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Balmus, M., Massing, A., Hoffman, J., Razavi, R. & Nordsletten, D. A. (2020). A partition of unity approach to fluid mechanics and fluid-structure interaction. Computer Methods in Applied Mechanics and Engineering, 362, Article ID 112842.
Open this publication in new window or tab >>A partition of unity approach to fluid mechanics and fluid-structure interaction
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2020 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 362, article id 112842Article in journal (Refereed) Published
Abstract [en]

For problems involving large deformations of thin structures, simulating fluid-structure interaction (FSI) remains a computationally expensive endeavour which continues to drive interest in the development of novel approaches. Overlapping domain techniques have been introduced as a way to combine the fluid-solid mesh conformity, seen in moving-mesh methods, without the need for mesh smoothing or re-meshing, which is a core characteristic of fixed mesh approaches. In this work, we introduce a novel overlapping domain method based on a partition of unity approach. Unified function spaces are defined as a weighted sum of fields given on two overlapping meshes. The method is shown to achieve optimal convergence rates and to be stable for steady-state Stokes, Navier-Stokes, and ALE Navier-Stokes problems. Finally, we present results for FSI in the case of 2D flow past an elastic beam simulation. These initial results point to the potential applicability of the method to a wide range of FSI applications, enabling boundary layer refinement and large deformations without the need for re-meshing or user-defined stabilization.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE SA, 2020
Keywords
Finite element methods, Fluid-structure interaction, Overlapping domains, Partition of unity
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-271266 (URN)10.1016/j.cma.2020.112842 (DOI)000515542500012 ()2-s2.0-85078801140 (Scopus ID)
Note

QC 20200401

Available from: 2020-04-01 Created: 2020-04-01 Last updated: 2020-04-01Bibliographically approved
Nguyen, V. D., Jansson, J., Goude, A. & Hoffman, J. (2019). Direct Finite Element Simulation of the Turbulent Flow Past a Vertical Axis Wind Turbine. Renewable energy, 135, 238-247
Open this publication in new window or tab >>Direct Finite Element Simulation of the Turbulent Flow Past a Vertical Axis Wind Turbine
2019 (English)In: Renewable energy, ISSN 0960-1481, E-ISSN 1879-0682, Vol. 135, p. 238-247Article in journal (Refereed) Published
Abstract [en]

There is today a significant interest in harvesting renewable energy, specifically wind energy, in offshore and urban environments. Vertical axis wind turbines get increasing attention since they are able to capture the wind from any direction. They are relatively easy to install and to transport, cheaper to build and maintain, and quite safe for humans and birds. Detailed computer simulations of the fluid dynamics of wind turbines provide an enhanced understanding of the technology and may guide design improvements. In this paper, we simulate the turbulent flow past a vertical axis wind turbine for a range of rotation angles in parked and rotating conditions. We propose the method of Direct Finite Element Simulation in a rotating ALE framework, abbreviated as DFS-ALE. The simulation results are validated against experimental data in the form of force measurements. We find that the simulation results are stable with respect to mesh refinement and that we capture well the general shape of the variation of force measurements over the rotation angles.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
VAWT, Direct FEM simulation, ALE
National Category
Energy Systems
Research subject
Computer Science; Applied and Computational Mathematics; Vehicle and Maritime Engineering
Identifiers
urn:nbn:se:kth:diva-224801 (URN)10.1016/j.renene.2018.11.098 (DOI)000459365600021 ()2-s2.0-85058018814 (Scopus ID)
Note

QC 20180326

Available from: 2018-03-26 Created: 2018-03-26 Last updated: 2019-11-01Bibliographically approved
Wendt, F., Nielsen, K., Hoffman, J., Jansson, J., Leoni, M. & Yasutaka, I. (2019). Ocean Energy Systems Wave Energy Modelling Task: Modelling, Verification and Validation of Wave Energy Converters. Journal of Marine Science and Engineering, 7(11), Article ID 379.
Open this publication in new window or tab >>Ocean Energy Systems Wave Energy Modelling Task: Modelling, Verification and Validation of Wave Energy Converters
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2019 (English)In: Journal of Marine Science and Engineering, E-ISSN 2077-1312, Vol. 7, no 11, article id 379Article in journal (Refereed) Published
Abstract [en]

The International Energy Agency Technology Collaboration Programme for Ocean Energy Systems (OES) initiated the OES Wave Energy Conversion Modelling Task, which focused on the verification and validation of numerical models for simulating wave energy converters (WECs). The long-term goal is to assess the accuracy of and establish confidence in the use of numerical models used in design as well as power performance assessment of WECs. To establish this confidence, the authors used different existing computational modelling tools to simulate given tasks to identify uncertainties related to simulation methodologies: (i) linear potential flow methods; (ii) weakly nonlinear Froude-Krylov methods; and (iii) fully nonlinear methods (fully nonlinear potential flow and Navier-Stokes models). This article summarizes the code-to-code task and code-to-experiment task that have been performed so far in this project, with a focus on investigating the impact of different levels of nonlinearities in the numerical models. Two different WECs were studied and simulated. The first was a heaving semi-submerged sphere, where free-decay tests and both regular and irregular wave cases were investigated in a code-to-code comparison. The second case was a heaving float corresponding to a physical model tested in a wave tank. We considered radiation, diffraction, and regular wave cases and compared quantities, such as the WEC motion, power output and hydrodynamic loading.

Place, publisher, year, edition, pages
MDPI, 2019
Keywords
wave energy, numerical modelling, simulation, boundary element method, computational fluid dynamics
National Category
Environmental Engineering
Identifiers
urn:nbn:se:kth:diva-266242 (URN)10.3390/jmse7110379 (DOI)000502261500002 ()2-s2.0-85075672461 (Scopus ID)
Note

QC 20200103

Available from: 2020-01-03 Created: 2020-01-03 Last updated: 2020-01-03Bibliographically approved
Nguyen, V. D., Leoni, M., Dancheva, T., Jansson, J., Hoffman, J., Wassermann, D. & Li, J.-R. (2019). Portable simulation framework for diffusion MRI. Journal of magnetic resonance, 309, Article ID 106611.
Open this publication in new window or tab >>Portable simulation framework for diffusion MRI
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2019 (English)In: Journal of magnetic resonance, ISSN 1090-7807, E-ISSN 1096-0856, Vol. 309, article id 106611Article in journal (Refereed) Published
Abstract [en]

The numerical simulation of the diffusion MRI signal arising from complex tissue micro-structures is helpful for understanding and interpreting imaging data as well as for designing and optimizing MRI sequences. The discretization of the Bloch-Torrey equation by finite elements is a more recently developed approach for this purpose, in contrast to random walk simulations, which has a longer history. While finite elements discretization is more difficult to implement than random walk simulations, the approach benefits from a long history of theoretical and numerical developments by the mathematical and engineering communities. In particular, software packages for the automated solutions of partial differential equations using finite elements discretization, such as FEniCS, are undergoing active support and development. However, because diffusion MRI simulation is a relatively new application area, there is still a gap between the simulation needs of the MRI community and the available tools provided by finite elements software packages. In this paper, we address two potential difficulties in using FEniCS for diffusion MRI simulation. First, we simplified software installation by the use of FEniCS containers that are completely portable across multiple platforms. Second, we provide a portable simulation framework based on Python and whose code is open source. This simulation framework can be seamlessly integrated with cloud computing resources such as Google Colaboratory notebooks working on a web browser or with Google Cloud Platform with MPI parallelization. We show examples illustrating the accuracy, the computational times, and parallel computing capabilities. The framework contributes to reproducible science and open-source software in computational diffusion MRI with the hope that it will help to speed up method developments and stimulate research collaborations.

Place, publisher, year, edition, pages
Academic Press, 2019
Keywords
Cloud computing, diffusion MRI, Bloch-Torrey equation, interface conditions, pseudo-periodic conditions, FEniCS.
National Category
Mathematics
Research subject
Applied and Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-256328 (URN)10.1016/j.jmr.2019.106611 (DOI)000497799500005 ()31574354 (PubMedID)2-s2.0-85072714990 (Scopus ID)
Note

QC 20190822

Available from: 2019-08-21 Created: 2019-08-21 Last updated: 2019-12-13Bibliographically approved
Nguyen, V. D., Jansson, J., Goude, A. & Hoffman, J. (2019). Technical Report -- Comparison of Direct Finite Element Simulation with Actuator Line Models and Vortex Models for Simulation of Turbulent Flow Past a Vertical Axis wind Turbine.
Open this publication in new window or tab >>Technical Report -- Comparison of Direct Finite Element Simulation with Actuator Line Models and Vortex Models for Simulation of Turbulent Flow Past a Vertical Axis wind Turbine
2019 (English)Report (Other (popular science, discussion, etc.))
Abstract [en]

We compare three different methodologies for simulation of turbulent flow past a vertical axis wind turbine: (i) full resolution of the turbine blades in a Direct Finite Element Simulation (DFS), (ii) implicit representation of the turbine blades in a 3D Actuator Line Method (ALM), and (iii) implicit representation of the turbine blades as sources in a Vortex Model (VM). The integrated normal force on one blade is computed for a range of azimuthal angles, and is compared to experimental data for the different tip speed ratios, 2.55, 3.44 and 4.09.

Publisher
p. 11
Keywords
VAWT, DFS-ALE, Actuator Line Models, Vortex Models
National Category
Engineering and Technology Natural Sciences
Identifiers
urn:nbn:se:kth:diva-257890 (URN)
Note

QC 20190909

Available from: 2019-09-08 Created: 2019-09-08 Last updated: 2019-11-01Bibliographically approved
Spühler, J. H., Jansson, J., Jansson, N. & Hoffman, J. (2018). 3D Fluid-Structure Interaction Simulation of Aortic Valves Using a Unified Continuum ALE FEM Model. Frontiers in Physiology, 9, Article ID 363.
Open this publication in new window or tab >>3D Fluid-Structure Interaction Simulation of Aortic Valves Using a Unified Continuum ALE FEM Model
2018 (English)In: Frontiers in Physiology, ISSN 1664-042X, E-ISSN 1664-042X, Vol. 9, article id 363Article in journal (Refereed) Published
Abstract [en]

Due to advances in medical imaging, computational fluid dynamics algorithms and high performance computing, computer simulation is developing into an important tool for understanding the relationship between cardiovascular diseases and intraventricular blood flow. The field of cardiac flow simulation is challenging and highly interdisciplinary. We apply a computational framework for automated solutions of partial differential equations using Finite Element Methods where any mathematical description directly can be translated to code. This allows us to develop a cardiac model where specific properties of the heart such as fluid-structure interaction of the aortic valve can be added in a modular way without extensive efforts. In previous work, we simulated the blood flow in the left ventricle of the heart. In this paper, we extend this model by placing prototypes of both a native and a mechanical aortic valve in the outflow region of the left ventricle. Numerical simulation of the blood flow in the vicinity of the valve offers the possibility to improve the treatment of aortic valve diseases as aortic stenosis (narrowing of the valve opening) or regurgitation (leaking) and to optimize the design of prosthetic heart valves in a controlled and specific way. The fluid-structure interaction and contact problem are formulated in a unified continuum model using the conservation laws for mass and momentum and a phase function. The discretization is based on an Arbitrary Lagrangian-Eulerian space-time finite element method with streamline diffusion stabilization, and it is implemented in the open source software Unicorn which shows near optimal scaling up to thousands of cores. Computational results are presented to demonstrate the capability of our framework.

Place, publisher, year, edition, pages
Frontiers Media S.A., 2018
Keywords
fluid-structure interaction, finite element method, Arbitrary Lagrangian-Eulerian method, parallel algorithm, blood flow, patient specific heart model
National Category
Physiology
Identifiers
urn:nbn:se:kth:diva-226752 (URN)10.3389/fphys.2018.00363 (DOI)000430119500001 ()2-s2.0-85045511659 (Scopus ID)
Funder
Swedish Foundation for Strategic Research Swedish Research Council
Note

QC 20180503

Available from: 2018-05-03 Created: 2018-05-03 Last updated: 2018-05-03Bibliographically approved
Nguyen, V. D., Jansson, J., Frachon, T., Degirmenci, C. & Hoffman, J. (2018). A fluid-structure interaction model with weak slip velocity boundary conditions on conforming internal interfaces. In: : . Paper presented at 6th European Conference on Computational Mechanics (ECCM), 7th European Conference on Computational Fluid Dynamics (ECFD 7), 1115 June 2018, Glasgow, UK.
Open this publication in new window or tab >>A fluid-structure interaction model with weak slip velocity boundary conditions on conforming internal interfaces
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2018 (English)Conference paper, Published paper (Other (popular science, discussion, etc.))
Abstract [en]

We develop a PUFEM–Partition of Unity Finite Element Method to impose slip velocity boundary conditions on conforming internal interfaces for a fluid-structure interaction model. The method facilitates a straightforward implementation on the FEniCS/FEniCS-HPC platform. We show two results for 2D model problems with the implementation on FEniCS: (1) optimal convergence rate is shown for a stationary Navier-Stokes flow problem, and (2) the slip velocity conditions give qualitatively the correct result for the Euler flow. 

Keywords
fluid-structure interaction, slip boundary conditions, conforming meshes, internal interfaces
National Category
Computational Mathematics
Research subject
Applied and Computational Mathematics; Computer Science
Identifiers
urn:nbn:se:kth:diva-225143 (URN)
Conference
6th European Conference on Computational Mechanics (ECCM), 7th European Conference on Computational Fluid Dynamics (ECFD 7), 1115 June 2018, Glasgow, UK
Note

QC 20190215

Available from: 2018-03-31 Created: 2018-03-31 Last updated: 2019-11-01Bibliographically approved
Nguyen, V. D., Jansson, J., Hoffman, J. & Li, J.-R. (2018). A partition of unity finite element method for computational diffusion MRI. Journal of Computational Physics, 375, 271-290
Open this publication in new window or tab >>A partition of unity finite element method for computational diffusion MRI
2018 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 375, p. 271-290Article in journal (Refereed) Published
Abstract [en]

The Bloch–Torrey equation describes the evolution of the spin (usually water proton) magnetization under the influence of applied magnetic field gradients and is commonly used in numerical simulations for diffusion MRI and NMR. Microscopic heterogeneity inside the imaging voxel is modeled by interfaces inside the simulation domain, where a discontinuity in the magnetization across the interfaces is produced via a permeability coefficient on the interfaces. To avoid having to simulate on a computational domain that is the size of an entire imaging voxel, which is often much larger than the scale of the microscopic heterogeneity as well as the mean spin diffusion displacement, smaller representative volumes of the imaging medium can be used as the simulation domain. In this case, the exterior boundaries of a representative volume either must be far away from the initial positions of the spins or suitable boundary conditions must be found to allow the movement of spins across these exterior boundaries.

Many approaches have been taken to solve the Bloch–Torrey equation but an efficient high-performance computing framework is still missing. In this paper, we present formulations of the interface as well as the exterior boundary conditions that are computationally efficient and suitable for arbitrary order finite elements and parallelization. In particular, the formulations are based on the partition of unity concept which allows for a discontinuous solution across interfaces conforming with the mesh with weak enforcement of real (in the case of interior interfaces) and artificial (in the case of exterior boundaries) permeability conditions as well as an operator splitting for the exterior boundary conditions. The method is straightforward to implement and it is available in FEniCS for moderate-scale simulations and in FEniCS-HPC for large-scale simulations. The order of accuracy of the resulting method is validated in numerical tests and a good scalability is shown for the parallel implementation. We show that the simulated dMRI signals offer good approximations to reference signals in cases where the latter are available and we performed simulations for a realistic model of a neuron to show that the method can be used for complex geometries.

Place, publisher, year, edition, pages
Elsevier, 2018
Keywords
Computational diffusion MRI, Bloch–Torrey equation, Partition of unity finite element method, Interface conditions, Weak pseudo-periodic conditions, FEniCS/FEniCS-HPC
National Category
Computational Mathematics
Research subject
Applied and Computational Mathematics; Biological Physics; Computer Science
Identifiers
urn:nbn:se:kth:diva-234286 (URN)10.1016/j.jcp.2018.08.039 (DOI)000450907600014 ()2-s2.0-85054048672 (Scopus ID)
Funder
Swedish Energy Agency, P40435-1
Note

QC 20180906

Available from: 2018-09-06 Created: 2018-09-06 Last updated: 2019-11-01Bibliographically approved
Degirmenci, N. C., Jansson, J., Hoffman, J., Arnela, M., Sánchez-Martín, P., Guasch, O. & Ternström, S. (2017). A Unified Numerical Simulation of Vowel Production That Comprises Phonation and the Emitted Sound. In: Proceedings of the Annual Conference of the International Speech Communication Association, INTERSPEECH 2017: . Paper presented at 18th Annual Conference of the International Speech Communication Association, INTERSPEECH 2017, Stockholm, Sweden, 20 August 2017 through 24 August 2017 (pp. 3492-3496). The International Speech Communication Association (ISCA)
Open this publication in new window or tab >>A Unified Numerical Simulation of Vowel Production That Comprises Phonation and the Emitted Sound
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2017 (English)In: Proceedings of the Annual Conference of the International Speech Communication Association, INTERSPEECH 2017, The International Speech Communication Association (ISCA), 2017, p. 3492-3496Conference paper, Published paper (Refereed)
Abstract [en]

A unified approach for the numerical simulation of vowels is presented, which accounts for the self-oscillations of the vocal folds including contact, the generation of acoustic waves and their propagation through the vocal tract, and the sound emission outwards the mouth. A monolithic incompressible fluid-structure interaction model is used to simulate the interaction between the glottal jet and the vocal folds, whereas the contact model is addressed by means of a level set application of the Eikonal equation. The coupling with acoustics is done through an acoustic analogy stemming from a simplification of the acoustic perturbation equations. This coupling is one-way in the sense that there is no feedback from the acoustics to the flow and mechanical fields. All the involved equations are solved together at each time step and in a single computational run, using the finite element method (FEM). As an application, the production of vowel [i] has been addressed. Despite the complexity of all physical phenomena to be simulated simultaneously, which requires resorting to massively parallel computing, the formant locations of vowel [i] have been well recovered.

Place, publisher, year, edition, pages
The International Speech Communication Association (ISCA), 2017
Series
Proceedings of the Annual Conference of the International Speech Communication Association, INTERSPEECH, ISSN 2308-457X ; 2017
Keywords
Numerical voice production, phonation, vocal tract acoustics, fluid-structure interaction, finite element method
National Category
Fluid Mechanics and Acoustics
Research subject
Applied and Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-219554 (URN)10.21437/Interspeech.2017-1239 (DOI)000457505000727 ()2-s2.0-85039159138 (Scopus ID)
Conference
18th Annual Conference of the International Speech Communication Association, INTERSPEECH 2017, Stockholm, Sweden, 20 August 2017 through 24 August 2017
Projects
Eunison
Funder
EU, FP7, Seventh Framework Programme, 308874
Note

QC 20171211

Available from: 2017-12-07 Created: 2017-12-07 Last updated: 2020-02-19Bibliographically approved
Jansson, J., Degirmenci, N. C. & Hoffman, J. (2017). Adaptive unified continuum FEM modeling of a 3D FSI benchmark problem. International Journal for Numerical Methods in Biomedical Engineering, 33(9), Article ID e2851.
Open this publication in new window or tab >>Adaptive unified continuum FEM modeling of a 3D FSI benchmark problem
2017 (English)In: International Journal for Numerical Methods in Biomedical Engineering, ISSN 2040-7939, E-ISSN 2040-7947, Vol. 33, no 9, article id e2851Article in journal (Refereed) Published
Abstract [en]

In this paper, we address a 3D fluid-structure interaction benchmark problem that represents important characteristics of biomedical modeling. We present a goal-oriented adaptive finite element methodology for incompressible fluid-structure interaction based on a streamline diffusion–type stabilization of the balance equations for mass and momentum for the entire continuum in the domain, which is implemented in the Unicorn/FEniCS software framework. A phase marker function and its corresponding transport equation are introduced to select the constitutive law, where the mesh tracks the discontinuous fluid-structure interface. This results in a unified simulation method for fluids and structures. We present detailed results for the benchmark problem compared with experiments, together with a mesh convergence study.

Place, publisher, year, edition, pages
Wiley-Blackwell, 2017
Keywords
adaptive finite element method, benchmark problem, fluid-structure interaction, Benchmarking, Computer programming, Diffusion in liquids, Finite element method, Mesh generation, Transport properties, Adaptive finite element, Adaptive finite element methods, Bench-mark problems, Bio-medical models, Fluid-structure interfaces, Incompressible fluid-structure interaction, Software frameworks, Streamline diffusion, Fluid structure interaction
National Category
Computer and Information Sciences
Identifiers
urn:nbn:se:kth:diva-216185 (URN)10.1002/cnm.2851 (DOI)000409217800004 ()27863119 (PubMedID)2-s2.0-85017639985 (Scopus ID)
Note

QC 20171124

Available from: 2017-11-24 Created: 2017-11-24 Last updated: 2020-03-09Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-4256-0463

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