Finite Element Discretization Research Articles

Statistical modelling of a tractor tractive performance during ploughing operation on a tropical Alfisol

Abstract Tractor is the most prominent off-road agricultural machinery that is significant to the global food security. The tractive modelling of tyre–soil interaction and agricultural implement dynamics is a complex phenomenon that require holistic approach. Terramechanics techniques such as empirical, semi-empirical, analytical, and numerical methods such as finite element models and discrete element models have gained traction in tractive performance studies. Some of these approaches are premised on large arrays of variables for modelling tractive performance based on the soil–tyre and tools interactions. In this study, soft computing in R software domain was used to model the tractor tractive performance during ploughing operations on a tropical Alfisol. The research farm at the National Centre for Agricultural Mechanization was used for the field experiment. The experimental design was a nested-factorial under a Randomized Complete Block Design having three replications. The input factors were tractor power size, T, (60, 65, and 70 hp); tyre inflation pressure, P, (83, 124, and 165 kPa); implement configuration, I, (2 and 3 bottoms disc plough); and operational speed, S, (6.31, 7.90, 9.47, 11.05, and 12.63 km/h). Standard procedures were followed to obtain the measured parameters in the field, which were statistically analysed. Correlation analysis and analysis of variance of the measured parameters at 5% significance level were established. Multiple linear regression was used to develop the model, validated using the 10-fold cross-validation method. The results revealed that the evaluated variables have a range of 1.56–7.79 kN, 5.15–27.20%, 9.10–32.00 cm, 4.50–13.94%, 1.31–1.67 g/cm3, 95.89–207.78 kPa, and 98.67–295.56 for draught, wheel slip, depth of cut, moisture content, bulk density, cone index (CI), and shear stress, respectively. A positive correlation exists between the towing force (TF) and the measured variables except for the shear stress and CI. The final developed model has seven variables for predicting TF with a 6.5% error and an average of 0.4735 cross validation root mean square error. The model quality of fit achieved an R Adj 2 = 0.8754 {R}_{\text{Adj}}^{2}=0.8754 which satisfactorily described the response variable. The study provides insights into tractive dynamic systems modelling of machine, tractive medium (soil), and agricultural tools anchored on soft computing approach. Its adoption will assist in quality ploughing operation integrating the variables established in the model.

Flow dynamics over cylinder in two‐dimensional benchmark problem: A finite element approximation

This research investigates 2D benchmark flow around a circular cylinder, utilizing the incompressible Navier–Stokes equations alongside the continuity and energy equations. The numerical solution is achieved through finite element discretization for space variable, combined with a second‐order Crank–Nicolson scheme for time integration. The computational results are derived using the FEATFLOW finite element based library package. Our study focuses on the dimensionless form of the flow equations and examines three key dimensionless parameters: drag, lift, and pressure drop. Upon applying finite element method (FEM) discretization, the system is converted into a set of linear or nonlinear ordinary differential equations or algebraic equations for steady‐state scenarios. We then apply the Newton–Raphson method as the outer nonlinear solver, and the multigrid method for efficiently resolving the linear subproblems. To ensure numerical accuracy, we evaluated the and errors, confirming that the experimental order of convergence matches the theoretical predictions. Flow profiles were both graphically represented and tabulated, offering a detailed understanding of the simulation results.

Size-Dependent Mechanical Properties and Excavation Responses of Basalt with Hidden Cracks at Baihetan Hydropower Station through DFN–FDEM Modeling

Basalt is an important geotechnical material for engineering construction in Southwest China. However, it has complicated structural features due to its special origin, particularly the widespread occurrence of hidden cracks. Such discontinuities significantly affect the mechanical properties and engineering stability of basalt, and related research is lacking and unsystematic. In this work, taking the underground caverns in the Baihetan Hydropower Station as the engineering background, the size-dependent mechanical behaviors and excavation responses of basalt with hidden cracks were systematically explored based on a synthetic rock mass (SRM) model combining the finite-discrete element method (FDEM) and discrete fracture network (DFN) method. The results showed that: (1) The DFN–FDEM model generated based on the statistical characteristics of the geometric parameters of hidden cracks can consider the real structural characteristics of basalt, whereby the mechanical behaviors found in laboratory tests and at the engineering site could be exactly reproduced. (2) The representative elementary volume (REV) size of basalt blocks containing hidden cracks was 0.5 m, and the mechanical properties obtained at this size were considered equivalent continuum properties. With an increase in the sample dimensions, the mechanical properties reflected in the stress–strain curves changed from elastic–brittle to elastic–plastic or ductile, the strength failure criterion changed from linear to nonlinear, and the failure modes changed from fragmentation failure to local structure-controlled failure and then to splitting failure. (3) The surrounding rock mass near the excavation face of underground caverns typically showed a spalling failure mode, mainly affected by the complex structural characteristics and high in situ stresses, i.e., a tensile fracture mechanism characterized by stress–structure coupling. The research findings not only shed new light on the failure mechanisms and size-dependent mechanical behaviors of hard brittle rocks represented by basalt but also further enrich the basic theory and technical methods for multi-scale analyses in geotechnical engineering, which could provide a reference for the design optimization, construction scheme formulation, and disaster prevention of deep engineering projects.

Divergence-free cut finite element methods for Stokes flow

We develop two unfitted finite element methods for the Stokes equations based on Hdiv\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{H}^{{{\\,\ extrm{div}\\,}}}$$\\end{document}-conforming finite elements. Both cut finite element methods exhibit optimal convergence order for the velocity, pointwise divergence-free velocity fields, and well-posed linear systems, independently of the position of the boundary relative to the computational mesh. The first method is a cut finite element discretization of the Stokes equations based on the Brezzi–Douglas–Marini (BDM) elements and involves interior penalty terms to enforce tangential continuity of the velocity at interior edges in the mesh. The second method is a cut finite element discretization of a three-field formulation of the Stokes problem involving the vorticity, velocity, and pressure and uses the Raviart–Thomas (RT) space for the velocity. We present mixed ghost penalty stabilization terms for both methods so that the resulting discrete problems are stable and the divergence-free property of the Hdiv\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{H}^{{{\\,\ extrm{div}\\,}}}$$\\end{document}-conforming elements is preserved also on unfitted meshes. In both methods boundary conditions are imposed weakly. We show that imposing Dirichlet boundary conditions weakly introduces additional challenges; (1) The divergence-free property of the RT and the BDM finite elements may be lost depending on how the normal component of the velocity field at the boundary is imposed. (2) Pressure robustness is affected by how well the boundary condition is satisfied and may not hold even if the incompressibility condition holds pointwise. We study two approaches of weakly imposing the normal component of the velocity at the boundary; we either use a penalty parameter and Nitsche’s method or a Lagrange multiplier method. We show that appropriate conditions on the velocity space has to be imposed when Nitsche’s method or penalty is used. Pressure robustness can hold with both approaches by reducing the error at the boundary but the price we pay is seen in the condition numbers of the resulting linear systems, independent of if the mesh is fitted or unfitted to the boundary.

Waveguide finite element modelling for broadband vibration analysis of tyres including rotation and prestress

In the framework of tyre/road noise prediction, our aim is to introduce a waveguide finite element (WFE) method for broadband vibration analysis of rotating inflated structures of arbitrary cross-section. Approximating the geometry as perfectly circular, the finite element discretization is restricted to the two-dimensional cross-section, enabling fast and high-frequency computations. Tyres are particularly challenging to model due to various complicating effects, often approximated or neglected in WFE models : rotation, inflation, structural anisotropy, heterogenetity, damping among others. Our formulation uses Lagrangian perturbations of displacement in Eulerian coordinates, providing a concise way to express equilibrium equations in vibrating media initially moving, prestressed and subjected to fixed point forces (typically, contact excitations in rotating tyres). The method comprises three steps: computing the steady rolling state (including rotation, inflation and centrifugal force), determining the undamped vibration modes superimposed onto the steady state (solving an eigenvalue problem of quadratic type owing to Coriolis acceleration), and obtaining the forced response of the damped structure through specific orthogonality relationships (considering a specific form of damping). The WFE method is compared with a rotating shell analytical model from existing literature and is subsequently applied to a rotating tyre with heterogeneous cross-section up to 4kHz.

Accelerated iterative DG finite element solvers for large-scale time-harmonic acoustic problems

Finite element methods are widely used to solve time-harmonic wave propagation problems, but solving large cases can be extremely difficult even with the computational power of parallel computers. In this work, the linear system resulting from the finite element discretization is solved with iterative solution methods, which are efficient in parallel but can require a large number of iterations. In standard discontinuous Galerkin (DG) methods, the numerical solution is discontinuous at the interfaces between the elements. In hybridizable DG methods, additional unknowns are introduced at the interfaces between the finite elements, and the physical unknowns are eliminated from the global system, resulting in a hybridized system. We have recently proposed a new strategy, called CHDG, where the additional unknowns correspond to transmission variables, whereas in the standard approach they are numerical fluxes. This strategy improves the properties of the hybridized system for faster iterative solution procedures. In this talk, we present and study a 3D CHDG implementation with nodal finite element basis functions. The resulting scheme has properties amenable to efficient parallel computing. Numerical results are presented to validate the method, and preliminary 3D computational results are proposed.

Uniform error analysis of an exponential IMEX-SAV method for the incompressible flows with large Reynolds number based on grad-div stabilization

Based on the grad-div stabilization and scalar auxiliary variable (SAV) methods, a first-order Euler implicit/explicit finite element scheme is studied for the Navier–Stokes equations with large Reynolds number. In the designing of numerical scheme, the nonlinear term is explicitly treated such that one only needs to solve a constant coefficient algebraic system at each time step. Meanwhile, the proposed scheme is unconditionally stable without any condition of the time step τ and mesh size h. In finite element discretization, we use the stable Taylor-Hood element for the approximation of the velocity and pressure. By a rigorous analysis, we derive an uniform L2 error estimate O(τ+h2) of the velocity in which the constant is independent of the viscosity coefficient. Finally, numerical experiments are given to support theoretical results and the efficiency of the proposed scheme.

Real-Time Aerodynamic Load Estimation for Hypersonics via Strain-Based Inverse Maps

This work develops an efficient real-time inverse formulation for inferring the aerodynamic surface pressures on a hypersonic vehicle from sparse measurements of the structural strain. The approach aims to provide real-time estimates of the aerodynamic loads acting on the vehicle for ground and flight testing, as well as guidance, navigation, and control applications. Specifically, the approach targets hypersonic flight conditions where direct measurement of the surface pressures is challenging due to the harsh aerothermal environment. For problems employing a linear elastic structural model, the inference problem can be posed as a least-squares problem with a linear constraint arising from a finite element discretization of the governing elasticity partial differential equation. Due to the linearity of the problem, an explicit solution is given by the normal equations. Precomputation of the resulting inverse map enables rapid evaluation of the surface pressure and corresponding integrated quantities, such as the force and moment coefficients. The inverse approach additionally allows for uncertainty quantification, providing insights for theoretical recoverability and robustness to sensor noise. Numerical studies demonstrate the estimator performance for reconstructing the surface pressure field, as well as the force and moment coefficients, for the Initial Concept 3.X (IC3X) conceptual hypersonic vehicle.

A novel FDEM-GSA method with applications in deformation and damage analysis of surrounding rock in deep-buried tunnels

In underground hydraulic tunnel engineering, particularlydeep-buried projects, the deformations and stability of the surrounding rock are critical to the construction process. Due to the complex depositional environment of such tunnels, multiple factors influence the stability of the surrounding rock during construction. This paper proposes a novel hybrid method combining Finite-Discrete Element Method (FDEM) with Global Sensitivity Analysis (GSA) and machine learning. The FDEM model is used to establish an approximate relationship between input and output parameters, and its accuracy is validated through comparison with monitoring data. On the basis of data simulated by the FDEM model, a meta-model is developed by Particle Swarm Optimization-Extreme Gradient Boosting (PSO-XGBoost). 10,000 data sets are generated using the meta-model for Sobol sensitivity analysis. The proposed analysis framework is applied to study the deep-buried water diversion tunnel in the Central Yunnan Water Diversion Project (CYWDP). The results indicate that in deep-buried tunnel environments, as the tunnel depth increases, the dominant factor influencing the deformation of the surrounding rock transitions from tunnel depth to the mechanical properties of the rock itself. These findings provide valuable insights for optimizing construction plans in similar tunnel projects and offer a new perspective on sensitivity analysis frameworks based on numerical computations.

Multi-Scale Integrated Corrosion-Adjusted Seismic Fragility Framework for Critical Infrastructure Resilience

This study presents a novel framework for integrating corrosion effects into critical infrastructure seismic risk assessment, focusing on reinforced concrete (RC) structures. Unlike traditional seismic fragility curves, which often overlook time-dependent degradation such as corrosion, this methodology introduces an approach incorporating corrosion-induced degradation into seismic fragility curves. This framework combines time-dependent corrosion simulation with numerical modeling, using the finite–discrete element method (FDEM) to assess the reduction in structural capacity. These results are used to adjust the seismic fragility curves, capturing the increased vulnerability due to corrosion. A key novelty of this work is the development of a comprehensive risk assessment that merges the corrosion-adjusted fragility curves with seismic hazard data to estimate long-term seismic risk, introducing a cumulative risk ratio to quantify the total risk over the structure’s lifecycle. This framework is demonstrated through a case study of a one-story RC moment frame building, evaluating its seismic risk under various corrosion scenarios and locations. The simulation results showed a good fit, with a 3% to 14% difference between the case study and simulations up to 75 years. This fitness highlights the model’s accuracy in predicting structural degradation due to corrosion. Furthermore, the findings reveal a significant increase in seismic risk, particularly in moderate and intensive corrosion environments, by 59% and 100%, respectively. These insights emphasize the critical importance of incorporating corrosion effects into seismic risk assessments, offering a more accurate and effective strategy to enhance infrastructure resilience throughout its lifecycle.

A new combined finite-discrete element method for stability analysis of soil-rock mixture slopes

PurposeThe purpose of this paper is to propose a new combined finite-discrete element method (FDEM) to analyze the mechanical properties, failure behavior and slope stability of soil rock mixtures (SRM), in which the rocks within the SRM model have shape randomness, size randomness and spatial distribution randomness.Design/methodology/approachBased on the modeling method of heterogeneous rocks, the SRM numerical model can be built and by adjusting the boundary between soil and rock, an SRM numerical model with any rock content can be obtained. The reliability and robustness of the new modeling method can be verified by uniaxial compression simulation. In addition, this paper investigates the effects of rock topology, rock content, slope height and slope inclination on the stability of SRM slopes.FindingsInvestigations of the influences of rock content, slope height and slope inclination of SRM slopes showed that the slope height had little effect on the failure mode. The influences of rock content and slope inclination on the slope failure mode were significant. With increasing rock content and slope dip angle, SRM slopes gradually transitioned from a single shear failure mode to a multi-shear fracture failure mode, and shear fractures showed irregular and bifurcated characteristics in which the cut-off values of rock content and slope inclination were 20% and 80°, respectively.Originality/valueThis paper proposed a new modeling method for SRMs based on FDEM, with rocks having random shapes, sizes and spatial distributions.

Numerical Analysis for a Non-isothermal Incompressible Navier–Stokes–Allen–Cahn System

In this paper we develop the numerical analysis for a non-isothermal diffuse-interface model, in dimension N=2,3,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N=2, 3,$$\\end{document} that describes the movement of a mixture of two incompressible viscous fluids. This model consists of modified Navier–Stokes equations coupled with a phase-field equation given by a convective Allen–Cahn equation, and energy transport equation for the temperature; which admits a dissipative energy inequality. We propose an energy stable numerical scheme based on the Finite Element Method, and we analyze optimal weak and strong error estimates, as well as convergence towards regular solutions. In order to construct the numerical scheme, we introduce two extra variables (given by the gradient of the temperature and the variation of the energy with respect to the phase-field function) which allows us to control the strong regularity required by the model, which is one of the main difficulties appearing from the numerical point of view. Having the equivalent model, we consider a fully discrete Finite Element approximation which is well-posed, energy stable and satisfies a set of uniform estimates which allow to analyze the convergence of the scheme. Finally, we present some numerical simulations to validate numerically our theoretical results.

Dislocation-based finite element method for homogenized limit domain characterization of structured metamaterials

PurposeHeterogeneous and micro-structured materials have been the object of multiscale and homogenization techniques aimed at recognizing the elastic properties of the equivalent continuum. The proposed investigation deals with the mechanical characterization of the heterogeneous material structured metamaterials through analyzing the ultimate strength using the limit analysis of the Representative Volume Element (RVE). To get the desired material strength, a novel finite element formulation based on the derivation of self-equilibrated solutions through the finite elements devoted to calculating the lower bound theorem has been implemented together with the limit analysis in Melàn’s formulation.Design/methodology/approachThe finite element formulation is based on discrete mapping of Volterra dislocations in the structure using isoparametric representation. Using standard finite element techniques, the linear operator V, which relates the self-equilibrated internal solicitation to displacement-like nodal parameters, has been built through finite element discretization of displacement and strain.FindingsThe proposed work presented an elastic homogenization of the mechanical properties of an elementary cell with a geometry known in the literature, the isotropic truss. The matrix of elastic constants was calculated by subjecting the RVE to numerical load tests, simulated with a commercial FEM calculation code. This step showed the dependence of the isotropy properties, verified with Zener theory, on the density of the RVE. The isotropy condition of the material is only achieved for certain section ratios between body-centered cubic (BCC) and face-centered cubic (FCC), neglecting flexural effects at the nodes. The density that satisfies Zener’s conditions represents the isotropic geomatics of the isotropic truss.Originality/valueFor the isotropic case, the VFEM procedure was used to evaluate the isotropy of the limit domain and was compared with the Mises–Schleicher limit domain. The evaluation of residual ductility and dissipation energy allowed a measurement parameter for the limit anisotropy to be defined. The novelty of the proposal consisted in the formulation of both the linearized and the nonlinear limit locus of the material; hence, it furnished the starting point for further limit analysis of the structures whose elementary volume has been described through the proposed approach.

Failure mechanism of a tunnel in a soil–rock mixture based on a new combined finite–discrete element method

The mechanical properties and failure characteristics of soil–rock mixtures (SRMs) directly affect the stability of tunnels constructed in SRMs. A new SRM modelling method based on the combined finite–discrete element method (FDEM) was proposed. Using this new SRM modelling method based on the FDEM, the mechanical characteristics and failure behaviour of SRM samples under uniaxial compression, as well as the failure mechanism of SRMs around a tunnel, were further investigated. The study results support the following findings: (1) The modelling of SRM samples can be achieved using a heterogeneous rock modelling method based on the Weibull distribution. By adjusting the relevant parameters, such as the soil–rock boundaries, element sizes and modelling control points, SRM models with different rock contents and morphologies can be obtained. (2) The simulation results of uniaxial compression tests of SRM samples with different element sizes and morphologies validate the reliability and robustness of the new modelling method. In addition, with increasing rock content, VBP (volumetric block proportion), the uniaxial compressive strength and Young’s modulus increase exponentially, but the samples all undergo single shear failure within the soil or along the soil–rock interfaces, and the shear failure angles are all close to the theoretical values. (3) Tunnels in SRMs with different rock contents all exhibit X-shaped conjugate shear failure, but the fracture network propagation depth, the maximum displacement around the tunnel, and the failure degree of the tunnel in the SRM roughly decreases via a power function as the rock content increases. In addition, as the rock content increases, such as when VBP = 40%, large rocks have a significant blocking effect on fracture propagation, resulting in an asymmetric fracture network around the tunnel. (4) The comparisons of uniaxial compression and tunnel excavation simulation results with previous theoretical results, laboratory test results, and numerical simulation results verify the correctness of the new modelling method proposed in this paper.

Two Nitsche-based mixed finite element discretizations for the seepage problem in Richards’ equation

This paper proposes two algorithms to impose seepage boundary conditions in the context of Richards’ equation for groundwater flows in unsaturated media. Seepage conditions are non-linear boundary conditions, that can be formulated as a set of unilateral constraints on both the pressure head and the water flux at the ground surface, together with a complementarity condition: these conditions in practice require switching between Neumann and Dirichlet boundary conditions on unknown portions on the boundary. Upon realizing the similarities of these conditions with unilateral contact problems in mechanics, we take inspiration from that literature to propose two approaches: the first method relies on a strongly consistent penalization term, whereas the second one is obtained by an hybridization approach, in which the value of the pressure on the surface is treated as a separate set of unknowns. The flow problem is discretized in mixed form with div-conforming elements so that the water mass is preserved. Numerical experiments show the validity of the proposed strategy in handling the seepage boundary conditions on geometries with increasing complexity.

A FDEM study on the mechanical properties and failure behavior of soft-hard interbedded rocks considering the size effect

Soft–hard interbedded rocks are widely distributed at the Earth’s surface, and their mechanical properties and failure behavior directly affect the stability of local tunnel and slope engineering projects. Previous studies have rarely considered the influence of size effects on the mechanical properties and failure behavior of such rocks. Therefore, this paper used the combined finite–discrete element numerical method (FDEM) to study the mechanical properties and failure behavior of soft–hard interbedded rock samples considering the size effect. First, appropriate input parameters were calibrated and verified by using a new parameter calibration method. Second, the effects of the element size and loading rate were studied to obtain appropriate model parameters. Finally, the effects of the layer number, sample size, and height–diameter ratio of composite rock samples on their mechanical properties and failure behavior at different layer dip angles and layer thickness ratios were investigated. The results support the following findings: (1) For the composite rock samples with a layer thickness of 10 mm, reliable simulation results can be obtained by using a 2.2 mm element size, and the loading rate should not exceed 0.2 m/s in FDEM numerical modeling. (2) The number of layers in the sample should be at least 5, and when the height–diameter ratio is a constant 2.0, the height of the sample should not be less than 110 mm. (3) As the height–diameter ratio of the composite rock samples increases, both the compressive strength and elastic modulus decrease for all layer dip angles considered, but the rock failure mode changes for layer dip angles of 15–75°; in addition, the sample size effect is most significant for layer dip angles of 60° and 75°. (4) Taking horizontally layered composite rock samples as examples, both the compressive strength and elastic modulus of samples with different layer thickness ratios decrease with increasing height–diameter ratio and their failure modes also depend on the height–diameter ratio.

A Space-Time Finite Element Method for the Eddy Current Approximation of Rotating Electric Machines

Abstract In this paper we formulate and analyze a space-time finite element method for the numerical simulation of rotating electric machines where the finite element mesh is fixed in a space-time domain. Based on the Babuška–Nečas theory we prove unique solvability both for the continuous variational formulation and for a standard Galerkin finite element discretization in the space-time domain. This approach allows for an adaptive resolution of the solution both in space and time, but it requires the solution of the overall system of algebraic equations. While the use of parallel solution algorithms seems to be mandatory, this also allows for a parallelization simultaneously in space and time. This approach is used for the eddy current approximation of the Maxwell equations which results in an elliptic-parabolic interface problem. Numerical results for linear and nonlinear constitutive material relations confirm the applicability and accuracy of the proposed approach.

Wall-Modeled Large-Eddy Simulation Method for Unstructured-Grid Navier–Stokes Solvers

This paper reports on the implementation and assessment of a wall-modeled large-eddy simulation (WMLES) methodology in an unstructured-grid, node-centered flow solver, FUN3D, that is developed and supported at the NASA Langley Research Center. Finite-volume (FV) and finite-element (FE) discretization schemes considered in the study provide formal second-order spatial accuracy. Large-eddy simulations (LES) resolve large-scale turbulent-flow features, and small-scale effects are modeled using the Vreman subgrid-scale model. At solid-wall boundaries, a shear-stress model is employed to provide a proper boundary-flux closure. The nonlinear equations are integrated in time using either an optimized backward difference formula or an implicit multistage Runge–Kutta temporal scheme. The implicit equations at each time step are solved by strong nonlinear iteration schemes. WMLES demonstrations are shown for two high-lift configurations, namely, the McDonnell Douglas 30P30N multi-element airfoil and a NASA High-Lift Common Research Model. Results show that the WMLES approaches implemented in the FV and FE discretization methods produce consistent solutions and are capable of capturing key aerodynamic characteristics and flow structures for high-lift configurations at a wide range of angles of attack, including maximum-lift conditions. In the 30P30N example, correct trends in the variations of integrated aerodynamic forces and moments, surface pressure distributions, and boundary-layer profiles are captured as the Reynolds number is increased.

Test and simulation of corroded high strength steel wires: From scanned morphology feature to mechanical degradation

This paper presents a coupled experimental-numerical study aimed at understanding the mechanical behavior of corroded high-strength steel wires. Accelerated corrosion tests were conducted on steel wires to achieve varying corrosion levels, and the mechanical properties of the corroded wires were characterized by tensile test. The surface morphology of the corroded wires was derived by 3D optical scanning and point cloud models was generated that precisely captured the surface pits. These models were then converted into solid models by surface reconstruction and finite element discretization. Numerical simulations, based on reconstructed surface morphology, effectively predict key mechanical characteristics and align closely with experimental data. The research establishes relationships between statistical pit parameters and macro-mechanical properties, providing valuable insights for predicting the mechanical performance of corroded wires and evaluating the integrity of structures compromised by corrosion.

Finite Element Method on locally refined composite meshes for Dirichlet fractional Laplacian

It is known that the solution of the Dirichlet fractional Laplacian in a bounded domain exhibits singular behavior near the boundary. Consequently, numerical discretizations on quasi-uniform meshes lead to low accuracy and nonphysical solutions. We adopt a finite element discretization on locally refined composite meshes, which consist in a combination of graded meshes near the singularity and uniform meshes where the solution is smooth. We also provide a reference strategy on parameter selection of locally refined composite meshes. Numerical tests confirm that finite element method on locally refined composite meshes has higher accuracy than uniform meshes, but the computational cost is less than that of graded meshes. Our method is applied to discrete the fractional-in-space Allen–Cahn equation and the fractional Burgers equation with Dirichlet fractional Laplacian, some new observations are discovered from our numerical results.