Mesh Parameters Research Articles

Digital Simulations for Three-dimensional Nonlinear Advection-diffusion Equations Using Quasi-variable Meshes High-resolution Implicit Compact Scheme

A two-level implicit compact formulation with quasi-variable meshes is reported for solving three-dimensions second-order nonlinear parabolic partial differential equations. The new nineteen-point compact scheme exhibit fourth and second-order accuracy in space and time on a variable mesh steps and uniformly spaced mesh points. We have also developed an operator-splitting technique to implement the alternating direction implicit (ADI) scheme for computing the 3D advection-diffusion equation. Thomas algorithm computes each tri-diagonal matrix that arises from ADI steps in minimal computing time. The operator-splitting form is unconditionally stable. The improved accuracy is achieved at a lower cost of computation and storage because the spatial mesh parameters tune the mesh location according to solution values' behavior. The new method is successfully applied to the Navier-Stokes equation, advection-diffusion equation, and Burger's equation for the computational illustrations that corroborate the order, accuracies, and robustness of the new high-order implicit compact scheme. The main highlight of the present work lies in obtaining a fourth-order scheme on a quasi-variable mesh network, and its superiority over the comparable uniform meshes high-order compact scheme.

Behavior of ions from medium-density plasma in electric field created by plate–grid–plate geometry

The behavior of the ions from a medium-density plasma in an electric field created by the plate–grid–plate geometry was simulated with a two-dimensional one-fluid model in which electrons are assumed to be in thermal equilibrium, and the accuracy of the model was verified by comparing with other research results. The results show that the wire mesh parameters of the grid, including the wire mesh diameter and the spacing between the two wires of the grid, have an important influence on the ion extraction time and the ion collection ratio of the cathode plate. The blocking rate of the grid obtained by the theoretical simulation is almost equal to the geometrical blocking rate, and it is minimally affected by the initial ion density. These results can provide guidance for the optimization of wire mesh parameters of the grid, especially for the ion extraction and collection from a pulsed plasma.

A numerical method on Bakhvalov-Shishkin mesh for Volterra integro-differential equations with a boundary layer

We construct a finite difference scheme for a first-order linear singularly perturbed Volterra integro-differential equation(SPVIDE) on Bakhvalov-Shishkin mesh. For the discretization of the problem, we use the integral identities and deal with the emerging integrals terms with interpolating quadrature rules which also yields remaining terms. The stability bound and the error estimates of the approximate solution are established. Further, we demonstrate that the scheme on Bakhvalov-Shishkin mesh is N ( O − 1 ) N(O−1) u n iformly convergent, where N is the mesh parameter. The numerical results are also provided for a couple of examples.

Modeling of the local anisotropic mechanical foam properties in polyisocyanurate metal panels using mesoscale FEM simulations

The local anisotropic mechanical foam properties of continuously produced polyisocyanurate metal panels were investigated. The main focus was the analysis of the anisotropic cell structure. Based on these investigations, a mesoscale FE-model of a representative volume element (RVE) was validated, which can provide a prediction of the mechanical properties of anisotropic foam structures with varying aspect ratios and orientations of the cells based on defined ellipsoid packings and an anisotropic tessellation model. During the validation of the model, the parameters mesh size, RVE size and strut partitioning were investigated. Due to the anisotropic cell structures, a method was developed to determine a directional RVE size, which has distinct advantages over cube-shaped RVEs. Finally, a comparison of experimental to numerical results was performed. Both in the experiment and the simulation, the structures show a strongly anisotropic behavior, whereby the degree of anisotropy tends to be slightly underestimated in the simulation. Despite small deviations, the simulation results are in good agreement with the experimental data. Accordingly, this simulation model is suitable for an estimation of the anisotropic mechanical foam properties.

Analysis of a finite difference method based on L1 discretization for solving multi‐term fractional differential equation involving weak singularity

In this article, we consider a multi‐term fractional initial value problem which has a weak singularity at the initial time . The fractional derivatives are defined in Caputo sense. Due to such singular behavior, an initial layer occurs near which is sharper for small values of γ1 where γ1 is the highest order among all fractional differential operators. In addition, the analytical properties of the solution are provided. The classical L1 scheme is introduced on a uniform mesh to approximate the fractional derivatives. The error analysis is carried out, and it is shown that the numerical solution converges to the exact solution. Further analysis proves that the scheme is of order over the entire region, but it is of order O(τ) on any subdomain away from the origin. τ denotes the mesh parameter. To show the efficiency of the proposed scheme, this method is tested on several model problems, and the results are in agreement with the theoretical findings.

Two-level Overlapping Schwarz Methods Based on Local Generalized Eigenproblems for Hermitian Variational Problems

The research of the two-level overlapping Schwarz (TL-OS) methods based on constrained energy minimizing coarse space is still in its infancy, and there exist some defects, e.g., mainly for a second order elliptic problem and too heavy computational cost of coarse space construction. In this paper, by introducing appropriate assumptions, we propose more concise coarse basis functions for general Hermitian positive and definite discrete systems, and establish the algorithmic and theoretical frameworks of the corresponding TL-OS methods. Furthermore, to enhance the practicability of the algorithm, we design two economical TL-OS preconditioners and prove the condition number estimate. As the first application of the frameworks, we prove that the assumptions hold for the linear finite element discretization of a second order elliptic problem with high contrast and oscillatory coefficient and the condition number of the TL-OS preconditioned system is robust with respect to the model and mesh parameters. In particular, we also prove that the condition number of the economically preconditioned system is independent of the jump range under a certain jump distribution. Experimental results show that the first kind of economical preconditioner is more efficient and stable than the existing one. Second, we construct TL-OS and the economical TL-OS preconditioners for the plane wave least squares discrete system of the Helmholtz equation by using the frameworks. The numerical results for homogeneous and nonhomogeneous cases illustrate that the preconditioned conjugate gradient method based on the proposed preconditioners has good stability in terms of the angular frequency, mesh parameters, and the number of degrees of freedom in each element.

TextureMe: High-Quality Textured Scene Reconstruction in Real Time

Three-dimensional (3D) reconstruction using an RGB-D camera has been widely adopted for realistic content creation. However, high-quality texture mapping onto the reconstructed geometry is often treated as an offline step that should run after geometric reconstruction. In this article, we propose TextureMe , a novel approach that jointly recovers 3D surface geometry and high-quality texture in real time. The key idea is to create triangular texture patches that correspond to zero-crossing triangles of truncated signed distance function (TSDF) progressively in a global texture atlas. Our approach integrates color details into the texture patches in parallel with the depth map integration to a TSDF. It also actively updates a pool of texture patches to adapt TSDF changes and minimizes misalignment artifacts that occur due to camera drift and image distortion. Our global texture atlas representation is fully compatible with conventional texture mapping. As a result, our approach produces high-quality textures without utilizing additional texture map optimization, mesh parameterization, or heavy post-processing. High-quality scenes produced by our real-time approach are even comparable to the results from state-of-the-art methods that run offline.

Combined parameterization of material distribution and surface mesh for stiffener layout optimization of complex surfaces

Stiffener layout optimization of complex surfaces is fulfilled within the framework of topology optimization. A combined parameterization method is developed in two aspects. One is to parameterize the material distribution of the stiffener layout by means of B-spline. The other is to build the mapping relationship from the known 3D surface mesh of the thin-walled structure to its parametric domain by means of mesh parameterization. The influence of mesh parameterization upon the stiffener layout is discussed to reveal the matching issue of the combined parameterization. 3D complex surfaces represented by the triangular mesh can be dealt with even though analytical parametric equations are not available. Some numerical examples are solved to demonstrate the direct advantage and effectiveness of the proposed method.

Dynamic characteristics of a straight bevel gear drive system considering multi-state meshing and time-varying parameters

In order to investigate the dynamic characteristics of the straight bevel gear drive system, its torsional-bending-axial dynamics model considered the multi-state meshing characteristics is established. The time-varying load distribution ratio and meshing stiffness of the system are calculated by micro element method according to the performance of the straight bevel gear. Three different Poincaré sections are defined to study the dynamic characteristics of the system. The mechanism of tooth disengagement and back-side contacting is studied according to the time history diagram of the total normal force. The nonlinear dynamics equation of the system is solved by the variable step fourth-order Runge-Kutta method when the bevel gear drive system in automobile reducer is taken as the research object. The transition process of system dynamic characteristics and the influences of the meshing frequency, load coefficient and the comprehensive transmission error are studied by using the time history diagram of the total normal force, phase portraits, Poincaré maps, bifurcation diagrams and the corresponded top Lyapunov exponent (TLE). The chaotic motion found in the research is unfavorable from a practical point of view which can be avoided by adjusting the value of parameters or the initial value of state variables in engineering. The research can provide a theoretical basis for the parameter design and dynamic characteristic control of straight bevel gear drive system.

Degradation of sulfadiazine in a cyclic V-SDBD plasma system: Parameters analysis and degradation pathway

A cyclic volume and surface dielectric barrier discharge (V-SDBD) plasma wastewater treatment system with stainless steel net as discharge electrode was established and applied to the sulfadiazine (SDZ) degradation. The discharge characteristics, active substance yield and relative emission spectra in different net electrode systems were compared. The SDZ degradation as well as the UV–vis spectra and COD removal of the SDZ solutions under different treatment conditions were investigated to achieve the appropriate mesh parameter of the net electrode and circulating velocity of the solution. The obtained results show that the SDZ had a better degradation in the cyclic V-SDBD system than that in the intermittent DBD system. 10-mesh stainless steel net and 333 mL min−1 circulating flow rate were the optimal reaction conditions for the SDZ degradation. Compared with the other three net electrodes (14, 20 and 40-mesh), the 10-mesh electrode system could produce more H2O2 and O3, and the relative emission spectrum had stronger intensity. The results of voltage and current waveform and Lissajous figures show that the air ionization in the V-SDBD system with 10-mesh electrode was higher, and more micro-discharge channels could be generated in the discharge space. UV–vis spectra and COD removal analysis of SDZ solutions also stated the SDZ degradation in the V-SDBD plasma system. According to the byproducts’ identification, SDZ degradation pathway was speculated and the change of solution toxicity was analyzed. The results verified that the total toxicity of the initial SDZ solution could be reduced after treating in the V-SDBD plasma system.

3DMesh-GAR: 3D Human Body Mesh-Based Method for Group Activity Recognition.

Group activity recognition is a prime research topic in video understanding and has many practical applications, such as crowd behavior monitoring, video surveillance, etc. To understand the multi-person/group action, the model should not only identify the individual person’s action in the context but also describe their collective activity. A lot of previous works adopt skeleton-based approaches with graph convolutional networks for group activity recognition. However, these approaches are subject to limitation in scalability, robustness, and interoperability. In this paper, we propose 3DMesh-GAR, a novel approach to 3D human body Mesh-based Group Activity Recognition, which relies on a body center heatmap, camera map, and mesh parameter map instead of the complex and noisy 3D skeleton of each person of the input frames. We adopt a 3D mesh creation method, which is conceptually simple, single-stage, and bounding box free, and is able to handle highly occluded and multi-person scenes without any additional computational cost. We implement 3DMesh-GAR on a standard group activity dataset: the Collective Activity Dataset, and achieve state-of-the-art performance for group activity recognition.

Error Analysis of an Unfitted HDG Method for a Class of Non-linear Elliptic Problems

We study Hibridizable Discontinuous Galerkin (HDG) discretizations for a class of non-linear interior elliptic boundary value problems posed in curved domains where both the source term and the diffusion coefficient are non-linear. We consider the cases where the non-linear diffusion coefficient depends on the solution and on the gradient of the solution. To sidestep the need for curved elements, the discrete solution is computed on a polygonal subdomain that is not assumed to interpolate the true boundary, giving rise to an unfitted computational mesh. We show that, under mild assumptions on the source term and the computational domain, the discrete systems are well posed. Furthermore, we provide a priori error estimates showing that the discrete solution will have optimal order of convergence as long as the distance between the curved boundary and the computational boundary remains of the same order of magnitude as the mesh parameter.

Математическое моделирование гидродинамических процессов в прибрежной акватории Японского моря

A three-dimensional mathematical model of coastal water dynamics in the Peter the Great Bay of the Sea of Japan is presented. The system of Navier-Stokes equations is written under the assumption of a hydrodynamic approximation of an inhomogeneous fluid and takes into account turbulent exchange, wind stresses, friction forces, complex topography of the bottom and coastline. On the basis of hydrographic information, a numerical method is used to reconstruct the bottom topography and coastline. The free water surface equation is replaced by a singularly perturbed problem. In the FreeFem++ application software package, a code was written for calculating the hydrodynamic characteristics of coastal waters. During the solution, the finite element mesh is built automatically, the mesh parameters are set by the user. To solve the singular problem, at each time layer, the grid is adapted around the numerical solution with the grid adaptation parameters.

РАЦИОНАЛЬНЫЕ НАСТРОЙКИ ЧИСЛЕННОЙ МОДЕЛИ ДЛЯ МОДЕЛИРОВАНИЯ РАБОЧЕГО ПРОЦЕССА ЛОПАТКИ ОСЕВОЙ ТУРБИНЫ С ПЛЕНОЧНЫМ ОХЛАЖДЕНИЕМ

To reliably determine the characteristics of cooled turbines in CFD simulation, it is necessary to take into account the inter-action of film cooling jets with the main flow. For a correct description of such processes, it is necessary to refine the grid of finite volume mesh, which requires significant resources for the calculation and high qualification of the engineer. An attempt to simplify the model reduces the reliability of the results obtained. There are no systematic recommendations in the available publications on the choice of settings for numerical models of film-cooled turbines. This paper presents results aimed at finding optimal settings for numerical models that allow accurate and cost-effective simulation of the workflow in cooled film-cooled turbines. As a result, practical recommendations were obtained on the choice of mesh parameters and turbulence models for such problems. – the value of y+ is not more than 2; – number of elements in the near-wall layer: at least 20; – cell growth factor in the near-wall layer: not less than 1.2. The use of these recommendations will make it possible to obtain results close to real ones while reducing the required time and computational costs.

Two-stage explicit schemes based on numerical approximations of convection-diffusion equations

A wide family of finite difference methods for the convection-diffusion problems based on an explicit two-stage scheme and a seemingly implicit method are presented. In this paper, to have a greater stability region while maintaining the second-order accuracy, a family of methods that combines the MacCormack and Saul'vey schemes is proposed. The stability analysis of the combined methods is investigated using the von Neumann approach. In each case, it is found that it is the convection term that limits the stability of the scheme. Based on the von Neumann analysis, valuable stability limits in terms of mesh parameters for maintaining accurate results are determined in an analytic manner and demonstrated through computer simulations. Two model problems consisting of linear advection-diffusion and nonlinear viscous Burgers equation are given to illustrate some properties of the present technique, such as stability and the ability to propagate discontinuities.

A Low Distortion Mesh Parameterization Mapping Method Based on Proxy Function and Combined Newton

To address the issues of low efficiencies and serious mapping distortions in current mesh parameterization methods, we present a low distortion mesh parameterization mapping method based on proxy function and combined Newton’s method in this paper. First, the proposed method calculates visual blind areas and distortion prone areas of a 3D mesh model, and generates a model slit. Afterwards, the method performs the Tutte mapping on the cut three-dimensional mesh model, measures the mapping distortion of the model, and outputs a distortion metric function and distortion values. Finally, the method sets iteration parameters, establishes a reference mesh, and finds the optimal coordinate points to get a convergent mesh model. When calculating mapping distortions, Dirichlet energy function is used to measure the isometric mapping distortion, and MIPS energy function is used to measure the conformal mapping distortion. To find the minimum value of the mapping distortion metric function, we use an optimal solution method combining proxy functions and combined Newton’s method. The experimental data show that the proposed method has high execution efficiency, fast descending speed of mapping distortion energy and stable optimal value convergence quality. When a texture mapping is performed, the texture is evenly colored, close laid and uniformly lined, which meets the standards in practical applications.

Performance comparison of hybrid functionals for describing narrow-gap semiconductors: A study on low-temperature thermoelectric material α-SrSi2

Narrow-bandgap thermoelectric semiconductors with precisely designed electronic structures are required for highly efficient energy-recycling societies. As a solution to the underestimation of the bandgap value, which is the most serious problem of first-principles calculations based on the density functional theory (DFT) especially for narrow-gap materials, we consider the PBE0 functional, Heyd–Scuseria–Ernzerhof screening hybrid functional (HSE06), and recently developed Gaussian–Perdew–Burke–Ernzerhof (Gau–PBE) hybrid functional. The convergence of the energy and bandgap of extremely narrow-gap semiconductor α-SrSi2 with respect to the mesh parameters, which are the number of k-point divisions in DFT and Hartree–Fock (HF) exchange integral calculations, was investigated using each functional, and the electronic structure and transport properties were then calculated. Consequently, Gau–PBE provided similar electronic and transport properties to those obtained using the other methods while lowering the calculation costs, i.e., with >80% less computation time and a smaller number of HF mesh points. These results provide insights to the low-cost practical calculation of the precise transport properties of low-temperature thermoelectric materials.

Semi-supervised video-driven facial animation transfer for production

We propose a simple algorithm for automatic transfer of facial expressions, from videos to a 3D character, as well as between distinct 3D characters through their rendered animations. Our method begins by learning a common, semantically-consistent latent representation for the different input image domains using an unsupervised image-to-image translation model. It subsequently learns, in a supervised manner, a linear mapping from the character images' encoded representation to the animation coefficients. At inference time, given the source domain (i.e., actor footage), it regresses the corresponding animation coefficients for the target character. Expressions are automatically remapped between the source and target identities despite differences in physiognomy. We show how our technique can be used in the context of markerless motion capture with controlled lighting conditions, for one actor and for multiple actors. Additionally, we show how it can be used to automatically transfer facial animation between distinct characters without consistent mesh parameterization and without engineered geometric priors. We compare our method with standard approaches used in production and with recent state-of-the-art models on single camera face tracking.

Development of hybrid steel-commingled composites CF/PEEK/BwM by filament winding and thermoforming

A hybrid material made of carbon fiber, poly(ether-ether-ketone) and metallic braided wire mesh was designed to improve the crashworthiness of thermoplastic composite structures. The filament winding process was adapted to enable the winding of carbon fiber/poly(ether-ether-ketone) commingled tow with five different patterns of braided wire mesh, which were later consolidated by thermoforming. Samples of the hybrid steel-commingled composites were subjected to interlaminar shear strength tests, dynamic mechanical and thermomechanical analysis. Thermal analysis determined the glass transition, secondary temperature transitions, melting point, and the thermal expansion coefficient of CF/PEEK hybrid composites. The shear and thermal properties were investigated using statistical techniques of analysis of variance and design of experiments, highlighting the effects of the braided wire mesh parameters, i.e., mesh physical dimensions, on the material behavior. The incorporation of wire mesh showed no significant difference in the thermal properties of the hybrid composites and the applicability of these materials has no restrictive effect on temperature variations. An improvement of 22.7% in interlaminar shear strength was obtained for the hybrid metal-composite compared to the material without the braided wire mesh. Finally, a multiple regression model was developed to predict the interlaminar shear strength of hybrid steel-commingled composites as a function of the mesh parameters.

Comparing Multi-Element Airfoil Flow Solutions Using Multiple Solvers with Output-Based Adapted Meshes

In this work, Reynolds-averaged Navier–Stokes (RANS) solutions for a multi-element airfoil computed with Massachusetts Institute of Technology Solution Adaptive Numerical Simulator (SANS), United States Department of Defense High Performance Computing Modernization Program CREATETM-AV Kestrel component Conservative Field Finite Elements (COFFE), and SU2 using output-based adapted meshes are compared with RANS solutions computed using manually generated meshes adhering to “best practices.” The adapted meshes are generated using the process implemented in SANS, which seeks to find a mesh that minimizes the error estimate of a given output functional. The manually generated meshes are the result of a systematic study of the influence of a range of meshing parameters on solution accuracy. Using the adapted meshes generally leads to a reduction of more than one order of magnitude in lift and drag error relative to the manually generated meshes of a comparable node count for all of the computational fluid dynamics solvers. Alternatively, the node counts of the adapted meshes are more than an order of magnitude smaller than the manually generated meshes for a given lift and drag error level. The improved accuracy in lift and drag computed with the adapted meshes can partially be attributed increased resolution around the stagnation points and trailing edges of the airfoil elements relative to the manually generated meshes. Notably, the adapted meshes provide accurate results despite having values generally significantly larger than one.