Reconstruction Scheme Research Articles

Modeling of Oil–Water Two-Phase Flow in Horizontal Pipes Using CFD for the Prediction of Flow Patterns

A computational fluid dynamics study of the horizontal oil–water flow was performed using the Eulerian–Eulerian and mixture multiphase models in conjunction with the realizable k–ε turbulence model for the characterization of flow patterns. The experimental tests were carried out using water and mineral oil with a density of 880 kg/m3 and a viscosity of 180 cP, varying the superficial velocities of both fluids in ranges of 0.1–1.2 m/s and 0.1–0.5 m/s, respectively. The numerical model was defined under the same initial and boundary conditions as in the experiment. Moreover, the model is defined such that entering the fluids in a mixed state, the stratified pattern could form adequately with the two multiphase models. Although the Eulerian–Eulerian model, together with the geometric reconstruction scheme, allowed us to visualize the three-dimensional dispersed patterns in a very similar way to the experimental results, the mixture model did not exhibit such similarity, especially in the oil-in-water dispersions. Additionally, the Eulerian–Eulerian model was able to predict the experimental holdup values with an average error of 15.2%.

Numerical aspects of gradient reconstruction schemes applied to complex geometries

Numerical aspects of gradient reconstruction schemes applied to complex geometries

Discretely nonlinearly stable weight-adjusted flux reconstruction high-order method for compressible flows on curvilinear grids

To achieve genuine predictive capability, an algorithm must consistently deliver accurate results over prolonged temporal integration periods, avoiding the unwarranted growth of aliasing errors that compromise the discrete solution. Provable nonlinear stability bounds the discrete approximation and ensures that the discretization does not diverge. Nonlinear stability is accomplished by satisfying a secondary conservation law, namely for compressible flows; the second law of thermodynamics. For high-order methods, discrete nonlinear stability and entropy stability, have been successfully implemented for discontinuous Galerkin (DG) and residual distribution schemes, where the stability proofs depend on properties of L2-norms. In this paper, nonlinearly stable flux reconstruction (NSFR) schemes are developed for three-dimensional compressible flow in curvilinear coordinates. NSFR is derived by merging the energy stable flux reconstruction (ESFR) framework with entropy stable DG schemes. NSFR is demonstrated to use larger time-steps than DG due to the ESFR correction functions, at the cost of larger error levels at design order convergence for equivalent degrees of freedom, while preserving discrete nonlinear stability. NSFR differs from ESFR schemes in the literature since it incorporates the FR correction functions on the volume terms through the use of a modified mass matrix. We also prove that discrete kinetic energy stability cannot be preserved to machine precision for quadrature rules where the surface quadrature is not a subset of the volume quadrature. This result stems from the inverse mapping from the kinetic energy variables to the conservative variables not existing for the kinetic energy projected variables. This paper also presents the NSFR modified mass matrix in a weight-adjusted form. This form reduces the computational cost in curvilinear coordinates because the dense matrix inversion is approximated by a pre-computed projection operator and the inverse of a diagonal matrix on-the-fly and exploits the tensor product basis functions to utilize sum-factorization. The nonlinear stability properties of the scheme are verified on a nonsymmetric curvilinear grid for the inviscid Taylor-Green vortex problem and the correct orders of convergence were obtained on a curvilinear mesh for a manufactured solution. Lastly, we perform a computational cost comparison between conservative DG, overintegrated DG, and our proposed entropy conserving NSFR scheme, and find that our proposed entropy conserving NSFR scheme is computationally competitive with the conservative DG scheme.

Optical Brewster interfaces enabled object identification and 3D reconstruction

Efficient and accurate object identification and 3D reconstruction are crucial for processing image information in visual imaging. Here, we propose a novel scheme for all-optical 2D contour identification and 3D reconstruction based on optical Brewster interfaces. It is revealed that 2D amplitude and phase contours for high-contrast and low-contrast objects can be identified, which is attributed to the 1D and 2D light fields manipulated by the photonic spin Hall and the Brewster effects. The 3D model can be reconstructed by rotating or slicing the high-contrast objects and by inverting the thickness of the low-contrast objects. The study potentially opens up opportunities in applications such as intelligent driving and microscopic imaging.

High order recovery of geometric interfaces from cell-average data

We consider the problem of recovering multivariate characteristic functions u := χΩ from cell-average data on a coarse grid, motivated in particular by the accurate treatment of interfaces in finite volume schemes. While linear recovery methods are known to perform poorly, nonlinear strategies based on local reconstructions of the jump interface Γ := ∂Ω by geometrically simpler interfaces may offer significant improvements. We study two main families of local reconstruction schemes the first one based on nonlinear least-squares fitting, the second one based on the explicit computation of a polynomial-shaped curve fitting the data, which yields simpler numerical computations and high order geometric fitting. For each of them, we derive a general theoretical framework which allows us to control the recovery error by the error of best approximation up to a fixed multiplicative constant. Numerical tests in 2d illustrate the expected approximation order of these strategies. Several extensions are discussed, in particular the treatment of piecewise smooth interfaces with corners.

Improving approximation accuracy in Godunov-type smoothed particle hydrodynamics methods

The study examines the origin of errors resulting from the approximation of the right hand sides of the Euler equations using the Godunov type contact method of smoothed particle hydrodynamics (CSPH). The analytical expression for the numerical shear viscosity in CSPH method is obtained. In our recent study the numerical viscosity was determined by comparing the numerical solution of momentum diffusion in the shear flow with theoretical one. In this study we deduce the analytical expression for the numerical viscosity which is found to be similar to numerical one, confirming the obtained results. To reduce numerical diffusion, diffusion limiters are typically applied to expressions for contact values of velocity and pressure, as well as higher-order reconstruction schemes. Based on the performed theoretical analysis, we propose a new method for correcting quantities at interparticle contacts in CSPH method, which can be easily extended to the MUSCL-type (Monotonic Upstream-centered Scheme for Conservation Laws) method. Original CSPH and MUSCL-SPH approaches and ones with aforementioned correction are compared.

Reconstruction of directional sources using physics-informed neural networks

In the context of augmented/virtual reality applications, replicating the directivity of sound sources is a critical step to ensure a high-quality immersive experience. However, accurate directivity measurements require complex experimental procedures involving a high number of microphones. In these scenarios, spatial interpolation allows to reconstruct the sound field with fewer sensors, which can be sparsely distributed around the source. The literature offers several interpolation schemes for sound field reconstruction, although they exhibit limited accuracy due to the lack of knowledge on the underlying physics. Recently, Physics-Informed Neural Networks (PINN) have been used to directly solve partial differential equations and thus better predict the evolution of dynamical systems. In this manuscript, we propose a spatial interpolation scheme based on PINN for the reconstruction of sound source directivity. PINN are used to solve the Helmholtz equation starting from acquisitions of the directivity over a limited set of sparsely distributed points. Results are compared with the outcomes of well-established methods based on Spherical Harmonics Decomposition (SH), Thin Plate Pseudo-Splines Interpolation (SPLI) and Piece-wise Linear Spherical Triangular Interpolation (TRI). PINN prove to provide better reconstruction of the directivity with respect to the proposed comparison methods, even when dealing with highly sparse sampling grids.

Flux reconstruction approach for long-time calculations of the linearized Euler equation

The Linearized Euler Equations (LEE) are one of the fundamental governing equations in acoustics research. Due to the relatively small magnitude of acoustic disturbances compared to the physical quantities of the background flow, ensuring highly precise solutions without dissipation and dispersion over time is essential. The Flux Reconstruction (FR) method, recognized as a high-order numerical method with flexible construction capabilities, has been extensively utilized in recent years for solving partial differential equations numerically. This paper introduces an offsetting numerical flux for one-dimensional LEE. Subsequently, it develops a flux reconstruction scheme with energy-conserving characteristics, referred to as the ECFR scheme, aimed at achieving high-precision numerical solutions for prolonged computations. The energy-conserving feature of the scheme is substantiated through theoretical derivation and further corroborated by numerical validation. Moreover, the impact of Mach numbers and the parameter of the offsetting flux on the scheme's performance is discussed. The stability of the scheme is also analyzed, with the limit of the CFL number being provided. The novel ECFR scheme facilitates obtaining high-precision acoustic numerical solutions, thereby providing strong support for the study of complex engineering problems such as aircraft, submarine, and automobile noise.

Deep-learning based single-shot 3D reconstruction with simulated color-crosstalk and randomized extrinsics

In recent years, many single-frame 3D reconstruction schemes based on fringe projection profilometry (FPP) have been proposed. However, most single-frame reconstruction schemes still face the following three issues: (1) obtaining large datasets is very time-consuming, (2) focusing only on achieving single-frame reconstruction for white objects, and (3) requiring fixing the camera-projector positional relationship, increasing operational difficulty. By building a virtual FPP simulation system, our method can quickly render the required datasets, avoiding cumbersome manual operations. When rendering the datasets, we simulate adverse factors such as color channel crosstalk, system extrinsic parameter variations, and object surface colors to guide the training of the neural network. Ultimately, from a single three-frequency color image, the corresponding three-frequency three-step phase-shift images are predicted, achieving single-frame 3D reconstruction of colored objects and allowing some variation in system extrinsic parameters. Real-world experiments demonstrate that the network trained with the diverse data generated by our virtual system has good accuracy, providing valuable guidance for the practical application of deep learning methods.

X-ray nano-holotomography reconstruction with simultaneous probe retrieval.

In conventional tomographic reconstruction, the pre-processing step includes flat-field correction, where each sample projection on the detector is divided by a reference image taken without the sample. When using coherent X-rays as a probe, this approach overlooks the phase component of the illumination field (probe), leading to artifacts in phase-retrieved projection images, which are then propagated to the reconstructed 3D sample representation. The problem intensifies in nano-holotomography with focusing optics, which, due to various imperfections creates high-frequency components in the probe function. Here, we present a new iterative reconstruction scheme for holotomography, simultaneously retrieving the complex-valued probe function. Implemented on GPUs, this algorithm results in 3D reconstruction resolving twice thinner layers in a 3D ALD standard sample measured using nano-holotomography.

Improving mimetic gravity with non-trivial scalar potential: Cosmology, black holes, shadow and photon sphere

It is not easy to treat the spacetime with horizon(s) in the standard mimetic gravity. The solution to this problem has been presented in Nojiri and Nashed (2022), where it was suggested to modify the Lagrange multiplier constraint.In this paper, by using the improved formulation, we investigate the cosmology and black holes in mimetic gravity with scalar potential and in the scalar mimetic F(R) gravity. The inflationary era and dark energy epoch for the above theories are presented as specific examples from the general reconstruction scheme which permits to realize any universe expansion history via the choice of the corresponding scalar potential or function F(R). Two black hole solutions including the Schwarzschild and Hayward ones are constructed. The shadow and the radius of the photon sphere for the above black holes are found. The explicit confrontation of the black hole shadow radius with the observational bounds from M87∗ and Sgr A∗ objects is done. It is demonstrated that they do not conflict with Event Horizon Telescope observations.

Surface pressure reconstruction from LPT data with boundary conforming grids

Abstract The coupling between fluid-structure interactions is governed by the pressure distribution over the interaction surface between the fluid and solid domains. The capabilities of non-intrusive optical techniques, such as particle image velocimetry and Lagrangian particle tracking (LPT), have been proven to provide accurate velocity and acceleration information within the flow field while simultaneously tracking the corresponding structural deformations. However, scattered data from LPT measurements are typically mapped onto Cartesian grids, independently of the shape of the solid objects in the measurement domain. The use of Cartesian grids poses challenges for the determination of the surface pressure because the velocity gradients close to the object’s surface are not captured accurately. Therefore, an alternative surface pressure reconstruction scheme utilizing LPT data based on the arbitrary Lagrangian–Eulerian approach is proposed to mitigate the error propagation associated with the use of uniform grids. The introduced method provides an exact surface conformation utilizing boundary fitted coordinate systems and radial basis function based mesh deformations, which eliminates the need to use extrapolations to obtain surface pressure distributions. The introduced approach is assessed by means of a synthetic hill surface probing a three-dimensional analytical flow field; its practical applicability is demonstrated through an experimental characterization of turbulent boundary layer interactions with a steadily and unsteadily deforming elastic membrane.

CoSeg: Cognitively Inspired Unsupervised Generic Event Segmentation.

Some cognitive research has discovered that humans accomplish event segmentation as a side effect of event anticipation. Inspired by this discovery, we propose a simple yet effective end-to-end self-supervised learning framework for event segmentation/boundary detection. Unlike the mainstream clustering-based methods, our framework exploits a transformer-based feature reconstruction scheme to detect event boundaries by reconstruction errors. This is consistent with the fact that humans spot new events by leveraging the deviation between their prediction and what is perceived. Thanks to their heterogeneity in semantics, the frames at boundaries are difficult to be reconstructed (generally with large reconstruction errors), which is favorable for event boundary detection. In addition, since the reconstruction occurs on the semantic feature level instead of the pixel level, we develop a temporal contrastive feature embedding (TCFE) module to learn the semantic visual representation for frame feature reconstruction (FFR). This procedure is like humans building up experiences with "long-term memory." The goal of our work is to segment generic events rather than localize some specific ones. We focus on achieving accurate event boundaries. As a result, we adopt the F1 score (Precision/Recall) as our primary evaluation metric for a fair comparison with previous approaches. Meanwhile, we also calculate the conventional frame-based mean over frames (MoF) and intersection over union (IoU) metric. We thoroughly benchmark our work on four publicly available datasets and demonstrate much better results. The source code is available at https://github.com/wang3702/CoSeg.

Thermal effect on the flow induced by a single-dielectric-barrier-discharge plasma actuator under steady actuation

The thermal effect of a single-dielectric-barrier-discharge plasma actuator under steady actuation is numerically investigated. A new actuator model is proposed and validated using experimental data. A discrete Galerkin method based on high-order flux reconstruction schemes is employed to solve the flow governing equations and the actuator model equations on unstructured quadrilateral grids. By comparing the induced heated and cold flow fields of the actuator with and without a plasma thermal source, its thermal effect is revealed. The actuator generates a thermal wall jet with rich vorticity, forming a monopolar starting vortex with a high-temperature and low-density core. Over time, the starting vortex becomes unstable and transforms into a dipole. Actuator heating enhances jet velocity and width, as well as vortex stability, while slowing down vorticity generation. The relative change in density and temperature fields due to actuator heating is four orders of magnitude greater than that without actuator heating. Additionally, the actuator heating causes the background thermodynamic fields to increase approximately linearly with time. Two stages in the actuator's thermal effect are distinguished due to time accumulation. Initially, the actuator heating minimally affects the monopolar starting vortex motion, and the temperature and density fields are treated as passive variables driven by the velocity field. During this stage, the momentum and thermal effects of the actuator can be studied separately. However, after the starting vortex becomes unstable, the actuator heating significantly impacts its motion and morphology, and these two effects are coupled with each other.

A family of TENOA-THINC-MOOD schemes based on diffuse-interface method for compressible multiphase flows

In this work, we develop a family of hybrid algorithms to simulate compressible multi-phase flows by solving the quasi-conservative five-equation model. The general numerical framework utilizes targeted essentially non-oscillatory schemes with adaptive dissipation (TENOA) to boost the resolution of high-frequency waves, whereas the Tangent of Hyperbola for INterface Capturing (THINC) scheme is activated near the shock and contact discontinuities as well as material interfaces to maintain their sharpness, based on a novel indicator. Also, the newly derived THINC reconstruction scheme is both simpler and better at preserving the flow symmetry. The robustness of our numerical approach is further fortified through the adaptation of a modified a posteriori multidimensional optimal order detection (MOOD) technique. Moreover, to mitigate carbuncle phenomenon encountered in two-dimensional simulations, a hybrid Riemann solver is also proposed based on the low Mach modification around shock for the Harten-Lax-van Leer contact (HLLC) approximate Riemann solver. Numerical results of the challenging one- and two-dimensional benchmark cases demonstrate the superiority of the proposed methods regarding oscillation-free, interface-sharpening, low-dissipation and robustness properties.

A virtual reconstruction method for corridor gable buildings based on the knowledge of structural dynamics: taking Leiyin Cave as an example

Virtual reconstruction of ancient buildings often has incomplete records of the original design and construction details, and can only be reconstructed based on limited data, drawings and photography, which is different from the actual conditions. The unique overhanging structure of the corridor gable building makes it vulnerable to damage in extreme weather conditions. In order to ensure that the virtual reconstruction results can not only reproduce the original appearance of history, but also ensure that the reconstructed model maintains structural stability in the long term. This paper proposes a reconstruction method of the original appearance of the corridor gable building remains based on structural dynamics analysis. This method comprehensively uses three-dimensional reconstruction, structural engineering, dynamic analysis, and computer simulation technology to ensure the structural accuracy and historical authenticity of the virtually reconstructed corridor gable building. First, through data collection and analysis, combined with ancient architectural construction techniques, a preliminary three-dimensional model was created, which included all structural elements and details. Several groups of reconstruction schemes are determined based on material properties. Then, using finite element analysis software, perform dynamic analysis on the three-dimensional model. Evaluate the stability of the reconstructed structure and optimize the material selection plan to ensure the feasibility and accuracy of the virtual reconstruction. Taking the virtual reconstruction of the eaves in front of Leiyin Cave as an example, it shows that this method is effective and feasible to achieve the virtual reconstruction of corridor gable buildings. It provides new ideas for virtual reconstruction of ancient buildings and has important practical application value.

A Hierarchical Point-spread Function Reconstruction Method

Reconstruction of the point-spread function (PSF) plays an important role in many areas of astronomy, including photometry, astrometry, galaxy morphology, and shear measurement. The atmospheric and instrumental effects are the two main contributors to the PSF, both of which may exhibit complex spatial features. Current PSF reconstruction schemes typically rely on individual exposures, and their ability to reproduce the complicated features of the PSF distribution is therefore limited by the number of stars. Interestingly, in conventional methods, after stacking the model residuals of the PSF ellipticities and (relative) sizes from a large number of exposures, one can often observe some stable and nontrivial spatial patterns on the entire focal plane, which could be quite detrimental to, e.g., weak-lensing measurements. These PSF residual patterns are caused by instrumental effects, as they consistently appear in different exposures. Taking this as an advantage, we propose a multilayer PSF reconstruction method to remove such PSF residuals, the second and third layers of which make use of all available exposures together. We test our method on the i-band data of the second release of the Hyper Suprime-Cam. Our method successfully eliminates most of the PSF residuals. Using the Fourier_Quad shear measurement method, we further test the performance of the resulting PSF fields on shear recovery using the field distortion effect. The PSF residuals have strong correlations with the shear residuals, and our new multilayer PSF reconstruction method can remove most of such systematic errors related to the PSF, leading to much smaller shear biases.

A Single-Frame and Multi-Frame Cascaded Image Super-Resolution Method.

The objective of image super-resolution is to reconstruct a high-resolution (HR) image with the prior knowledge from one or several low-resolution (LR) images. However, in the real world, due to the limited complementary information, the performance of both single-frame and multi-frame super-resolution reconstruction degrades rapidly as the magnification increases. In this paper, we propose a novel two-step image super resolution method concatenating multi-frame super-resolution (MFSR) with single-frame super-resolution (SFSR), to progressively upsample images to the desired resolution. The proposed method consisting of an L0-norm constrained reconstruction scheme and an enhanced residual back-projection network, integrating the flexibility of the variational model-based method and the feature learning capacity of the deep learning-based method. To verify the effectiveness of the proposed algorithm, extensive experiments with both simulated and real world sequences were implemented. The experimental results show that the proposed method yields superior performance in both objective and perceptual quality measurements. The average PSNRs of the cascade model in set5 and set14 are 33.413 dB and 29.658 dB respectively, which are 0.76 dB and 0.621 dB more than the baseline method. In addition, the experiment indicates that this cascade model can be robustly applied to different SFSR and MFSR methods.

Hybridized formulations of flux reconstruction schemes for advection-diffusion problems

We present the hybridization of flux reconstruction methods for advection-diffusion problems. Hybridization introduces a new variable into the problem so that it can be reduced via static condensation. This allows the solution of implicit discretizations to be done more efficiently. We derive an energy statement from a stability analysis considering a range of correction functions on hybridized and embedded flux reconstruction schemes. Then, we establish connections to standard formulations. We devise a post-processing scheme that leverages existing flux reconstruction operators to enhance accuracy for diffusion-dominated problems. Results show that the implicit convergence of these methods for advection-diffusion problems can result in performance benefits of over an order of magnitude. In addition, we observe that the superconvergence property of hybridized methods can be extended to the family of FR schemes for a range of correction functions.

One-shot structured light illumination based on shearlet transform.

Balancing speed and accuracy has always been a challenge in 3D reconstruction. One-shot structured light illuminations are of perfect performance on real-time scanning, while the related 3D point clouds are typically of relatively poor quality, especially in regions with rapid height changes. To solve this problem, we propose a one-shot reconstruction scheme based on shearlet transform, which combines spatial and frequency domain information to enhance reconstruction accuracy. First, we apply the shearlet transform to the deformed fringe pattern to obtain the transform coefficients. Second, pixel-wise select the indices associated with the N largest coefficients in magnitude to obtain a new filter. Finally, we refocus globally to extract phase using these filters and generate a reliable quality map based on coefficient magnitudes to guide phase unwrapping. Simultaneously, we utilize the maximum coefficient value to generate a quality map for guiding the phase unwrapping process. Experimental results show that the proposed method is robust in discontinuous regions, resulting in more accurate 3D point clouds.