Open-source Computational Fluid Dynamics Solver Research Articles

Lifex-cfd: An open-source computational fluid dynamics solver for cardiovascular applications

Computational fluid dynamics (CFD) is an important tool for the simulation of the cardiovascular function and dysfunction. Due to the complexity of the anatomy, the transitional regime of blood flow in the heart, and the strong mutual influence between the flow and the physical processes involved in the heart function, the development of accurate and efficient CFD solvers for cardiovascular flows is still a challenging task. In this paper we present life▪-cfd, an open-source CFD solver for cardiovascular simulations based on the life▪ finite element library, written in modern C++ and exploiting distributed memory parallelism. We model blood flow in both physiological and pathological conditions via the incompressible Navier-Stokes equations, accounting for moving cardiac valves, moving domains, and transition-to-turbulence regimes. In this paper, we provide an overview of the underlying mathematical formulation, numerical discretization, implementation details and examples on how to use life▪-cfd. We verify the code through rigorous convergence analyses, and we show its almost ideal parallel speedup. We demonstrate the accuracy and reliability of the numerical methods implemented through a series of idealized and patient-specific vascular and cardiac simulations, in different physiological flow regimes. The life▪-cfd source code is available under the LGPLv3 license, to ensure its accessibility and transparency to the scientific community, and to facilitate collaboration and further developments. Program summaryProgram Title:life▪-cfdCPC Library link to program files:https://doi.org/10.17632/hzsnc3jgds.1Developer's repository link:https://gitlab.com/lifex/lifex-cfdLicensing provisions:LGPLv3Programming language: C++ (standard ≥17)Supplementary material:https://doi.org/10.5281/zenodo.7852088 contains the application executable in binary form, compatible with any recent enough x86-64 Linux system, assuming that glibc version ≥ 2.28 is installed. Data and parameter files necessary to replicate the test cases described in this manuscript are also available.Nature of problem: The program allows to run computational fluid dynamics simulations of cardiovascular blood flows in physiological and pathological conditions, modeled through incompressible Navier-Stokes equations, including moving cardiac valves, moving domains (such as contracting cardiac chambers) in the arbitrary Lagrangian-Eulerian framework, and transition-to-turbulence flow. Given the scale of the typical applications, the program is designed for parallel execution.Solution method: The equations are discretized using the Finite Element method, on either tetrahedral or hexahedral meshes. The software builds on top of deal.II, implementing the mathematical models and numerical methods specific for CFD cardiovascular simulations. Parallel execution exploits the MPI paradigm. The software supports both Trilinos and PETSc as linear algebra backends.Additional comments including restrictions and unusual features: The program provides a general-purpose executable that can be used to run CFD simulations without having to access or modify the source code. The program allows to setup simulations through a user-friendly yet flexible interface, by means of readable and self-documenting parameter files. On top of that, more advanced users can modify the source code to implement more sophisticated test cases. life▪-cfd supports checkpointing, i.e. simulations can be stopped and restarted at a later time.

A graph neural network-based framework to identify flow phenomena on unstructured meshes

Driven by the abundant data generated from computational fluid dynamics (CFD) simulations, machine learning (ML) methods surpass the deterministic criteria on flow phenomena identification in the way that they are independent of a case-by-case threshold by combining the flow field properties and the topological distribution of the phenomena. The current most popular and successful ML models based on convolutional neural networks are limited to structured meshes and unable to directly digest the data generated from unstructured meshes, which are more widely used in real industrial CFD simulations. We proposed a framework based on graph neural networks with the proposed fast Gaussian mixture model as the convolution kernel and U-Net architecture to detect flow phenomena based on a graph hierarchy generated by the algebraic multigrid method embedded in the open-source CFD solver, code_saturne. We demonstrate the superiority of the proposed kernel and U-Net architecture, along with the generality of the framework to unstructured mesh and unseen case, on detecting the vortices once trained on a single backward-facing step case. Our proposed framework can be trivially extended to detect more flow phenomena in three dimensional cases, which is ongoing work.

A verified and validated moving domain computational fluid dynamics solver with applications to cardiovascular flows.

Computational fluid dynamics (CFD) in combination with patient-specific medical images has been used to correlate flow phenotypes with disease initiation, progression and outcome, in search of a prospective clinical tool. A large number of CFD software packages are available, but are typically based on rigid domains and low-order finite volume methods, and are often implemented in massive low-level C++ libraries. Furthermore, only a handful of solvers have been appropriately verified and validated for their intended use. Our goal was to develop, verify and validate an open-source CFD solver for moving domains, with applications to cardiovascular flows. The solver is an extension of the CFD solver Oasis, which is based on the finite element method and implemented using the FEniCS open source framework. The new solver, named OasisMove, extends Oasis by expressing the Navier-Stokes equations in the arbitrary Lagrangian-Eulerian formulation, which is suitable for handling moving domains. For code verification we used the method of manufactured solutions for a moving 2D vortex problem, and for validation we compared our results against existing high-resolution simulations and laboratory experiments for two moving domain problems of varying complexity. Verification results showed that the error followed the theoretical convergence rates. The temporal accuracy was second-order, while the spatial accuracy was second- and third-order using and finite elements, respectively. Validation results showed good agreement with existing benchmark results, by reproducing lift and drag coefficients with less than 1% error, and demonstrating the solver's ability to capture vortex patterns in transitional and turbulent-like flow regimes. In conclusion, we have shown that OasisMove is an open-source, accurate and reliable solver for cardiovascular flows in moving domains.

An uncertainty-quantification framework for assessing accuracy, sensitivity, and robustness in computational fluid dynamics

Combining different existing uncertainty quantification (UQ) techniques, a framework is obtained to assess a set of metrics in computational physics problems, in general, and computational fluid dynamics (CFD), in particular. The metrics include accuracy, sensitivity and robustness of the simulator’s outputs with respect to uncertain inputs and parameters. These inputs and parameters are divided into two groups: based on the variation of the first group (e.g. numerical/computational parameters such as grid resolution), a computer experiment is designed, the data of which may become uncertain due to the parameters of the second group (e.g. finite time-averaging). To construct a surrogate model based on uncertain data, Gaussian process regression (GPR) with observation-dependent (heteroscedastic) noise is used. To estimate the propagated uncertainties in the simulator’s outputs from the first group of parameters, a probabilistic version of the polynomial chaos expansion (PCE) is employed Global sensitivity analysis is performed using probabilistic Sobol indices. To illustrate its capabilities, the framework is applied to the scale-resolving simulations of turbulent channel and lid-driven cavity flows using the open-source CFD solver Nek5000. It is shown that at wall distances where the time-averaging uncertainty is high, the quantities of interest are also more sensitive to numerical/computational parameters. In particular for high-fidelity codes such as Nek5000, a thorough assessment of the results’ accuracy and reliability is crucial. The detailed analyses and the resulting conclusions can enhance our insight into the influence of different factors on physics simulations, in particular the simulations of high-Reynolds-number turbulent flows including wall turbulence.

Hybrid Large Eddy Simulation for low-order Discontinuous Galerkin methods using an explicit filter

In this paper we present a simple, easily implemented and effective approach for explicitly-filtered Large Eddy Simulation with a Discontinuous Galerkin (DG) discretisation for velocity. DG formulations are often desirable due to their stability and increased accuracy, however this can come at greater computational expense due to the additional degrees of freedom in the velocity field. Additionally, data output can also be an issue, due to the increased storage requirements. Here we present a hybrid approach, based upon the construction of an approximation of the velocity shear tensor using information from a projected Continuous Galerkin (CG) version of the discontinuous velocity field. The resulting turbulence algorithm is implemented within Fluidity, an open-source computational fluid dynamics solver. The model is then validated with a well known test case, and shown to agree favourably with published results. Comparisons are also made between the CG/DG hybrid LES with DG-only LES, which demonstrate the superior computational performance of the hybrid model.

ADflow: An Open-Source Computational Fluid Dynamics Solver for Aerodynamic and Multidisciplinary Optimization

Computational fluid dynamics through the solution of the Navier–Stokes equations with turbulence models has become commonplace. However, simply solving these equations is not sufficient to be able to perform efficient design optimization with a flow solver in the loop. This paper discusses the recommendations for developing a flow solver that is suitable for efficient aerodynamic and multidisciplinary design optimization. One of the major recommendations is to be able to load the flow solver as a library that provides direct memory access to the relevant data. Other recommendations are to use a higher-level language for scripting and to pay special attention to solution warm starting, code efficiency, flow solver robustness, and solution failure handling. As an example of a flow solver that follows these recommendations, the open-source flow solver ADflow is presented. Results from aerodynamic optimization, aerostructural analysis, and aerostructural optimization using ADflow demonstrate the performance advantages claimed in the recommendations. The publication of these recommendations and the availability of the source code open the door for other solvers to adopt the same application programming interface. ADflow is part of a wider aerodynamic shape optimization tool suite that is also available under an open-source license.

Investigation of Zero Moment Point in a Partially Filled Liquid Vessel Subjected to Roll Motion

Liquid-handling robots are designed to dispense sub-microliter quantities of fluids for applications including laboratory tests. When larger amounts of liquids are involved, sloshing must be considered as a parameter affecting stability, which is of significance for autonomous vehicles. The measurement and quantification of slosh in enclosed volumes poses a challenge to researchers who have traditionally resorted to tracking the air–liquid interface for two-phase flow analysis. There is a need for a simpler method to predict rollover in these applications. In this work, a novel solution to address this problem is proposed in the form of the Zero Moment Point (ZMP) of a dynamic liquid region. Computational experiments of a partially filled, two-dimensional liquid vessel were carried out using the Volume of Fluid (VOF) method in a finite volume based open-source computational fluid dynamics solver. The movement of the air–liquid interface was tracked, while the Center of Mass and the resulting Zero Moment Point were determined from the numerical simulations at each time step. The computational model was validated by comparing the wall pressure and movement of the liquid-free surface to experimentally obtained values. It was concluded that for a dynamic liquid domain, the Zero Moment Point can be instrumental in determining the stability of partially filled containers subjected to sloshing.

A Correlation for the Discontinuity of the Temperature Variance Dissipation Rate at the Fluid-Solid Interface in Turbulent Channel Flows

Discontinuity of the dissipation rate associated with the temperature variance at the fluid-solid interface is analyzed in a turbulent channel flow at a Reynolds number, based on the friction velocity of 395 and a Prandtl number of 0.71. The analysis is performed with a wall-resolved Large Eddy Simulation and the results are used to derive a regression for the dissipation rate discontinuity, which depends only on the fluid-solid thermal diffusivity and conductivity ratios. Wall-resolved Large Eddy Simulations at a higher Reynolds number and a higher Prandtl number are used to investigate the validity of two correlations derived from the regression for the selected thermal properties ratios. The present results are obtained with the open-source Computational Fluid Dynamics solver Code_Saturne, and use the fully conservative fluid-solid thermal coupling capability introduced by the authors in version 5.0.

Accurate numerical simulation on the structural response of the VEGA payload fairing using modal coupling approach

Structural aeroacoustic interactions are of great interest in the design and manufacture of aerospace structures. During the lift off and the early phases of the launch various external loads like steady accelerations, random and broadband frequency vibrations, acoustic loads due to jet noise and fluid–structure interactions act on the lightweight panel structure of the payload fairing. Thereby internal vibrational loads and instability effects may be caused by the interaction of various mechanical loads and acoustic noise acting on the cylindrical shell structure. Within the project “Prediction of Acoustic Loads on Space Structures” funded by the European Space Agency (ESA) an aeroelastic coupling approach has been built up. Therein, the aerodynamic loads on the VEGA payload fairing (PLF) have been determined for different flight conditions by the use of the open-source CFD solver SU2. Due to the different discretization between the computational fluid dynamics (CFD) and computational structural dynamics (CSD) mesh the approach of Radial Basis Function (RBF) has been used to interpolate the resulting pressure distribution onto the structural model. According to that the dynamic response of the PLF has been analyzed by taking the basic aerodynamic forces, structural vibration and acoustic pressure fluctuations into account. An intrinsic part of this work is the numerical simulation and assessment of the interaction between structural vibrations, transonic flow and acoustic pressure fluctuations during the early launch phase.

PUFoam : A novel open-source CFD solver for the simulation of polyurethane foams

In this work a transient three-dimensional mathematical model is formulated and validated for the simulation of polyurethane (PU) foams. The model is based on computational fluid dynamics (CFD) and is coupled with a population balance equation (PBE) to describe the evolution of the gas bubbles/cells within the PU foam. The front face of the expanding foam is monitored on the basis of the volume-of-fluid (VOF) method using a compressible solver available in OpenFOAM version 3.0.1. The solver is additionally supplemented to include the PBE, solved with the quadrature method of moments (QMOM), the polymerization kinetics, an adequate rheological model and a simple model for the foam thermal conductivity. The new solver is labelled as PUFoam and is, for the first time in this work, validated for 12 different mixing-cup experiments. Comparison of the time evolution of the predicted and experimentally measured density and temperature of the PU foam shows the potentials and limitations of the approach.Program summaryProgram Title: PUFoamProgram Files doi:http://dx.doi.org/10.17632/62ggzx623g.1Licensing provisions: GNU General Public License 3 (GPL)Programming language: C++.Supplementary material: In order to test the main solver all the required input files have been provided within the testCase directory. This could be either directly used or modified according to user’s needs.Nature of problem: The CFD solver developed through this research work provides a numerical mean for the simulation of polyurethane foam. The problem includes a reacting multi-phase system in which the liquid mixture expands due to the polymerization phenomenon and the presence of different additives. In that, the gas bubbles nuclei within the reacting liquid mixture start to grow owing to the diffusion of gases produced due to the chemical reactions. Further, industrial applications such as mould-filling seek for capturing the foam front face and the evolution of its physical and thermal properties during the foaming process. Thus, the solver shall facilitate the evolution of gas bubbles via a population balance equation, capturing the foam interface using a volume-of-fluid method, and eventually predicts the foam characteristics.Solution method: Conservation equations for mass and momentum as well as phase fraction equations are solved using the standard finite volume method. The indicator function (i.e., the phase fraction equation in this case) is solved for the primary phase taking into account the density variation of the foam which is implemented as the compressibility effect. Additional transport equations are also solved to yield the progress of the polymerization process through the conversions of water, isocyanate, and the amount of gases produced. Finally, the evolution of the cell size distribution inside the foam phase is evaluated by using a population balance equation. The solution of PBE inside the CFD code is performed by transforming the problem into a set of transport equations for the moments of bubble/cell size distribution. The quadrature method of moments (QMOM) is applied to approximate the right hand side of moments equations which represent the growth and coalescence of bubbles.External routines/libraries: OpenFOAM® (version 3.0.1) (http://www.openfoam.org)Restrictions: Due to lack of available experimentally-based or analytical models, the current version of the solver supports two different blowing agents including n-pentane and R-11. Further, the growth rate of the bubbles is assumed to be diffusion-controlled and its rate associated with the concentration gradient around the bubbles. This restriction will be relaxed in near future by adopting a detailed model for the bubble growth rate. It must be also reminded that the solver is compiled with OpenFOAM version 3.0.1 and compiling it with other versions might require additional efforts.

A semi-parabolic wake model for large offshore wind farms based on the open source CFD solver OpenFOAM

Wake effect represents one of the main sources of energy loss and uncertainty when designing offshore wind farms. Traditionally analytical models have been used to optimize and estimate power deficits. However these models have shown to underestimate wake effect and consequently overestimate output power (1, 2). This means that analytical models can be very helpful at optimizing preliminary layouts but not as accurate as needed for an ultimate fine design. Different techniques can be found in the literature to study wind turbine wakes that include simplified kinematic models and more advanced field models, that solve flow equations with different turbulence closure schemes. See the review papers of Crespo et al. (3), Vermeer et al. (4), and Sanderse et al. (5). Purely elliptic Computational Fluid Dynamics (CFD) models based on the actuator disk technique have been developed during the last years (6-8). They consider wind turbine rotor as a disk where a distribution of axial forces act over the incoming air. It is a fair approach but it can still be computationally expensive for big wind farms in an operative mode. With this technique still active, an alternative approach inspired on the parabolic wake models (9, 10) is proposed. Wind turbine rotors continue to be represented as actuator disks but now the domain is split into subdomains containing one or more wind turbines. The output of each subdomain is mapped onto the input boundary of the next one until the end of the domain is reached, getting a considerable decrease on computational time, by a factor of order 10. As the model is based on the open source CFD solver OpenFOAM, it can be parallelized to speed-up convergence. The near wake is calculated so no initial wind speed deficit profiles have to be supposed as in totally parabolic models and alternative turbulence models, such as the anisotropic Reynolds Stress Model (RSM) can be used. Traditional problems of elliptic models related to the estimation of the reference wind speed at each rotor position are mitigated due to the semi-parabolic algorithm. The model has been validated at the ECN test farm and at the offshore Horns Rev wind farm with significant results and also have been compared to other wake models.

Fluid-structure interaction coupling CFD and FEA

Fluid-structure interaction (FSI) is becoming of high importance and influence to examine and understand difficult engineering problems. FSI is defined as the interaction between a moving or deforming structure with an internal or external fluid flow, where the change in boundary conditions in one aspect influences the other. The iteration method between computational fluid dynamics (CFD) for the fluid domain and finite element analysis (FEA) for the structural domain will be examined in further detail. The coupling method between CFD and FEA will be shown to have been verified on the HA145E flutter benchmark by Rodden and Johnson (1994). In this study, a coupling solution between the FEA solver MSC.Nastran and the open source CFD solver OpenFOAM was used to perform a rear spoiler test case. The problem focuses on the airflow over a simple deformable spoiler as air accelerates over it from initial rest.