Johan Hoffman

KTH Royal Institute of Technology | KTH · Department of Computer Science

In this work we propose a new stabilized approach for solving the incompressible Navier-Stokes equations on fixed overlapping grids. This new approach is based on the partition of unity finite element method, which defines the solution fields as weighted sums of local fields, supported by the different grids. Here, the discrete weak formulation of...

In the context of flow visualization a triple decomposition of the velocity gradient was proposed by Kolat in 2007 who demonstrated the technique in 2D, which was later realized in 3D by Nagata et al. in 2020. The triple decomposition opens for a refined energy stability analysis of the Navier-Stokes equations, with implications for the mathematica...

An interface tracking finite element methodology is presented for 3D turbulent flow fluid‐structure interaction, including full‐friction contact and topology changes, with specific focus on heart valve simulations. The methodology is based on a unified continuum fluid‐structure interaction model, which is a monolithic approach where the fundamental...

We present a high performance computing framework for finite element simulation of blood flow in the left ventricle of the human heart. The mathematical model is described together with the discretization method and the parallel implementation in Unicorn which is part of the open source software framework FEniCS-HPC. We show results based on patien...

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...

To date, it is unclear how fluid dynamics stimulate mechanosensory cells to induce an osteoprotective or osteodestructive response. We investigated how murine hematopoietic progenitor cells respond to 2 minutes of dynamic fluid flow stimulation with a precisely controlled sequence of fluid shear stresses. The response was quantified by measuring ex...

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...

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...

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...

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...

For problems involving large deformations of thin structures, simulating fluid-structure interaction (FSI) remains challenging largely due to the need to balance computational feasibility, efficiency, and solution accuracy. Overlapping domain techniques have been introduced as a way to combine the fluid-solid mesh conformity, seen in moving-mesh me...

The Bloch-Torrey partial differential equation can be used to describe the evolution of the transverse magnetization of the imaged sample under the influence of diffusion-encoding magnetic field gradients inside the MRI scanner. The integral of the magnetization inside a voxel gives the simulated diffusion MRI signal. This paper proposes a finite e...

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 h...

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 h...

The Bloch-Torrey partial differential equation describes the evolution of the transverse magnetization under the influence of diffusion-encoding magnetic field gradients inside a three-dimensional medium. The integral of the magnetization inside a voxel gives the simulated diffusion MRI signal. This paper proposes a finite element discretization on...

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 disconti...

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)...

We present an adaptive finite element method for time-resolved simulation of aerodynamics without any turbulence-model parameters, which is applied to a benchmark problem from the HiLiftPW-3 workshop to compute the flow past a JAXA Standard Model (JSM) aircraft model at realistic Reynolds numbers. The mesh is automatically constructed by the method...

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...

We develop a general high performance computing framework in FEniCS-HPC for mesh conforming interface conditions with two concrete examples: (1) diffusion in biological tissues and (2) turbulent flow fluid-structure interaction (FSI) models.

We give a brief introduction to research on adaptive computational methods for laminar compressible and incompressible flows and then focus on computability and adaptivity for turbulent incompressible flow, where we present a framework for adaptive finite element methods with duality-based a posteriori error control for chosen output quantities of...

We present a locally adapted parametric finite element method for interface problems. For this adapted finite element method we show optimal convergence for elliptic interface problems with a discontinuous diffusion parameter. The method is based on the adaption of macroelements where a local basis represents the interface. The macroelements are in...

This is the first joint reference paper for the Ocean Energy Systems (OES) Task 10 Wave Energy Converter modeling verification and validation group. The group is established under the OES Energy Technology Network program under the International Energy Agency. OES was founded in 2001 and Task 10 was proposed by Bob Thresher (National Renewable Ener...

The combination of medical imaging with computational fluid dynamics (CFD) has enabled the study of 3D blood flow on a patient-specific level. However, with models based on gated high-resolution data, the study of transient flows, and any model implementation into routine cardiac care, is challenging. The present paper presents a novel pathway for...

We combine the unified continuum fluid-structure interaction method with a mul-tiphase flow model to simulate turbulent flow and fluid-structure interaction of rotating vertical axis turbines in offshore environments. This work is part of a project funded by the Swedish Energy Agency, which focuses on energy systems combining ecological sustainabil...

Echocardiography is the most commonly used image modality in cardiology, assessing several aspects of cardiac viability. The importance of cardiac hemodynamics and 4D blood flow motion has recently been highlighted, however such assessment is still difficult using routine echo-imaging. Instead, combining imaging with computational fluid dynamics (C...

We present a framework for coupled multiphysics in computational fluid dynamics, targeting massively parallel systems. Our strategy is based on general problem formulations in the form of partial differential equations and the finite element method, which open for automation, and optimization of a set of fundamental algorithms. We describe these al...

In this paper we address a 3D fluid-structure interaction (FSI) benchmark problem that represents important characteristics of biomedical modeling. We present a goal-oriented adaptive finite element methodology for incompressible FSI based on a streamline-diffusion type stabilization of the balance equations for mass and momentum for the entire con...

We present a locally adapted parametric finite element method for interface problems. Optimal convergence for elliptic interface problems with a discontinuous diffusion parameter is shown. The method is based on adaption of macro elements where a local basis represents the interface.

The combination of refined medical imaging techniques and computational fluid dynamics (CFD) models has enabled the study of complex flow behavior on a highly regional level. Recently, we have developed a platform for patient-specific CFD modelling of blood flow in the left ventricle (LV), with input data and required boundary conditions acquired f...

In diffusion nuclear magnetic resonance (NMR) and diffusion magnetic resonance imaging (MRI), the multi-compartment Bloch-Torrey equation plays an important role in probing the diffusion characteristics from a nanometer scale to a macroscopic scale. The signal attenuation can be computed by solving the equation. If the volume of interest is compose...

We present a new mathematical theory explaining the fluid mechanics of subsonic flight, which is fundamentally different from the existing boundary layer-circulation theory by Prandtl–Kutta–Zhukovsky formed 100 year ago. The new theory is based on our new resolution of d’Alembert’s paradox showing that slightly viscous bluff body flow can be viewed...

This work presents a direct comparison of unsteady, turbulent flow simulations with measurements performed using a Gulfstream G550 nose landing gear model. The experimental campaign, which was carried out by researchers from the NASA Langley Research Center, provided a series of detailed, well documented wind-tunnel measurements for comparison and...

In recent years, computational fluid dynamics (CFD) simulations on in-silico models of the heart have provided a valuable insight into cardiac hemodynamic behaviour. However, so far most models have been either based on simplified geometries or on imaging acquisitions with relatively low temporal resolution. It has been suggested that models based...

Developing multiphysics finite element methods (FEM) and scalable HPC implementations can be very challenging in terms of software complexity and performance, even more so with the addition of goal-oriented adaptive mesh refinement. To manage the complexity we in this work present general adaptive stabilized methods with automated implementation in...

Offshore floating platforms for wind turbines represent challenging concepts for designers trying to combine an optimal compromise between cost effectiveness and performance. Modelling of the hydrodynamic behaviour of the structure is still the subject of wide debate in the technical communities. The assessment of the hydrodynamics of the support s...

This article is a review of our work towards a parameter-free method for simulation of turbulent flow at high Reynolds numbers. In a series of papers we have developed a model for turbulent flow in the form of weak solutions of the Navier-Stokes equations, approximated by an adaptive finite element method, where: (i) viscous dissipation is assumed...

We present our simulation results for the benchmark problem of the flow past a rudimentary landing gear using a General Galerkin FEM, also referred to as adaptive DNS/LES. In General Galerkin, no explicit subgrid model is used; instead, the computational mesh is adaptively refined with respect to an a posteriori error estimate of a quantity of inte...

We present a time-resolved, adaptive finite element method for aerodynamics, together with the results from the HiLiftPW-2 workshop, where this method is used to compute the ow past a DLR-F11 aircraft model at realistic Reynolds number. The mesh is automatically constructed by the method as part of the computation, and no explicit turbulence model...

As a step toward building a more complete model of voice production mechanics, we assess the feasibility of a fluid-structure simulation of the vocal fold mechanics in the Unicorn incompressible Unified Continuum framework. The Unicorn framework consists of conservation equations for mass and momentum, a phase function selecting solid or fluid cons...

We report the latest results obtained in the development of an adaptive finite element method for computational aeroacoustics (CAA). The new methodology is based on the General Galerkin (G2) method, which has been successfully used for the computation of incompressible, turbulent flow. Here, we simulate the flow past an in-duct mixer plate and comp...

This is a summary of preliminary results from simulations with the 30P30N high-lift device. We used the General Galerkin finite element method (G2), where no explicit subgrid model is used, and where the computational mesh is adaptively refined with respect to a posteriori error estimates for a quantity of interest. The mesh is fully unstructured a...

We present developments in the Unicorn-HPC framework for unified continuum mechanics, enabling adaptive finite element computation of fluid-structure interaction, and an overview of the larger FEniCS-HPC framework for automated solution of partial diffential equations of which Unicorn-HPC is a part. We formulate the basic model and finite element d...

In this paper we describe a general adaptive finite element framework for unstructured tetrahedral meshes without hanging nodes suitable for large scale parallel computations. Our framework is designed to scale linearly to several thousands of processors, using fully distributed and efficient algorithms. The key components of our implementation, lo...

This chapter provides a description of the technology of Unicorn focusing on simple, efficient and 10597 general algorithms and software for the Unified Continuum (UC) concept and the adaptive General 10598 Galerkin (G2) discretization as a unified approach to continuum mechanics.

The FEniCS project aims towards the goals of generality, efficiency, and simplicity, concerning mathematical methodology, implementation and application, and the Unicorn project is an imple- mentation aimed at FSI and high Re turbulent flow guided by these principles. Unicorn is based on the DOLFIN/FFC/FIAT suite and the linear algebra package PETS...

We present a framework for adaptive finite element computation of turbulent flow and fluid–structure interaction, with focus on general algorithms that allow for complex geometry and deforming domains. We give basic models and finite element discretization methods, adaptive algorithms and strategies for efficient parallel implementation. To illustr...

In this paper we first review our recent work on a new framework for adaptive turbulence simulation: we model turbulence by weak solutions to the Navier–Stokes equations that are wellposed with respect to mean value output in the form of functionals, and we use an adaptive finite element method to compute approximations with a posteriori error cont...

In this article we describe an incompressible Unified Continuum (UC) model in Euler (laboratory) coordinates with a moving mesh for tracking the fluid-structure interface as part of the discretization, allowing simple and general formulation and efficient computation. The model consists of conservation equations for mass and momentum, a phase conve...

We show by computational solution of the incompressible Navier-Stokes equa- tions with friction force boundary conditions, that the cla ssical inviscid circulation theory by Kutta-Zhukovsky for lift and laminar viscous boundary layer theory by Prandtl for drag, which have dominated 20th century fluid dyn amics, do not cor- rectly describe the real...

We present a deterministic foundation of thermodynamics for slightly viscous fluids or gases based on a 1st Law in the form of the Euler equations express-ing conservation of mass, momentum and energy, and a 2nd Law formulated in terms of kinetic energy, internal (heat) energy, work and shock/turbulent dissipa-tion, without reference to entropy. Th...

We propose a resolution of d’Alembert’s Paradox comparing observation of substantial drag/lift in fluids with very small viscosity such as air and water, with the mathematical prediction of zero drag/lift of stationary irrotational solutions of the incompressible inviscid Euler equations, referred to as potential flow. We present analytical and com...

In this paper, we identify and propose solutions for several issues encountered when designing a mesh adaptation package, such as mesh-to-mesh projections and mesh database design, and we describe an algorithm to integrate a mesh adaptation procedure in a physics solver. The open-source MAdLib package is presented as an example of such a mesh adapt...

General Galerkin (G2) is a new computational method for turbulent flow, where a stabilized Galerkin finite element method is used to compute approximate weak solutions to the Navier–Stokes equations directly, without any filtering of the equations as in a standard approach to turbulence simulation, such as large eddy simulation, and thus no Reynold...

We show by computational solution of the incompressible Navier-Stokes equa- tions with friction force boundary conditions, that the cla ssical inviscid circulation theory by Kutta-Zhukovsky for lift of a wing and laminar viscous boundary layer theory by Prandtl for drag, which have dominated 20th century flight mechan- ics, do not correctly describ...

Abstract We present a new matematical and physical explanation of the generation of lift and drag of an airplane wing, which is fundamentally different from the explana- tions by Kutta-Zhukovsky connecting lift to circulation and by Prandtl connecting drag to boundary layer friction, which have dominated 20th century flight mechan- ics and still re...

We discuss the formulation of the Clay Mathematics Institute Millen-nium Prize Problem on the Navier-Stokes equations in the perspective of Hadamard's notion of wellposedness. 1 The Clay Navier-Stokes Millennium Problem The Clay Mathematics Institute Millennium Prize Problem on the incompress-ible Navier-Stokes equations [3, 7] asks for a proof of...

We present evidence that the problem of breakdown/blowup of smooth solutions of the Euler and Navier-Stokes equations, is closely related to Hadamard's concepts of wellposedness and illposedness. We present a combined criterion for blowup, based on detecting increasing L2-residuals and stability factors, which can be tested computationally on meshe...

We present analytical and computational evidence of blowup of initially smooth solutions of the incompressible Euler equations into non-smooth turbulent solutions. We detect blowup by observing increasing L 2-residuals of computed solutions under decreasing mesh size.

We review our work on adaptivity and error control for turbulent flow, and we present recent developments on turbulent boundary layer flow. The computational method G2 is not based on filtering of the Navier-Stokes (NS) equations, and thus no Reynolds (subgrid) stresses are introduced. Instead the mathematical basis is ϵ-weak solutions to the NS eq...

We propose a new resolution to d'Alembert's Paradox from 1752 comparing the mathematical prediction of zero drag (resistance to motion) through an ideal (zero viscosity) incompressible uid, with massive observations of non-zero drag in uids with very small viscosity, such as air and water. Our resolution is fundamentally dieren t from the accepted...

We identify, by computing turbulent solutions of the incompressible Navier- Stokes equations with friction force boundary conditions, the physical mechanisms generating lift and drag of a wing, which make it possible to fl y with a lift/drag ra- tio larger than 10. We discover mechanisms fundamentally different from those of the classical inviscid...

Applied Mathematics: Body&Soul is a mathematics education reform program including a series of books, together with associated educational material and open source software freely available from the project web page at www.bodysoulmath.org. Body&Soul reflects the revolutionary new possibilities of mathematical modeling opened by the modern computer...

This is Volume 4 of the book series of the Body & Soul mathematics education reform program, and presents a unified new approach to computational simulation of turbulent flow starting from the general basis of calculus and linear algebra of Vol 1-3. The book puts the Body & Soul computational finite element methodology in the form of General Galerk...