Benchmark Test Cases Research Articles

Benchmarked simulations of natural convection airflow in a square cavity

An open-source code, OpenFOAM, and two commercial finite volume packages are benchmarked for accuracy and convergence speed in solving steady natural convection airflows in a square cavity with adiabatic horizontal boundaries and with high temperature difference on the two vertical side walls. The compressible two-dimensional Navier–Stokes equations are solved at Rayleigh numbers 106 and 107 (steady flow for Rayleigh numbers less than 2 × 108) using seven different CFD algorithms, including both transient and steady flow solvers. Velocity fields, pressures, temperatures and Nusselt numbers are compared against well-established results for three benchmark test cases from the literature. Relative accuracy and CPU time are reported for each algorithm and for each of the three test cases, yielding benchmarked comparisons of OpenFOAM, STAR-CCM+, and ANSYS-Fluent solvers for low Mach number compressible airflows.

Improved Volume-Of-Solid Formulations for Micro-Continuum Simulation of Mineral Dissolution at the Pore-Scale

We present two novel Volume-of-Solid (VoS) formulations for micro-continuum simulation of mineral dissolution at the pore-scale. The traditional VoS formulation (VoS-ψ) uses a diffuse interface localization function ψ to ensure stability and limit diffusion of the reactive surface. The main limitation of this formulation is that accuracy is strongly dependent on the choice of the localization function. Our first novel improved formulation (iVoS) uses the divergence of a reactive flux to localize the reaction at the fluid-solid interface, so no localization function is required. Our second novel formulation (VoS-ψ′) uses a localization function with a parameter that is fitted to ensure that the reactive surface area is conserved globally. Both novel methods are validated by comparison with experiments, numerical simulations using an interface tracking method based on the Arbitrary Eulerian Lagrangian (ALE) framework, and numerical simulations using the VoS-ψ. All numerical methods are implemented in GeoChemFoam, our reactive transport toolbox and three benchmark test cases in both synthetic and real pore geometries are considered: 1) dissolution of a calcite post by acid injection in a microchannel and experimental comparison, 2) dissolution in a 2D polydisperse disc micromodel at different dissolution regimes and 3) dissolution in a Ketton carbonate rock sample and comparison to in-situ micro-CT experiments. We find that the iVoS results match accurately experimental results and simulation results obtained with the ALE method, while the VoS-ψ method leads to inaccuracies that are mostly corrected by the VoS-ψ’ formulation. In addition, the VoS methods are significantly faster than the ALE method, with a speed-up factor of between 2 and 12.

Large deflection analysis of functionally graded beams based on geometrically exact three-dimensional beam theory and isogeometric analysis

The main aim of this study is to develop a numerical model based on Isogeometric Analysis to investigate the large deflection response of curved functionally graded beams. In this regard, an exact three-dimensional beam theory is employed to model the spatial behavior of the beams. The beam theory has been considered as an up-to-date one, which effectively fulfills the requirements large deflection representation, objectively, and geometrical exactness. The C1-continuity requirement of interpolation functions to develop the beam elements is treated naturally and efficiently by adopting the Isogeometric Analysis approach. To validate the accuracy and efficiency of the proposed approach, five standard benchmark test cases are conducted. In additions, various numerical examples are presented to study the influence of material variations on the behavior of curved functionally graded beam under different loading conditions.

A reconstructed discontinuous Galerkin method based on variational formulation for compressible flows

A new reconstructed discontinuous Galerkin (rDG) method based on variational formulation is developed for compressible flows. In the presented method, a higher-order piece-wise polynomial is reconstructed based on the underlying discontinuous Galerkin (DG) solution. This reconstruction is done by using a newly developed variational formulation. The variational reconstruction (VR) can be seen as an extension of the compact finite difference (FD) schemes to unstructured grids. The reconstructed variables are obtained by solving an extreme-value problem, which minimizes the jumps of the reconstructed piece-wise polynomials across the cell interfaces, and therefore maximizes the smoothness of the reconstructed solution. Intrinsically, the stencils of the presented reconstruction are the entire mesh, so this method is robust even on tetrahedral grids. A variety of benchmark test cases are presented to assess the accuracy, efficiency and robustness of this rDG method. The numerical experiments demonstrate that the developed rDG method based on variational formulation can maintain the linear stability, obtain the designed high-order accuracy, and outperform the rDG counterpart based on the least-squares reconstruction for both inviscid and viscous compressible flows.

Border mapping multi-resolution (BMMR) technique for incompressible projection-based particle methods

A novel multi-resolution technique called border mapping multi-resolution (BMMR) is proposed for projection-based particle methods. The BMMR aims to obtain background equivalent particle distributions in the two sides of a border between sub-domains with a 2:1 resolution ratio so that a single resolution framework is adopted to near-border particles calculations. The novelty of the BMMR is that it obtains the background grid from the mapping of the actual particle distribution in the border and, as a result, the location of the particles in the background grid exactly matches the location of the actual particles. In this way, such technique aims to reduce the error from the interpolation of the physical quantities in the background grid and to avoid sudden changes in the particle distribution that may lead to unstable local pressure calculation. In the coarse side of the border, the refinement is made by a triangulation and by placing fictitious particles in the midpoints of the triangles. In the fine side of the border, the derefinement is made by defining a set of fine particles that result in a particle distribution that best resembles a coarse one. The accuracy and computational performance of the BMMR implemented in a moving particle semi-implicit (MPS) simulation system are verified by using benchmark test cases of 2D free surface flows.

BR2 discontinuous Galerkin methods for finite hyperelastic deformations

In this work we introduce a DG framework for nonlinear elasticity based on a Bassi-Rebay (BR2) formulation. The framework encompasses compressible and incompressible hyperelastic materials and is capable of dealing with large deformations. In order to achieve stability, we combine higher-order lifting operators for the BR2 stabilisation term with an adaptive stabilisation strategy which relies on the BR2 Laplace operator stabilisation and a penalty parameter based on the spectrum of the fourth-order elasticity tensor. Dirichlet boundary conditions for the displacement can be imposed by means of Lagrange multipliers and Nitsche method. Efficiency of the solution strategy is achieved by means of state-of-the-art agglomeration based h-multigrid preconditioners and the code implementation supports distributed memory execution on modern parallel architectures. Several benchmark test cases are proposed in order to investigate some relevant computational aspects, namely the performance of the h-multigrid iterative solver varying the stabilisation parameters and the influence of Dirichlet boundary conditions on Newton's method globalisation strategy.

A cell-centered finite volume formulation of geometrically exact Simo-Reissner beams with arbitrary initial curvatures.

This article presents a novel total Lagrangian cell‐centered finite volume formulation of geometrically exact beams with arbitrary initial curvatures undergoing large displacements and finite rotations. The choice of rotation parameterization, the mathematical formulation of the beam kinematics, conjugate strain measures, and the linearization of the strong form of governing equations are described. The finite volume based discretization of the computational domain and the governing equations for each computational volume are presented. The discretized integral form of the equilibrium equations is solved using a block‐coupled Newton–Raphson solution procedure. The efficacy of the proposed methodology is presented by comparing the simulated numerical results with classic benchmark test cases available in the literature. The objectivity of strain measures for the current formulation and mesh convergence studies for both initially straight and curved beam configurations are also discussed.

A tool for rapid simulation and sizing of hybrid traction systems with fuel cells

Diesel multiple units (DMU) offer an affordable alternative to electric trains on lines in which infrastructural and maintenance costs of electrification are not justified. A further improvement of sustainability involves the abandonment of internal combustion engines in favour of an electric power train sustained by an on-board storage system. In this work, the authors propose a model to perform a rapid simulation of hybrid storage systems based on hydrogen fuel cells,a technology that should be complementary with respect to battery-operated trains. The proposed tool is applied, as a benchmark test case, to a modular passenger train devoted to regional service. Obtained results clearly demonstrate the capabilities of proposed tools and give useful indications for a feasible optimization and integration of fuel cells for railway applications.

A new strategy for solving store separation problems using OpenFOAM

The ability of OpenFOAM to solve the problem of a store separating from an air vehicle (store separation problem) has been evaluated using a dynamic mesh (Overset/Chimera) technique for an industry-class (transonic and generic) benchmark test case. The major limitations of the standard libraries have been determined. To tackle these challenges, a new strategy has been proposed and implemented using only open-source libraries and tools. The strategy combines porting, modifying, and adapting an overset library from the OpenFOAM fork platform (foam-extend) to the standard OpenFOAM platform (ESI). Furthermore, in order to overcome the well-known weakness of the standard OpenFOAM compressible solvers, the newly adapted overset library was integrated with an open-source, density-based, and coupled solver ( HiSA), which uses the OpenFOAM technology. Additionally, a force restrained model was developed to consider the externally applied forces on the store by the store ejectors. The accuracy of the developed strategy has been compared with wind tunnel tests and the solutions of two well-known commercial codes, showing good agreements with them. While the study has focused on simulations with inviscid Euler equations (typical of the test case considered here), the viscosity effect on the solution has also been studied with Navier–Stokes equations and compared with other results in the literature, showing minor differences. To the best of the authors’ knowledge, this is the first work which studies and validates the store separation problem in transonic regime with OpenFOAM.

Numerical investigation on influences of injection flow rate on bubbling flow at submerged orifices

In this study, we numerically investigated the formation of bubbles by gas injection through an orifice in a stagnant liquid column and the flow field surrounding the bubbles after detachment under several flow conditions. To this end, we employed an enhanced coupling method that combines the advantages of mass conservation property of the volume-of-fluid (VOF) method with the boundedness and continuity of a conservative level-set (LS) function for multiphase computations to achieve a smoothened and sharpened interface. The coupling method was integrated into an incompressible Navier–Stokes solver to investigate the bubbling flow under various injection conditions. The simulated results were first validated against the experimental data of a benchmark test case to assess its reliability. The capability of the solver was also confirmed by examining the computed results and comparing them with those of the other studies. Subsequently, we simulated bubbling flow under different injected gas conditions and several orifice radii. The simulated results indicated that at low gas injection flow rates, the detachment time of bubbles, pinched off the orifice rim, could be predicted depending on the orifice radius and volume flow rate of the gas, whereas orifice radius had a notable influence on the detached volume of bubbles. In addition, the gas injection flow rate had a significant influence on the pressure field surrounding the bubbles after detachment, which is useful for studying of the bubbling flows and for the optimal design of small-scale systems.

Superconvergence of the MINI mixed finite element discretization of the Stokes problem: An experimental study in 3D

Stokes flows are a type of fluid flow where convective forces are small in comparison with viscous forces, and momentum transport is entirely due to viscous diffusion. Besides being routinely used as benchmark test cases in numerical fluid dynamics, Stokes flows are relevant in several applications in science and engineering including porous media flow, biological flows, microfluidics, microrobotics, and hydrodynamic lubrication. The present study concerns the discretization of the equations of motion of Stokes flows in three dimensions utilizing the MINI mixed finite element, focusing on the superconvergence of the method which was investigated with numerical experiments using five purpose-made benchmark test cases with analytical solution. Despite the fact that the MINI element is only linearly convergent according to standard mixed finite element theory, a recent theoretical development proves that, for structured meshes in two dimensions, the pressure superconverges with order 1.5, as well as the linear part of the computed velocity with respect to the piecewise-linear nodal interpolation of the exact velocity. The numerical experiments documented herein suggest a more general validity of the superconvergence in pressure, possibly to unstructured tetrahedral meshes and even up to quadratic convergence which was observed with one test problem, thereby indicating that there is scope to further extend the available theoretical results on convergence.

A vertex-centered finite volume method with interface sharpening technique for compressible two-phase flows

A robust and efficient finite volume method with interface sharpening technique has been developed to solve the six-equation multi-fluid single-pressure model for compressible two-phase flows. The numerical method is implemented in a three-dimensional vertex-centered code. A least-squares reconstruction with Kuzmin's vertex-based (VB) limiter is implemented for the volume fraction and a set of primitive variables in the presented finite volume framework. In regions where two different fluid components are present within a cell, a sharpening technique based on THINC (Tangent of Hyperbola for Interface Capturing) is adopted to provide a sharp resolution for the transitioning interface. These reconstructed values are then used as the initial data for Riemann problems. The enhanced AUSM+ -up scheme is applied to both liquid and gas flows. The multi-stage Runge-Kutta method is used for time marching. A number of benchmark test cases are presented to assess the performance of the present method. These include: an air-water interface moving at a constant velocity, Ransom's faucet problem, air-water/water-air shock tube problems with high pressure ratios, a shock in air impacting a water column case, an underwater explosion case and an air bubble blast case. In all of these cases, the shock and rarefaction waves are captured accurately, especially with the THINC interface sharpening technique.

Multi-Objective Hidden Genes Genetic Algorithm for Multigravity-Assist Trajectory Optimization

In multigravity-assist trajectory optimization, the size of the design space is a variable itself. The objective functions are usually replete with local minima. This paper presents a multi-objective hidden genes genetic algorithm (MOHGGA) for trajectory optimization. The length of the chromosome is selected large enough to enable modeling a given maximum number of swing-bys and maximum number of deep space maneuvers (DSMs). Binary tags are appended to those genes that control the swing-bys and DSMs. These binary tags are used to remove/add swing-bys and DSMs to a trajectory solution, and hence enable optimization among solutions of different sizes (different topologies). The MOHGGA generates Pareto fronts that have solutions of, in general, different number of swing-bys, swing-by planets, launch and arrival dates, and number of DSMs. Two objectives are considered in this paper: the total mission cost and total time of flight. An elitist nondominated sorting genetic algorithm is used. Local optimization is conducted on one objective function, holding the other objective function constant, to further improve the resulting Pareto front. Numerical results of four benchmark test cases for missions to Mars, Jupiter, Saturn, and Mercury are presented. The results demonstrate the capability of MOHGGA in searching for optimal trajectory topologies while optimizing two objectives.

Simulation of conjugate mass transfer in multiphase flow: A new unified approach based on the phase field method

Conjugate mass transfer phenomena are commonly found in industries and nature. It raises a serious challenge for numerical research, because at interfaces not only the continuity of mass flux but also the concentration jump (i.e. Henry's law) must be guaranteed. A complicated interface will further increase the complexity of numerical research of conjugate mass transfer. The phase field method has an intrinsic advantage over the other available numerical methods to model complicated interfaces, but so far there is no efforts to investigate interphase mass transfer with the aid of phase field method. The challenge is to design an appropriate governing equation for concentration field, which can be coupled with the phase field method and meanwhile can describe conjugate mass transfer in a unified manner. In this study, a new governing equation for concentration field is proposed to address the challenge. A number of benchmark test cases are employed to validate the present approach. The excellent agreement of the present numerical results with the analytical solutions and published data can demonstrate the applicability of the present approach for simulating conjugate mass transfer not only with a flat stationary interface but also with a moving/curved interface.

A hybrid-mixed finite element method for single-phase Darcy flow in fractured porous media

We present a hybrid-mixed finite element method for a novel hybrid-dimensional model of single-phase Darcy flow in a fractured porous media. In this model, the fracture is treated as a (d−1)-dimensional interface within the d-dimensional fractured porous domain, for d=2,3. Two classes of fracture are distinguished based on the permeability magnitude ratio between the fracture and its surrounding medium: when the permeability in the fracture is (significantly) larger than in its surrounding medium, it is considered as a conductive fracture; when the permeability in the fracture is (significantly) smaller than in its surrounding medium, it is considered as a blocking fracture. The conductive fractures are treated using the classical hybrid-dimensional approach of the interface model where pressure is assumed to be continuous across the fracture interfaces, while the blocking fractures are treated using the recent Dirac-δ function approach where normal component of Darcy velocity is assumed to be continuous across the interface. Due to the use of Dirac-δ function approach for the blocking fractures, our numerical scheme allows for nonconforming meshes with respect to the blocking fractures. This is the major novelty of our model and numerical discretization. Moreover, our numerical scheme produces locally conservative velocity approximations and leads to a symmetric positive definite linear system involving pressure degrees of freedom on the mesh skeleton only. As an application, we extend the idea to a simple transport model. The performance of the proposed method is demonstrated by various benchmark test cases in both two- and three-dimensions. Numerical results indicate that the proposed scheme is highly competitive with existing methods in the literature

A decomposition-based many-objective ant colony optimization algorithm with adaptive solution construction and selection approaches

The ant colony optimization algorithm (ACO) had an exceptional performance in solving discrete optimization problems because of its design in solution construction and search strategy. However, the study of ACO in discrete many-objective optimization remains insufficient. This paper proposes a decomposition-based ACO for discrete many-objective optimization. The proposed algorithm utilizes a reinforcement learning-based adaptive pheromone updating strategy that enhances the solution construction phase’s searching ability in the high-dimensional objective space. Furthermore, an adaptive selection strategy is adopted to improve its convergence performance using different reference points. And A comparative experimental study is conducted on many-objective benchmark test cases. The experimental results indicate that the proposed algorithm achieves competitive performance on optimization quality.

Artificial Intelligence Techniques for Power System Transient Stability Assessment

The high penetration of renewable energy sources, coupled with decommissioning of conventional power plants, leads to the reduction of power system inertia. This has negative repercussions on the transient stability of power systems. The purpose of this paper is to review the state-of-the-art regarding the application of artificial intelligence to the power system transient stability assessment, with a focus on different machine, deep, and reinforcement learning techniques. The review covers data generation processes (from measurements and simulations), data processing pipelines (features engineering, splitting strategy, dimensionality reduction), model building and training (including ensembles and hyperparameter optimization techniques), deployment, and management (with monitoring for detecting bias and drift). The review focuses, in particular, on different deep learning models that show promising results on standard benchmark test cases. The final aim of the review is to point out the advantages and disadvantages of different approaches, present current challenges with existing models, and offer a view of the possible future research opportunities.

Injection-Constrained State Estimation

In applications of state estimation involving data assimilation over a spatial region, it is often convenient, and sometimes necessary, to confine the state correction to a prescribed subspace of the state space that corresponds to the measurement location. This is the injection-constrained state-estimation problem, where the injection of the output error is constrained to a specified subspace of the state space. Unlike full-state output-error injection, which is the dual of static full-state feedback, constrained output-error injection is the dual of static output feedback. To address the injection-constrained state-estimation problem, this paper develops the injection-constrained unscented Kalman filter (IC-UKF) and the injection-constrained retrospective cost filter (IC-RCF). The performance of these filters is evaluated numerically for linear and nonlinear state-estimation problems in order to compare their accuracy and determine their suboptimality relative to full-state output-error injection. As a benchmark test case, IC-UKF and IC-RCF are applied to the viscous Burgers equation for state and parameter estimation.

Topology optimization to maximize eigenfrequencies of multi-material structures

A multi-material structure that is composed of several different material properties is promising for achieving an ideal functionality that can outperform a single material structure. In particular, increasing the value of the fundamental eigenfrequency is important because it can increase dynamic stability. Since the beginning, Topology optimization (TO) to maximize the fundamental eigenfrequency of a single-material structure has been investigated. However, there are few research papers on multi-material topology optimization (MMTO) for the eigenfrequency maximization problem thus far. Therefore, we propose a novel framework for the MMTO of the eigenfrequency problem. From a theoretical standpoint, two key features are addressed: (i) multi-material level set (MMLS) method is developed. In this method, interfaces between different material phases are represented by iso-surfaces of multiple level set functions. Hence, the optimal solutions have a 1/0 binary structure and are free from greyscale elements; (ii) The proposed design methodology uses a reaction-diffusion equation (RDE) to update the level-set functions based on the topological derivative, allowing new holes to form during the optimization process. The effectiveness of our methodology is demonstrated by benchmark test cases.

Condition Monitoring in a Wind Turbine Planetary Gearbox Using Sensor Fusion and Convolutional Neural Network

To meet the requirements of reducing operations and maintenance costs of wind turbines, we present a machine learning framework for early damage detection in gearboxes based on the cyclostationary analysis of sensor data. The application focus is the condition monitoring of wind turbine gearboxes under varying load scenarios, in particular turbulent wind conditions. Faults in the rotating components in the gearbox can leave their signature in the vibrations that can be measured by accelerometers. We analyze data stemming from a simulated vibration response of a 5MW multibody wind turbine model in a healthy and damaged scenarios and under different wind conditions. With cyclostationary analysis applied on acquired sensor data, we generate cyclic spectral coherence maps that highlight signatures related to the fault damage and enable its identification. These maps are used to train convolutional neural networks that then identify faults, including those of small magnitude, in test data with a high accuracy. Benchmark test cases inspired by an NREL study are tested and faults successfully detected.