We describe the Adaptive Euler methodology, and results from the 5th High Lift Prediction Workshop, showing good validation and high efficiency, building on our good results from the 4th workshop [74]. Adaptive Euler is first principles FEM simulation with adjoint-based adaptive error control, realized with automated discretization from mathematical notation in our FEniCS [81] framework. We describe a prototype extension of the methodology to aeroelasticity also with adjoint-based adaptive error control, such methods are highlighted as having “great potential” in the field of aeroelasticity in [80]. In the 5th workshop a tail was added to the aircraft, and we have been able to show good validation for such cases, and showing a wake-tail interaction at stall. One aim has been to investigate the limits of performance - how coarse meshes are possible with Adaptive Euler? We have been able to show mesh-independent results already on extremely coarse meshes of appx. 200k vertices for the full span - appx. 10x coarser than our results for the 4th workshop. These extremely coarse meshes have been generated by Helden Aerospace with their HeldenMesh mesh generator. We show that the Adaptive Euler by the scientific method in our reproducible Digital Math framework predicts drag, lift, pitch moment and pressure distribution in close correspondence with experiments in the 5th High Lift PredictionWorkshops, with very high efficiency, estimated to 100x faster and cheaper than RANS, the industry standard for efficient aerodynamics, corresponding to appx. 100 core hours on a commodity computational resource. Reproducibility and Open Science is described as the goal of all NASA activities in [87], we see that we realize this already today. One guiding incentive for thiswork is to develop an efficient and versatile tool for aeroelasticity modeling with the Adaptive Euler methodology. Such a product is highly sought after and is motivated in part by the CFD Vision 2030 [86] set by NASA and the Certification by Analysis 2040 Vision [77] set by Boeing. The consequences of this would include-but are not limited to-the eventual development of a full fluid-structure interaction (FSI) framework that may be used for applications in aerospace engineering, including in the general Unified Continuum FSI (UC-FSI) framework we have previously developed. As such, we present numerical simulations designed to test benchmark problems in the field of aeroelasticity. These problems are chosen based on their relevance to current challenges and potential for extension, and the results are compared to experimental data when available. We view these simulations as critical building blocks towards the development of a full Adaptive Euler framework for aeroelasticity.

We show that computing turbulent solutions to Euler’s equations with a slip boundary condition offers a Theory of Everything ToE for slightly viscous incompressible fluid flow as a parameter-free model, covering a vast area of applications in vehicle aero/hydrodynamics including airplanes, ships and cars. This work resolves the Grand Challenges of fluid dynamics described in NASA Vision 2030. The foundation of the methodology is an extremely efficient Direct FEM Simulation (DFS) method. We describe a breakthrough in efficiency, allowing extrenely small numerical dissipation by choosing very small stabilization coefficients, while allowing very large time step size. This work is developed as part of the Digital Math framework [2]-as the foundation of modern science based on constructive digital mathematical computation. We show that Euler CFD by the scientific method in Digital Math predicts drag, lift and pressure distribution in close correspondence with observations for real problems with complex geometry and so can serve to deliver complete realistic aero/hydro-data for simulators without input from model experiments in wind tunnel and towing tank or full-scale experiments, as a new revolutionary capability. 

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 patient-specific data that capture essential features observed with other computational models and imaging techniques, and thus indicate that our framework possesses the potential to provide relevant clinical information for diagnosis and medical treatment. Several other studies have been conducted to simulate the three dimensional blood flow in the left ventricle of the human heart with prescribed wall movement. Our contribution to the field of cardiac research lies in establishing an open source framework modular both in modelling and numerical algorithms.

Radiofrequency catheter ablation (RFCA) is an effective treatment for cardiac arrhythmias. Although generally safe, it is not completely exempt from the risk of complications. The great flexibility of computational models can be a major asset in optimizing interventional strategies if they can produce sufficiently precise estimations of the generated lesion for a given ablation protocol. This requires an accurate description of the catheter tip and the cardiac tissue. In particular, the deformation of the tissue under the catheter pressure during the ablation is an important aspect that is overlooked in the existing literature, which resorts to a sharp insertion of the catheter into an undeformed geometry. As the lesion size depends on the power dissipated in the tissue and the latter depends on the percentage of the electrode surface in contact with the tissue itself, the sharp insertion geometry has the tendency to overestimate the lesion obtained, which is a consequence of the tissue temperature rise overestimation. In this paper, we introduce a full 3D computational model that takes into account the tissue elasticity and is able to capture tissue deformation and realistic power dissipation in the tissue. Numerical results in FEniCS-HPC are provided to validate the model against experimental data and to compare the lesions obtained with the new model and with the classical ones featuring a sharp electrode insertion in the tissue.

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 element discretization on manifolds in order to efficiently simulate the diffusion MRI signal in domains that have a thin layer or a thin tube geometrical structure. The variable thickness of the three-dimensional domains is included in the weak formulation established on the manifolds. We conducted a numerical study of the proposed approach by simulating the diffusion MRI signals from the extracellular space (a thin layer medium) and from neurons (a thin tube medium), comparing the results with the reference signals obtained using a standard three-dimensional finite element discretization. We show good agreements between the simulated signals using our proposed method and the reference signals for a wide range of diffusion MRI parameters. The approximation becomes better as the diffusion time increases. The method helps to significantly reduce the required simulation time, computational memory, and difficulties associated with mesh generation, thus opening the possibilities to simulating complicated structures at low cost for a better understanding of diffusion MRI in the brain.

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.

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.

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.

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.