Exact Velocity Research Articles

A two-level semi-hybrid-mixed model for Stokes–Brinkman flows with divergence-compatible velocity–pressure elements

A two-level version for a recent semi-hybrid-mixed finite element approach for modeling Stokes and Brinkman flows is proposed. In the context of a domain decomposition of the flow region Ω, composite divergence-compatible finite elements pairs in H(div,Ω)×L2(Ω) are utilized for discretizing velocity and pressure fields, using the same approach previously adopted for two-level mixed Darcy and stress mixed elasticity models. The two-level finite element pairs of spaces in the subregions may have richer internal resolution than the boundary normal trace. Hybridization occurs by the introduction of an unknown (traction) defined over element boundaries, playing the role of a Lagrange multiplier to weakly enforce tangential velocity continuity and Dirichlet boundary condition. The well-posedness of the method requires a proper choice of the finite element space for the traction multiplier, which can be achieved after a proper velocity FE space enrichment with higher order bubble fields. The method is strongly locally conservative, yielding exact divergence-free velocity fields, demonstrating pressure robustness, and facilitating parallel implementations by limiting the communication of local common data to at most two elements. Easier coupling strategies of finite elements regarding different polynomial degree or mesh widths are permitted, provided that mild mesh and normal trace consistency properties are satisfied. Significant improvement in computational performance is achieved by the application of static condensation, where the global system is solved for coarse primary variables. The coarse primary variables are a piecewise constant pressure variable over the subregions, velocity normal trace and tangential traction over subdomain interfaces, as well as a real number used as a multiplier ensuring global zero-mean pressure. Refined details of the solutions are represented by secondary variables, which are post-processed by local solvers. Numerical results are presented for the verification of convergence histories of the method.

Numerical Algorithms for Divergence-Free Velocity Applications

This work focuses on the well-known issue of mass conservation in the context of the finite element technique for computational fluid dynamic simulations. Specifically, non-conventional finite element families for solving Navier–Stokes equations are investigated to address the mathematical constraint of incompressible flows. Raviart–Thomas finite elements are employed for the achievement of a discrete free-divergence velocity. In particular, the proposed algorithm projects the velocity field into the discrete free-divergence space by using the lowest-order Raviart–Thomas element. This decomposition is applied in the context of the projection method, a numerical algorithm employed for solving Navier–Stokes equations. Numerical examples validate the approach’s effectiveness, considering different types of computational grids. Additionally, the presented paper considers an interface advection problem using marker approximation in the context of multiphase flow simulations. Numerical tests, equipped with an analytical velocity field for the surface advection, are presented to compare exact and non-exact divergence-free velocity interpolation.

A hybrid FEM-IBM-level set algorithm for water entry of deformable body

Water entry of deformable bodies has been investigated extensively despite the major challenges in precise simulations of the whole physical process. Inspired by the basic idea of immersed boundary method (IBM), a hybrid FEM-IBM-level set algorithm is proposed where structural compliance is considered. The flow is described by Navier-Stokes equations with an added body force while the drastically moving object of arbitrary geometry is represented by several Lagrangian points on solid boundary. The direct forcing IBM is enhanced and coupled with finite element method (FEM) to facilitate simulation of severe fluid-structure interactions. Consequently, the added body force is calculated implicitly based on the exact velocity boundary condition with divergence-free condition ensured simultaneously. The improved conservative level set technique is adopted for accurate depiction of instantaneously distorted water surface, and the strongly coupled system is resolved iteratively through a partitioned scheme. Examples including sedimentation of a disk, water entry of deformable wedge and cylindrical shell are performed for validation. Specifically, hydroelastic impact of a three-dimensional conical shell is investigated, and the influence factors of entry dynamics are discussed. The results demonstrate the reliability and great potential of present algorithm for practical applications in ocean engineering, naval architecture and military engineering, etc.

Four-quadrant propeller hydrodynamic performance mapping for improving ship motion predictions

On the path toward fully autonomous sea vessels, forecasting a ship’s exact velocity and position during its route plays a crucial role in dynamic positioning, target tracking, and autopilot operations of the unmanned body navigating toward predetermined locations. This paper addresses the prediction of the operational performance of a free-running submarine advancing in a straight route (in surge motion). Along with the forward advancing vessel (straight-ahead motion) the study covers all possible scenarios of ship’s surge, including crash-ahead, crash-back, and astern motions. Conventional maneuvering models cannot handle motions other than forward advancement due to the absence of propeller data in all four quadrants of hydrodynamic performance map. This study proposes an approach for predicting submarine performance in all these surge conditions by utilizing four-quadrant propeller performance and resistance test data. We developed an in-house code, SMot4QP, to simulate ship speed and position in the time domain. We obtained satisfying results for the straight-ahead and crash-ahead motions, while the crash-back and astern maneuvers require further refinement due to propeller wake interaction with the hull. The proposed method is capable of predicting the motions of all types of vessels using the ship’s resistance and four-quadrant propeller test results. Thus, SMot4QP offers a fast and robust alternative to computationally expensive free-running self-propulsion simulations for operational performance prediction in broader naval applications.

Numerical Investigations on Wake Effects of Fish Cages

Abstract A typical fish farm in Norway usually consists of 6 to 12 fish cages, and these fish cages are moored together in a grid shape. Due to wake effects, individual fish cages may experience different flow velocities depending on their positions in the fish farm. Hereby, the drag forces on individual fish cages can be different. The drag forces on the downstream fish cages are difficult to be estimated without knowing the exact flow velocity, which will lead to challenges with the mooring system design. In this study, the computational fluid dynamic (CFD) method combined with a porous media model is employed to investigate the wake effects on the fish farm. The flow field through the fish cages and the drag forces on the downstream fish cages are investigated and discussed.

Classical dynamics of vortex solitons from perturbative scattering amplitudes

We introduce a novel point-particle effective description of ANO vortex solitons in the critical Abelian Higgs Model (AHM) in d = 2 + 1 based on the small winding expansion. Identifying the effective vortices with the elementary quanta of a complex scalar field, relativistic vortex-vortex scattering amplitudes are calculated as a diagrammatic, perturbative expansion in the winding number N. Making use of powerful techniques recently developed for analyzing the post-Minkowskian two-body problem in general relativity, we efficiently extract the contribution to the loop integrals from the classical potential region, with the resulting velocity expansion subsequently resummed to all orders. The main result of this paper is an analytic expression for the classical, vortex-vortex potential at O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(N2), or one-loop, with exact velocity dependence. By truncating the resulting effective Hamiltonian at O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(p2) we derive an analytic, perturbative expression for the metric on the 2-vortex moduli space. Finally, the emergence of the critical AHM from the classical limit of the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 supersymmetric AHM, and the resulting constraints on the point-particle EFT is described in detail using an on-shell superspace construction for BPS states in d = 2 + 1.

Wide-binary Stars Formed in the Turbulent Interstellar Medium

The ubiquitous interstellar turbulence regulates star formation and the scaling relations between the initial velocity differences and the initial separations of stars. We propose that the formation of wide binaries with initial separations r in the range ∼103 au ≲ r ≲ 105 au is a natural consequence of star formation in the turbulent interstellar medium. With the decrease of r, the mean turbulent relative velocity v tur between a pair of stars decreases, while the largest velocity v bon at which they still may be gravitationally bound increases. When v tur < v bon, a wide binary can form. In this formation scenario, we derive the eccentricity distribution p(e) of wide binaries for an arbitrary relative velocity distribution. By adopting a turbulent velocity distribution, we find that wide binaries at a given initial separation generally exhibit a superthermal p(e), irrespective of the exact turbulent velocity scaling. This provides a natural explanation for the observed superthermal p(e) of the wide binaries in the solar neighborhood.

Azimuthal seismic reflection characteristics with quality factor Q in viscoelastic horizontal transverse isotropic media

Abstract In seismic exploration, a precise description of the seismic reflection property is critical for reservoir prediction and fluid identification. In the study of seismic wave transmission effects, taking into account both the viscoelastic and anisotropic properties of a medium is compatible with the features of the earth. Moreover, it is advantageous to the characterization of complicated reservoirs. According to the elastic medium foundation and the imaginary component with quality factor Q, seismic reflection properties of viscoelastic media are described in the complex domain. The complex wave number is expressed by phase velocity and Q. The attenuation angle is introduced when the complex wave number is represented by a propagation vector and an attenuation vector. The exact velocity and polarization direction of a viscoelastic medium are expressed using a complex stiffness matrix incorporating Q matrix elements. The quasi-Zoeppritz equation for viscoelastic horizontal transverse isotropic (VHTI) media is derived by using boundary conditions based on the wave function of viscoelastic media. The numerical simulation of reflectivity reveals that the reflection coefficient in a viscoelastic medium is clearly different from that of an elastic medium. Moreover, the difference in reflection coefficient in various orientations has distinct characteristics.

Binary Dynamics through the Fifth Power of Spin at O(G^{2}).

We use a previously developed scattering-amplitudes-based framework for determining two-body Hamiltonians for generic binary systems with arbitrary spin S. By construction this formalism bypasses difficulties with unphysical singularities or higher-time derivatives. This framework has been previously used to obtain the exact velocity dependence of the O(G^{2}) quadratic-in-spin two-body Hamiltonian. We first evaluate the S^{3} scattering angle and two-body Hamiltonian at this order in G, including not only all operators corresponding to the usual worldline operators, but also an additional set due to an interesting subtlety. We then evaluate S^{4} and S^{5} contributions at O(G^{2}) which we confirm by comparing against aligned-spin results. We conjecture that a certain shift symmetry together with a constraint on the high-energy growth of the scattering amplitude specify the Wilson coefficients for the Kerr black hole to all orders in the spin and confirm that they reproduce the previously obtained results through S^{4}.

Convergence analysis of pressure reconstruction methods from discrete velocities

Magnetic resonance imaging allows the measurement of the three-dimensional velocity field in blood flows. Therefore, several methods have been proposed to reconstruct the pressure field from such measurements using the incompressible Navier–Stokes equations, thereby avoiding the use of invasive technologies. However, those measurements are obtained at limited spatial resolution given by the voxel sizes in the image. In this paper, we propose a strategy for the convergence analysis of state-of-the-art pressure reconstruction methods. The methods analyzed are the so-called Pressure Poisson Estimator (PPE) and Stokes Estimator (STE). In both methods, the right-hand side corresponds to the terms that involving the field velocity in the Navier–Stokes equations, with a piecewise linear interpolation of the exact velocity. In the theoretical error analysis, we show that many terms of different order of convergence appear. These are certainly dominated by the lowest-order term, which in most cases stems from the interpolation of the velocity field. However, the numerical results in academic examples indicate that only the PPE may profit of increasing the polynomial order, and that the STE presents a higher accuracy than the PPE, but the interpolation order of the velocity field always prevails. Furthermore, we compare the pressure estimation methods on real MRI data, assessing the impact of different spatial resolutions and polynomial degrees on each method. Here, the results are consistent with the academic test cases in terms of sensitivity to polynomial order as well as the STE showing to be potentially more accurate when compared to reference pressure measurements.

Dynamic effects of nuclear surface in isoscalar dipole modes

Dynamic surface effects in the isoscalar dipole modes of heavy nuclei are studied within a semiclassical model based on the solution of the Vlasov kinetic equation for finite Fermi systems with a moving surface. The isoscalar dipole strength function and the velocity field associated with the isoscalar dipole modes obtained in previous papers using the semiclassical model are considered in the dynamic-surface approximation, which takes into account only the part of the variation of the phase-space distribution function caused by the dynamic surface. It is found that the dynamic surface effects have an essential influence on the features of the isoscalar dipole modes. The isoscalar dipole strength function has a two-resonance structure already in the dynamic-surface approximation, and the centroid energies of both the low-energy resonance and the high-energy resonance are close to corresponding centroid energies of exact strength function. Calculations of the velocity field in the dynamic-surface approximation show the vortex character of the low-energy isoscalar dipole resonance and the compression character of the high-energy one, which are similar to the corresponding exact velocity fields.

Dissipation factor and phase velocity approximate formulas for P-waves in fluid-saturated porous media

Actual sedimentary rocks are generally homogeneous porous media saturated by fluid, which are described by poroelastic media. Wave velocity and dissipation factor in poroelastic media provide essential information about rock and fluid properties and are widely used in many fields. The exact wave velocity and dissipation factor can be obtained from wavenumbers determined by dispersion equation through complex mathematic operations. Reported approximate formulas are most given under the assumption that the characteristic angular frequency (ωc ) is far larger than the angular frequency (ω) and becomes invalid for high frequency. Thus, this paper derived phase velocity and dissipation factor approximation of the two P-waves in poroelastic media for the whole low-frequency range. Based on the Geertsma–Smit approximation, we modified the infinite-frequency limiting velocity for fast P-wave approximation and removed the ω/ωc <<1 assumption for slow P-wave approximation. Numerical analysis shows that the proposed approximate formulas for P-waves in porous media can reveal the exact variations of phase velocity and dissipation factor in the low-frequency range, which is from zero frequency for isotropic media to the characteristic frequency. Phase velocity approximations of the two P-waves in poroelastic media are very close to exact values, with maximum relative errors being far less than 1%.

Estimation of Vehicle Longitudinal Velocity with Artificial Neural Network

Vehicle dynamics control systems have a fundamental role in smart and autonomous mobility, where one of the most crucial aspects is the vehicle body velocity estimation. In this paper, the problem of a correct evaluation of the vehicle longitudinal velocity for dynamic control applications is approached using a neural networks technique employing a set of measured samples referring to signals usually available on-board, such as longitudinal and lateral acceleration, steering angle, yaw rate and linear wheel speed. Experiments were run on four professional driving circuits with very different characteristics, and the vehicle longitudinal velocity was estimated with different neural network training policies and validated through comparison with the measurements of the one acquired at the vehicle's center of gravity, provided by an optical Correvit sensor, which serves as the reference (and, therefore, exact) velocity values. The results obtained with the proposed methodology are in good agreement with the reference values in almost all tested conditions, covering both the linear and the nonlinear behavior of the car, proving that artificial neural networks can be efficiently employed onboard, thereby enriching the standard set of control and safety-related electronics.

Field-driven domain wall motion in ferrimagnetic nanowires

The fascinating high-speed field-driven domain wall (DW) motion along ferrimagnetic nanowires near the angular momentum compensation point (AMCP) is solved based on the generic ferrimagnetic dynamics. The physics of the absences of precessional torque and infinite high Walker breakdown field at the AMCP is proved under general conditions. Based on the energy conservation principle, an almost exact DW velocity formula, valid beyond the Walker breakdown field, is obtained. Our results agree with all existing experiments and simulations. This theory provides useful guidances to DW manipulation.

Adaptive Neural Network Output Feedback Control of Uncertain Underactuated Systems With Actuated and Unactuated State Constraints

Underactuated systems are widely applied in industry, construction, manufacturing, etc., and the complex working environment puts forward higher demands for safety and transient performance. Hence, it is necessary to consider how to simultaneously ensure actuated and unactuated motion constraints by fewer control inputs, especially when systems suffer from model uncertainties, unavailable velocities, etc. Unfortunately, it is still a significant challenge to overcome in real applications and theoretical analysis. Additionally, most existing studies merely consider the specific control objects and few general methods are applicable to a class of underactuated systems. To this end, we design a new adaptive output-feedback controller for a class of uncertain underactuated systems. Compared with existing methods only handling actuated constraints, an important merit of this article is that by introducing the elaborately designed coupling term composed of actuated and unactuated constraints together, all state variables are kept within the preset time-variant ranges and converge to their desired values. Furthermore, a new Lyapunov function candidate is utilized to provide a theoretical guarantee. As far as we know, without the need of exact model knowledge and velocity feedback, this article provides the first solution to achieve accurate motion control and state constraints for both actuated and unactuated variables, which is meaningful both theoretically and practically. Meanwhile, the asymptotic stability of the equilibrium point for the closed-loop system is proven by utilizing Lyapunov techniques and Barbalat’s lemma. For verification, the presented controller is applied to underactuated overhead and rotary cranes, respectively, together with detailed theoretical analysis and experimental validations.

Reflection seismic-based imaging of meandering channels of Lower Indus Plain using wavelet transform-based density-porosity hydro-geophysical simulations: Implications on water exploration

Water-bearing meandering channel streams (MCS) are very attractive targets for the exploration of fresh drinking water for meeting the demands of human needs. There are various techniques that are used for the exploration and management of water-bearing reservoirs. Seismic reflection data (SRD) is an effective method used in groundwater exploration. SRD is the product of density and velocity information, which are hidden inside this data. The sub-surface layers of the earth’s crust have specific tuning frequency contents, which can be used to predict the exact density, velocity, thicknesses, and porosity of the water-bearing reservoirs. The clean, sandstone-filled, water-bearing channels have a better quality of water compared to the shale- and clay-filled zones. Therefore, the discrimination of this reservoir facies becomes difficult using the SRD. This study utilizes the seismic reflection method for the exploration of water-bearing zones at depths of 25 to 65 m for a confined aquifer inside the Miano area, Lower Indus Platform (LIP), Pakistan. The wavelet-transform-based density-porosity and velocity-porosity hydro-geophysical simulations (WDVHS) are used as a key exploration tools for the quantitative prediction of the water-bearing stratigraphic trap. The full spectrum (bandlimited) seismic amplitudes do not have the tuning frequency contents, which could be used for the quantitative prediction of the exact density and velocity of the channel stream. The WDVHS has predicted the quantitative attributes of this confined aquifer. The least angle of the sandstone lens’s layer implicates the equilibrium position of the hydraulic head. The water table was present at a depth of 8 m. The clean, water-bearing sandstones have the lowest densities of 1.2, 1.5, and 2 g/c.c. and a porosity of 20 to 30%. Shale-clay-filled impure sediments have a density of 2.3 g/cc and < 10% porosity. The total thickness of this confined aquifer was 29.8 m, which has the least velocity of 554, 1024, and 1494 m/s for clean water-bearing sandstones and 3372 m/s for impurities in shale or clay-filled sediments. This study can be used for drilling exploratory wells for water exploration inside the LIP and world-leading water zones.

Classical physics from amplitudes on curved backgrounds

We generalise the Kosower-Maybee-O’Connell (KMOC) formalism relating classical observables and scattering amplitudes to curved backgrounds. We show how to compute the final semiclassical state for a particle moving in a curved background in terms of scattering amplitudes on that background. Two-point amplitudes in this framework correspond to conservative physics with background-dependent memory effects. As an application, we consider plane wave and shock wave backgrounds both in electromagnetism and general relativity. We determine the final semiclassical state, showing it satisfies a notion of double copy on curved backgrounds. We then conclude by computing the impulse of a particle on such backgrounds, deriving exact results and velocity memory effects.

Analytical solutions of PDEs by unique polynomials for peristaltic flow of heated Rabinowitsch fluid through an elliptic duct

In this research, we have considered the convective heat transfer analysis on peristaltic flow of Rabinowitsch fluid through an elliptical cross section duct. The Pseudoplastic and Dilatant characteristics of non-Newtonian fluid flow are analyzed in detail. The Rabinowitsch fluid model shows Pseudoplastic fluid nature for sigma > 0 and Dilatant fluid behaviour for sigma < 0. The governing equations are transformed to dimensionless form after substituting pertinent parameters and by applying the long wavelength approximation. The non-dimensional momentum and energy equations are solved analytically to obtain the exact velocity and exact temperature solutions of the flow. A novel polynomial of order six having ten constants is introduced first time in this study to solve the energy equation exactly for Rabinowitsch fluid flow through an elliptic domain. The analytically acquired solutions are studied graphically for the effective analysis of the flow. The flow is found to diminish quickly in the surrounding conduit boundary for Dilatant fluid as compared to the Pseudoplastic fluid. The temperature depicted the opposite nature for Pseudoplastic and Dilatant fluids. The flow is examined to plot the streamlines for both Pseudoplastic and Dilatant fluids by rising the flow rate.

Analysis of Pressure-Robust Embedded-Hybridized Discontinuous Galerkin Methods for the Stokes Problem Under Minimal Regularity

We present analysis of two lowest-order hybridizable discontinuous Galerkin methods for the Stokes problem, while making only minimal regularity assumptions on the exact solution. The methods under consideration have previously been shown to produce \(H(\text {div})\)-conforming and divergence-free approximate velocities. Using these properties, we derive a priori error estimates for the velocity that are independent of the pressure. These error estimates, which assume only \(H^{1+s}\)-regularity of the exact velocity fields for any \(s \in [0, 1]\), are optimal in a discrete energy norm. Error estimates for the velocity and pressure in the \(L^2\)-norm are also derived in this minimal regularity setting. Our theoretical findings are supported by numerical computations.

Convolutional neural network-based moment tensor inversion using domain adaptation for microseismicity monitoring

Microseismic monitoring is widely used to analyze the locations and growth directions of fractures formed at sites of hydraulic fracturing treatment and CO2 geologic sequestration. Because moment tensors can provide focal mechanisms, moment tensor inversion has received considerable attention in microseismic monitoring; the real-time processing of moment tensor inversion is important for rapid decision-making. Pre-trained machine learning (ML) models can make nearly instantaneous predictions in the application stage and thus present an attractive alternative to real-time processing. However, prior information regarding the velocity model at the target site is a prerequisite for generating the dataset used to train the ML model that is applied in moment tensor inversion. In addition, it is difficult to create the training dataset because it requires three-dimensional numerical modelling when the velocity model is complex; numerous simulations must be executed for sources with various locations and moment tensors. To overcome these limitations, we applied the domain adaptation technique to the convolutional neural network (CNN)-based moment tensor inversion method, which uses peak amplitudes and arrival times of P- and S-waves as input features. The CNN model was pre-trained with the dataset generated from a homogeneous velocity model. Then, in the domain adaptation stage, the pre-trained model was fine-tuned along with the target dataset. To validate the performance of the domain adaptation, moment tensors from both horizontal and tilted three-layer models were predicted. In each case, the domain-adapted model performance was similar to the performances of the CNN-based models that had been trained using the dataset generated with the exact target velocity models.