and transported probability density function (PDF) methods. Here it accounts for inhomogeneous effects that have been found significant in flames with relatively low Damköhler numbers. Today there are only a few simple models available for the conditional mean velocity and these are discussed with reference to the DNS results. We find that both the linear model of Kutznetzov and the Li and Bilger model are unsuitable for multi stream flows, whereas the gradient diffusion model of Pope shows very close agreement with DNS over the whole range of the DSML. The gradient diffusion model relies on a model for the conserved scalar PDF and here we have used a presumed mapping function PDF, that is known to give an excellent representation of the DNS. A new model for the conditional mean velocity is suggested by arguing that the Gaussian reference field represents the velocity field, a statement that is evidenced by a near perfect agreement with DNS. The model still suffers from an inconsistency with the unconditional flux of conserved scalar variance, though, and a strategy for developing fully consistent models is suggested.

A numerical investigation of intrathecal isobaric drug dispersion within the cervical subarachnoid space

Intrathecal drug and gene vector delivery is a procedure to release a solute within the cerebrospinal fluid. This procedure is currently used in clinical practice and shows promise for treatment of several central nervous system pathologies. However, intrathecal delivery protocols and systems are not yet optimized. The aim of this study was to investigate the effects of injection parameters on solute distribution within the cervical subarachnoid space using a numerical platform. We developed a numerical model based on a patient-specific three dimensional geometry of the cervical subarachnoid space with idealized dorsal and ventral nerve roots and denticulate ligament anatomy. We considered the drug as massless particles within the flow field and with similar properties as the CSF, and we analyzed the effects of anatomy, catheter position, angle and injection flow rate on solute distribution within the cerebrospinal fluid by performing a series of numerical simulations. Results were compared quantitatively in terms of drug peak concentration, spread, accumulation rate and appearance instant over 15 seconds following the injection. Results indicated that solute distribution within the cervical spine was altered by all parameters investigated within the time range analyzed following the injection. The presence of spinal cord nerve roots and denticulate ligaments increased drug spread by 60% compared to simulations without these anatomical features. Catheter position and angle were both found to alter spread rate up to 86%, and catheter flow rate altered drug peak concentration up to 78%. The presented numerical platform fills a first gap towards the realization of a tool to parametrically assess and optimize intrathecal drug and gene vector delivery protocols and systems. Further investigation is needed to analyze drug spread over a longer clinically relevant time frame.

High performance Python for direct numerical simulations of turbulent flows

Abstract Direct Numerical Simulations (DNS) of the Navier Stokes equations is an invaluable research tool in fluid dynamics. Still, there are few publicly available research codes and, due to the heavy number crunching implied, available codes are usually written in low-level languages such as C/C++ or Fortran. In this paper we describe a pure scientific Python pseudo-spectral DNS code that nearly matches the performance of C++ for thousands of processors and billions of unknowns. We also describe a version optimized through Cython, that is found to match the speed of C++. The solvers are written from scratch in Python, both the mesh, the MPI domain decomposition, and the temporal integrators. The solvers have been verified and benchmarked on the Shaheen supercomputer at the KAUST supercomputing laboratory, and we are able to show very good scaling up to several thousand cores. A very important part of the implementation is the mesh decomposition (we implement both slab and pencil decompositions) and 3D parallel Fast Fourier Transforms (FFT). The mesh decomposition and FFT routines have been implemented in Python using serial FFT routines (either NumPy, pyFFTW or any other serial FFT module), NumPy array manipulations and with MPI communications handled by MPI for Python ( mpi4py ). We show how we are able to execute a 3D parallel FFT in Python for a slab mesh decomposition using 4 lines of compact Python code, for which the parallel performance on Shaheen is found to be slightly better than similar routines provided through the FFTW library. For a pencil mesh decomposition 7 lines of code is required to execute a transform.