Prismatic Meshes Research Articles

Design and Analysis of UAV Profile for Agriculture and Surveying Application

This study represents the aerodynamic design of an Unmanned aerial vehicle intended for surveillance or agriculture with a maximum take weight of 125 kg. Weight estimation and constraint analysis were done based on the Mission profile. Design of Computer-Aided Design (CAD) models were generated for three different configurations using CATIA V5R20 as a high wing, mid-wing, and low wing. Flow analysis was done for the above configurations at various angles of attack. ANSYS 15 was used for the flow Analysis. A Tetrahedron element meshed the model with the minimum required orthogonal quality. Five microns were given to the initial layer height of the prism mesh. Spalart Allmaras model is used as the Turbulence model in the solver. The aerodynamic characteristics of the above configuration obtained from Computational Fluid Dynamics (CFD) results were compared with the DATCOM program and validated with the wind tunnel experimental test data. The open-circuited suction-type Subsonic wind tunnel was employed for the test. The aerodynamic properties for the angle of attack in the range of -2° to 14° angle of attack are calculated using a six-component balance. The study aims to find the Unmanned Aerial Vehicle (UAV) configuration based on the aerodynamic characteristics obtained from the CFD and DATCOM results. High-wing UAVs have better aerodynamic efficiency than the other two configurations.

Design and performance of a space–time virtual element method for the heat equation on prismatic meshes

We present a space–time virtual element method for the discretization of the heat equation, which is defined on general prismatic meshes and variable degrees of accuracy. Strategies to handle efficiently the space–time mesh structure are discussed. We perform convergence tests for the h- and hp-versions of the method in case of smooth and singular solutions, and test space–time adaptive mesh refinements driven by a residual-type error indicator.

Neutronics and thermal-hydraulics coupling analysis for a small lead-based fast reactor based on the discrete ordinate nodal and parallel channel method

The full-core neutronics/thermal-hydraulics (NE/TH) coupling analysis for a small lead-based fast reactor (SLFR) was presented. The NE-to-TH coupling occurs via power distribution, whereas the TH-to-NE coupling occurs via the material cross section, which is related to the temperature distribution. In the NE module, a discrete ordinate (SN) nodal solver is implemented based on the hexagonal prism mesh. In the TH module, a parallel channel model is implemented with each hexagonal fuel assembly as a channel. The mass flow of each channel is searched according to the same pressure drop, the temperature and density of the coolant within each channel is calculated with a one-dimensional axial heat convection model, and the temperature distribution along the fuel pin is calculated with a one-dimensional radial heat conduction model. In order to update the cross section, a temperature-dependent homogenized microscopic cross-section library is prepared in advance, and based on the temperature distribution obtained from the TH calculation, the cross-section data required by the NE calculation are obtained by interpolation. The results of the NE/TH coupling analysis for SLFR indicate that the TH parameters (the maximum temperature of the fuel, cladding, and coolant and the maximum velocity of the coolant) are all within the design limits, and the TH feedback provides negative reactivity feedback (about −200 pcm) and has a fairly small effect on the power distribution (<1.0%).

Multiple normals configuration on an arbitrary manifold for viscous mesh generation

AbstractMarching normal calculation is considered the focus of the commonly used advancing layer method for viscous mesh generation, and the local configuration of multiple normals for complex corners locally is a rather complicated problem that has not been completely solved yet. In some extremely complex corners, even the advanced commercial software cannot generate positive prismatic meshes. To address this issue, this article presents a novel method to generate multiple normals on an arbitrary manifold. In the proposed method, we abstract the multiple normals displacement and topology connection calculation into a geometric problem on the unit sphere and prove that visible conditions can always be satisfied in finite multiple normals. After that, an engineering implementation is proposed, including an initial normal calculation using visual dependency graph analysis and spherical mesh optimization. The results show that our method can generate multiple normals at extremely complex corners where even advanced commercial software failed. The experiments of the industrial model proved the reliability and effectiveness of the first layer mesh generated by our method.

Prismatic mesh generation based on anisotropic volume harmonic field

In this paper, we present an effective prismatic mesh generation method for viscous flow simulations. To address the prismatic mesh collisions in recessed cavities or slit areas, we exploit 3D tensors controlled anisotropic volume harmonic field to generate prismatic meshes. Specially, a well-fitting tetrahedral mesh is first constructed to serve as the discrete computation domain of volume harmonic fields. Then, 3D tensors are exploited to control the volume harmonic field that better fits the shape geometry. From the topological perspective, the generation of the prismatic mesh can be treated as a topology-preserved morphing of the viscous wall. Therefore, iso-surfaces in the volume harmonic field should be homeomorphic to the viscous wall while fitting its shapes. Finally, a full prismatic mesh can be induced by estimating the forward directions and visible regions in the volume harmonic field. Moreover, to be compatible with different simulation situations, the thickness of prismatic meshes should be variable. Our approach provides local adjustable thickness of prismatic meshes, which can be achieved by controlling local 3D tensors. The proposed anisotropic volume harmonic field based prismatic meshes are efficient and robust, and a full prismatic mesh can be guaranteed without low quality collisions. Various experiments have shown that our proposed prismatic meshes have obvious advantages in terms of efficiency and effectiveness.

Single and multiple springback technique for construction and control of thick prismatic mesh layers

Abstract We suggest an algorithm for construction of semi-structured thick prismatic mesh layers which guarantees an absence of inverted prismatic cells in resulting layer and allows one to control near-surface mesh orthogonality. Initial mesh is modelled as a thin layer of highly compressed prisms made of hyperelastic material glued to the triangulated surface. In order to compute robust normals at the vertices of the surface mesh we use quadratic programming algorithm based on the nearest ball concept. This pre-stressed material expands, possibly with self-penetration and extrusion to exterior of computational domain until target layer thickness is attained. Special preconditioned relaxation procedure is proposed based on the solution of stationary springback problem. It is shown that preconditioner can handle very stiff problems. Once an offset prismatic mesh is constructed, self-intersections are eliminated using iterative prism cutting procedure.Next, variational advancing front procedure is applied for refinement and precise orthogonalization of prismatic layer near boundaries. We demonstrate that resulting mesh layer is ‘almost mesh-independent’ in a sense that the dependence of thickness and shape of the layer on mesh resolution and triangle quality is weak. It is possible to apply elastic springback technique sequentially layer by layer. We compare single springback technique with multiple springback technique in terms of mesh quality, stiffness of local variational problems and mesh orthogonality or/and layer thickness balance.

Об использовании элементно-центрированной конечно-объёмной схемы на призматических сетках в пристеночном слое

We consider the cell-centered finite-volume scheme with the quasi-one-dimensional reconstruction and generalize it to anisotropic prismatic meshes suitable for high-Reynolds-number problems. We offer a new algorithm of flux computation based on the reconstruction along the wall surface, whereas in the original schemes it was along the tangent to the wall surface. We also study how does the curvature of mesh elements influence the accuracy if taken into account.

Conservative high-order discontinuous Galerkin remap scheme on curvilinear polyhedral meshes

A data transfer (remap) between two meshes is an important step of each arbitrary Lagrangian-Eulerian (ALE) simulation. We develop a conservative scheme for remapping high-order discontinuous Galerkin fields on high-order polytopal meshes with curved faces. This scheme uses a virtual element function to define the remap velocity. We show that the optimal accuracy is achieved when the remap problem is written and is solved as a coupled system of two conservative equations. The properties of the proposed scheme are studied numerically for smooth and discontinuous fields on cubic and prismatic meshes.

Prismatic mesh generation using minimum distance fields

Anisotropic prismatic/strand meshes are often used to capture viscous boundary layer effects in Reynolds Averaged Navier Stokes (RANS) simulations of high Reynolds number flows. This paper describes a new algorithm for generation of prismatic meshes using the minimum distance field of the surface tessellation. The algorithm starts with initial point placement using both the direction of best visibility and the direction to the closest point on the minimum distance iso-surface. Initial point placement is followed by a constrained smoothing operation based on an elastic spring analogy. The constraints ensure movement of nodes is restricted to the iso-surface of the distance field and within the region of visibility. Simulations are performed using a dual-mesh infrastructure, where the prismatic meshes transition to a Cartesian background mesh a short distance from the wall. This overset mesh system is processed by a domain connectivity method to establish connections between self-intersecting strand meshes and strand/Cartesian mesh systems. Mesh and flow simulation results are presented for test cases of varying complexity.

Validation Method for Finite-Element Modeling of Acoustic Re-emission of Bodies in the Turbulent Fluid Flow

In this paper, we generalize the previously developed method of finite element modeling of the noise emission produced by inhomogeneities of bodies in a turbulent flow for the prismatic mesh discretization of a compressible fluid. The method was validated based on well-known analytical solutions for prediction problems of noise emission produced when two-dimensional and three-dimensional streamlining cylindrical or spherical bodies that are small in comparison with the acoustic wavelength.

Dfemtoolz: An open-source C++ framework for efficient imposition of material and boundary conditions in finite element biomedical simulations

We propose a novel C++ open-source package dfemtoolz that enables highly efficient: (1) discretization of a triangular surface mesh into volumetric tetrahedral elements (by using the Tetgen); (2) splitting of prism or tetrahedral meshes into hexahedral meshes; and (3) application of boundary conditions for modeling various physical phenomena (i.e. fluid flow, structural analysis, heat transfer, mass transport, etc.). The novelty of the proposed library is two-fold: (1) it avoids computationally expensive merging by performing a more efficient search of neighboring nodes; and (2) it enables highly efficient manipulation of nodes’ BCs in the bitwise manner. The framework is initially proposed and validated for biomedical simulations; however, it could have wide-scale applications. Program summaryProgram Title: dfemtoolzProgram Files doi:http://dx.doi.org/10.17632/9xy4x3ggch.1Licensing provisions: GNU General Public License 3Programming language: C++Nature of the problem: In silico trials assume reproducing medical phenomena on computers with the aim to reduce harms, costs and time required for performing traditional clinical trials. A typical in silico workflow consists of the following six steps: (1) Segmentation of medical scans; (2) Reconstruction of the segmented region; (3) Meshing of the obtained volume; (4) Application of appropriate materials and boundary conditions (BCs); (5) Solving governing equations that describe how the considered phenomena will behave under the specified conditions and (6) Visualization of the obtained results. At the moment, there are available mature open-source frameworks for solving the following tasks: segmentation (i.e. ITK, ImageJ), meshing (i.e. Tetgen, Triangle), simulation (i.e. OpenFOAM, Elmer, FEniCS) and visualization (i.e. VTK, OpenGL). However, the step 4 (application of materials and boundary conditions) remains an open question in terms of open-source packages. To the best of our knowledge, there is no robust and publically available framework for these purposes – which inspired us to propose the dfemtoolz with the aim to improve compatibility and ease integration of the overall six in silico trials steps.Solution method: The dfemtoolz is provided as both stand-alone executable modules and C++ library that could be integrated into an existing software package. The dfemtoolz supports two use-case scenarios: (1) a user has a surface geometry of the FEM model that needs to be discretized before further application of boundary conditions; and (2) a user has an existing FE mesh and only needs to prescribe BCs. Since it is generic, the dfemtoolz is capable of processing any FEM model represented as a list of nodes (defined with coordinates in an arbitrary dimension) and a list of elements (of an arbitrary type).Additional comments: The source code, working examples and benchmarks are available for download at the URL: https://github.com/dmilashinovic/dfemtoolz and are tested to work under Linux and Windows OS. The library was developed using the Code::Blocks IDE and the g++ compiler.

A Novel Subdomain 2D/Q-2D Finite Element Method for Power/Ground Plate-Pair Analysis

Upon excitation by a surface magnetic current, a power/ground plate-pair supports only $\mathrm{TM}^{z}$ modes. This means that the magnetic field has only azimuthal components permitting a simple but effective domain decomposition method (DDM) to be used. In the proximity of an antipad, field interactions are rigorously modeled by a quasi-two-dimensional (Q-2D) finite element method (FEM) making use of three-dimensional (3D) triangular prism mesh elements. Since high-order $\mathrm{TM}^{z}$ modes are confined in the close proximity of the antipad, field interactions in the region away from the antipad only involve the fundamental mode and are rigorously modeled by a 2D FEM. This approach reduces 3D computation domain into a hybrid 2D/Q-2D domain. The discretization of this hybrid domain results in a global matrix system consisting of two globally coupled matrix equations pertinent to 2D and Q-2D domains. In this article, these two matrix equations are “decoupled” using a Riemann solver and the information exchange between the two domains is facilitated using numerical flux. The resulting decoupled two matrix equations are iteratively solved using the Gauss–Seidel algorithm. The accuracy, efficiency, and robustness of the proposed DDM are verified by four representative examples.

IFDF acceleration method with adaptive diffusion coefficients for SN nodal calculation in SARAX code system

SN nodal method has been successfully applied to fast reactor core neutronics analysis. The computational efficiency can be enhanced efficiently by the popular coarse-mesh finite difference (CMFD) method. However, the CMFD method suffers from the problem of instability, especially for optically thick problems. In this paper, another efficient nonlinear acceleration method, named interface flux discontinuity factor (IFDF) acceleration, was studied and improved for the SN nodal calculation in hexagonal prism and cuboid meshes. With adaptive diffusion coefficients, the IFDF is guaranteed to be positive and within a reasonable region, which makes the acceleration stable. It was found that the IFDF and CMFD methods obtained similar speedups for the tested fast reactor problems. However, the stability of the IFDF method was much better than the CMFD method even with artificial diffusion improvement. Additionally, the rebalance accelerated IFDF method was applied to the external-source multiplication problem besides the common eigenvalue problem.

Accurate and efficient surface reconstruction from volume fraction data on general meshes

Simulations involving free surfaces and fluid interfaces are important in many areas of engineering. There is, however, still a need for improved simulation methods. Recently, a new efficient geometric VOF method called isoAdvector for general polyhedral meshes was published. We investigate the interface reconstruction step of isoAdvector, and demonstrate that especially for unstructured meshes the applied isosurface based approach can lead to noisy interface orientations. We then introduce a novel computational interface reconstruction scheme based on calculation of a reconstructed distance function (RDF). By iterating over the RDF calculation and interface reconstruction, we obtain second order convergence of both the interface normal and position within cells even with a strict L∞ error norm. In 2D this is verified with reconstruction of a circle on Cartesian meshes and on unstructured triangular and polygonal prism meshes. In 3D the second order convergence is verified with reconstruction of a sphere on Cartesian meshes and on unstructured tetrahedral and polyhedral meshes. The new scheme is combined with the interface advection step of the isoAdvector algorithm. Significantly reduced absolute advection errors are obtained, and for CFL number 0.2 and below we demonstrate second order convergence on all the mentioned mesh types in 2D and 3D. The implementation of the proposed interface reconstruction schemes is straightforward and the computational cost is significantly reduced compared to contemporary methods. The schemes are implemented as an extension to the Computational Fluid Dynamics (CFD) Open Source software package, OpenFOAM®. The extension module and all test cases presented in this paper are released as open source.

Bi-directional integral pumping devices for dual mechanical seals: Influence of mesh type on accuracy of numerical simulations

A numerical study is conducted to simulate the performance of barrier fluid flow through a bi-directional dual mechanical seal with an integral radial pumping ring. Standard K-ε model is implemented as a turbulence model. Multiple Reference Frame approach is implemented to model the rotation of the pumping ring. The present study is a sequel to a previous companion work done in the area of visualization of barrier fluid flow. Improvements to the previous work depended on two aspects. First, a multi-block hybrid (tetra, prism and hexa) mesh is used where it is aimed to reduce numerical false diffusion by orienting the cells to be aligned with flow direction as much as possible. Second, expanding model’s boundaries to include inboard sealing faces. The numerical results are validated against Q-ΔP curves produced from experimental tests where an experimental setup is constructed, and appropriate instrumentation is employed to measure the pressure, temperature, and flow rate of the barrier fluid.Moreover, implementation of two spatial discretization schemes is illustrated to verify the numerical performance of each method. Second order Upwind and QUICK (Quadratic Upstream Interpolation for Convective Kinematics) schemes are used for the discretization of convective terms. The validity of implementation of each method is investigated since higher-order methods are known to be more computationally expensive but their accuracy are higher. The results by the hybrid mesh indicate that the use of the Second-order scheme provides more accurate prediction of Q-ΔP curves than the previous companion work. Moreover, the impact of using the QUICK scheme is the increased computational time while providing slightly more accurate Q-H curve relative to the second-order scheme.Finally, expanding model’s boundaries to include inboard sealing faces revealed that closed barrier fluid circulation takes place in the vicinity of the inboard sealing faces indicating poor renewal of the barrier fluid contained within this zone compared to the outboard sealing faces.

An Efficient Mode-Based Domain Decomposition Hybrid 2-D/Q-2D Finite-Element Time-Domain Method for Power/Ground Plate-Pair Analysis

Generally, with a surface magnetic current excitation, only the $\mathrm {TM}_{\mathrm {zmn}}$ modes are activated between the power/ground plate pair. As a result, the magnetic field only has azimuthal component while the longitude component is zero. To make full use of this quasi-2-D (Q-2D) property, a Q-2D finite-element time-domain (FETD) method combined with the basic 3-D triangular prism mesh elements is firstly proposed to solve the magnetic field wave equation. It is further noted that the higher order modes are confined in the proximity of the antipads (labeled as via domain) due to the exponential attenuation property along the propagating direction. Therefore, in the region sufficiently far from the antipad (marked as plate-pair domain), only the fundamental mode needs to be considered. In this way, a Q-2D FETD analysis is required in the via domain while in the plate-pair domain, only a 2-D FETD solver is needed. As a result, the proposed algorithm is actually a hybrid 2-D and Q-2D FETD method. Besides, to handle arbitrarily shaped antipads, the wave-port excitation is implemented, and the corresponding mode-based S-parameter extraction methodology is developed according to the orthogonal property of different eigenmodes. The efficiency, accuracy, and generality of the proposed approach are verified by several representative examples.

3D-FVM anisotropic model for eddy current problems related to composite materials

ABSTRACTIn this paper, a 3D-finite volume method model is developed to analyse eddy current problems related to anisotropic conductive materials. Two unidirectional composite materials (boron fibres reinforced aluminium alloy, carbon fibres reinforced polymer) are studied. To be adapted to such problem, the finite volume implementation of the A–V formulation has been carried out by using the unstructured mesh, where the prism shape of the elementary volume is introduced. The effects of the mesh type either prism mesh or hexahedral mesh on the accuracy and the CPU time are carefully analysed. The anisotropy ratio on the eddy current distribution is also discussed. The developed numerical model is validated by comparison to experimental results.

Engineering applications of 2D and 3D finite element mesh generation in hydrogeology and water resources

This paper develops an automatic density-controlled 2-D and 3-D finite element mesh generation system to solve practical engineering applications in geology, hydraulics, hydrology, water resources, etc. The Delaunay triangulation method is adopted to create triangular meshes based on the required density specified by users. A triangle-to-quadrilateral conversion method is used to generate quadrilateral meshes adaptively. Density control algorithms of adaptive 2-D mesh generation are presented to satisfy the various requirements of the overland and subsurface hydrogeology and water resources in the actual target area. According to the alignment of boundary edges and distribution of surface nodes, this paper proposes the main algorithm and basic criteria to generate supplementary triangle and quadrilateral meshes for filling the water regions of river reaches and junctions with storage. A stretch mode is proposed to generate triangular prism and hexahedral meshes by stretching the 2-D mesh into 3-D space based on the materials of geometric regions. The 1-D/2-D/3-D correspondence between the finite element mesh and the river reaches, junctions with and without storage, ponds, lakes, control structures and fractures is established. Finally, practical 2-D and 3-D meshing applications are provided to demonstrate the accuracy and effectiveness of the finite element mesh generator developed in this paper.

Influence of mesh non-orthogonality on numerical simulation of buoyant jet flows

In the present research, we discuss the influence of mesh non-orthogonality on numerical solution of a type of buoyant flow. Buoyant jet flows are simulated numerically with hexahedral and prismatic mesh elements in an open source Computational Fluid Dynamics (CFD) code called “OpenFOAM”. Buoyant jet instability obtained with the prismatic meshes may be overestimated compared to that obtained with the hexahedral meshes when non-orthogonal correction is not applied in the code. Although the non-orthogonal correction method can improve the instability generated by mesh non-orthogonality, it may increase computation time required to reach a convergent solution. Thus, we propose modified solvers that can reduce the influence of mesh non-orthogonality and reduce the computation time compared to the existing solvers in OpenFOAM. It is demonstrated that calculations for a buoyant jet with a large temperature difference are performed faster by the modified solver.

Reduced storage nodal discontinuous Galerkin methods on semi-structured prismatic meshes

We present a high order time-domain nodal discontinuous Galerkin method for wave problems on hybrid meshes consisting of both wedge and tetrahedral elements. We allow for vertically mapped wedges which can be deformed along the extruded coordinate, and present a simple method for producing quasi-uniform wedge meshes for layered domains. We show that standard mass lumping techniques result in a loss of energy stability on meshes of vertically mapped wedges, and propose an alternative which is both energy stable and efficient. High order convergence is demonstrated, and comparisons are made with existing low-storage methods on wedges. Finally, the computational performance of the method on Graphics Processing Units is evaluated.