Mesh Scheme Research Articles

Improved Delayed Detached-Eddy Simulation of Turbulent Vortex Shedding in Inert Flow over a Triangular Bluff Body

The Improved Delayed Detached-Eddy Simulation (IDDES) is a modification of the original Detached-Eddy Simulation (DES) design to incorporate Wall Modeled Large Eddy Simulation (WMLES) capabilities and to extend the class of flows suitable for this methodology. For thin attached boundary layers, typically seen in external aerodynamic flows, the DES branch of the model is active, whereas with thick boundary layers, typically seen in internal flows and also wake flows, the WMLES branch is active, thus providing a numeric method suited to handling most flow cases automatically. The flow over a triangular bluff body is used to validate the suitability of the IDDES model and compare the results with experimental, DDES, and LES data. The IDDES model is found to be relatively accurate when compared with the experimental results, with recirculation length, streamwise velocity, and Reynolds stresses all showing good agreement with the experimental data. However, when compared with the DDES model, there is a ~4% overprediction of the recirculation length using the same mesh and numerical scheme. The code, with its extra complexity, is also ~3% slower to solve. The IDDES model has also been tested against different meshes, and the results show that even for a coarse mesh, there is still good agreement with the experimental data.

Investigation of Aerodynamic Performance of Multi-element Airfoil in Free Surface Effect

Abstract This study examines the aerodynamic performance of the 30P30N multi-element airfoil flying on a free surface, a numerical computational model is established, the governing equations are addressed through the application of the finite volume method, while the volume of fluid method is utilized for the simulation of two-phase flow. Different mesh strategies and turbulence models are compared, with the numerical methods validated against experimental data. The aerodynamic properties of the 30P30N multi-element airfoil on the free surface at different wavelengths and wave heights are given by numerical computations, which show that the ground effect of the 30P30N multi-element airfoil differ from those on a clean airfoil, the aerodynamic coefficients of the 30P30N multi-element airfoil decrease as flight altitude lowers, with the pitching and drag moment of the slat is opposite to that of the main airfoil and the flap. Additionally, when the 30P30N multi-element airfoil flies over a regular wave surface, the aerodynamic coefficients of each component exhibit periodic behavior.

Theoretical and Numerical Analysis of Singular Perturbation Problems in Ordinary Differential Equations

Background: Singular perturbation troubles in everyday differential equations (ODEs) involve a small parameter ϵ that causes answers to show off behaviors on multiple scales, main to massive challenges in both theoretical and numerical evaluation. Objective: This paper at targets to comprehensively look at the theoretical and numerical techniques for reading and solving singular perturbation troubles in ODEs. Focus is located on know-how the behaviors precipitated through the small parameter and developing strong numerical techniques to accurately seize these behaviors. Methods: Theoretical approaches employed include matched asymptotic expansions and multiple scale analysis. These methods decompose the solution domain into regions with different scales, constructing and matching approximate solutions to ensure smooth transitions. Numerical techniques such as finite difference methods, finite element methods, and spectral methods are utilized, with particular emphasis on adaptive mesh refinement to handle boundary layers effectively Results: Theoretical evaluation demonstrates the effectiveness of matched asymptotic expansions and multiple scale analysis in presenting correct approximations and easy transitions among one of a kind solution regions. Numerical techniques showed high accuracy and performance, particularly whilst blended with adaptive techniques. Finite distinction strategies with non-uniform grids and adaptive mesh refinement, finite detail techniques with adaptive mesh strategies, and spectral strategies with special handling of boundary layers all proved successful. Stability and convergence analyses showed the reliability of those techniques. Conclusions: This comprehensive evaluation highlights the strengths and applicability of each theoretical and numerical strategies in tackling singular perturbation issues in ODEs. The mixed use of these techniques lets in for correct and green answers, presenting treasured equipment for applications in diverse clinical and engineering fields.

Error Estimates for First- and Second-Order Lagrange–Galerkin Moving Mesh Schemes for the One-Dimensional Convection–Diffusion Equation

A new moving mesh scheme based on the Lagrange–Galerkin method for the approximation of the one-dimensional convection–diffusion equation is studied. The mesh movement is prescribed by a discretized dynamical system for the nodal points. This system is related to the velocity and diffusion coefficient in the convection–diffusion equation such that the nodal points follow the convective flow of the model. It is shown that under a restriction of the time step size the mesh movement cannot lead to an overlap of the elements and therefore an invalid mesh. Using a piecewise linear approximation, optimal error estimates in the ℓ∞(L2)∩ℓ2(H01)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell ^\\infty (L^2) \\cap \\ell ^2(H_0^1)$$\\end{document} norm are proved in case of both, a first-order backward Euler method and a second-order two-step method in time. These results are based on new estimates of the time dependent interpolation operator derived in this work. Preservation of the total mass is verified for both choices of the time discretization. Numerical experiments are presented that confirm the error estimates and demonstrate that the proposed moving mesh scheme can circumvent limitations that the Lagrange–Galerkin method on a fixed mesh exhibits.

Inclisiran: A Systematic Review Exploring the Revolutionary Approach of Twice-Yearly Dosing Regimen in the Treatment of Hypercholesterolemia.

The global burden of hyperlipidemia is on the rise, along with an increase in associated cardiovascular complications. Since most of the patients affected by hyperlipidemia are elderly individuals with multiple comorbidities, the introduction of even a single additional drug for asymptomatic conditions such as hyperlipidemia can drastically reduce treatment compliance due to their long medication history. Hence, researchers are trying to come up with a drug with a long duration of action requiring less frequent dosing without compromising compliance and improving the outcome. This led to the discovery of inclisiran, a "wonder drug" that utilizes small interference RNA and requires only twice-yearly administration to maintain patients' lipid levels at optimal levels. We conducted a systematic review by following standardized guidelines on the long-term efficacy and safety of the new drug, inclisiran, in the treatment of hypercholesterolemia. We conducted an advanced search on PubMed using the MeSH strategy and then employed appropriate keywords to search other major databases, such as PubMed Central and Medline, using various inclusion and exclusion criteria, which yielded 94 articles from various databases.We narrowed down the search to 10 randomized controlled trials (ORION trials) after removing duplicates and screening for irrelevant titles for inclusion in the study. The ORION trials on inclisiran evaluated the drug's impact on various parameters, such as low-density lipoprotein-cholesterol (LDL-C), proprotein convertase subtilisin/kexin type 9 (PCSK9), high-density lipoprotein (non-HDL), apolipoprotein B (apoB), and so on, whileconsidering the safety aspects of the drug. All the trials indicate greater efficacy of inclisiran and long-term maintenance of the results achieved when compared to a placebo and showed a long dosing interval, thereby increasing treatment compliance. Additionally, as the drug's dose increased, we observed greater reductions in the mentioned parameters without a significant increase in the incidence of adverse events. According to the review's data analysis, inclisiran, with its greater efficacy, has the potential to replace conventional pharmacological therapy in the near future, with the best results achieved when combined with lifestyle modifications. However, a long-term assessment of the drug's efficacy and safety is required before implementing it in clinical practice to identify any potential safety concerns, particularly related to the administration of higher dosage over a longer period.

Combined loading of unreinforced and Z-pin reinforced composite pi joints: An experimental and numerical study

Blind predictions of experimental responses of non-reinforced and z-pin reinforced composite pi joints were established using a progressive damage and failure model. The finite element model used a novel mixed-mode cohesive formulation to model intra-laminar and inter-laminar damage. A deliberate meshing strategy was used for cohesive interlayers to capture the interaction between intra- and inter-laminar damage modes. A smeared cohesive zone modeling approach was implemented to efficiently include the effects of z-pinning for the z-pin reinforced specimens. Using material properties obtained through experimental correlation of simpler joint configurations, blind predictions for large element specimens subjected to combined loading (axial compression and push-off loading) were established. To assess the predictive capabilities of the model, experimental and numerical comparisons were made in terms of load-displacement response, critical loads, and failure progression. Comparisons between the experimental results and predictions for the unreinforced joints were found to be in good agreement across the range of compressive loads tested. For the z-pin reinforced joints, initial responses were accurately predicted; however, ultimate loads and the toughening effect of the z-pin reinforcement was overpredicted.

Enhancing heat transfer with a synthetic jet for thermal management applications

AbstractThis article explores the utilization of a synthetic jet as an approach to cool microelectronic devices, addressing their thermal management needs. The study includes both experimental measurements and numerical simulations to gain a comprehensive understanding of the heat transfer characteristics and fluid flow patterns generated by the synthetic jet actuator. The average Nusselt number (Nu) of the synthetic jet impinging flow with the dimensionless separation distances of the orifice to the heated surface (H/D) is investigated at different Reynolds numbers. A dynamic mesh scheme is employed in performing the simulations of the fluid domain to showcase the diaphragm's vibration and its deformation over time. The velocity profiles exhibit that the synthetic jet flow prompts the formation of two countervortices during every vibrating cycle of the diaphragm. The experimental results align closely with the predicted outcomes, indicating that the synthetic jet significantly enhances heat transfer by 3.1 times relative to the natural convection in the case of (H/D = 8.4) across different Reynolds numbers while maintaining low power consumption, a compact size, and a noise‐free operation.

Error estimates of exponential wave integrators for the Dirac equation in the massless and nonrelativistic regime

AbstractWe present exponential wave integrator Fourier pseudospectral (EWI‐FP) methods and establish their error estimates of the fully discrete schemes for the Dirac equation in the massless and nonrelativistic regime. This regime involves a small dimensionless parameter where , and is inversely proportional to the speed of light. The solution exhibits highly oscillatory behavior in time and rapid wave propagation in space in this regime. Specifically, the time oscillations have a wavelength of , while the spatial oscillations have a wavelength of , with a wave speed of . We employ (symmetric) exponential wave integrators for temporal derivatives and Fourier spectral discretization for spatial derivatives. We rigorously derive the error bounds which explicitly depend on the mesh size , the time step and the small dimensionless parameter . The error estimates for the EWI‐FP methods demonstrate that their meshing strategy requirement (‐scalability) necessitates setting and when . Finally, some numerical examples are provided to validate the error bounds.

Adaptive Mesh Strategy for Efficient Use of Interface Elements in a 3D Probabilistic Explicit Cracking Model for Concrete.

In this paper, the development of a 3D adaptive probabilistic explicit cracking model for concrete is reported. The contribution offered herein consists in a new adaptive mesh strategy designed to optimize the use of interface elements in probabilistic explicit cracking models. The proposed adaptive mesh procedure is markedly different from other strategies found in the literature, since it takes into account possible influences on the redistribution of stresses after cracking and can also be applied to purely deterministic cracking models. The process of obtaining the most appropriate adaptive mesh procedure involved the development and evaluation of three different adaptivity strategies. Two of these adaptivity strategies were shown to be inappropriate due to issues related to stress redistribution after cracking. The validation results demonstrate that the developed adaptive probabilistic model is capable of predicting the scale effect at a level similar to that experimentally observed, considering the tensile failure of plain concrete specimens. The results also show that different softening levels can be obtained. The proposed adaptive mesh strategy proved to be advantageous, being able to promote significant reductions in the simulation time in comparison with the classical strategy commonly used in probabilistic explicit cracking models.

Optimisation of Bridge Pier Winding Flow Numerical Simulation Scheme Based on Delft3D

The majority of existing numerical simulations of the effect of bridge piers on water’s movement are based on a limited number of bridge piers at a laboratory scale. Furthermore, some 2D numerical simulations for actual bridge projects have deficiencies, including the use of overly large meshes and an inadequate treatment of bridge piers. In this study, we compare three methods (structural mesh encryption, suspension mesh, and non-structural mesh) based on Delft3D, and we apply the optimisation scheme to a real bridge project. It is demonstrated that optimal results can be achieved by utilising a grid size comparable to the pier diameter (Dp) in the region away from the pier. In the vicinity of the pier, the grid cell size should be no larger than 1/9 Dp. The suspended grid technique (DD Boundary) can yield results consistent with those obtained using a full-area high-resolution grid, provided that the total grid number can be reduced and the computational time is considerably reduced. In this study, the unstructured mesh (Delft3D Flexible Mesh) scheme was unable to capture the oscillations in the wake flow behind the bridge piers. However, the application of the optimised scheme in bridge engineering demonstrated its practical value. The findings of this study on mesh resolution and suspension mesh schemes can be applied to the Delft3D software and are also useful for other numerical simulation work.

Binary Opacity Grids: Capturing Fine Geometric Detail for Mesh-Based View Synthesis

While surface-based view synthesis algorithms are appealing due to their low computational requirements, they often struggle to reproduce thin structures. In contrast, more expensive methods that model the scene's geometry as a volumetric density field (e.g. NeRF) excel at reconstructing fine geometric detail. However, density fields often represent geometry in a "fuzzy" manner, which hinders exact localization of the surface. In this work, we modify density fields to encourage them to converge towards surfaces, without compromising their ability to reconstruct thin structures. First, we employ a discrete opacity grid representation instead of a continuous density field, which allows opacity values to discontinuously transition from zero to one at the surface. Second, we anti-alias by casting multiple rays per pixel, which allows occlusion boundaries and subpixel structures to be modelled without using semi-transparent voxels. Third, we minimize the binary entropy of the opacity values, which facilitates the extraction of surface geometry by encouraging opacity values to binarize towards the end of training. Lastly, we develop a fusion-based meshing strategy followed by mesh simplification and appearance model fitting. The compact meshes produced by our model can be rendered in real-time on mobile devices and achieve significantly higher view synthesis quality compared to existing mesh-based approaches. Our interactive webdemo is available at https://binary-opacity-grid.github.io.

A Review of Computational Fluid Dynamics Approaches Used to Investigate Lubrication of Rolling Element Bearings

Abstract Optimizing bearing performance is based on effective lubrication, especially in high-speed machinery, where minimizing churning and drag losses is of significant importance. Over the past few decades, extensive research has been conducted into the better understanding of different aspects of bearing lubrication. These investigations have employed a combination of experimental methods and advanced computational fluid dynamics (CFD) models. This article provides a comprehensive overview of critical aspects of bearing lubrication, with a specific emphasis on recent advances in CFD models. Lubricant flow and distribution patterns are discussed while examining their impact on drag and churning losses. An extensive discussion is provided on the meshing strategies and modeling approaches used to simulate various flow phenomena within bearings. In addition, relevant trends and impacts of cage design on bearing lubrication and fluid friction have been explored, along with a discussion of prevailing limitations that can be addressed in future bearing CFD models.

Evaluating numerical models for the prediction of pollutant dispersion over Tokyo's Polytechnic University campus

This paper focuses on assessing how different Computational Fluid Dynamics (CFD) methodologies perform in modelling pollutant dispersion over extended urban areas. The case selected for evaluating the proposed methodologies is based on an extensive experimental study conducted by Tachibana et al. (2022), in which outdoor field measurements and wind tunnel experiments were carried out for monitoring tracer gas dispersion over the Atsugi Campus of Tokyo's Polytechnic University (TPU). Numerical results obtained by solving steady Reynolds Averaged Navier Stokes (RANS) governing equations, as well as using a scale resolving Large Eddy Simulation (LES) approach are compared against experimental data, in terms of both dimensionless local velocities and pollutant concentrations. The different meshing strategies that are employed for each methodology are also discussed in detail. The aim of the paper is to help gain further insights about the extent to which the Menter's Shear Stress Transport (SST) k-ω RANS model and LES can be used in the Architectural, Engineering and Construction (AEC) industry for pollutant dispersion modelling.

Non-uniform knot (NUK) SIAC post-processing of flow fields produced through unstructured grid adaptation and optimization

As the finite element method (FEM) and the finite volume method (FVM), both their traditional and high-order variants, continue their proliferation into various applied engineering disciplines, adaptive mesh refinement and optimization strategies have increased in their importance when solving real-world computational fluid mechanics applications. The post-processing and visualization of the resulting flow fields present two significant analysis and visualization challenges. The first challenge is the handling of elemental continuity, which is often only C0 continuous (in continuous Galerkin methods) or piecewise discontinuous (in discontinuous Galerkin methods). The second challenge is that, depending on the flow regime and the geometric configurations for which adaptive meshing strategies are used, the meshes generated are often highly anisotropic. The (uniform knot) line-SIAC (L-SIAC) filter has been proposed as a way of handling elemental continuity issues in an accuracy-conserving manner with the added benefit of casting the data in a smooth context even if the representation is element discontinuous. In this paper, we demonstrate that the state-of-the-art adaptive L-SIAC filter, designed for mildly anisotropic meshes, suffers degradation in the quality of the post-processed solution when applied to the types of highly anisotropic meshes produced through adaptive mesh refinement and optimization. Hence, a new Non-Uniform Knot (NUK) L-SIAC filter is proposed that automatically conforms to the underlying mesh anisotropy. We demonstrate that the new filter behaves similarly to the adaptive L-SIAC filter when applied to uniform and mildly anisotropic meshes, and furthermore we show the superiority of the NUK L-SIAC filter when applied to highly anisotropic meshes. The newly formulated filter is applied to 2D canonical scalar fields and used to visualize 2D and 3D fluid flow simulation results.

Mesh morphing-based pre-processing and numerical simulation of blockage accident in lead–bismuth fast reactor fuel assembly

This paper presents a CFD modeling approach for a 19-rod bundle fuel assembly with spiral semi-cylindrical ribs, which potentially can be used for liquid metal cooled fast reactor, as well as a numerical simulation of flow and thermal behavior under partially blocked conditions. The ribs on fuel rod surface are integrally formed with the cladding to enhance heat transfer while preventing detachment. However, the complex channel geometry presents challenges for grid generation, as using a large number of tetrahedral or polyhedral elements would consume significant computational resources. Therefore, this paper proposes a mesh morphing-based pre-processing method to establish a structured hexahedral mesh for such complex geometry. Using this approach, the 19-rods assembly is analyzed, and the result has been verified by conventional mesh scheme as well as experiment.

A computational study for simulating MHD duct flows at high Hartmann numbers using a stabilized finite element formulation with shock-capturing

The concern of this manuscript is stabilized finite element simulations of two-dimensional incompressible and viscous magnetohydrodynamic (MHD) duct flows governed by a coupled system of partial differential equations of the convection–diffusion type. In such flows, the high values of the Hartmann numbers (Ha) indicate that the convection process dominates the flow field. As is typical trouble encountered in convection-dominated flow simulations, classical discretization methods fail to function properly for MHD flows at high Hartmann numbers, yielding several numerical instabilities. In this study, the core computational tool we employ in order to overcome such challenges is the streamline-upwind/Petrov–Galerkin (SUPG) formulation. Beyond that, since the SUPG-stabilized formulation requires additional treatment where solutions experience rapid changes, we also enhance the SUPG-stabilized finite element formulation with a shock-capturing operator for achieving better solution profiles around sharp layers. The formulations are derived for both steady-state and time-dependent models. The proposed method, the so-called SUPG-YZβ formulation, techniques used, and in-house-developed finite element solvers are evaluated on a comprehensive set of numerical experiments. The test computations reveal that the SUPG-YZβ formulation yields quite good solution profiles near strong gradients without any significant numerical instabilities, even for quite challenging values of Ha, whereas the SUPG usually fails alone. Furthermore, by using only linear elements on relatively coarser meshes, the proposed formulation achieves this without the need for any adaptive mesh strategy, in contrast to most previously reported studies.

An efficient 3D finite element procedure for simulating wheel–rail cyclic contact and ratcheting

Various models for simulating rail ratcheting behaviour were developed to study rolling contact fatigue (RCF) damage in rails. However, limitations remain in terms of the accuracy of wheel–rail contact modelling and computational efficiency of the cyclic loading simulation. This study developed an efficient 3D finite element (FE) procedure to simulate ratcheting in rails subjected to numerous load cycles. The procedure simulates a wheel rolling repeatedly over a rail section with updated stress–strain states, enabling automatically executed cyclic loading simulation given a predefined number of cycles. To ensure the accuracy of the contact modelling, the effect of meshing schemes on subsurface stress distribution was examined. In addition, the FE contact model with the selected meshing scheme, which balances accuracy and computational efficiency, was verified against the widely accepted CONTACT program. Subsequently, a non-linear kinematic hardening (NLKH) steel material was used in the FE model for ratcheting simulations with up to 100 wheel-loading cycles. The rail surface and subsurface stress states were replicated under partial-slip wheel–rail rolling contact conditions with traction coefficients of 0.10, 0.20 and 0.35, respectively. The ratcheting behaviour was extensively analysed in terms of plastic deformation, contact patch evolution, and ratcheting rates. The simulated plastic deformation was found to alter the contact geometry and thus contact stresses, which in turn affect further accumulation of plastic deformation and subsequent ratcheting strains. These findings highlighted the importance of considering the interplay between the rail ratcheting behaviour of the rail and evolving contact conditions for predicting ratcheting and RCF damage in rails.

Skin and Proximity Effect Calculation of a System of Rectangular Conductors Using the Proper Generalized Decomposition Technique

This paper presents the application of a numerical approach known as proper generalized decomposition (PGD) to calculate the per-unit length (PUL) ac resistance of rectangular conductors. PGD has been successfully used in areas such as fluid mechanics and biomedical applications. It solves a partial differential equation (PDE) by decomposing the answer into a set of unknown one-dimensional (1D) functions in an iterative approach until it reaches a predetermined convergence. In this paper, a frequency-dependent meshing scheme is employed in the PGD technique at each frequency to properly take skin and proximity effects into account. One of the main advantages of PGD over traditional numerical approaches such as finite element or finite difference methods is that it confines the answers within a set of one-dimensional functions, which require fewer computational resources. Different examples of single and multiple rectangular conductors are considered to study skin and proximity effects. The PGD results are compared with those obtained using a commercial finite element method (FEM) software to verify the accuracy of the model. This approach can be used in applications such as white box modeling of transformers, EMC analysis, hairpin winding design used in electric vehicles, and busbar simulation.

An adaptive mesh scheme of the lattice spring model based on geometrical continuity

An adaptive mesh scheme is introduced for the lattice spring model (LSM), where the original triangular cells are subdivided into a set of smaller triangular cells. The scheme is based on geometrical continuity at the heterogeneous mesh boundary, where the refined grid cells intersect the original cell edge. The LSM simulations on the refined grid show a superior computational efficiency to the uniform grid. Each subdivision reduces the original cell edges by a factor of two. The refinement procedure was recursively applied ten times before any marked loss in accuracy was observed. The accuracy of the adaptive model is on par with a regular grid approach. More specifically, the characteristics of fracture cavity are comparable with a uniform grid of the same mesh density as the smallest cells in the adaptive approach. The fracture criterion such as J-integral, the elastic energy of the grid and potential energy change due to fracture growth and strain loading agree well with the theory of a mode I fracture, which enables simulations of process such as sub-critical fracture with a wide dynamic range.

SUPG-based stabilized finite element computations of convection-dominated 3D elliptic PDEs using shock-capturing

This study is interested in stabilized finite element computations of advection-dominated convection–diffusion-type partial differential equations. The governing equations are assumed to be defined on the 3D unit cube and stationary. Towards that end, we stabilize the standard (Bubnov–) Galerkin finite element method (GFEM), which typically suffers from yielding numerical approximations polluted with node-to-node nonphysical oscillations in convection dominance, by employing the streamline-upwind/Petrov–Galerkin (SUPG) formulation. In order to achieve better shock representations near sharp layers, the SUPG-stabilized formulation is also enhanced with a simple and residual-based shock-capturing mechanism, the so-called YZβ technique. Several test computations are performed to assess the efficiency and robustness of the proposed formulation. The test problems are examined under more challenging conditions than those previously studied in the literature, i.e., for flows substantially dominated by convection phenomena. The numerical results and comparisons demonstrate that the SUPG-YZβ combination significantly eliminates both globally spread and localized numerical instabilities. Beyond that, the proposed formulation accomplishes that by using only linear elements on relatively coarser meshes and without making use of any adaptive mesh strategies.