Benchmark Test Cases Research Articles

Probabilistic machine learning to improve generalisation of data-driven turbulence modelling

A probabilistic machine learning model is introduced to augment the k−ωSST turbulence model in order to improve the modelling of separated flows and the generalisability of learnt corrections. Increasingly, machine learning methods have been used to leverage experimental and high-fidelity simulation data, improving the accuracy of the Reynolds Averaged Navier–Stokes (RANS) turbulence models widely used in industry. A significant challenge for such methods is their ability to generalise to unseen geometries and flow conditions. Furthermore, heterogeneous datasets containing a mix of experimental and simulation data must be efficiently handled. In this work, field inversion and an ensemble of Gaussian Process Emulators (GPEs) is employed to address both of these challenges. The ensemble model is applied to a range of benchmark test cases, demonstrating improved turbulence modelling for cases involving separated flows with adverse pressure gradients, where RANS simulations are understood to be unreliable. Perhaps more significantly, the simulation reverted to the uncorrected model in regions of the flow exhibiting physics outside of the training data.

A very fast high-order flux reconstruction for Finite Volume schemes for Computational Aeroacoustics

AbstractGiven the small wavelengths and wide range of frequencies of the acoustic waves involved in Aeroacoustics problems, the use of very accurate, low-dissipative numerical schemes is the only valid option to accurately capture these phenomena. However, as the order of the scheme increases, the computational time also increases. In this work, we propose a new high-order flux reconstruction in the framework of finite volume (FV) schemes for linear problems. In particular, it is applied to solve the Linearized Euler Equations, which are widely used in the field of Computational Aeroacoustics. This new reconstruction is very efficient and well suited in the context of very high-order FV schemes, where the computation of high-order flux integrals are needed at cell edges/faces. Different benchmark test cases are carried out to analyze the accuracy and the efficiency of the proposed flux reconstruction. The proposed methodology preserves the accuracy while the computational time relatively reduces drastically as the order increases.

Flow reduction due to arterial catheterization during stroke treatment - A computational study using a distributed compartment model.

The effectiveness of various stroke treatments depends on the anatomical variability of the cerebral vasculature, particularly the collateral blood vessel network. Collaterals at the level of the Circle of Willis and distal collaterals, such as the leptomeningeal arteries, serve as alternative avenues of flow when the primary pathway is obstructed during an ischemic stroke. Stroke treatment typically involves catheterization of the primary pathway, and the potential risk of further flow reduction to the affected brain area during this treatment has not been previously investigated. To address this clinical question, we derived the lumped parameters for catheterized blood vessels and implemented a corresponding distributed compartment (0D) model. This 0D model was validated against an experimental model and benchmark test cases solved using a 1D model. Additionally, we compared various off-center catheter trajectories modeled using a 3D solver to this 0D model. The differences between them were minimal, validating the simplifying assumption of the central catheter placement in the 0D model. The 0D model was then used to simulate blood flows in realistic cerebral arterial networks with different collateralization characteristics. Ischemic strokes were modeled by occlusion of the M1 segment of the middle cerebral artery in these networks. Catheters of different diameters were inserted up to the obstructed segment and flow alterations in the network were calculated. Results showed up to 45% maximum blood flow reduction in the affected brain region. These findings suggest that catheterization during stroke treatment may have a further detrimental effect for some patients with poor collateralization.

Symmetrical fully coupled numerical model for efficient dam–reservoir interaction analysis in time domain

ABSTRACT A numerical model is presented for solving the dam–reservoir interaction (DRI) problem in the time domain. The primary aim of this paper is to introduce a coupling method that could be simply implemented in a monolithic DRI model, yields a symmetrical system of equations, and maintains accuracy comparable to existing studies. The finite element method is employed to solve the equation of motion for the structure, and the finite volume method is for the Navier–Stokes equations in the fluid domain. These two solvers are coupled using an innovative approach to generate a pressure-based symmetric system of equations, which is resolved implicitly. Moreover, unlike most previous DRI studies, free surface waves are considered in the modeling procedure, and their effects are investigated. Comparison of the results with benchmark test cases from the literature demonstrates that the proposed numerical method is both straightforward and precise.

An efficient hybrid WENO scheme with minimized dispersion and adaptive dissipation properties for compressible flows

A numerical scheme with good spectral properties is important for the simulation of compressible flows with various of length scales for fine flow scales resolving. The MDAD-HY scheme (Li et al., 2022) using a discontinuity detector and scale sensor achieves the minimized dispersion and adaptive dissipation property. However, the discontinuity detector is devised based on the ratio of the 1st-order and 2nd-order derivatives on two sides of the interface introducing excessive numerical cost. To address this issue, an efficient hybrid WENO scheme with minimized dispersion and adaptive dissipation properties is proposed in this work. Based on the characteristic-decomposition approach, the numerical flux of the present hybrid scheme is achieved by switching between the linear MDAD scheme and the MDAD-WENO scheme according to a new efficient non-dimensional discontinuity detector. The linear flux is reconstructed in a component-wise method to decrease the characteristic-projection operations. To further improve the spectral property of the present scheme, an adaptive parameter controlling the contribution of the optimal linear scheme according to the discontinuity indicator is introduced. Several benchmark test cases involving broadband of length scales and discontinuities are adopted to verify the efficiency and the high-resolution capability of the present scheme.

Fault classification and localization of multi-machine-based ieee benchmark test case power transmission lines using optimizable weighted extreme learning machine

Accurate fault diagnosis in transmission lines is crucial to ensure the reliability and stability of power grids. Conventional approaches often rely on expert knowledge or complex feature extraction methods, which are subjective and time-consuming. Additionally, many existing approaches use separate sub-algorithms for fault classification and localization. These are operating independently and sequentially. This research work proposes an innovative method for fault classification and localization in transmission lines using phasor measurement unit (PMU) data. The proposed method employs a Weighted Extreme Learning Machine (WELM) algorithm, which uses the variable data distribution across different fault classes through a weighted approach. The PMU data is generated by simulation using an IEEE 9-bus test system in the MATLAB simulation environment. The Maximal Overlap Discrete Wavelet Transform-based feature extraction technique is applied to derive input feature data to facilitate fault classification and localization. The WELM classifier is also optimized using the Grey Wolf Optimization (GWO) algorithm. The resulting GWO-optimized WELM (GWO-WELM) model, when trained on PMU data, achieves a remarkable fault classification accuracy of 99.83 % and fault localization accuracy of 95.48 %, respectively. These results demonstrate that the GWO-WELM model outperforms commonly used classifiers. Moreover, the proposed model shows robustness by accurately classifying the noisy data with a signal-to-noise ratio (SNR) of 10 dB (achieving 91.5 % accuracy in classification and 88.1 % accuracy in localization, respectively).

Synchronous high-speed measurements of a flexible structure under wind gust load

Simultaneously measuring the fluid flow around a flexible structure and the resulting deformations during short-term yet highly dynamic flow events is the focus of this fluid–structure interaction (FSI) study. These scenarios occur when a wind gust impacts a flexible structure, leading to extreme loads and significant deflections. To mimic such gusts, a specifically designed wind gust generator is used within a wind tunnel featuring an open test section. A high-speed particle-image velocimetry system records the flow field, while the digital-image correlation technique captures the structural deformations. That allows us to perform synchronized coupled fluid–structure measurements for a T-structure under wind gust load. The time-resolved measurements are repeated up to 104 times, allowing for phase-averaging of both the flow and the structural data, and to examine the convergence of the statistics. A comprehensive analysis of the instantaneous and phase-averaged data reveals that the flow field in the vicinity of the structure undergoes noticeable changes during the gust impact. The recirculation region behind the T-structures perceptibly increases when the gust hits the structure. A maximum deformation of about 10% of its height is observed during the highly dynamic gust event. Given (1) the availability of synchronously recorded data for both the fluid flow and the structure deformation, (2) the simplicity of the structure's geometry, and (3) the moderate Reynolds number of about 4×104, this case also serves as a well-suited benchmark test case for evaluating simulation methodologies for strongly coupled, highly dynamic FSI problems.

High resolution optimized high-order schemes for discretization of non-linear straight and mixed second derivative terms

In this paper, we propose a new set of midpoint-based high-order discretization schemes for computing straight and mixed nonlinear second derivative terms that appear in the compressible Navier-Stokes equations. Firstly, we detail a set of conventional fourth and sixth-order baseline schemes that utilize central midpoint derivatives for the calculation of second derivatives terms. To enhance the spectral properties of the baseline schemes, an optimization procedure is proposed that adjusts the order and truncation error of the midpoint derivative approximation while still constraining the same overall stencil width and scheme order. A new filter penalty term is introduced into the midpoint derivative calculation to help achieve high wavenumber accuracy and high-frequency damping in the mixed derivative discretization. Fourier analysis performed on the both straight and mixed second derivative terms show high spectral efficiency and minimal numerical viscosity with no odd-even decoupling effect. Numerical validation of the resulting optimized schemes is performed through various benchmark test cases assessing their theoretical order of accuracy and solution resolution. The results highlight that the present optimized schemes efficiently utilize the inherent viscosity of the governing equations to achieve improved simulation stability - a feature attributed to their superior spectral resolution in the high wavenumber range. The method is also tested and applied to non-uniform structured meshes in curvilinear coordinates, employing a supersonic impinging jet test case.

Harnessing collaborative learning automata to guide multi-objective optimization based inverse analysis for structural damage identification

Structural damage identification based on physical models is often transformed into an optimization problem that minimizes the difference between measurement information of structure being monitored and the model prediction in the parametric space. However, the objective function in this context often exhibits multimodality, involving high-dimensional variables due to the reliance on finite element models for damage identification. These features pose challenges to optimization algorithms, where entrapment in local solutions can lead to false positives and false negatives in damage identification. In this research, we propose a reinforcement learning based multi-swarm optimizer to tackle such challenges in pursuit of a small yet diverse solution set that can capture the true damage scenario as one of the solutions. The proposed method leverages the flexibility of the particle swarm optimizer and incorporates novel strategies of metaheuristics to realize targeted improvement. To enable the particle swarm to adaptively select the appropriate search strategy based on the current environment, we adopt the learning automata technique, which sidesteps the need for reward strategy selection that is usually ad hoc at each step of the search. The integration harnesses the automatic learning and self-adaptation capabilities of learning automata, enabling the particles to navigate based on environmental signals. This leads to accumulated probabilities tied to advantageous movements, fostering an adaptive exploration of particles in the search space. The proposed approach is first validated through implementing into benchmark test cases with comparisons. It is then applied to structural damage identification with piezoelectric admittance experimental signals. `The results highlight the capability of the algorithm to identify a small solution set with high accuracy to match the actual damage scenario.

A hybrid method combining ISPH with graph neural network for simulating free-surface flows

The incompressible Smoothed Particle Hydrodynamics (ISPH) is a popular Lagrangian Particle method. In the conventional ISPH method for simulating free-surface flows, the pressure-projection phase, which solves the pressure Poisson's equation (PPE), is the most time-consuming. In this paper, we propose a novel hybrid method by combining the graph neural network (GNN) with the ISPH for modelling the free-surface flows. In the new hybrid method, the graph neural network (GNN) is employed to replace solving the PPE for pressure in the conventional ISPH. To the best of knowledge of the authors, this is the first attempt to combine the GNN with ISPH model in a Lagrangian formulation. The performance of the hybrid method will be evaluated by comparing its results with experimental data, analytical solution or numerical results from other methods for three benchmark test cases: dam breaking, sloshing wave and solitary wave propagation. In addition, the potential of generalization of the hybrid method will be studied by applying it with the GNN model trained on data for relatively simple cases to simulate more complex cases. It will be demonstrated that the hybrid method does not only give satisfactory results, but also shows good potential of generalization. In addition, the new method will be demonstrated to require the computation time which can be 80 times less than the conventional ISPH for estimating pressure for cases with a large number of particles that is usually needed in the practical free-surface flows simulation using ISPH.

A multi-fidelity transfer learning strategy based on multi-channel fusion

Multi-fidelity strategies leverage a large amount of low-fidelity data combined with a smaller set of high-fidelity data, thereby achieving satisfactory results at a reasonable cost. In our research, we introduce an innovative multi-fidelity strategy that integrates the concepts of multi-fidelity data fusion and transfer learning. In the proposed framework, we incorporate auto-encoders and a multi-channel transfer learning strategy, enabling the network model to comprehend the relationship between the low-fidelity and high-fidelity models in both explicit and implicit manners. This approach not only enhances prediction accuracy but also mitigates issues such as overfitting and negative transfer, which may arise in scenarios with sparse samples. Additionally, Bayesian optimization is employed for effective hyperparameter selection. To evaluate and analyze the performance of our proposed method, we present a series of benchmark test cases. Furthermore, we also show the application of the proposed method to engineering problems. Firstly, we consider a parametrized partial differential equation problem, where high-fidelity and low-fidelity data are obtained using exact methods and simplified algorithms, respectively. Subsequently, we extend this strategy to convolutional neural network architectures, specifically addressing a pressure Poisson equation problem. We also explore the effect of the reliability of the low-fidelity data and the number of high-fidelity data on the results. The results show that the proposed method exhibits low requirements in terms of both the reliability of the low-fidelity data and the number of high-fidelity data while maintaining satisfactory accuracy metrics.

Anisotropic evolution of viscous strain in soft biological materials

We propose a model for anisotropic viscoelastic biological materials that can handle large deformations, based on the kinematic assumption that the reinforcing fibre structure undergoes affine deformation with the underlying matrix. A generalized orientation tensor approach is used to account for the dispersion of the fibres. Moreover, we consider a strain energy function that features both an elastic and an overstress component, corresponding to distinct natural states. As a consequence of this choice, the remodelled state is not necessarily stress-free, and the material does not completely relax the stress. Notably, we consider that viscous remodelling also alters the fibre distribution, leading to a dependence of the overstress energy on the remodelled orientation tensor. An anisotropic evolution equation for the viscous strain is then derived, which has five distinct characteristic times if a single fibre family is considered and requires no additional assumptions on the viscous spin. To implement the model, we prove that the evolution of the viscous strain can be recast in a variational form by an Onsager variational principle. Finally, we discuss the algorithm used for the simulations and show numerical examples that serve as benchmark test cases for viscoelastic materials.

Fully higher-order coupling of finite element and level set methods for two-phase flow with a new explicit projection method

This work presents the development of a higher-order finite element method for modeling unsteady, incompressible and inviscid two-phase flows using the level set method. A new explicit projection method is introduced to solve the incompressible Euler equation, where the pressure and the velocity fields are solved separately. To implement high order temporal schemes, the Hodge decomposition in this projection method is not applied to the velocity but to its time derivative. A discontinuous Galerkin discretization is used to solve both the level set and the nonlinear advection terms present in the Euler equations, while a Galerkin discretization is used to solve the pressure Poisson equation. The present method is a fully high order numerical approach, both in space and temporal dimensions. Numerical results provided by several 2D benchmark test cases in naval hydrodynamics (i.e hydrostatic equilibrium, sloshing and dam break) validate the computational code, illustrating the power of the proposed method. Compared to the CFD codes based on low order VOF/finite-volume methods, the present approach demonstrates greater accuracy on coarse meshes, leading to reduced CPU time.

Numerical Evaluation of Aircraft Aerodynamic Static and Dynamic Stability Derivatives by a Mid-Fidelity Approach

The present study aimed to investigate the capability of mid-fidelity aerodynamic solvers in performing a preliminary evaluation of the static and dynamic stability derivatives of aircraft configurations in their design phase. In this work, the mid-fidelity aerodynamic solver DUST, which is based on the novel vortex particle method (VPM), was used to perform simulations of the static and dynamic motion conditions of the Stability And Control CONfiguration (SACCON): an unmanned combat aerial vehicle geometry developed by NATO’s Research and Technology Organisation (RTO), which is used as a benchmark test case in the literature for the evaluation of aircraft stability derivatives. Two different methods were exploited to extract the dynamic stability derivative values from the aerodynamic coefficient time histories that were calculated with DUST. The results for the mid-fidelity approach were in good agreement with the obtained experimental data, as well as with the results obtained using more demanding high-fidelity CFD simulations. This demonstrates its suitability when implemented in DUST for predicting the static and dynamic behavior of airloads in different conditions, as well as in reliably predicting the values of stability derivatives, with the advantage of requiring limited computational effort with respect to classical high-fidelity numerical approaches and the use of wind tunnel tests.

Prediction of energy performance of residential buildings using regularised neural models

Human habitats are one of the major consumers of energy. Therefore, in the current age of increasing carbon dioxide footprints, analysing energy efficiency of a building is important and is the subject of the current study. Machine-learning-based artificial neural network (ANN) approaches are used in the current study to investigate building energy performance. Eight parameters – relative compactness, surface area, wall area, roof area, overall height and orientation of the building, as well as the glazing area and its distribution – are selected as the input parameters and heating and cooling loads (CLs) as the output parameters. The network prediction capability was checked by comparing the predictions of the ANN architecture with the benchmark test case. A well-trained and validated ANN is used to predict 96 conditions by varying glazing area and glazing area distribution. The ANN is found to capture the physics efficiently. This study revealed that there is a significant potential to improve the energy efficiency of a building and the maximum saving in the CL can be as high as 20.67% for a fraction of the glazing areas equal to 0.15 if the glazing area distribution is 32.5% in the north and 22.5% each in the east, south and west.

Numerical Simulation of Supersonic Turbulent Separated Flows Based on k–ω Turbulence Models with Different Compressibility Corrections

The accurate prediction of supersonic turbulent separated flows involved in aerospace vehicles is a great challenge for current numerical simulations. Based on the k–ω equations, several different compressibility corrections are incorporated in turbulence models to improve their prediction capabilities. Two benchmark test cases, namely the ramped cavity and the compression corner, are adopted for the numerical validation. Detailed comparisons between simulations and experiments are conducted to evaluate the effect of compressibility corrections on turbulence models. The computed results indicate that compressibility corrections have a significant impact on turbulence model performance. The compressibility correction, considering the effects of both dilatation dissipation and pressure dilatation, is suitable for the prediction of compressible free shear layers, but it may have a negative impact on the prediction of low-speed flows in the near-wall region due to the severe underprediction of the wall skin friction coefficient. In comparison, the compressibility correction only considering the effects of dilatation dissipation is conservative, with decreased predictability of free shear layers in supersonic flows, although it improves the predictions of the original models without corrections.

Shock capturing for a high-order ALE discontinuous Galerkin method with applications to fluid flows in time-dependent domains

In recent decades, the arbitrary Lagrangian–Eulerian (ALE) approach has been one of the most popular choices to deal with the fluid flows having moving boundaries. The ALE finite volume (FV) method is well-known for its capability of shock capturing. Several ALE discontinuous Galerkin (DG) methods are developed to fully explore the advantages of high-order methods, especially in complex flows. The DG scheme is highly efficient and has high resolution in smooth parts of the flow while the FV scheme has advantage on the robustness against shocks. In this paper, we present a novel algorithm to combine both the ALE FV and ALE DG methods into one stable and efficient hybrid approach. The main challenge for a mixed ALE FV method and ALE DG method is to reduce the inconsistency between both discretizations. Of particular concern are the same mesh velocity distribution between DG and FV elements and a continuous mesh velocity at the coupling interfaces. Since the computational efficiency of the proposed algorithm is of major concern, performance aspects will be considered during the construction of the scheme. To investigate the accuracy of the new scheme, several benchmark test cases with prescribed movements are included. Afterwards, the algorithm is applied to more general and complex scenarios to show its ability to cope with complex setups. In our paper, the scheme is implemented into a loosely-coupled fluid–structure interaction (FSI) framework. With a shock-driven cylinder movement in a channel flow and a transonic flow-induced airfoil vibration, we demonstrate our method for FSI applications.

A numerical method for MHD Stokes model with applications in blood flow

Abstract The magnetohydrodynamic (MHD) Stokes equations have several applications in the field of biofluid dynamics. In the present study, we propose the staggered finite volume method (S-FVM) for MHD Stokes equations and establish its equivalence to a nonconforming finite element approximation. We also theoretically establish the convergence of the proposed S-FVM. The error estimation is carried out in an unstructured grid framework which is known for its flexibility and robustness in dealing with complex domains. The apriori estimate shows that the L 2 {L}_{2} -norm of the error for the pressure and velocity components is of order h h , the spacial grid size. After validating the numerical performance of the scheme against benchmark test cases, we do numerical simulations for the blood flow through an injured arteriole and analyze the influence of the magnetic force on hemodynamics in the arteriole under an injured condition.

Development of an implicit high-order Flux Reconstruction solver for high-speed flows on simplex elements

In this study, a significant emphasis is placed on the extension of high-order Flux Reconstruction (FR) schemes to cater to high-speed flows, specifically those involving high Mach numbers. The paper delves into the development and implementation of these FR schemes on both straight and curved-edged 2D and 3D simplex elements within the open-source COOLFluiD (Computational Object-Oriented Libraries for Fluid Dynamics) platform. The proposed FR solver provides more accurate detection of complex flow features over relatively coarser meshes when compared to their low-order peers (particularly in presence of shock waves), is fully implicit and able to simulate compressible flow problems governed by the Euler or Navier-Stokes equations on triangular and tetrahedral meshes. In order to simulate cases with shocks, a shock-capturing scheme previously developed for quadrilateral elements, was extended to tackle supersonic and hypersonic simulations. Extensive verification of the resulting FR solver (up to 7th order, a.k.a P6, for the solution polynomial and 3rd order a.k.a Q2 for the geometrical representation) has been performed on benchmark test cases with flow speeds ranging from subsonic to hypersonic, up to Mach 9.6. The obtained results have been favorably compared to those available in the literature.

Accuracy verification of fast adaptive galerkin finite volume solver for thermal and mechanical load crack propagation in triangular meshes

This study presents the details of the Galerkin finite volume method for triangular unstructured meshes and its application for the fracture analysis of 2D elasticity problems under simultaneous thermal and mechanical loading. The heat diffusion and elasticity equations are discretized using the Galerkin finite volume method (which, due to omitting matrix manipulation calculations, computations are considerably faster than FEM and XFEM Solvers). The maximum tangential stress criterion is presented after briefly describing the interaction integral formulation used to calculate the stress intensity factors in thermo-mechanical problems. The accuracy of the computed results of the present strategy under thermo-mechanical loads is demonstrated using some benchmark test cases. First, a thermal stress analysis of a plate with an inclined central crack under thermal boundary conditions is performed. Second, the development of a crack under mechanical stress boundary conditions is modeled. Third, crack propagation under both thermal and mechanical boundary conditions is simulated. The present modeling strategy's results are compared with those reported in previous numerical works to verify the accuracy. The stress intensity factors and predicted crack trajectories are utilized to assess the accuracy of computed results and investigate the quality of crack simulation by the proposed numerical method.