Integration Scheme Research Articles

Simplified conservative discretization of the Cahn-Hilliard-Navier-Stokes equations

In this paper we construct a novel discretization of the Cahn-Hilliard equation coupled with the Navier-Stokes equations. The Cahn-Hilliard equation models the separation of a binary mixture. We construct a very simple time integration scheme for simulating the Cahn-Hilliard equation, which is based on splitting the fourth-order equation into two second-order Helmholtz equations. We combine the Cahn-Hilliard equation with the Navier-Stokes equations to simulate phase separation in a two-phase fluid flow in two dimensions. The scheme conserves mass and momentum and exhibits consistency between mass and momentum, allowing it to be used with large density ratios. We introduce a novel discretization of the surface tension force from the phase-field variable that has finite support around the transition region. The model has a parameter that allows it to transition from a smoothed continuum surface force to a fully sharp interface formulation. We show that our method achieves second-order accuracy, and we compare our method to previous work in a variety of experiments.

Multi-step Hermite-Birkhoff predictor-corrector schemes

In this study, we introduce a multi-step multi-derivative predictor-corrector time integration scheme analogous to the schemes in Schütz et al. (2022) [13], incorporating a multi-step quadrature rule. We conduct stability analysis up to order eight and optimize the schemes to achieve A(α)-stability for large α. Numerical experiments are performed on ordinary differential equations exhibiting diverse stiffness conditions, as well as on partial differential equations showcasing non-linearity and higher-order terms. Results demonstrate the convergence and flexibility of the proposed schemes across diverse situations.

Конечно-элементное моделирование нелинейных задач упругости в абсолютных узловых координатах на неструктурированных шестигранных сетках

We consider a finite element approach to solving the problem of elasticity theory in terms of absolute nodal coordinate formulation (ANCF), in which large body displacements are described in a global reference frame without using any local coordinate system. The main feature of the method is the absence of gyroscopic effects and, as a result, constancy of the mass matrix and the vector of the generalized force of gravity. In contrast to the traditional ANCF approach, the sets of nodal degrees of freedom of the finite element are formed only on the basis of absolute coordinates of nodes, which allows us to solve the problem using, in particular, unstructured hexahedral meshes. To construct the stiffness matrix, we apply a second-order automatic differentiation algorithm, which ensures its symmetrical form (Hessian matrix) and is analytically accurate in calculating the derivative. This approach also makes it possible to carry out calculations for models of hyperelastic materials without the corresponding Piola-Kirchhoff tensor. It has been shown that within the framework of discretization of the equation of motion, along with the well-known Newmark numerical integration scheme, it is possible to use the HTT-α scheme, which is unconditionally stable, second-order accurate and dissipative for high frequencies. We present several examples of solving static and dynamic elasticity problems for compressible and incompressible models of hyperelastic materials, in which the functions of internal energy density of the body are specified in terms of the deformation gradient.

Impact of multiple slips and thermal radiation on heat and mass transfer in MHD Maxwell hybrid nanofluid flow over porous stretching sheet

This study investigates the two-dimensional magnetohydrodynamic (MHD) boundary-layer flow over a stretching sheet embedded in a porous medium, focusing on the innovative use of hybrid nanofluids. The research has practical applications in heat exchangers, nanofluid technology, porous media, and MHD systems. Key governing parameters, including internal heat sources/sinks, multiple slips, and thermal radiation, are analyzed for their impact on the flow. The nanofluid consists of hybridized nanoparticles (Alumina-Magnetite) dispersed in a water and ethylene glycol mixture (WEG-50:50). Assuming steady-state, incompressible, and laminar flow with small boundary layer thickness and constant nanofluid properties, the governing equations for continuity, momentum, energy, and species concentration are formulated. The fluid is modeled as a non-Newtonian (Maxwell) fluid. The resulting nonlinear ordinary differential equations system, with specified boundary conditions, is solved using the Runge-Kutta integration scheme implemented in MAPLE 23. Numerical results of heat transfer rates are validated against existing data, showing a 12 % increase in the Nusselt number for the WEG-Al2O3 nanofluid and a 20 % increase for the hybrid WEG- Al2O3–Fe3O4 nanofluid. It is demonstrated that skin friction decreases by up to 15 % with increased thermal Grashof number and that the Nusselt number can be reduced by up to 10 % due to magnetic effects. Overall, hybrid nanofluids generally demonstrate higher Nusselt and Sherwood numbers, enhancing heat transfer efficiency.

Nonlinear dynamic analysis of shear- and torsion-free rods using isogeometric discretization and outlier removal

AbstractIn this paper, we present a discrete formulation of nonlinear shear- and torsion-free rods introduced by Gebhardt and Romero (Acta Mechanica 232(10):3825–3847, 2021) that uses isogeometric discretization and robust time integration. Omitting the director as an independent variable field, we reduce the number of degrees of freedom and obtain discrete solutions in multiple copies of the Euclidean space $$\left( \mathbb {R}^3\right) $$ R 3 , which is larger than the corresponding multiple copies of the manifold $$\left( \mathbb {R}^3 \varvec{\times } S^2\right) $$ R 3 × S 2 obtained with standard Hermite finite elements. For implicit time integration, we choose the same integration scheme as Gebhardt and Romero in (2021) that is a hybrid form of the midpoint and the trapezoidal rules. In addition, we apply a recently introduced approach for outlier removal by Hiemstra et al. (Comput Methods Appl Mech Eng 387:114115, 2021) that reduces high-frequency content in the response without affecting the accuracy, ensuring robustness of our nonlinear discrete formulation. We illustrate the efficiency of our nonlinear discrete formulation for static and transient rods under different loading conditions, demonstrating good accuracy in space, time and the frequency domain. Our numerical example coincides with a relevant application case, the simulation of mooring lines.

A gradient-based optimization algorithm to solve optimal control problems with conformable fractional-order derivatives

In this paper, we solve numerically a class of fractional optimal control problems in the conformable sense. We first propose a nonlinear fractional optimal control problem subject to general equality and inequality constraints. Then, based on a novel numerical integration scheme, we present a discretization method for the governed fractional-order system as well as the cost and constraint functionals, which yields a discretized approximate problem. We further derive the gradients of the cost and constraint functionals in regard to the discretized controls. On the basis of this result, a numerical optimization approach to solve the approximate problem is developed. Finally, three non-trivial example problems are solved to illustrate the applicability and effectiveness of the developed approach.

An Integrated Quality Inspection Scheme for Updated Basic Geographic Data Results in DWG and SHP Formats

An Integrated Quality Inspection Scheme for Updated Basic Geographic Data Results in DWG and SHP Formats

Rocking block simulation based on numerical dissipation.

In this paper, a computational approach based on numerical dissipation is proposed to simulate rocking blocks. A rocking block is idealized as a solid body interacting with its foundation through a contact-based formulation. An implicit time integration scheme with numerical dissipation, set to optimally treat dissipation in contact problems, is employed. The numerical dissipation is ruled by the time step and the rocking dissipative phenomenon at impacts is accurately predicted without any damping model. A broad numerical campaign is conducted to define a regression law in analytic form for the setting of the time step, depending on the block size and aspect ratio, the contact stiffness, as well as the coefficient of restitution selected. The so-obtained regression law appears accurate and an a posteriori validation with cases not in the training dataset confirms the effectiveness of the approach. Finally, the comparison with available experimental tests highlights the approach efficacy for free rocking and harmonic loading cases (in a deterministic sense), and for earthquake-like loading cases (in a statistical sense). It is found that rocking blocks with sizes of interest for structural engineering (e.g., cultural heritage structures) can be simulated with time steps within 10-3 ÷ 10-1s, so allowing very fast computations.

Online and Offline Integration Scheme of College English Education Under Big Data Technology

How to use big data technology to promote the integration and complementarity of English online education and offline education has become an urgent problem in the field of higher education. This paper mainly studies the integration and complementary strategies of online and offline English education in higher vocational colleges based on big data technology. This paper first analyzes the current situation of English teaching in higher vocational colleges, then discusses the application of big data technology in online English education in higher vocational colleges and puts forward relevant strategies of integration and complementarity. Finally, it expounds the important role of big data technology in promoting the integration and complementarity of online and offline English education in higher vocational colleges. In the future, we can further strengthen the application depth and breadth of big data technology in higher education, so as to promote the reform and development of English teaching in higher vocational colleges and improve the teaching quality.

Scalable and adaptable tactile sensor array with island-bridge-form sensing units for multi-directional stimuli recognition

Multiple mechanical stimuli recognition ability with direction discrimination function is of importance for a tactile sensor. However, typical multi-directional tactile sensor needs complex analysis to classify ambiguous output signals because of the nonspecific response. Besides, conventional sensor array layout with separate output ports for each sensor unit limits the integration and adaptability of the sensor system. This work proposes a novel sensor array configuration with island-bridge-form sensing units to isolate pressure and shear loading. Meanwhile, the reasonable integration scheme with specially-designed circuit effectively reduces the total output ports and data acquisition cost, capable of scaling up the sensor array according to application scenarios easily. A series of experiments and analysis from the characterization of sensing units to real-time recording of multiple mechanical stimuli are conducted, showing the independent, timely and high-sensitivity response of the tactile sensor array, exhibiting the application potential in human–machine interaction, wearable electronics and soft robotics.

Projective integration methods in the Runge–Kutta framework and the extension to adaptivity in time

Projective Integration methods are explicit time integration schemes for stiff ODEs with large spectral gaps. In this paper, we show that all existing Projective Integration methods can be written as Runge–Kutta methods with an extended Butcher tableau including many stages. We prove consistency and order conditions of the Projective Integration methods using the Runge–Kutta framework. Spatially adaptive Projective Integration methods are included via partitioned Runge–Kutta methods. New time adaptive Projective Integration schemes are derived via embedded Runge–Kutta methods and step size variation while their accuracy, stability, convergence, and error estimators are investigated analytically and numerically.

Lucas decomposition and extrapolation methods for the evaluation of infinite integrals involving the product of three Bessel functions of arbitrary order

A method to efficiently evaluate integrals containing the product of three Bessel functions of the first kind and of any non negative real order is presented. The numerical problem is particularly challenging since standard integration techniques are completely unsuccessful in integrating such anomalously oscillating (and possibly slow decaying) functions. The proposed method is based on a decomposition of such a product into a sum of functions which asymptotically approach sinusoidal functions, for which integration schemes based on integration then summation procedures followed by extrapolation methods can be applied. Different extrapolation procedures are compared in order to identify the most efficient extrapolation strategy. Several numerical examples and comparisons with known analytic results are provided to show the robustness and the accuracy of the proposed approach and to help in identifying the most efficient and reliable extrapolation scheme. Particular attention is given to a class of integrals emerging in many fields of physics, in particular in quantum mechanics and particle physics, showing that the proposed method can be even more efficient (sometimes hundred of times faster) than the available analytical formulas.

Simplicits: Mesh-Free, Geometry-Agnostic Elastic Simulation

The proliferation of 3D representations, from explicit meshes to implicit neural fields and more, motivates the need for simulators agnostic to representation. We present a data-, mesh-, and grid-free solution for elastic simulation for any object in any geometric representation undergoing large, nonlinear deformations. We note that every standard geometric representation can be reduced to an occupancy function queried at any point in space, and we define a simulator atop this common interface. For each object, we fit a small implicit neural network encoding spatially varying weights that act as a reduced deformation basis. These weights are trained to learn physically significant motions in the object via random perturbations. Our loss ensures we find a weight-space basis that best minimizes deformation energy by stochastically evaluating elastic energies through Monte Carlo sampling of the deformation volume. At runtime, we simulate in the reduced basis and sample the deformations back to the original domain. Our experiments demonstrate the versatility, accuracy, and speed of this approach on data including signed distance functions, point clouds, neural primitives, tomography scans, radiance fields, Gaussian splats, surface meshes, and volume meshes, as well as showing a variety of material energies, contact models, and time integration schemes.

Seeking Efficiency for the Accurate Draping of Digital Garments in Production.

Digital garments are set to revolutionize the apparel industry in the way we design, produce, market, sell and try-on real garments. But for digital garments to play a central role, from designer to consumer, they must be a faithful digital replica of their real counterpart: a digital twin. Yet, most industry-grade tools used in the apparel industry do not focus on accuracy, but rather on producing fast and plausible drapes for interactive editing and quick feedback, thus limiting the value and the potential of digital garments. The key to accuracy lies in using the proper underlying simulation technology, well documented in the academic literature but historically sidelined in the apparel industry in favor of simulation speed. In this paper, we describe our industry-grade cloth simulation engine, built with a strong focus on accuracy rather than sheer speed. Using a global integration scheme and adopting state of the art simulation practices from the Computer Graphics field, we evaluate a wide range of algorithms to improve its convergence and overall performance. We provide qualitative and quantitative insights on the cost and capabilities of each of these features, with the aim of giving valuable feedback and useful guidelines to practitioners seeking to implement an accurate and robust draping simulator.

Calibrating Car-Following Models Using SUMO-in-the-Loop and Vehicle Trajectories From Roadside Radar

This paper presents an innovative calibration method for car-following (CF) models in the Simulation of Urban MObility (SUMO) using real-world trajectory data from a 1.5 km signalized urban corridor, captured by roadside radars. By applying a sophisticated track-level association and fusion methodology, the study extends trajectory analysis beyond individual radar fields of view. The enhanced data is then utilized to refine the Krauss, IDM, and W99 CF models within SUMO, addressing the literature gap by integrating SUMO into the calibration loop, thereby accommodating the simulator's integration scheme and any model adaptations. The research identifies that default SUMO models tend to exhibit shorter time headways compared to real-world data, with calibration effectively reducing this discrepancy. Moreover, the W99 model, despite its unrealistic acceleration profiles when calibrated without considering acceleration, most accurately captures the higher-end energy consumption distribution. Conversely, the IDM model, with its default parameters, provides the closest approximation to observed acceleration behaviors, highlighting the nuanced performance of CF models in traffic simulation and their implications for energy consumption estimation. Detailed results of optimized parameters for each CF model are provided in appendix in addition to distribution information that may be useful for other modelers to use directly or other datasets to be compared in the future (including expansion of the work to include vehicle classification).

Latin American regionalism and integration in the ongoing process of hegemonic transition

When observing the critical balance of Latin America and the Caribbean (LAC) in the 21st century, caught between the withdrawal of the United States and the rise of China in the global and regional political and economic stage, one cannot but wonder on what course the processes of regional integration and regionalism will follow in Latin America and the Caribbean in this context. Our hypothesis is that regionalism and the processes of regional integration cannot be understood as “autonomist” processes—that is, as mere processes of facilitating consensus between different regional political actors—but must rather be perceived as a convergence with extraregional hegemonic powers, even amidst an absolute ideological diversity. Therefore, this work looks into the changes taking place within regionalism and the schemes of regional integration led by the Organization of American States (OAS) and the Community of Latin American and Caribbean States (CELAC) in the face of the ongoing anomalous and interstitial process of hegemonic transition from the United States to China that appears to be taking place; these are, undoubtedly, the extraregional references shaping LAC regionalism in the 21st century.

Maximum bound principle preserving additive partitioned Runge-Kutta schemes for the Allen-Cahn equation

In this paper, a novel framework for constructing the temporal high-order numerical schemes that inherit the maximum bound principle (MBP) of the Allen-Cahn equation is proposed. The original Allen-Cahn equation is converted into an equivalent system by introducing an auxiliary variable. Based on the new system, we put forward and analyze high-order (up to the fourth-order) additive partitioned Runge-Kutta (APRK) schemes for the time integration of the Allen-Cahn equation, which satisfies the discrete MBP under reasonable time step constraints. A simple sufficient condition is also given to ensure that a class of APRK methods preserves the discrete MBP and that the resulting scheme is linearly implicit. The convergence order in the discrete L∞-norm is further provided by utilizing the established discrete MBP, which plays a vital role in the analysis. Several numerical experiments are carried out to validate our theoretical results.

Machine learning for the identification of phase transitions in interacting agent-based systems: A Desai-Zwanzig example.

Deriving closed-form analytical expressions for reduced-order models, and judiciously choosing the closures leading to them, has long been the strategy of choice for studying phase- and noise-induced transitions for agent-based models (ABMs). In this paper, we propose a data-driven framework that pinpoints phase transitions for an ABM-the Desai-Zwanzig model-in its mean-field limit, using a smaller number of variables than traditional closed-form models. To this end, we use the manifold learning algorithm Diffusion Maps to identify a parsimonious set of data-driven latent variables, and we show that they are in one-to-one correspondence with the expected theoretical order parameter of the ABM. We then utilize a deep learning framework to obtain a conformal reparametrization of the data-driven coordinates that facilitates, in our example, the identification of a single parameter-dependent ordinary differential equation(ODE) in these coordinates. We identify this ODE through a residual neural network inspired by a numerical integration scheme (forward Euler). We then use the identified ODE-enabled through an odd symmetry transformation-to construct the bifurcation diagram exhibiting the phase transition.

Optical solitons for the concatenation model with power–law of self–phase modulation by lie symmetry

This paper investigates the concatenation model under the influence of power-law self-phase modulation through the Lie symmetry. We employ two integration schemes, namely the extended tanh approach and the F-expansion algorithm, to rigorously integrate the reduced ordinary differential equations governing the system. Through this methodological framework, we uncover a diverse array of soliton solutions and systematically classify them, shedding light on their intricate dynamics and characteristics. Our research unveils previously undiscovered soliton solutions, enriching the existing understanding of concatenation models. We introduce a comprehensive classification scheme for these solitons, providing valuable insights into their behavior and interactions. Numerical simulations validate the stability and persistence of the identified soliton solutions across various parameter regimes. Our findings contribute to the theoretical framework of nonlinear wave dynamics and hold potential for innovative applications in fields such as nonlinear optics and information processing.

Simulation of impacts between spherical rigid bodies with frictional effects

AbstractThis work studies the impact between spherical rigid bodies in the frame of nonsmooth contact dynamics considering friction effects. A new impact element formulation based on the classical instantaneous local Newton impact law is presented. The kinematics properties of the spheres are described by a rigid body formulation with translational and rotational degrees of freedom referred to an inertial frame. In addition, an extension of the nonsmooth generalized‐ time integration scheme applied to collisions with multiple impacts including Coulomb's friction law is given. Six numerical examples are presented to evaluate the robustness and the performance of the proposed methodology.