Global Mesh Research Articles

An implicit large-eddy simulation perspective on the flow over periodic hills

The periodic hills simulation case is a well-established benchmark for computational fluid dynamics solvers due to its complex features derived from the separation of a turbulent flow from a curved surface. We study the case with the open-source implicit large-eddy simulation (ILES) software Lethe. Lethe solves the incompressible Navier–Stokes equations by applying a stabilized continuous finite element discretization. The results are validated by comparison to experimental and computational data available in the literature for Re = 5600. We study the effect of the time step, averaging time, and global mesh refinement. The ILES approach shows good accuracy for average velocities and Reynolds stresses using less degrees of freedom than the reference numerical solution. The time step has a greater effect on the accuracy when using coarser meshes, while for fine meshes the results are rapidly time-step independent when using an implicit time-stepping approach. A good prediction of the reattachment point is obtained with several meshes and this value approaches the experimental benchmark value as the mesh is refined. We also run simulations at Reynolds equal to 10600 and 37000 and observe promising results for the ILES approach.

Advancing Parsimonious Deep Learning Weather Prediction Using the HEALPix Mesh

AbstractWe present a parsimonious deep learning weather prediction model to forecast seven atmospheric variables with 3‐hr time resolution for up to 1‐year lead times on a 110‐km global mesh using the Hierarchical Equal Area isoLatitude Pixelization (HEALPix). In comparison to state‐of‐the‐art (SOTA) machine learning (ML) weather forecast models, such as Pangu‐Weather and GraphCast, our DLWP‐HPX model uses coarser resolution and far fewer prognostic variables. Yet, at 1‐week lead times, its skill is only about 1 day behind both SOTA ML forecast models and the SOTA numerical weather prediction model from the European Center for Medium‐Range Weather Forecasts. We report several improvements in model design, including switching from the cubed sphere to the HEALPix mesh, inverting the channel depth of the U‐Net, and introducing gated recurrent units (GRU) on each level of the U‐Net hierarchy. The consistent east‐west orientation of all cells on the HEALPix mesh facilitates the development of location‐invariant convolution kernels that successfully propagate weather patterns across the globe without requiring separate kernels for the polar and equatorial faces of the cube sphere. Without any loss of spectral power after the first 2 days, the model can be unrolled autoregressively for hundreds of steps into the future to generate realistic states of the atmosphere that respect seasonal trends, as showcased in 1‐year simulations.

A global adaptive discretization of velocity space for discrete velocity methods in predictions of rarefied and multi-scale flows

By introducing a discrete velocity space (DVS), deterministic methods in gas-kinetic theory, such as the discrete velocity method (DVM) and unified methods, can accurately capture complex nonequilibrium distribution functions and describe rarefied flow behaviors. However, describing high-speed flows with conventional Cartesian DVS is prohibitively costly due to the large number of discrete velocity points. Therefore, to enable deterministic solvers to handle complex, rarefied, and multi-scale flows effectively, a novel adaptive velocity space (AVS) is proposed. First, a global velocity mesh is intentionally adopted instead of a local velocity mesh to maintain a high level of DVS parallelism and facilitate extension to implicit algorithms. The global AVS is robust as it avoids the instability of information transformation between different cell-local AVS. Second, a new strategy is developed for reconstructing the distribution function in the tree-structured AVS, which is a low-order reconstruction with forced macroscopic conservation. This low-order reconstruction facilitates the direct value assignment between farther and child nodes, avoiding the derivative calculation of the distribution function (which is sometimes discontinuous). Additionally, the integration error of the low-order reconstruction is fixed by the forced macroscopic conservation. With these two important improvements, the proposed global AVS is then integrated into general DVM frameworks, such as the unified gas-kinetic scheme. Finally, a number of numerical tests are carried out to validate the proposed method, including steady and unsteady multi-scale flows.

Strategy for simulating high-speed crack propagation in 3D-plate structures based on S-version FEM

Plate structures serve as the fundamental components of many large structures; therefore, dynamic crack propagation in plates is a significant safety concern. This paper proposes a novel strategy based on the s-version finite element method (s-method) for simulating high-speed crack propagation in a 3D plate structure. We employed a combination of the nodal force release technique and local mesh update method to simulate a dynamically propagating crack front. The global mesh was generated based on the entire domain geometry without considering crack propagation, which significantly simplified the mesh generation procedure, whereas the local mesh was generated only in the vicinity of the crack front with fine elements to ensure high accuracy. In the proposed strategy, the local mesh completely covered the crack front beyond the surface of the 3D plate structure. Such an incompatibility between the surface of the target domain and boundaries of the local mesh causes non-negligible errors in the conventional s-method. Hence, we propose an approach based on Heaviside enrichment to eliminate these errors. To investigate the effectiveness of the proposed strategy, numerical examples to analyse the experimental results of high-speed crack propagation in double cantilever beam-type plate specimens made of polymethyl methacrylate are presented. The numerical results demonstrated the effectiveness of the proposed strategy for simulating high-speed crack propagation in 3D plate structures. Therefore, the proposed strategy has the potential to serve as a fundamental numerical framework for simulating dynamic crack propagation in engineering structures.

Stress field and interaction forces between dislocations and precipitate distributions

AbstractA computational method is developed for calculation of the stress field and interaction forces between dislocations and precipitates of arbitrary shape and distribution. The internal stress generated by precipitates due to coherency strain is implemented within the discrete dislocation dynamics (DDD) framework. The s‐version finite element method (s‐FEM), which models a precipitate of arbitrary shape using a local mesh is used to calculate coherency stress fields. The method facilitates meshing precipitate volumes of arbitrary geometry, and multiple local meshes can be superimposed at various positions of the global mesh. Accuracy and convergence conditions of the method are established. For a single precipiate, the method is shown to be 3.5 times faster than a standard FEM calculation for the same accuracy, and the gain in speed increases with the number of precipitates. The CRSS of spherical precipitates is found to be higher than disk‐shaped precipitates of the same volume fraction.

A parallel grad‐div stabilized finite element algorithm for the Navier–Stokes equations with a nonlinear damping term

AbstractIn this work, we propose a parallel grad‐div stabilized finite element algorithm for the Navier–Stokes equations attached with a nonlinear damping term, using a fully overlapping domain decomposition approach. In the proposed algorithm, we calculate a local solution in a defined subdomain on a global composite mesh which is fine around the defined subdomain and coarse in other regions. The algorithm is simple to carry out on the basis of available sequential solvers. By a local a priori estimate of the finite element solution, we deduce error bounds of the approximations from our presented algorithm. We perform also some numerical experiments to verify the effectiveness of the proposed algorithm.

3D hand pose and shape estimation from monocular RGB via efficient 2D cues

Estimating 3D hand shape from a single-view RGB image is important for many applications. However, the diversity of hand shapes and postures, depth ambiguity, and occlusion may result in pose errors and noisy hand meshes. Making full use of 2D cues such as 2D pose can effectively improve the quality of 3D human hand shape estimation. In this paper, we use 2D joint heatmaps to obtain spatial details for robust pose estimation. We also introduce a depth-independent 2D mesh to avoid depth ambiguity in mesh regression for efficient hand-image alignment. Our method has four cascaded stages: 2D cue extraction, pose feature encoding, initial reconstruction, and reconstruction refinement. Specifically, we first encode the image to determine semantic features during 2D cue extraction; this is also used to predict hand joints and for segmentation. Then, during the pose feature encoding stage, we use a hand joints encoder to learn spatial information from the joint heatmaps. Next, a coarse 3D hand mesh and 2D mesh are obtained in the initial reconstruction step; a mesh squeeze-and-excitation block is used to fuse different hand features to enhance perception of 3D hand structures. Finally, a global mesh refinement stage learns non-local relations between vertices of the hand mesh from the predicted 2D mesh, to predict an offset hand mesh to fine-tune the reconstruction results. Quantitative and qualitative results on the FreiHAND benchmark dataset demonstrate that our approach achieves state-of-the-art performance.

Two-phase CFD simulations of COSI tests and evaluation of condensation distribution

This study presents the two-phase CFD simulation of experiments carried out on COSI facility in the frame of Pressurized Thermal Shock (PTS). PTS may occur during a cold-water injection, by the Emergency Core Cooling System (ECCS) during a Loss-Of-Coolant Accident (LOCA). The simulations were carried out using the Neptune_CFD code. A sensitivity study on Direct Contact Condensation (DCC) models was performed with a comparison with experimental data. At the end of this study, it appears that the turbulence of the free surface is rather low. Consequently, a low-turbulence heat transfer model is more appropriate. Then, two sensitivity studies on global and local mesh refinement are carried out, with the creation of an optimized mesh. This optimized mesh is used with the low-turbulence model to simulate the 40 test cases with no water level and co-current steam flow. Deviations in temperature and total condensation rate are less than 5% and 25% respectively. Finally, the condensation rate between stratified and non-stratified regions is evaluated. Condensation tends to occur in non-stratified zones, with imbalance that can be very high, reaching almost 80% of total condensation.

SolidWorks Flow Simulation: Selecting the optimal mesh for conducting CFD analysis on a centrifugal fan

The accuracy of mesh use determines the suitability of simulation results with experimental test results, therefore it is necessary to study the type and number of mesh used for flow simulation. This study aims to investigate the type of mesh and the number of cells that are appropriately used in the simulation of centrifugal fans using the Solidworks Flow Simulation module. The research was conducted by comparing the simulation results with the experimental results on centrifugal fans that have been carried out by previous studies. In this research, the type of mesh used is global mesh. The parameter of determining the number of cells is done by varying the mesh level because the mesh level affects the number of cells. In this simulation study, the boundary condition is set to one flow volume of 5 m3/h and a rotation speed of 92.362 rad/s. In this study, the total pressure and efficiency of the centrifugal fan are the things that are seen from the comparison of flow simulation with the experiment. Based on the simulation results that have been carried out, mesh levels 1 to 4 show results that differ significantly from the experimental results. At machine levels 5 to 7, the results are close to the experimental results, but the closest total pressure and efficiency values are at mesh level 5. The results of this study can be a reference for research that simulates centrifugal fans.

Simulating Atmospheric Dust With a Global Variable‐Resolution Model: Model Description and Impacts of Mesh Refinement

AbstractIn this study, a global variable‐resolution modeling framework of atmospheric dust and its radiative feedback is established and evaluated. In this model, atmospheric dust is simulated simultaneously with meteorological fields, and dust‐radiation interactions are included. Five configurations of global mesh with refinement at different resolutions and over different regions are used to explore the impacts of regional refinement on modeling dust lifecycle at regional and global scales. The model reasonably produces the overall magnitudes and spatial variabilities of global dust metrics such as surface mass concentration, deposition, aerosol optical depth, and radiative forcing compared to observations and previous modeling results. Two global variable‐resolution simulations with mesh refinement over major deserts of North Africa (V16 km‐NA) and East Asia (V16 km‐EA) simulate less dust emissions and smaller dry deposition rates inside the refined regions due to the weakened near‐surface wind speed caused by better resolved topographic complexity at higher resolution. The dust mass loadings over North Africa are close to each other between V16 km‐NA and the quasi‐uniform resolution (∼120 km) (U120 km), while over East Asia, V16 km‐EA simulates higher dust mass loading. Over the non‐refined areas with the same resolution, the difference between global variable‐resolution and uniform‐resolution experiments also exists, which is partly related to their difference in dynamic time‐step and the coefficient for horizontal diffusion. Refinement at convection‐permitting resolution around the Tibetan Plateau (TP) simulates less dust due to its more efficient wet scavenging from resolved convective precipitation around the TP against coarse resolution.

Finite element modeling of spherical indentation behavior of 3D mesh fabric at the yarn level

This paper reports an experimental and numerical study on the spherical indentation behavior of three-dimensional (3D) warp-knitted mesh fabrics. A full-size finite element (FE) model of a typical 3D mesh fabric is established at the yarn level based on the realistic monofilament architecture from micro-computed tomography (μCT) scanning and verified with experiments. The structural change of the fabric in the spherical indentation process is quantitatively analyzed in terms of fabric global deformation, local deformation, mesh deformation, and spacer monofilament deformation from the FE simulation. The numerical results show that the fabric shrinks walewise and expands coursewise from the spherical indentation of the continuous intermeshed monofilament architecture, showing counterintuitive partial auxeticity. The coursewise symmetry and walewise asymmetry of the 3D mesh fabric produce relatively symmetrical coursewise deformation and asymmetrical walewise deformation under spherical indentation. The symmetrical coursewise deformation includes even widening, good fitting of the indenter, and almost identical mesh sizes in the coursewise direction. Walewise asymmetry leads to uneven shortening, inferior fitting of the indenter, and considerably varied mesh sizes in the walewise direction. Spacer monofilaments in different positions relative to the spherical indenter have different deformations. The closer to the indenter, the greater bending and twisting of the spacer monofilament. The spacer monofilament knitted earlier of the tested fabric has smaller deformation than that knitted later due to the walewise asymmetry. The coursewise symmetry and walewise asymmetry of the inhomogeneous 3D mesh fabric structure result in a highly nonlinear spherical indentation behavior.

Finite Element Discretizations for Variable-Order Fractional Diffusion Problems

We present a finite element discretization scheme for multidimensional fractional diffusion problems with spatially varying diffusivity and fractional order. We consider the symmetric integral form of these nonlocal equations defined on general geometries and in arbitrary bounded domains. A number of challenges are encountered when discretizing these equations. The first comes from the heterogeneous kernel singularity in the fractional integral operator. The second comes from the formally dense discrete operator with its quadratic growth in memory footprint and arithmetic operations. An additional challenge comes from the need to handle volume conditions—the generalization of classical local boundary conditions to the nonlocal setting. Satisfying these conditions requires that the effect of the whole domain, including both the interior and exterior regions, be computed on every interior point in the discretization. Performed directly, this would result in quadratic complexity. In order to address these challenges, we propose a strategy that decomposes the stiffness matrix into three components. The first is a sparse matrix that handles the singular near-field separately, and is computed by adapting singular quadrature techniques available for the homogeneous case to the case of spatially variable order. The second component handles the remaining smooth part of the near-field as well as the far-field, and is approximated by a hierarchical {mathcal {H}}^2 matrix that maintains linear complexity in storage and operations. The third component handles the effect of the global mesh at every node, and is written as a weighted mass matrix whose density is computed by a fast-multipole type method. The resulting algorithm has therefore overall linear space and time complexity. Analysis of the consistency of the stiffness matrix is provided and numerical experiments are conducted to illustrate the convergence and performance of the proposed algorithm.

Application of Bilinear Softening Laws and Fracture Toughness of Foamed Concrete

This study examined the fracture and failed performance of foamed concrete materials by testing normalized notched beams under three-point bending via three methods: inverse analysis, digital image correlation (DIC), and finite element modeling (FEM). It also discussed both experimental and FEM characteristics. However, inverse analysis is only applicable for specimens with a notch height of 30 mm. Bilinear softening of the tested beams was estimated to identify the fracture energy (GF), critical crack length (ac), and elastic modulus (E). Additionally, the fracture toughness was calculated by adopting the double-K method (initiation fracture, unstable fracture, and cohesive fracture). Two-dimensional FEA modeling of the fracture was conducted using the traction-separation law (TSL), incorporating the extended finite element method (XFEM) and cohesive zone (CZM) techniques. A finite element sensitivity for the XFEM and CZM was performed, with the global mesh size of 2 and the damage stabilization cohesion of 1 × 10−5 showed good convergence and were used in other models. Further comparison of the DIC experiment findings with those from the FEM demonstrated good agreement in terms of crack propagation simulation.

Finite element analysis of three-dimensional cracks by connecting global and local meshes

In this paper, a novel method for the finite element analysis of three-dimensional cracks is developed by connecting global and local meshes using polyhedral elements. A local mesh including a fine spider-web mesh around the crack tip is arbitrary placed in a coarse global mesh of hexahedral elements. Polyhedral elements are generated by modifying the hexahedral elements at the interface between global and local meshes. The present polyhedral elements provide a seamless connection between global and local meshes. Numerical results show that the present method can be effectively used to analyze three-dimensional cracks by connecting global and local meshes using polyhedral elements.

Modeling of Severe Plastic Deformation by HSHPT of As-Cast Ti-Nb-Zr-Ta-Fe-O Gum Alloy for Orthopedic Implant.

The High Speed High Pressure Torsion (HSHPT) is the severe plastic deformation method (SPD) designed for the grain refinement of hard-to-deform alloys, and it is able to produce large, rotationally complex shells. In this paper, the new bulk nanostructured Ti-Nb-Zr-Ta-Fe-O Gum metal was investigated using HSHPT. The biomaterial in the as-cast state was simultaneously compressed up to 1 GPa and torsion was applied with friction at a temperature that rose as a pulse in less than 15 s. The interaction between the compression, the torsion, and the intense friction that generates heat requires accurate 3D finite element simulation. Simufact Forming was employed to simulate severe plastic deformation of a shell blank for orthopedic implants using the advancing Patran Tetra elements and adaptable global meshing. The simulation was conducted by applying to the lower anvil a displacement of 4.2 mm in the z-direction and applying a rotational speed of 900 rpm to the upper anvil. The calculations show that the HSHPT accumulated a large plastic deformation strain in a very short time, leading to the desired shape and grain refinement.

Superposed element method for the numerical simulation of structure crack

Crack is a key factor for the normal operation of structures. In this paper, a new method called Superposed Element Method (SEM) is proposed for the numerical simulation of crack analysis. Firstly, the structure containing crack is divided into two independent meshes. One is the global mesh without crack, the other is the local mesh of the crack and its vicinity. Then, the two independent meshes are coupled together, finite element method (FEM) is used for the local mesh and the complete elements outside of the coverage of the local mesh, and numerical manifold technique is applied to the incomplete elements. Finally, in order to couple the global mesh with the local mesh, the penalty stiffness is imposed on the boundaries of local mesh. The results of the numerical examples show that the pre-processing of SEM is quite simple, and the accuracy of the solution is relatively high. The method proposed is expected to be widely used for dynamic simulation of crack propagation.

An adaptive mesh refinement strategy for 3D phase modeling of brittle fracture

In order to improve the calculation accuracy and efficiency of the phase field method (PFM), an adaptive mesh refinement strategy suitable for 3D problems is proposed. The refined area is selected in terms of both the phase field value and the phase field increment value. The transition area is then chosen based on the transition element determination algorithm. The corresponding areas are refined using three basic and two advanced refinement templates. The new mesh is made up of hexahedrons and has no hanging nodes. The improved backtracking algorithm based on distance judgment is used in 3D adaptive mesh refinement and has proven its capacity to increase calculation efficiency. The accuracy and applicability of PFM to low-quality meshes with 3D adaptive mesh refinement are verified through benchmark tests, and the errors are all within 1%. Compared with the global refinement mesh, the number of elements in the PF model with 3D adaptive mesh refinement is reduced by more than 80%, and the computational efficiency is increased by 16 times. Combined with virtual crack insertion technology, mode I-II-III fracture is successfully simulated. The accurate and efficient calculation of cracked structures is realized. 3D multi-level adaptive mesh refinement is preliminary developed, and compared with single-level adaptive mesh, the computational efficiency is about two times higher, which provides a potential way to solve the efficient simulation of crack propagation in large-volume structures.

Barotropic tides in MPAS-Ocean (E3SM V2): impact of ice shelf cavities

Abstract. Oceanic tides are seldom represented in Earth system models (ESMs) owing to the need for high horizontal resolution to accurately represent the associated barotropic waves close to coasts. This paper presents results of tides implemented in the Model for Prediction Across Scales–Ocean or MPAS-Ocean, which is the ocean component within the U.S. Department of Energy developed Energy Exascale Earth System Model (E3SM). MPAS-Ocean circumvents the limitation of low resolution using unstructured global meshing. We are at this stage simulating the largest semidiurnal (M2, S2, N2) and diurnal (K1, O1) tidal constituents in a single-layer version of MPAS-O. First, we show that the tidal constituents calculated using MPAS-Ocean closely agree with the results of the global tidal prediction model TPXO8 when suitably tuned topographic wave drag and bottom drag coefficients are employed. Thereafter, we present the sensitivity of global tidal evolution due to the presence of Antarctic ice shelf cavities. The effect of ice shelves on the amplitude and phase of tidal constituents are presented. Lower values of complex errors (with respect to TPXO8 results) for the M2 tidal constituents are observed when the ice shelf is added in the simulations, with particularly strong improvement in the Southern Ocean. Our work points towards future research with varying Antarctic ice shelf geometries and sea ice coupling that might lead to better comparison and prediction of tides and thus better prediction of sea-level rise and also the future climate variability.

A parallel grad-div stabilized finite element algorithm for the Stokes equations with damping

This work studies a parallel grad-div stabilized finite element algorithm for the damped Stokes equations. In this algorithm, in the light of a fully overlapping domain decomposition technique, we solve a global grad-div stabilized problem to compute a local solution in an intersecting subdomain on a global composite mesh, which is fine in the subdomain and rough elsewhere, making the proposed algorithm easy to implement based on an available sequential solver. We derive error bounds of the approximate solutions from our presented algorithm by the theoretical tool of local a priori estimate for the grad-div stabilized finite element solution. Numerical results verify the validity of the theoretical analysis and demonstrate the benefits of the proposed algorithm. On the one hand, compared with the counterpart one excluding grad-div stabilization, this algorithm can reduce significantly the effect of pressure on the approximate velocities, and hence, yields much better approximate velocities in the case of small viscosities. On the other hand, it takes much less computational time in getting approximate solutions with a comparable accuracy than the standard grad-div stabilization method.

A parallel subgrid stabilized algorithm for incompressible flows with nonlinear slip boundary conditions

We present and study a parallel subgrid stabilized algorithm for simulating the incompressible Navier-Stokes equations with nonlinear slip boundary conditions. The algorithm uses finite element discretizations and an approach of completely overlapping region division for the parallelization, where an elliptic projection operator is applied to define the stabilization term. It has the following appealing features: 1) each subproblem used to calculate a local solution in a subdomain is actually a global problem defined on a global mesh that is locally refined around the subdomain; 2) it can re-use existing sequential software in coding, where both parallelization and stabilization are easy to implement based on existing sequential codes without extensive effort; 3) it inherits the advantages of the subgrid stabilization method and the completely overlapping region division approach; 4) with suitable algorithmic parameters, it is able to yield an optimal convergence rate for the approximate solutions with a comparable accuracy to that of the solutions from the global subgrid stabilized method, with considerable reduction in computational time. With the help of a local a priori estimate, we estimate error bounds of the obtained solutions from the algorithm, and perform some numerical tests to validate the theoretical prediction and illustrate the applicability of the proposed algorithm.