Global Mesh Research Articles

A parallel stabilized finite element variational multiscale method based on fully overlapping domain decomposition for the incompressible Navier-Stokes equations

Based on a fully overlapping domain decomposition approach, a parallel stabilized finite element variational multiscale method for the incompressible Navier-Stokes equations is proposed, where the stabilizations both for the velocity and pressure are based on two local Gauss integrations at the element level. The basic idea of the method is to use a locally refined global mesh to compute a stabilized solution in the given subdomain of interest. The proposed method only requires the application of an existing Navier-Stokes sequential solver on the locally refined global mesh associated with each subdomain, and thus can reuse the existing sequential solver without substantial recoding. Error bound of the approximate solutions from the proposed method is estimated with the use of local a priori error estimate for the stabilized solution. Algorithmic parameter scalings of the method are also derived. Some numerical simulations are presented to demonstrate the effectiveness of the method.

A novel scheme for modelling and analysis of spot-welded shell structures using interface shell elements

In this study, a novel scheme for modelling and analysis of spot-welded shell structures is presented by placing local spider-web shell meshes representing the weld nugget region in a global shell mesh. Interface shell elements are employed for trimmed shell elements with arbitrary number of nodes created by cutting a global shell mesh with the boundaries of local spider-web shell meshes. Transverse shear and membrane locking phenomena in interface shell elements are effectively alleviated by introducing assumed natural strain fields. Conventional elastic beam elements with six degrees of freedom are used to connect the center nodes of local spider-web shell meshes. The present method can construct high-quality shell meshes around spot welds without any global remeshing, which makes it very efficient and effective for the analysis of spot-welded shell structures.

Performance and Accuracy Implications of Parallel Split Physics‐Dynamics Coupling in the Energy Exascale Earth System Atmosphere Model

AbstractSimultaneous calculation of atmospheric processes is faster than calculating processes one at a time. This type of parallelism is beneficial or perhaps even necessary to provide good performance on modern supercomputers, which achieve faster performance through increased processor count rather than improved clock speed. The scalability of the Energy Exascale Earth System Model (E3SM) Atmosphere Model (EAM) is limited by the fluid dynamics which scales up to the number of mesh cells in the global mesh. In contrast, the suite of physics parameterizations in EAM is scalable up to the total number of physics columns, which is an order of magnitude greater than the number of mesh cells. A proposed solution to unlocking the greater potential performance from the physics suite is to solve the physics and dynamics in parallel. This work represents a first attempt at parallel splitting of the grid‐scale fluid dynamics model and the subgrid‐scale physics parameterizations in a global atmosphere model. We will demonstrate that switching to parallel physics‐dynamics coupling extends the scalability of the EAM to up to 3 times the previous peak scalability limit and is up to 20% faster than the sequentially split coupling at the highest core counts and the same time step. Decadal simulations of both coupling approaches show very little impact to the model climate. This improved performance does not come without drawbacks, however. Parallel splitting requires a shorter time step and other modifications which largely offset performance gains. A mass fixer is required for conservation. Techniques for mitigating these issues are also discussed.

Simulation-driven optimization of high-order meshes in ALE hydrodynamics

In this paper we propose tools for high-order mesh optimization and demonstrate their benefits in the context of multi-material Arbitrary Lagrangian-Eulerian (ALE) compressible shock hydrodynamic applications. The mesh optimization process is driven by information provided by the simulation which uses the optimized mesh, such as shock positions, material regions, known error estimates, etc. These simulation features are usually represented discretely, for instance, as finite element functions on the Lagrangian mesh. The discrete nature of the input is critical for the practical applicability of the algorithms we propose and distinguishes this work from approaches that strictly require analytical information. Our methods are based on node movement through a high-order extension of the Target-Matrix Optimization Paradigm (TMOP) of [1]. The proposed formulation is fully algebraic and relies only on local Jacobian matrices, so it is applicable to all types of mesh elements, in 2D and 3D, and any order of the mesh. We discuss the notions of constructing adaptive target matrices and obtaining their derivatives, reconstructing discrete data in intermediate meshes, node limiting that enables improvement of global mesh quality while preserving space-dependent local mesh features, and appropriate normalization of the objective function. The adaptivity methods are combined with automatic ALE triggers that can provide robustness of the mesh evolution and avoid excessive remap procedures. The benefits of the new high-order TMOP technology are illustrated on several simulations performed in the high-order ALE application BLAST [2].

Numerical simulation of crack propagation in shell structures using interface shell elements

In this study, we present a novel finite element approach to simulate crack propagation in shell structures. A local spider-web mesh is placed at the tip of a crack propagating through a global background mesh. Interface shell elements with assumed natural strains are used to connect a non-matching interface between the background mesh and the local spider-web mesh. Interface shell elements are also employed for trimmed shell elements created by cutting shell elements with the crack line. Numerical simulation of crack propagation in shell structures can be easily performed by moving the local spider-web mesh with an incremental crack growth. Numerical experiments show that the present method is very efficient and effective to accurately simulate crack propagation in shell structures without significantly increasing computational burden and implementation complexity of remeshing process.

Dynamic crack propagation analysis based on the s-version of the finite element method

A strategy to efficiently analyse dynamic crack propagation based on the s-version of the finite element method (s-method) is proposed. This strategy superimposes a local mesh over the area that includes the propagating crack tip, which is made possible by the flexible definition of the local mesh. For a strictly accurate evaluation based on the local fracture stress criterion, we introduce the nodal force release technique to the local mesh to simulate dynamic crack propagation. Based on the numerical results, we identify the appropriate global and local mesh conditions required to achieve accurate and efficient local stress evaluations. Comparisons with the standard finite element method using equivalent accuracies show that the proposed strategy can successfully reduce numerical costs. Our results thus demonstrate that the proposed strategy for dynamic crack propagation analysis based on the s-method significantly improves the efficiency of dynamic crack propagation analysis.

Mesh Size Optimization of Unidirectional Fiber-Reinforced Composite Model for Precisely Characterizing the Effective Elastic Property

Structural representative volume unit (RVU) has been extensively used to characterize the real effective elastic properties (EEPs) of fiber-reinforced composites (FRCs). The focus of this study is to optimize the optimum mesh size of a multiscale unidirectional RVU (UD-RVU) model to precisely characterize the EEPs of unidirectional FRCs (UD-FRCs). First, a variety of mechanical properties test experiments are carried out to obtain the real EEPs of UD-FRCs for the preparation of the optimization analysis. Then, a microscopic structural UD-RVU is established according to the fiber distribution of the UD-FRCs, and the corresponding ABAQUS/Python code that is used to characterize the EEPs is developed based on asymptotic homogenization theory. Finally, a complete optimization analysis, which is used for balancing simulation time and characterization accuracy, is performed to obtain the optimum mesh size of the multiscale finite element model. The optimized results reveal that the global mesh size of approximately 0.7 μm is the most optimal mesh, which has high accuracy and high simulation efficiency for characterizing the EEPs of UD-FRCs. The maximum error is close to 4.23% compared with experiments, which has a higher precision than the conventional calculation model, and the characterization model is reported in the literature.

Numerical Study on the Extreme Impact Load of Wavy-Water Ditching

In this paper, numerical method is used study the extreme impact load and its physical causes during the wavy aircraft ditching. the finite volume method and VOF method are used to capture the free surface, six degrees of freedom model and global motion mesh to deal with the relative motion between water and aircraft. and simulate the forced landing process of the aircraft. By choosing the place with the largest vertical velocity relative to the water as the impact position, the extreme impact load on the fuselage is predicted. In this paper, during the impact stage of the wavy water surface, the fuselage encountered an impact peak which is unforeseen on the calm water surface, and the magnitude of the impact peak was related to the sinking speed of the aircraft relative to the water surface. This paper also compares the movement attitude and overload history of aircraft ditching under five sea conditions with different wave height, and gives the influence rules of wave height on the extreme impact load and the peak values of other parameters, which provides a reference for the design of aircraft load distribution.

A large‐scale parallel hybrid grid generation technique for realistic complex geometry

SummaryHigh‐Performance Computing (HPC) systems and Computational Fluid Dynamics (CFD) have made significant progress in recent years; however, as the basis of the large‐scale parallel computing, the massive grid generation of billions of cells has become a bottleneck problem. In this study, a parallel grid generation technique is proposed to generate large‐scale mixed grids with arbitrary cell types and scales. The basic idea of our method is analogous to the global mesh refinement technique. An initial coarse grid with arbitrary cell types is regarded as a background mesh which is partitioned into subzones, and subzones are assigned onto different CPU cores. After the cells and faces in each subzone are split, the inserted new points of the solid wall are projected onto the original CAD entities to preserve the geometry accurately. Finally, the tangled cells caused by the projection in the boundary layer are untangled by a local Radial Basis Function mesh deformation technique. Furthermore, a parallel partition approach and an efficient wall distance computing technique for massive grids are developed also to shorten the preprocessing time. The tests show that the preprocessing efficiency has been increased by two or three orders compared with traditional methods. Billions of grids are generated for the AIAA JSM high‐lift model and the Chinese CHN‐T1 transport model to test the ability of the parallel grid generation technique. The maximum scale up to 19 billion mixed elements is generated using 16 384 CPU cores in parallel, and the mesh quality is acceptable for CFD simulations.

Numerical Analysis of Full-Scale Ship Self-Propulsion Performance with Direct Comparison to Statistical Sea Trail Results

Accurate prediction of the self-propulsion performance is one of the most important factors for the energy-efficient design of a ship. In general, the hydrodynamic performance of a full-scale ship could be achieved by model-scale simulation or towing tank tests with extrapolations. With the development of CFD methods and computing power, directly predict ship performance with full-scale CFD is an important approach. In this article, a numerical study on the full-scale self-propulsion performance with propeller operating behind ship at model- and full-scale is presented. The study includes numerical simulations using the RANS method with a double-model and VOF (Volume-of-Fluid) model respectively and scale effect analysis based on overall performance, local flow fields and detailed vortex identification. The verification study on grid convergence is also performed for full-scale simulation with global and local mesh refinements. A series of sea trail tests were performed to collect reliable data for the validation of CFD predictions. The analysis of scale effect on hull-propeller interaction shows that the difference of hull boundary layer and flow separation is the main source of scale effect on ship wake. The results of the fluctuations of propeller thrust and torque along with circulation distribution and local flow field show that the propeller’s loading is significantly higher for model-scale ship. It is suggested that the difference of vortex evolution and interaction is more pronounced and has larger effects on the ship’s powering performance at model-scale than full-scale according to the simulation results. From the study on self-propulsion prediction, it could be concluded that the simplification on free surface treatment does not only affect the wave-making resistance for bare hull but also the propeller performance and propeller induced ship resistance which can be produced up to 5% uncertainty to the power prediction. Roughness is another important factor in full-scale simulation because it has up to an approximately 7% effect on the delivery power. As a result of the validation study, the numerical simulations of full-scale ship self-propulsion shows good agreement with the sea trail data especially for cases that have considered both roughness and free surface effects. This result will largely enhance our confidence to apply full-scale simulation in the prediction of ship’s self-propulsion performance in the future ship designs.

An Enhanced Steepest Descent Method for Global Optimization-Based Mesh Smoothing

In order to speed up the global optimization-based mesh smoothing, an enhanced steepest descent method is presented in the paper. Numerical experiment results show that the method performs better than the steepest descent method in the global smoothing. We also presented a physically-based interpretation to explain why the method works better than the steepest descent method.

CFD analysis of the effects of multiple semicircular blades on Savonius wind turbine performance

The goal of this work is to simulate and improve the efficiency of an innovative multiple semicircular-bladed Savonius wind turbine, which is identified as belonging to the vertical axis wind turbine (VAWT) category. It is characterized as a low speed turbine that is simpler and cheaper to build than traditional turbines. This makes it appropriate for generating mechanical energy in lower wind speed regions, and it can be coupled with solar panels in urban agglomerations. The objective of this paper is to compare the aerodynamic characteristics and power efficiency of four different geometries of the Savonius wind turbine (two-conventional and two-modified rotors) in order to estimate the most efficient design. The proposed Savonius design comprises multiple semicircular blades added to conventional two- and three-bladed Savonius rotor configurations. The comparison of the efficiency in terms of the torque coefficient (C T ) and power coefficient (C P ) of the new system configurations with the conventional ones finds that the multiple semicircular two-bladed Savonius rotor is more efficient than others. The numerical simulation of the conventional Savonius rotor is developed and validated against experimental and numerical data derived from a literature review. The choice of turbulence model and local or global mesh refinement play essential roles in the accuracy of the numerical simulation results. In this work, we adopted a Shear Stress Transport (SST) model for modelling turbulence, which incorporates the near wall fluctuation capturing capability of the k-w model, and the robust k-ei€ model for modelling the whole numerical domain. An average improvement in the power coefficient of 8.43% for different tip speed ratios (TSRs) is observed for the new configuration compared with the others.

Three-dimensional fatigue crack growth simulation of embedded cracks using s-version FEM

PurposeSince the most of structures and structural components suffers from cyclic loadings, the study on the fatigue failure due to the crack growth has a great importance. The purpose of this paper is to present a three-dimensional fatigue crack growth simulation of embedded cracks using s-version finite element method (SFEM). Using the numerical results, the validity of the fitness-for-service (FFS) code evaluation method is verified.Design/methodology/approachIn this paper, three-dimensional fatigue crack propagation analysis of embedded cracks is performed using the SFEM. SFEM is a numerical analysis method in which the shape of the structure is represented by a global mesh, and cracks are modeled by local meshes independently. The independent global and local meshes are superimposed to obtain the displacement solution of the problem simultaneously.FindingsThe fatigue crack growth of arbitrary shape of cracks is slow compared to that of the simplified circular crack and the crack approximated based on the FFS code of the Japan Society of Mechanical Engineers (JSME). The results tell us that the FFS code of JSME can provide a conservative evaluation of the fatigue crack growth and the residual life time.Originality/valueThis paper presents a three-dimensional fatigue crack growth simulation of embedded cracks using SFEM. Using this method, it is possible to apply mixed mode loads to complex shaped cracks that are closer to realistic conditions.

On a multiscalea posteriorierror estimator for the stokes and Brinkman equations

AbstractThis work proposes and analyzes a residual a posteriori error estimator for the multiscale hybrid-mixed (MHM) method for the Stokes and Brinkman equations. The error estimator relies on the multi-level structure of the MHM method and considers two levels of approximation of the method. As a result the error estimator accounts for a first-level global estimator defined on the skeleton of the partition and second-level contributions from element-wise approximations. The analysis establishes local efficiency and reliability of the complete multiscale estimator. Also, it yields a new face-adaptive strategy on the mesh’s skeleton, which avoids changing the topology of the global mesh. Specially designed to work on multiscale problems, the present estimator can leverage parallel computers since local error estimators are independent of each other. Academic and realistic multiscale numerical tests assess the performance of the estimator and validate the adaptive algorithms.

Assessing Adaptive Mesh Refinement (AMR) in a Forced Shallow-Water Model with Moisture

AbstractTwo forced shallow-water flow scenarios are explored in a 2D fourth-order finite-volume dynamical core with adaptive mesh refinement (AMR) to investigate AMR’s ability to track and resolve complex evolving features. Traditional shallow-water test cases are mainly characterized by large-scale smooth flows that do not effectively test the multiscale abilities of variable-resolution and AMR models to resolve sharp gradients and small-scale flow filaments. Therefore, adding forcing mechanisms to the shallow-water system to model key atmospheric processes adds complexity and creates small-scale phenomena. These can serve as foci for dynamic grid refinement while remaining simple enough to study the numerical design of a model’s dynamical core. The first shallow-water flow scenario represents a strengthening, tropical cyclone–like, vortex that is driven by a Betts–Miller-like convection scheme. The second shallow-water test is built upon a barotropically unstable jet with an added Kessler-like warm rain scheme that leads to precipitating frontal zones. The key feature of both tests is that there is significant sensitivity to the model grid while converging (structurally) at high resolution. Both test cases are investigated for a series of uniform resolutions and a variety of AMR tagging criteria. The AMR simulations demonstrate that grid refinement can resolve local features without requiring global high-resolution meshes. However, the results are sensitive to the refinement criteria. Criteria that trigger refinement early in a simulation reproduce the uniform-resolution reference solutions most reliably. In contrast, AMR criteria that delay refinement for several days require careful tuning of the AMR thresholds to improve results compared with uniform-resolution simulations.

Parallel two-step finite element algorithm based on fully overlapping domain decomposition for the time-dependent natural convection problem

Purpose This paper aims to propose two parallel two-step finite element algorithms based on fully overlapping domain decomposition for solving the 2D/3D time-dependent natural convection problem. Design/methodology/approach The first-order implicit Euler formula and second-order Crank–Nicolson formula are used to time discretization respectively. Each processor of the algorithms computes a stabilized solution in its own global composite mesh in parallel. These algorithms compute a nonlinear system for the velocity, pressure and temperature based on a lower-order element pair (P1b-P1-P1) and solve a linear approximation based on a higher-order element pair (P2-P1-P2) on the same mesh, which shows that the new algorithms have the same convergence rate as the two-step finite element methods. What is more, the stability analysis of the proposed algorithms is derived. Finally, numerical experiments are presented to demonstrate the efficacy and accuracy of the proposed algorithms. Findings Finally, numerical experiments are presented to demonstrate the efficacy and accuracy of the proposed algorithms. Originality/value The novel parallel two-step algorithms for incompressible natural convection problem are proposed. The rigorous analysis of the stability is given for the proposed parallel two-step algorithms. Extensive 2D/3D numerical tests demonstrate that the parallel two-step algorithms can deal with the incompressible natural convection problem for high Rayleigh number well.

Numerical modeling of rock failure under dynamic loading with polygonal elements

SummaryPolygonal finite elements are gaining an increasing attention in the computational mechanics literature, but their application in rock mechanics is very rare. This paper deals with numerical modeling of rock failure under dynamic loading based on polygonal finite elements. For this end, a damage‐viscoplastic constitutive model for rock based on the Mohr‐Coulomb criterion with the Rankine criterion as a tensile cutoff is employed and implemented with the polygonal finite element method. Moreover, the mineral mesostructure or rock is described by randomly mapping groups of polygonal elements representing the constituent minerals into a global mesh and assigning these groups with the corresponding mineral material properties. The performance of the polygonal elements is compared with that of the linear and quadratic triangular and bilinear quadrilateral elements in numerical simulations of controlled shear band formation under uniaxial compression and lateral splitting failure in the dogbone tension test. Numerical simulations of uniaxial tension and compression tests as well as dynamic Brazilian disc test under increasing loading rates demonstrate that the present approach predicts the correct failure modes as well as the dynamic increase in strength of rock.

A fully Lagrangian meshfree framework for PDEs on evolving surfaces

We propose a novel framework to solve PDEs on moving manifolds, where the evolving surface is represented by a moving point cloud. This has the advantage of avoiding the need to discretize the bulk volume around the surface, while also avoiding the need to have a global mesh. Distortions in the point cloud as a result of the movement are fixed by local adaptation. We first establish a comprehensive Lagrangian framework for arbitrary movement of curves and surfaces given by point clouds. Collision detection algorithms between point cloud surfaces are introduced, which also allow the handling of evolving manifolds with topological changes. We then couple this Lagrangian framework with a meshfree Generalized Finite Difference Method (GFDM) to approximate surface differential operators, which together give a method to solve PDEs on evolving manifolds. The applicability of this method is illustrated with a range of numerical examples, which include advection-diffusion equations with large deformations of the surface, curvature dependent geometric motion, and wave equations on evolving surfaces.

Semi-supervised Semantic Mapping Through Label Propagation with Semantic Texture Meshes

Scene understanding is an important capability for robots acting in unstructured environments. While most SLAM approaches provide a geometrical representation of the scene, a semantic map is necessary for more complex interactions with the surroundings. Current methods treat the semantic map as part of the geometry which limits scalability and accuracy. We propose to represent the semantic map as a geometrical mesh and a semantic texture coupled at independent resolution. The key idea is that in many environments the geometry can be greatly simplified without loosing fidelity, while semantic information can be stored at a higher resolution, independent of the mesh. We construct a mesh from depth sensors to represent the scene geometry and fuse information into the semantic texture from segmentations of individual RGB views of the scene. Making the semantics persistent in a global mesh enables us to enforce temporal and spatial consistency of the individual view predictions. For this, we propose an efficient method of establishing consensus between individual segmentations by iteratively retraining semantic segmentation with the information stored within the map and using the retrained segmentation to re-fuse the semantics. We demonstrate the accuracy and scalability of our approach by reconstructing semantic maps of scenes from NYUv2 and a scene spanning large buildings.

A parallel stabilized finite element method based on the lowest equal-order elements for incompressible flows

Based on a fully overlapping domain decomposition technique, a parallel stabilized equal-order finite element method for the steady Stokes equations is presented and studied. In this method, each processor computes a local stabilized finite element solution in its own subdomain by solving a global problem on a global mesh that is locally refined around its subdomain, where the lowest equal-order finite element pairs (continuous piecewise linear, bilinear or trilinear velocity and pressure) are used for the finite element discretization and a pressure-projection-based stabilization method is employed to circumvent the discrete inf–sup condition that is invalid for the used finite element pairs. The parallel stabilized method is unconditionally stable, free of parameter and calculation of derivatives, and is easy to implement based on an existing sequential solver. Optimal error estimates are obtained by the theoretical tool of local a priori error estimates for finite element solutions. Numerical results are also given to verify the theoretical predictions and illustrate the effectiveness of the method.