Boundary Mesh Research Articles

Simulating cold shear flows on a moving mesh

ABSTRACT Rotationally supported, cold, gaseous discs are ubiquitous in astrophysics and appear in a diverse set of systems, such as protoplanetary discs, accretion discs around black holes, or large spiral galaxies. Capturing the gas dynamics accurately in these systems is challenging in numerical simulations due to the low sound speed compared to the bulk velocity of the gas, the resolution limitations of full disc models, and the fact that numerical noise can easily source spurious growth of fluid instabilities if not suppressed sufficiently well, negatively interfering with real physical instabilities present in such discs (like the magnetorotational instability). Here, we implement the so-called shearing-box approximation in the moving-mesh code arepo in order to facilitate achieving high resolution in local regions of differentially rotating discs and to address these problems. While our new approach offers manifest translational invariance across the shearing-box boundaries and offers continuous local adaptivity, we demonstrate that the unstructured mesh of arepo introduces unwanted levels of ‘grid-noise’ in the default version of the code. We show that this can be rectified by high-order integrations of the flux over mesh boundaries. With our new techniques we obtain highly accurate results for shearing-box calculations of the magnetorotational instability that are superior to other Lagrangian techniques. These improvements are also of value for other applications of the code that feature strong shear flows.

A Trefftz based meshfree local method for bending analysis of arbitrarily shaped laminated composite and isotropic plates

A simple meshfree method is developed in the context of Trefftz approaches to solve bending problem of arbitrarily shaped laminated composite and isotropic plates. Widely used deformation theories including classical plate theory, first-order and third-order shear deformation theory are adapted to the method, so the solution range contains thin to thick plates without any restrictions on geometry, genus, layer sequences or boundary conditions. The solution domain is discretized by a set of nodes at which the degrees of freedom are defined. A sub-domain (cloud) centered at each node and containing several adjacent nodes is considered, over which the corresponding Partial Differential Equation (PDE) is split into homogeneous and particular parts. The solution of the homogeneous PDE is formed using a series of exponential basis functions capable of exactly satisfying the PDE, thus putting the method in the context of Trefftz approaches. The boundary conditions are applied in a point-wise manner without the need for boundary meshes. No integration is enforced throughout the solution procedure. By investigating several sample problems compared the literature or the Finite Element Method (FEM), perfect agreement and high convergence rate have been appeared, while the required nodes in the present method is considerably fewer than FEM.

Three-dimensional transient finite element cooling simulation for injection molding tools

Plastic injection molding is one of the most popular manufacturing processes for mass production, and optimizing the mold cooling system is critical for reducing the cycle time and improving the final part quality. This paper develops a three-dimensional transient cooling simulation model based on the finite element method. Comparing with the conventional cycle-averaged cooling model that uses boundary element method, this method has two major advantages: First, the transient mold temperature is more accurate than the cycle-averaged mold temperature. Second, this method allows performing cooling simulation directly on the real-world mold models without the simplifications that required by the boundary element method. To speed up the transient cooling simulation, this method uses the cycle-averaged cooling model as initial condition and applies the heat flux conservation equations at the discontinuous mesh boundaries to eliminate the interface iterations. It is shown that this method finishes the transient cooling analysis in 478 s on the real-world injection molding mold with more than 6.9 million tetrahedral elements, which is a satisfactory time for practical usages. The simulation result is validated by the actual molding experiment. It is found that the maximum temperature error is less than 4% and the average temperature error is less than 1%. The validation proves the accuracy of this simulation method.

Deep learning for biomechanical modeling of facial tissue deformation in orthognathic surgical planning.

Orthognathic surgery requires an accurate surgical plan of how bony segments are moved and how the face passively responds to the bony movement. Currently, finite element method (FEM) is the standard for predicting facial deformation. Deep learning models have recently been used to approximate FEM because of their faster simulation speed. However, current solutions are not compatible with detailed facial meshes and often do not explicitly provide the network with known boundary type information. Therefore, the purpose of this proof-of-concept study is to develop a biomechanics-informed deep neural network that accepts point cloud data and explicit boundary types as inputs to the network for fast prediction of soft-tissue deformation. A deep learning network was developed based on the PointNet++ architecture. The network accepts the starting facial mesh, input displacement, and explicit boundary type information and predicts the final facial mesh deformation. We trained and tested our deep learning model on datasets created from FEM simulations of facial meshes. Our model achieved a mean error between 0.159 and 0.642mm on five subjects. Including explicit boundary types had mixed results, improving performance in simulations with large deformations but decreasing performance in simulations with small deformations. These results suggest that including explicit boundary types may not be necessary to improve network performance. Our deep learning method can approximate FEM for facial change prediction in orthognathic surgical planning by accepting geometrically detailed meshes and explicit boundary types while significantly reducing simulation time.

Geometrical discretisations for unfitted finite elements on explicit boundary representations

Unfitted (also known as embedded or immersed) finite element approximations of partial differential equations are very attractive because they have much lower geometrical requirements than standard body-fitted formulations. These schemes do not require body-fitted unstructured mesh generation. In turn, the numerical integration becomes more involved, because one has to compute integrals on portions of cells (only the interior part). In practice, these methods are restricted to level-set (implicit) geometrical representations, which drastically limit their application. Complex geometries in industrial and scientific problems are usually determined by (explicit) boundary representations. In this work, we propose an automatic computational framework for the discretisation of partial differential equations on domains defined by oriented boundary meshes. The geometrical kernel that connects functional and geometry representations generates a two-level integration mesh and a refinement of the boundary mesh that enables the straightforward numerical integration of all the terms in unfitted finite elements. The proposed framework has been applied with success on all analysis-suitable oriented boundary meshes (almost 5,000) in the Thingi10K database and combined with an unfitted finite element formulation to discretise partial differential equations on the corresponding domains.

Untangling all-hex meshes via adaptive boundary optimization

We propose a novel method to untangle and optimize all-hex meshes. Central to this algorithm is an adaptive boundary optimization process that significantly improves practical robustness. Given an all-hex mesh with many inverted hexahedral elements, we first optimize a high-quality quad boundary mesh with a small approximation error to the input boundary. Since the boundary constraints limit the optimization space to search for the inversion-free meshes, we then relax the boundary constraints to generate an inversion-free all-hex mesh. We develop an adaptive boundary relaxation algorithm to implicitly restrict the shape difference between the relaxed and input boundaries, thereby facilitating the next step. Finally, an adaptive boundary difference minimization is developed to effectively and efficiently force the distance difference between the relaxed boundary and the optimized boundary of the first step to approach zero while avoiding inverted elements. We demonstrate the efficacy of our algorithm on a data set containing 1004 all-hex meshes. Compared to previous methods, our method achieves higher practical robustness.

Digital design and stability simulation for large underground powerhouse caverns with parametric model based on BIM-based framework

Large infrastructures involving underground engineering like the underground powerhouse caverns constitute multi-medium, complicated and interaction systems, which require geotechnical data management, parametric model construction, optimal design alternatives, and real-time safety assessment. However, even though the data needed for numerical analysis is recorded in the Building Information Modeling (BIM) parametric models, the transformation of geometric characteristics between BIM and numerical models is cumbersome. Therefore, an automatic numerical simulation analysis framework was proposed, which can not only convert 3D parametric structural geometry model by indirect method, but also realize automatic pre-treatment and analysis, such as mechanical properties definition, boundary conditions assignment and mesh generation. In this study, the digital model of underground powerhouse caverns accompanying with cavern support system could be constructed automatically via secondary development on CATIA software. Reorganized borehole logs at geological profiles accompanying with topographic-geologic map are also used to define the 3D subsoil model. Python codes are programmed for pre-treatment of numerical model to enhance the calculation efficiency and alleviate the manual interventions by linking differ-format data files. Furthermore, a case study of Suki Kinari underground powerhouse caverns was exemplified the advantages of this framework in terms of modeling and pre-treatment efficiency, and error-free geometric information translation. The proposed framework provides a fundamental process for automatic design-to-analysis, hence mitigates user intervention and error-free structural calculation for design-making.

Safety Assessment of Ship Collision with Piers under the Protection of Anti-Collision Floating Box Based on BIM Technology

In order to research the force state of the piers subjected to a ship collision under the protection of floating anti-collision facilities, this study uses nonlinear spring connections to simulate the impact of ship damping and incidental water quality in the collision area. BIM technology is used to realize a safety evaluation method for the anti-collision floating box protection when the ship is colliding with piers. Established a BIM-based parametric preprocessing model for ships, piers, and anti-collision facilities, and opened the interface with ABAQUS longitudinally. After realizing the parameter adjustment of the BIM model, the visual parameter adjustment can be realized without destroying the boundary conditions, load conditions, and meshing. Taking a rigid frame bridge as an example, the most disadvantage position of the bridge pier under ship collision is determined by the parameterization method. At the same time, multi-condition analysis was carried out on the ship impacting the pier anti-collision floating box at different angles, different tonnages, and different speeds. Finally, the analysis results are traced back to the BIM model, achieving the unified integration of BIM model information and finite element analysis results and the purpose of visual analysis of any working conditions. The results show that the use of BIM parameterization technology to achieve linkage with the finite element preprocessing model can improve the efficiency of multi-condition sensitivity analysis and achieve the purpose of visual dynamic adjustment. The safety assessment analysis of the pier under the protection of the anti-collision pontoon on the pier under various working conditions shows that the anti-collision pontoon effectively reduces the hazard of the ship colliding with the pier, and the impact force gradually increases with the change from the oblique collision to the frontal collision. The peak impact force increases with the weight of the ship and shows a nonlinear relationship, such that the peak value of impact force increases with the speed increase, and the speed and the peak values of impact force show basically a linear relationship.

Large Eddy Simulation of the Flow Past a Soccer Ball

The football game is the most popular, played, and loved sport around the world. The advent of technological breakthroughs and the continuous increase in consumer demand have led to a revolution in football’s design and manufacturing process. In the past, studies in soccer ball aerodynamics mainly were limited to the investigation of lift and drag forces inside a wind tunnel apparatus. A few researchers have analyzed the flow around the different soccer balls using computational fluid dynamics simulations with the Reynolds-Averaged-Navier–Stokes equations model. This study primarily intends to simulate a modern soccer ball (Adidas Telstar 18) using the Large Eddy Simulations technique. The whole research is divided into two phases. In the first phase, the flow around a smooth sphere is simulated numerically to validate the meshing strategy, boundary conditions, and solution methodology. The same modeling approach is used in the later stage to simulate the flow around a soccer ball. The effect of panels and seam on the boundary layer flow separation and overall turbulent flow structure around the soccer ball are visualized. The results indicate that the large-eddy simulations help predict the flow intricacies by resolving small eddies near the panels.

Digital Twin for Fatigue Analysis

As part of fatigue from finite elements (FE) analysis inputs (geometry, material, and loading), the stress level in a component is a key input for representativity of simulation. To illustrate, assuming a simplified power law between stress and life in excluding all plasticity, sequence effect and any other non-linearities, a small variation in the stress input value may propagate into a large variation in the output simulated life.To reduce these epistemic uncertainties, correlation with strain gages is a fundamental added value to any FE model, as it permits to validate mesh convergence, model, stiffness, and boundary conditions. The construction of a robust digital twin heavily benefits from this important tool for further usage and to improve predictability.The current work shows how to extract insights from strain gages measurements. First of all, improving FE/test correlation may be helped by virtual strain gage analysis. However, strain gage measurement accuracy highly relies on strain gage position and orientation. Consequently, the optimization of sensors positions and orientations, regarding representativity of each independent load case, will reinforce Test Engineer expertise in his test plan specification. Then, the core subject of this paper depicts the load reconstruction process, which means how to get load histories from both strain gage measurements and independent unitary FE load cases, in quasi-static and dynamic framework. As a result, obtaining input loads is a way to extrapolate stress level and life results from discrete points (strain gages) to full component, accessing life results in hot spots with large stress concentration.The theorical background will be described and the methodology on an application case illustrated.

Computational fluid dynamics for turbomachinery technologies with a focus on high-speed rotor blades

NASA's SR3 8-bladed rotor with a rotational speed of 6350 rpm, an advance ratio of 3.6, and a transonic Mach Number of 0.8 is utilized to evaluate the aerodynamic and rotor effectiveness predictive ability of a CFD simulation using the Ansys commercial software. The experimentally tested model [1] included eight 45° swept blades that were tested at a design operating altitude of 10.68 km (35,000 ft.) and it is the one with the most data in the public domain. In the model, blade sweep and the distinct contour of the spinner and nacelle design were implemented to reduce compressibility losses. The primary goal of this research is to compare performance predictions with the experimental results for power coefficient and efficiency evaluation. Analyses are carried out on a single rotating zone separated by a sliding mesh boundary. We also look at the accuracy of recording downward velocities and swirling angles in the propeller's wake, with the goal to use the RANS technique to investigate how these wake parameters react with aerodynamic surface and the results are compared with the experimental results. Initial computational findings demonstrate increased correlation with wind tunnel measurements at 63.3° degrees pitch.

Crack propagation analysis in masonry structures via an inter-element cohesive fracture approach: assessment of mesh dependency issues

Inter-element cohesive methodologies have proved to be very effective to simulate complex cracking phenomena in quasi-brittle materials, by virtue of their capability of naturally handling multiple crack nucleation and propagation along unknown paths, also including crack bifurcation and coalescence. Nevertheless, in several computational implementations, such methodologies suffer from a certain mesh bias, since crack propagation is restricted to occur along inter-element mesh boundaries. Besides, the resulting structural response is inevitably affected by the additional compliance provided by the embedded cohesive elements with finite stiffness even prior to the crack onset. In this work, the diffuse inter-element cohesive method has been applied to masonry structures, focusing the attention on the role of related mesh dependency issues. In particular, the aim of this work is twofold. First, a novel calibration approach of the initial cohesive stiffness is developed to reduce the aforementioned artificial compliance effect. Second, an effective strategy is proposed to avoid the occurrence of multiple solutions, which are typical of diffuse inter-element cohesive approaches, especially in structured meshes. To assess the validity of the proposed method, numerical simulations of the failure behavior of simple masonry specimens are performed. The results show that a rational calibration of the cohesive properties (i.e., stiffness and strength) of diffuse embedded interfaces is useful to ensure numerical stability and accuracy, in terms of both load-bearing capacity and related crack pattern.

Numerical study on a thermoacoustic refrigerator with continuous and staggered arrangements

Thermoacoustic devices require heat exchangers with oscillating flow, but there is currently no viable design approach for them. A heat exchanger with a staggered structure can efficiently improve the velocity disturbance and promote heat transfer in steady flow. The flow and heat transfer characteristics of a standing-wave thermoacoustic refrigerator and an ambient heat exchanger with staggered parallel plates under the oscillating flow condition are investigated in this study, primarily focusing on the geometric influences and differences between staggered and non-staggered (continuous) arrangements. The CFD simulation is a mainstream tool for the numerical simulation of complex thermoacoustic phe?nomena. The flow field around the stack and heat exchanger plate is simulated by introducing the dynamic mesh boundary conditions. Through numerical simulation, the flow field characteristics of non-linear vortices generation around the heat exchanger are presented. By changing the staggered column number in the ambient heat exchanger, it is observed that the larger the column number of staggered parallel plates, the more significant the refrigeration effect through the thermoacoustic effect.

METHODOLOGIES TO PREDICT HYDRODYNAMIC CHARACTERISTICS OF PUSHER AND PULLER PODDED PROPULSORS IN OBLIQUE FLOWS

This paper presents the outcome of a numerical simulation based research program to evaluate the propulsive characteristics of puller and pusher podded propulsors in a straight course and at static azimuthing conditions while operating in open water. Methodologies to predict the propeller thrust and torque, and pod forces and moments in three dimensions using a Reynolds-Averaged Navier Stokes (RANS) solver at multiple azimuthing conditions and pod configurations are presented. To obtain insight into the reliability and accuracy of the results, grid and time step dependency studies are conducted for a podded propulsor in straight-ahead condition. The simulation techniques and results are first validated against measurements of a bare propeller and a podded propulsor in straight ahead condition for multiple loading scenarios and in both puller and pusher configurations. Next, simulations were carried out to model the podded propulsors in the two configurations at multiple loading conditions and at various azimuthing angles from +30° to –30° in 15° increments. The majority of the simulations are carried out using both steady state and unsteady state conditions, primarily to evaluate the effect of setup conditions on the computation time and prediction accuracy. The predicted performance characteristics of the pod unit using the unsteady RANS method were within 1% to 5% of the corresponding experimental measurements for all the loading conditions, azimuthing angles and pod configurations studied. The non-linear behaviour of the performance coefficients of the pod unit are well captured at various loading and azimuthing conditions in the predicted results. This study demonstrates that the RANS solver, with proper meshing arrangement, boundary conditions and setup techniques can predict the performance characteristics of the podded propulsor in multiple azimuthing angles, pod configurations and in the various loading conditions with a same level of accuracy as experimental results. Additionally, the velocity and pressure distributions on and around the pod-strut- propeller bodies are discussed as derived from the RANS predictions.

Iso-scallop tool path planning for triangular mesh surfaces in multi-axis machining

• A robust and universal isoscallop tool path planning method for multi-axis machining is proposed. • The tool path with the constant scallop height is generated from the first contour of a normalized geodesic distance field (GDF) on triangular mesh surfaces. • The proposed algorithm starts from the boundary curve and runs forward recursively to ensure that the surface is covered completely by the isoscallop tool path. • The feasibility and superiority are studied by several simulations and experiments. Triangular mesh enables the flexible construction of complex surface geometry and has become a general representation of 3D objects in computer graphics. However, the creation of a tool path with constant residual scallop height on triangular mesh surfaces in multi-axis machining is not a convenient task for current algorithms. In this study, an isoscallop tool path planning method for triangular mesh surfaces, in which the tool path is derived directly from the contours of a normalized geodesic distance field (GDF), without any post-processing is proposed. First, the GDF is built to determine the shortest geodesic distance from each vertex to the mesh boundary. Then, the normalizing process is performed on the GDF to ensure that its first contour meets the isoscallop height requirement considering the mesh curvature and effective cutter radius. To improve the computational efficiency, the GDF is only built in the mesh area related to the first contour by specifying a stop distance. Moreover, an adaptive refinement process is conducted on the mesh to improve the smoothness and accuracy of the tool path. Finally, the triangular mesh is trimmed along this first contour for a new round of tool path planning. The proposed method is organized recursively and terminated when no new paths are generated. Simulations and experiments are conducted to verify the effectiveness and superiority of the proposed tool path planning method.

BFEMP: Interpenetration-free MPM–FEM coupling with barrier contact

This paper introduces BFEMP, a new approach for monolithically coupling the Material Point Method (MPM) with the Finite Element Method (FEM) through barrier energy-based particle–mesh frictional contact using a variational time-stepping formulation. The fully implicit time integration of the coupled system is recast into a barrier-augmented unconstrained nonlinear optimization problem. A modified line-search Newton’s method is adopted to strictly prevent material points from penetrating the FEM domain, ensuring convergence and feasibility regardless of the time step size or the mesh resolutions. The proposed coupling scheme also reduces to a new approach for imposing separable frictional kinematic boundaries for MPM when all nodal displacements in the FEM domain are prescribed with Dirichlet boundary conditions. Compared to standard implicit time integration, the extra algorithmic components associated with the contact treatment only depend on simple point-segment (or point-triangle in 3D) geometric queries which robustly handle arbitrary FEM mesh boundaries represented with codimension-1 simplices. Experiments and analyses are performed to demonstrate the robustness and accuracy of the proposed method.

Effect of Computational Parameters on Output Properties of Underwater Explosion by Intelligent Numerical Simulation

The computational parameters are of great influence on underwater explosion load. A one-dimensional wedge model is established to analyze the influence of boundary condition (BC), water domain and mesh density on the numerical simulation results. The results show that flowout BC is rigid boundary and transmit BC is not suitable for simulating the collapses phase of bubble pulsation. According to propagation distance of shock wave and its reflected wave, a simple method to calculate appropriate water domain is proposed. A positive correlation between mesh density (λ) and calculated peak pressure of shock wave (P m) is found. When λ tends to infinity, simulated Pm in near field is quite reliable, but the values in relatively far field are lower than empirical results.

Quadratic splines on quad-tri meshes: Construction and an application to simulations on watertight reconstructions of trimmed surfaces

Given an unstructured mesh consisting of quadrilaterals and triangles (we allow both planar and non-planar meshes of arbitrary topology), we present the construction of quadratic splines of mixed smoothness — C1 smooth away from the unstructured regions of T and C0 smooth otherwise. The splines have several useful B-spline-like properties – partition of unity, non-negativity, local support and linear independence – and allow for straightforward imposition of boundary conditions. We propose a non-nested refinement process for the splines with multiple advantages — a simple computer implementation, reduction in the footprint of C0 smoothness, boundary preservation, and excellent approximation behaviour in simulations. Furthermore, the refinement process leaves the splines invariant on the mesh boundary. Numerical tests indicate that the spline spaces demonstrate optimal approximation behaviour in the L2 and H1 norms under mesh refinement, and provide a viable approach to simulations on watertight reconstructions of trimmed surfaces.

Viscoelastic biomechanical models to predict inward brain-shift using public benchmark data

Brain-shift during neurosurgery compromises the accuracy of tracking the boundaries of the tumor to be resected. Although several studies have used various finite element models (FEMs) to predict inward brain-shift, evaluation of their accuracy and efficiency based on public benchmark data has been limited. This study evaluates several FEMs proposed in the literature (various boundary conditions, mesh sizes, and material properties) by using intraoperative imaging data (the public REtroSpective Evaluation of Cerebral Tumors [RESECT] database). Four patients with low-grade gliomas were identified as having inward brain-shifts. We computed the accuracy (using target registration error) of several FEM-based brain-shift predictions and compared our findings. Since information on head orientation during craniotomy is not included in this database, we tested various plausible angles of head rotation. We analyzed the effects of brain tissue viscoelastic properties, mesh size, craniotomy position, CSF drainage level, and rigidity of meninges and then quantitatively evaluated the trade-off between accuracy and central processing unit time in predicting inward brain-shift across all models with second-order tetrahedral FEMs. The mean initial target registration error (TRE) was 5.78 ± 3.78 mm with rigid registration. FEM prediction (edge-length, 5 mm) with non-rigid meninges led to a mean TRE correction of 1.84 ± 0.83 mm assuming heterogeneous material. Results show that, for the low-grade glioma patients in the study, including non-rigid modeling of the meninges was significant statistically. In contrast including heterogeneity was not significant. To estimate the optimal head orientation and CSF drainage, an angle step of 5° and an CSF height step of 5 mm were enough leading to <0.26 mm TRE fluctuation.

Sensitivity analysis for numerical simulations of disturbed flows aiming ultrasonic flow measurement

A detailed parametric sensitivity analysis reveals the effect on the numerically calculated profile factor of ultrasonic flow meters of various modeling parameters such as mesh refinement, boundary conditions, turbulence model, wall treatment, interpolation schemes and numerical integration. The flow field is solved using a commercial CFD code and the profile factor is obtained by numerical integration of the three velocity components along the acoustic path. Interesting relations of these numerical parameters concerning the inertia of the flow are observed, suggesting that the higher the Reynolds number, the more precaution is needed in the simulation of pipe flows, especially when the goal is to infer the profile factor of ultrasonic flow measurements, which are related to strict uncertainties. The main finding is that quantitative conclusions may be mistaken or distorted if a proper analysis of how sensitive the simulation results are with respect to its modeling parameters is not carried out.