Mesh Transformation Research Articles

Deep learning-based reduced order model for three-dimensional unsteady flow using mesh transformation and stitching

Artificial intelligence-based three-dimensional fluid modeling has gained significant attention recently. However, the accuracy of such models is often limited by the preprocessing of irregular flow data. In order to bolster the credibility of near-wall flow prediction, we present a deep learning-based reduced order model for three-dimensional unsteady flow using the transformation and stitching techniques for multi-block structured meshes. To begin with, full-order flow data is provided by numerical simulations that rely on multi-block structured meshes. The mesh transformation technique is applied to convert each structured grid with data into a corresponding uniform and orthogonal grid, which is subsequently stitched and filled. The resulting snapshots in the transformed domain contain accurate flow information for multiple meshes and can be directly fed into a structured neural network without requiring any interpolation operation. Subsequently, a network model based on a fully convolutional neural network is constructed to predict flow dynamics accurately. To validate the strategy's feasibility, the flow around a sphere with Re=300 was investigated, and the results obtained using traditional Cartesian interpolation were used as the baseline for comparison. All the results demonstrate the preservation and accurate prediction of flow details near the wall, with the pressure correlation coefficient on the wall achieving a remarkable value of 0.9997. The stitching scheme that follows the proposed standard can effectively reduce the accumulation of inferring errors. Moreover, the periodic behavior of flow fields can be faithfully predicted during long-term inference. This work demonstrates that the proposed strategy has the advantage of high efficiency while providing accuracy assurance for downstream tasks.

Solving high-dimensional parametric engineering problems for inviscid flow around airfoils based on physics-informed neural networks

Engineering problems often involve solving partial differential equations (PDEs) over a range of similar problem setups, leading to high computational costs when using traditional numerical approaches to solve each setup individually. Recently developed physics-informed neural networks (PINNs) offer a novel approach to solving parametric problems, enabling the simultaneous solution of a series of similar problems. Our previous research combined PINNs with mesh transformation to learn PDE solutions in the computational space, effectively solving inviscid flow around airfoils. In this study, we expand the input dimensions of the model to include shape parameters and flow conditions, forming an input encompassing the complete state-space (i.e., all parameters determining the solution are included in the input). We spend about 18.8 h achieving the continuous solutions in a large state-space in one go, encompassing various subsonic inviscid airfoil flows encountered in engineering, thereby highlighting the model's significant advantages in addressing high-dimensional parametric problems. Once established, the model can efficiently complete airfoil flow simulation and shape inverse design tasks in about 1 s. Furthermore, we introduce a pretraining-finetuning method, enabling the fine-tuning of the model for the task of interest and quickly achieving accuracy comparable to the finite volume method.

A solver for subsonic flow around airfoils based on physics-informed neural networks and mesh transformation

Physics-informed neural networks (PINNs) have recently become a new popular method for solving forward and inverse problems governed by partial differential equations. However, in the flow around airfoils, the fluid is greatly accelerated near the leading edge, resulting in a local sharper transition, which is difficult to capture by PINNs. Therefore, PINNs are still rarely used to solve the flow around airfoils. In this study, we combine physical-informed neural networks with mesh transformation, using a neural network to learn the flow in the uniform computational space instead of physical space. Mesh transformation avoids the network from capturing the local sharper transition and learning flow with internal boundary (wall boundary). We successfully solve inviscid flow and provide an open-source subsonic flow solver for arbitrary airfoils. Our results show that the solver exhibits higher-order attributes, achieving nearly an order of magnitude error reduction over second-order finite volume method (FVM) on very sparse meshes. Limited by the learning ability and optimization difficulties of the neural network, the accuracy of this solver will not improve significantly with mesh refinement. Nevertheless, it achieves comparable accuracy and efficiency to second-order FVM on fine meshes. Finally, we highlight the significant advantage of the solver in solving parametric problems, as it can efficiently obtain solutions in the continuous parameter space about the angle of attack.

Numerical Assessment of Combustion Behavior and Emission Formations in an Ultrasonic-Assisted Ignition Engine.

By effective utilization of the dynamic mesh and coordinate transformation techniques, an ultrasonic horn is physically integrated in the chamber of an internal combustion engine. The consequences of multiple ultrasonic-fed strategies on the flow field, combustion process, and emission formation under the same working conditions are studied by numerical simulation. Based precisely on the bench test data, GT-Power and CONVERGE set up the original engine one-dimension (1d) and three-dimension (3d) simulation models. The chamber pressure and heat release rate of the 1d and 3d models under a full load condition of 3000 r·min-1 were validated, and the maximum relative error is less than 5%, proving the accuracy of the model. By reforming the 3d numerical model, ultrasonics is added to the gasoline engine's combustion chamber. Six different ultrasonic-fed schemes with 20 kHz amplitude of 30-300 μm are typically selected for in-depth research. The larger the amplitude, the stronger the turbulent kinetic energy (TKE), and the maximum TKE exceeds 46.6% at the ignition time. Stronger TKE can energetically encourage the generation of OH, O, and H radicals and improve the combustion reaction rate, and the peak pressure (PMAX) is increased by 1.9 MPa compared with scheme No. However, NOX and HC emissions gradually increase, reaching a maximum of 32.4 and 43.8%, respectively, while CO and soot emissions decrease, reaching a maximum of 11.4 and 11%, respectively. Four groups of ultrasonic-fed schemes with an amplitude of 100 μm and frequency of 20-50 kHz are scientifically studied. The findings indicated that the TKE level steadily increases as the frequency increases and the in-cylinder TKE increases by 16.4% at ignition time. The increase in ultrasonic frequency can promote the generation of active free radicals and meaningfully improve the combustion reaction rate to a certain extent. The PMAX can be increased up to 1 MPa compared with scheme No. At the same time, the NOX, HC, and soot also increased considerably, reaching 31.8, 17.9, and 21.9%, respectively. The CO showed a downward trend but gradually slowed, with a maximum decline of 6.5% at 20 kHz. The above simulation analysis is based on the full load condition of 3000 r·min-1, sufficiently proving that ultrasonics has a regulation effect on emissions and can achieve specific emissions through later optimization.

Temporal predictions of periodic flows using a mesh transformation and deep learning-based strategy

This paper focuses on the temporal prediction of unsteady flow based on a combination of mesh transformation and deep learning technology. To this end, a body-fitted mesh interpolation was first implemented to extract the flow information in the region of interest and maintain the detailed flow information in the boundary layer. Subsequently, a mesh transformation technique was applied to map the physical coordinates into the curvilinear coordinates to obtain a structural uniform mesh, which is facilitated for the implementation the structural neural networks. Ultimately, two advanced neural networks, i.e., Unet and Fourier Neural Operator (FNO), were used for establishing the relationship between flow at previous time steps and that at future time steps. Two flow configurations numerically simulated—i.e., a laminar flow around a cylinder at Re=200 and a transonic buffet of a supercritical airfoil at Ma=0.73—were selected as the benchmarks to demonstrate the effectiveness and robustness of the proposed strategy. The results indicated that the flow at future time steps can be accurately obtained using that at the previous time steps via both neural networks, even in a complicated flow scenario. The velocity and pressure of the periodic flow can be faithfully predicted with a remarkable accuracy. Additionally, the derived flow physical quantities were comprehensively compared, which demonstrated that better performance can be achieved using FNO with a lower relative loss and a shorter training time-consuming.

Coupled Numerical Scheme for Vascular Fluid-Tube Interaction using Large Deformation Theory

A methodological approach is elaborated to study the vascular fluid-tube interaction under pulsatile blood flow within an asymmetrical nonlinear aneurysm and large deformation models. The aneurysm dynamics were modeled using a simplified Lagrangian nonlinear system describing the arterial wall motion with large deformation. The flow is governed by the Navier-Stokes equations in two-dimensional domain. A semi-implicit splitting scheme coupled with the finite difference method is developed to solve the flow equation in an irregular domain using a mesh transformation. On the other hand, the wall equations are solved using the Runge-Kutta method combined with the shooting technique by reducing the resulted boundary value problem to an initial value problem. Rigid and elastic aneurysms are considered and the effect of various geometrical and fluid parameters on the flow are investigated, mainly the Reynolds number, the aneurysm length and height. The study focused on the effect of the asymmetric curvatures of the tube walls and their deformations due to the pulsatile flow. The flow is examined under a steady inlet flow as well as under a pulsatile one for various aneurysm forms. The obtained numerical results validate the fluid and structure solvers and demonstrate significant differences between the rigid and elastic models of the structure as well as the effect of the asymmetric propriety of the arterial aneurysm.

Foids

We present a bio-inspired fish simulation platform, which we call "Foids", to generate realistic synthetic datasets for an use in computer vision algorithm training. This is a first-of-its-kind synthetic dataset platform for fish, which generates all the 3D scenes just with a simulation. One of the major challenges in deep learning based computer vision is the preparation of the annotated dataset. It is already hard to collect a good quality video dataset with enough variations; moreover, it is a painful process to annotate a sufficiently large video dataset frame by frame. This is especially true when it comes to a fish dataset because it is difficult to set up a camera underwater and the number of fish (target objects) in the scene can range up to 30,000 in a fish cage on a fish farm. All of these fish need to be annotated with labels such as a bounding box or silhouette, which can take hours to complete manually, even for only a few minutes of video. We solve this challenge by introducing a realistic synthetic dataset generation platform that incorporates details of biology and ecology studied in the aquaculture field. Because it is a simulated scene, it is easy to generate the scene data with annotation labels from the 3D mesh geometry data and transformation matrix. To this end, we develop an automated fish counting system utilizing the part of synthetic dataset that shows comparable counting accuracy to human eyes, which reduces the time compared to the manual process, and reduces physical injuries sustained by the fish.

The Magneto-Natural Convection Flow of a Micropolar Hybrid Nanofluid over a Vertical Plate Saturated in a Porous Medium

In this study, we investigate the convective flow of a micropolar hybrid nanofluid through a vertical radiating permeable plate in a saturated porous medium. The impact of the presence or absence of the internal heat generation (IHG) in the medium is examined as well as the impacts of the magnetic field and thermal radiation. We apply similarity transformations to the non-dimensionalized equations and render them as a system of non-linear ODEs (Ordinary Differential Equations) subject to appropriate boundary conditions. This system of non-linear ODEs is solved by an adaptive mesh transformation Chebyshev differential quadrature method. The influence of the governing parameters on the temperature, microrotation and velocity is examined. The skin friction coefficient and the Nusselt number are tabulated. We determine that the skin friction coefficient and heat transport rate increase with the increment in the magnetic field. Moreover, the increment in the micropolarity and nanoparticle volume fraction enhances the skin friction coefficient and the Nusselt number. We also conclude that the IHG term improved the flow of the hybrid nanofluid. Finally, our results indicate that employing a hybrid nanofluid increases the heat transfer compared with that in pure water and a nanofluid.

3D mesh transformation preprocessing system in the real space for augmented reality services

Abstract We propose a preprocessing system that transforms the real world into 3D mesh virtual world to provide augmented reality (AR) services. The proposed system uses a monocular RGB camera to obtain sequential images to generate real space. First, we create 3D real-world space composed of point clouds using sequential color images. And then, we segment the objects in each color image and assign an identification number for each object. Also, we execute ‘3D point labeling’, which assigns identification numbers from 2D segmented object to 3D point cloud through a simple projection manner with several parameters. This process could collect 3D point cloud with same the label by as an object. Finally, only the 3D point clouds that have the same identification number by as an object are used to generate 3D mesh. This paper confirmed that 3D mesh could be created using the only general monocular camera without the help of special 3D sensors.

Discontinuous Galerkin via Interpolation: The Direct Flux Reconstruction Method

The discontinuous Galerkin (DG) method is based on the idea of projection using integration. The recent direct flux reconstruction (DFR) method by Romero et al. (J Sci Comput 67(1):351–374, 2016) is derived via interpolation and results in a scheme identical to DG (on hexahedral meshes). The DFR method is further studied and developed here. Two proofs for its equivalence with the DG scheme considerably simpler than the original proof are presented. The first proof employs the $$ 2K - 1 $$ degree of precision by a $$ K $$-point Gauss quadrature. The second shows the equivalence of DG, FR, and DFR by using the property that the derivative of the degree $$ K + 1 $$ Lobatto polynomial vanishes at the $$ K $$ Gauss points. Fourier analysis for these schemes are presented using an approach more geometric compared with existing analytic approaches. The effects of nonuniform mesh and those of high-order mesh transformation (a precursor for curved meshes in two and three spatial dimensions) on stability and accuracy are examined. These nonstandard analyses are obtained via an in-depth study of the behavior of eigenvalues and eigenvectors.

Iterative freeform lens design for prescribed irradiance on curved target

Current freeform illumination optical designs are mostly focused on producing prescribed irradiance distributions on planar targets. Here, we aim to design freeform optics that could generate a desired illumination on a curved target from a point source, which is still a challenge. We reduce the difficulties that arise from the curved target by involving its varying z-coordinates in the iterative wavefront tailoring (IWT) procedure. The new IWT-based method is developed under the stereographic coordinate system with a special mesh transformation of the source domain, which is suitable for light sources with light emissions in semi space such as LED sources. The first example demonstrates that a rectangular flat-top illumination can be generated on an undulating surface by a spherical-freeform lens for a Lambertian source. The second example shows that our method is also applicable for producing a non-uniform irradiance distribution in a circular region of the undulating surface.

The scaling and skewness of optimally transported meshes on the sphere

In the context of numerical solution of PDEs, dynamic mesh redistribution methods (r-adaptive methods) are an important procedure for increasing the resolution in regions of interest, without modifying the connectivity of the mesh. Key to the success of these methods is that the mesh should be sufficiently refined (locally) and flexible in order to resolve evolving solution features, but at the same time not introduce errors through skewness and lack of regularity. Some state-of-the-art methods are bottom-up in that they attempt to prescribe both the local cell size and the alignment to features of the solution. However, the resulting problem is overdetermined, necessitating a compromise between these conflicting requirements. An alternative approach, described in this paper, is to prescribe only the local cell size and augment this an optimal transport condition to provide global regularity. This leads to a robust and flexible algorithm for generating meshes fitted to an evolving solution, with minimal need for tuning parameters. Of particular interest for geophysical modelling are meshes constructed on the surface of the sphere. The purpose of this paper is to demonstrate that meshes generated on the sphere using this optimal transport approach have good a-priori regularity and that the meshes produced are naturally aligned to various simple features. It is further shown that the sphere's intrinsic curvature leads to more regular meshes than the plane. In addition to these general results, we provide a wide range of examples relevant to practical applications, to showcase the behaviour of optimally transported meshes on the sphere. These range from axisymmetric cases that can be solved analytically to more general examples that are tackled numerically. Evaluation of the singular values and singular vectors of the mesh transformation provides a quantitative measure of the mesh anisotropy, and this is shown to match analytic predictions.

From MOF membrane to 3D electrode: a new approach toward an electrochemical non-enzymatic glucose biosensor

A three-dimensional (3D) nickel oxide (NiO) catalytic electrode was fabricated by annealing Ni2(L-asp)2bipy MOF membrane and was subsequently applied for electrochemical glucose sensor. This 3D self-supported MOF membrane precursor provided uniform and porous architecture, and it was used for fabricating 3D NiO electrode in the first time. The SEM and XRD data showed that the NiO was evenly distributed on Ni mesh and complete transformation from Ni2(L-asp)2bipy to NiO. This catalytic electrode, using a chronoamperometric approach, demonstrated linear range up to 400 μM with high sensitivity of 478.9 μA mM−1 cm−2 and low limit of detection of 4.34 μM. Uric acid, urea and ascorbic acid showed negligible interferences to the detection of glucose. The excellent performance of this electrode was attributed to the uniformly distributed NiO on the Ni substrate, direct electron transformation from Ni substrate to electrochemical active NiO and the porosity of such electrode design.

Manual construction of continuous cartograms through mesh transformation

ABSTRACTA computer-assisted framework is proposed to support the manual construction of cartograms. The framework employs a joint triangulation, similar to that used in rubber-sheeting, to define a piecewise affine transformation between map space and cartogram space. This guarantees preservation of all topological relations within and among transformed datasets with insertion of a finite number of points. To support intuitive user control of cartogram appearance, methods are developed to translate generically defined user adjustments of the cartogram into mesh vertex positions on either the source map mesh or cartogram mesh. The framework is implemented in a working prototype application and used to create sample cartograms of the USA and China. Results are compared with cartograms produced using diffusion and carto3f algorithms in terms of accuracy, aesthetic appearance, and approximate construction time. Qualitative aspects of the manual construction process are also discussed.

An immersed-boundary method based on the gas kinetic BGK scheme for incompressible viscous flow

In this paper, an immersed-boundary (IB) method based on the gas kinetic Bhatnagar–Gross–Krook (BGK) scheme is proposed to simulate the incompressible viscous flow around stationary and moving rigid bodies. In the presented IB method, a set of Lagrangian points represent the solid boundary and will exert force on the surrounding Eulerian points which are the cell centers within the finite-volume framework. This force is calculated by a special iterative procedure and has an effect on the flux at the interface of cell, which guarantees the fulfillment of the no-slip boundary condition and entirely avoids the flow penetration. The flow field is obtained from the BGK scheme with local grid refinement. Without complex mesh generation and transformation, the present technique can be conveniently applied to simulations with complex and moving solid boundaries. The second-order temporal accuracy and better than first-order spatial accuracy in L2 norm are testified by the simulation of Stokes' first problem. Other three different test cases, including flows around a stationary circular cylinder, two circular cylinders in tandem and an oscillating circular cylinder, demonstrate the good capability of the present method.

Iterative mesh transformation for 3D segmentation of livers with cancers in CT images

Segmentation of diseased liver remains a challenging task in clinical applications due to the high inter-patient variability in liver shapes, sizes and pathologies caused by cancers or other liver diseases. In this paper, we present a multi-resolution mesh segmentation algorithm for 3D segmentation of livers, called iterative mesh transformation that deforms the mesh of a region-of-interest (ROI) in a progressive manner by iterations between mesh transformation and contour optimization. Mesh transformation deforms the 3D mesh based on the deformation transfer model that searches the optimal mesh based on the affine transformation subjected to a set of constraints of targeting vertices. Besides, contour optimization searches the optimal transversal contours of the ROI by applying the dynamic-programming algorithm to the intersection polylines of the 3D mesh on 2D transversal image planes. The initial constraint set for mesh transformation can be defined by a very small number of targeting vertices, namely landmarks, and progressively updated by adding the targeting vertices selected from the optimal transversal contours calculated in contour optimization. This iterative 3D mesh transformation constrained by 2D optimal transversal contours provides an efficient solution to a progressive approximation of the mesh of the targeting ROI. Based on this iterative mesh transformation algorithm, we developed a semi-automated scheme for segmentation of diseased livers with cancers using as little as five user-identified landmarks. The evaluation study demonstrates that this semi-automated liver segmentation scheme can achieve accurate and reliable segmentation results with significant reduction of interaction time and efforts when dealing with diseased liver cases.

On balanced moving mesh methods

Moving mesh methods are a widely used approach in the numerical solution of PDEs where the original PDEs are transformed from a physical domain to a computational domain. The objective is to utilize a uniform mesh in the computational domain to get a non-uniform physical mesh that better captures the behavior of the solution. The movement of the physical mesh points can be governed by a moving mesh PDE associated with a corresponding monitor function and both the original PDEs and the moving mesh PDEs must be solved simultaneously. The motivation for this paper is to study a balanced moving mesh method, where the aim is to strike a balance between the properties of the solution of the original PDE and that of the moving mesh PDE. We focus on particular choices of the monitor function that give both a well-behaved mesh transformation and a well-behaved solution in the computational domain. Both theoretical analysis and numerical experiments are presented as illustrations.

Automatic mesh generation and transformation for topology optimization methods

This paper presents automatic tools aimed at the generation and adaptation of unstructured tetrahedral meshes in the context of composite or heterogeneous geometry. These tools are primarily intended for applications in the domain of topology optimization methods but the approach introduced presents great potential in a wider context. Indeed, various fields of application can be foreseen for which meshing heterogeneous geometry is required, such as finite element simulations (in the case of heterogeneous materials and assemblies, for example), animation and visualization (medical imaging, for example). Using B-Rep concepts as well as specific adaptations of advancing front mesh generation algorithms, the mesh generation approach presented guarantees, in a simple and natural way, mesh continuity and conformity across interior boundaries when trying to mesh a composite domain. When applied in the context of topology optimization methods, this approach guarantees that design and non-design sub-domains are meshed so that finite elements are tagged as design and non-design elements and so that continuity and conformity are guaranteed at the interface between design and non-design sub-domains. The paper also presents how mesh transformation and mesh smoothing tools can be successfully used when trying to derive a functional shape from raw topology optimization results.

Adaptively deformed mesh based interface method for elliptic equations with discontinuous coefficients

Mesh deformation methods are a versatile strategy for solving partial differential equations (PDEs) with a vast variety of practical applications. However, these methods break down for elliptic PDEs with discontinuous coefficients, namely, elliptic interface problems. For this class of problems, the additional interface jump conditions are required to maintain the well-posedness of the governing equation. Consequently, in order to achieve high accuracy and high order convergence, additional numerical algorithms are required to enforce the interface jump conditions in solving elliptic interface problems. The present work introduces an interface technique based adaptively deformed mesh strategy for resolving elliptic interface problems. We take the advantages of the high accuracy, flexibility and robustness of the matched interface and boundary (MIB) method to construct an adaptively deformed mesh based interface method for elliptic equations with discontinuous coefficients. The proposed method generates deformed meshes in the physical domain and solves the transformed governed equations in the computational domain, which maintains regular Cartesian meshes. The mesh deformation is realized by a mesh transformation PDE, which controls the mesh redistribution by a source term. The source term consists of a monitor function, which builds in mesh contraction rules. Both interface geometry based deformed meshes and solution gradient based deformed meshes are constructed to reduce the L ∞ and L 2 errors in solving elliptic interface problems. The proposed adaptively deformed mesh based interface method is extensively validated by many numerical experiments. Numerical results indicate that the adaptively deformed mesh based interface method outperforms the original MIB method for dealing with elliptic interface problems.

의복 디자인 시스템을 이용한 웹 3차원 의복 애니메이션 구현

본 논문에서는 가상 공간에서 의상을 직접 입어보는 체험을 해 볼 수 있는 웹 3차원 의복 애니메이션을 구현하기 위하여 2차원 및 2.5차원 의복 디자인 시스템을 이용한 3차원 의복 애니메이션 시스템을 설계하였고, 자연스러운 드레이핑을 구현하기 위하여 메시 생성 및 변형 알고리즘, 영역 추출 알고리즘, 워프 알고리즘, 명암 추출 및 적용 알고리즘을 이용하였다. 그리고 2차원 및 2.5차원 의복 디자인 시스템에서 추출된 좌표 점은 텍스트 형식의 데이터로 받아 의복 정보 파일로 입력하게 된다. 또한 이 의복 정보 파일은 3차원 의복 애니메이션에 활용할 수 있도록 구현하였다. In this paper, we designed 2D, 2.5D cloth design system and a 3D cloth animation system. They make the 3D cloth animation possible by using coordinate points extracted from 2D and 2.5D cloth design system in order to realize a system that allows customers to wear clothes in the virtual space. To make natural draping, it uses for description the mesh creation and transformation algorithms, path extraction algorithm, warp algorithm, and brightness extraction and application algorithms. The coordinate points extracted here are received as text format data and inputted as clothing information in the cloth file. Moreover, the cloth file has a 2D pattern and is realized to be used in the 3D cloth animation system. The 3D cloth animation system generated in this way builds a web-based fashion mall using ISB (Internet Space Builder) and lets customers view the clothing animation on the web by adding the animation process to the simulation result.