Momentum Preserving Research Articles

Mass, momentum and energy preserving FEEC and broken-FEEC schemes for the incompressible Navier–Stokes equations

Abstract In this article we propose two finite-element schemes for the Navier–Stokes equations, based on a reformulation that involves differential operators from the de Rham sequence and an advection operator with explicit skew-symmetry in weak form. Our first scheme is obtained by discretizing this formulation with conforming FEEC (Finite Element Exterior Calculus) spaces: it preserves the point-wise divergence free constraint of the velocity, its total momentum and its energy, in addition to being pressure robust. Following the broken-FEEC approach, our second scheme uses fully discontinuous spaces and local conforming projections to define the discrete differential operators. It preserves the same invariants up to a dissipation of energy to stabilize numerical discontinuities. For both schemes we use a middle point time discretization that preserve these invariants at the fully discrete level and we analyze its well-posedness in terms of a CFL condition. While our theoretical results hold for general finite elements preserving the de Rham structure, we consider one application to tensor-product spline spaces. Specifically, we conduct several numerical test cases to verify the high order accuracy of the resulting numerical methods, as well as their ability to handle general boundary conditions.

Honeycomb-configured dissipative nanofluid flow within a squeezed channel with entropy generation: regression and numerical evaluations

PurposeNanosized honeycomb-configured materials are used in modern technology, thermal science and chemical engineering due to their high ultra thermic relevance. This study aims to scrutinize the heat transmission features of magnetohydrodynamic (MHD) honeycomb-structured graphene nanofluid flow within two squeezed parallel plates under Joule dissipation and solar thermal radiation impacts.Design/methodology/approachMass, energy and momentum preservation laws are assumed to find the mathematical model. A set of unified ordinary differential equations with nonlinear behavior is used to express the correlated partial differential equations of the established models, adopting a reasonable similarity adjustment. An approximate convergent numerical solution to these equations is evaluated by the shooting scheme with the Runge–Kutta–Fehlberg (RKF45) technique.FindingsThe impression of pertinent evolving parameters on the temperature, fluid velocity, entropy generation, skin friction coefficients and the heat transference rate is explored. Further, the significance of the irreversibility nature of heat transfer due to evolving flow parameters are evaluated. It is noted that the heat transference rate performance is improved due to the imposition of the allied magnetic field, Joule dissipation, heat absorption, squeezing and thermal buoyancy parameters. The entropy generation upsurges due to rising magnetic field strength while its intensification is declined by enhancing the porosity parameter.Originality/valueThe uniqueness of this research work is the numerical evaluation of MHD honeycomb-structured graphene nanofluid flow within two squeezed parallel plates under Joule dissipation and solar thermal radiation impacts. Furthermore, regression models are devised to forecast the correlation between the rate of thermal heat transmission and persistent flow parameters.

CFD Investigation of a Co-Flow Nozzle for Cold Spray Additive Manufacturing Applications

This current work evaluates the efficacy of a co-flow nozzle for cold spray applications with the aim of mitigating nozzle clogging issues, which can occur during long-duration operations, by replacing the solid wall of a divergent nozzle section with an annular co-flow fluid boundary. Simulations were conducted on high-pressure nitrogen flowing through convergent–divergent (C–D) axisymmetric nozzles, with a stagnation pressure of 6 MPa and a stagnation temperature of 1273 K. In these simulations, Inconel 718 particles of varying sizes (15 µm to 35 µm) were modeled using a 2-way Lagrangian technique, and the model’s accuracy was confirmed through validation against experimental results. An annular co-flow nozzle with a circular cross section and straight passage covering the primary C–D nozzle has been designed and modeled for cold spray application. Co-flow was introduced to the reduced nozzle length to compensate for particle velocity loss at higher operating conditions. It was found that co-flow facilitates momentum preservation for primary flow by providing an annular gas boundary, resulting in increased particle speed for a longer axial distance beyond the nozzle exit of the reduced divergent length nozzle. The particle acceleration performance of the reduced divergent section nozzle, when combined with co-flow, is comparable to the original length nozzle.

Sisko nanofluid flow through exponential stretching sheet with swimming of motile gyrotactic microorganisms: An application to nanoengineering

Abstract The swimming of motile gyrotactic microorganism’s phenomenon has recently become one of the most important topics in research due to its applicability in biotechnology, many biological systems, and numerous engineering fields. The gyrotactic microorganisms improve the stability of the nanofluids and enhance the mass/heat transmission. This research investigates the MHD fluid flow of a dissipative Sisko nanofluid containing microorganisms moving along an exponentially stretched sheet in the current framework. The mathematical model comprises equations that encompass the preservation of mass, momentum, energy, nanoparticle concentration, and microorganisms. The equations that govern are more complicated because of nonlinearity, and therefore to obtain the combination of ordinary differential equations, similarity transformations are utilized. The numerical results for the converted mathematical model are carried out with the help of the bvp4c solver. The resulting findings are compared to other studies that have already been published, and a high level of precision is found. The graphical explanations for velocity, temperature, and nanoparticles volume fraction distribution are shown with physical importance. Physical characteristics like Peclet number, Sisko fluid parameter, thermophoresis and Brownian motion parameter, and Hartmann number are taken into consideration for their effects. Based on the numerical outcomes, the bioconvection Peclet number enhances the density of mobile microorganisms, whereas thermal radiation contributes to an elevation in temperature. The velocity field decreases with the enhancement of magnetic parameter; however, the temperature field increases with increased magnetic parameter and thermophoresis parameter augmentation. Our numerical findings are ground breaking and distinctive, and they are used in microfluidic devices including micro instruments, sleeve electrodes, and nerve development electrodes. This study has various applications in nanoengineering, including nanomaterial synthesis, drug delivery systems, bioengineering, nanoscale heat transfer, environmental engineering.

Contrasting the Implicit Method in Incoherent Lagrangian and the Correction Map Method in Hamiltonian

The equations of motion for a Lagrangian mainly refer to the acceleration equations, which can be obtained by the Euler–Lagrange equations. In the post-Newtonian Lagrangian form of general relativity, the Lagrangian systems can only maintain a certain post-Newtonian order and are incoherent Lagrangians since the higher-order terms are omitted. This truncation can cause some changes in the constant of motion. However, in celestial mechanics, Hamiltonians are more commonly used than Lagrangians. The conversion from Lagrangianto Hamiltonian can be achieved through the Legendre transformation. The coordinate momentum separable Hamiltonian can be computed by the symplectic algorithm, whereas the inseparable Hamiltonian can be used to compute the evolution of motion by the phase-space expansion method. Our recent work involves the design of a multi-factor correction map for the phase-space expansion method, known as the correction map method. In this paper, we compare the performance of the implicit algorithm in post-Newtonian Lagrangians and the correction map method in post-Newtonian Hamiltonians. Specifically, we investigate the extent to which both methods can uphold invariance of the motion’s constants, such as energy conservation and angular momentum preservation. Ultimately, the results of numerical simulations demonstrate the superior performance of the correction map method, particularly with respect to angular momentum conservation.

Variational Framework for Structure-Preserving Electromagnetic Particle-in-Cell Methods

In this article we apply a discrete action principle for the Vlasov–Maxwell equations in a structure-preserving particle-field discretization framework. In this framework the finite-dimensional electromagnetic potentials and fields are represented in a discrete de Rham sequence involving general finite element spaces, and the particle-field coupling is represented by a set of projection operators that commute with the differential operators. With a minimal number of assumptions which allow for a variety of finite elements and shape functions for the particles, we show that the resulting variational scheme has a general discrete Poisson structure and thus leads to a semi-discrete Hamiltonian system. By introducing discrete interior products we derive a second type of space discretization which is momentum preserving, based on the same finite elements and shape functions. We illustrate our method by applying it to spline finite elements, and to a new spectral discretization where the particle-field coupling relies on discrete Fourier transforms.

Momentum Preserving Simulation of Cooperative Multirotors With Flexible-Cable Suspended Payload

Abstract In this paper, a momentum-preserving integration scheme is implemented for the simulation of single and cooperative multirotors with a flexible-cable suspended payload by employing a Lie group–based variational integrator (VI), which provides the preservation of the configuration manifold and geometrical constraints. Due to the desired properties of the implemented VI method, e.g., symplecticity, momentum preservation, and the exact fulfillment of the constraints, exponentially long-term numerical stability, and good energy behavior are obtained for more accurate simulations of aforementioned systems. The effectiveness of Lie group VI method with the corresponding discrete systems are demonstrated by comparing the simulation results of two example scenarios for the single and cooperative systems in terms of the preserved quantities and constraints, where a conventional fixed-step Runge–Kutta 4 (RK4) and variable-step integrator are utilized for the simulation of continuous-time models. It is shown that the implemented VI method successfully performs the simulations with a long-time stable behavior by preserving invariants of the system and the geometrical constraints, whereas the simulation of continuous-time models by RK4 and variable step are incapable of satisfying these desired properties, which inherently results in divergent and unstable behavior in simulations.

Variational integrators for forced Lagrangian systems based on the local path fitting technique

Variational integrators are particularly suitable for simulation of mechanical systems, where features such as symplecticity and momentum preservation are essential. They also exhibit excellent long-time energy behavior even if external forcing is involved. Motivated by this fact, we present a new approach, that is based on the local path fitting technique, to construct variational integrators for forced mechanical systems. The core technology exploited is to fit the local trajectory as the Lagrange interpolation polynomial by requiring that the forced Euler–Lagrange equations hold at the internal interpolation nodes. This operation also yields the essential terms of the discrete forced Euler–Lagrange equations and consequently formulates the final integrator. This new approach not only avoids numerical quadrature involved in the classical construction, but also significantly improves the precision of the resulting integrator, as illustrated by the given examples.

КВАЗІОДНОВИМІРНА МАТЕМАТИЧНА МОДЕЛЬ ПРОЦЕСІВ В ХОЛЛІВСЬКОМУ ТА ПЛАЗМОВО-ІОННОМУ ДВИГУНІ

Plasma-ion thrusters with a radial magnetic field in ionization chamber and Hall effect thrusters are electrostatic electric propulsion thrusters with closed electron drift. Axial symmetry in the dynamics of the components of propellant in these thrusters allows to write the equations of plasma-dynamics for electrons, ions and neutral atoms in two-dimensional axial-radial form. Attempts to reduce the equations to simpler one-dimensional form by simply removing the components with radius differentiation lead to the loss in the description of important effects, responsible for values of thruster performance. At the same time, a significant disadvantage of gas dynamics equation set is its fundamental openness – the correspondence between the number of unknown variables and equations is achieved approximately basing on some assumptions. In traditional form of gas dynamics, such closeness is made under the assumption of thermodynamic equilibrium with velocity distribution functions of components close to Maxwell one, which is the limit result of collisions. The use of such approximation to plasma components dynamics in electric propulsion thrusters is impossible due to the rarefaction of the substance in them. A mathematical model of two-component plasma-dynamics is represented in stationary form to describe the processes in the Hall effect thruster channel and the ionization chamber of plasma-ion thruster with radial magnetic field. Due to the impossibility of using the method of local thermodynamic equilibrium to describe the rarefied substance in electric propulsion thruster, a more advanced form of equations is used. A more reliable means of approximate closure of the set of equations is proposed in the description of the rarified gas. An approach to the description of the specifics of electrons energy transfer from the plasma to the walls of the channel, as well as the non-mirror reflection of electrons from the potential barrier within the Langmuir layer is shown. A method of averaging the parameters over the cross section of the channel is proposed, which allows to convert the equation into a quasi-one-dimensional form with the preservation of charge, momentum and energy losses on the channel walls.

Time-varying materials in the presence of dispersion: plane-wave propagation in a Lorentzian medium with temporal discontinuity

We study the problem of a temporal discontinuity in the permittivity of an unbounded medium with Lorentzian dispersion. More specifically, we tackle the situation in which a monochromatic plane wave forward-traveling in a (generally lossy) Lorentzian-like medium scatters from the temporal interface that results from an instantaneous and homogeneous abrupt temporal change in its plasma frequency (while keeping its resonance frequency constant). In order to achieve momentum preservation across the temporal discontinuity, we show how, unlike in the well-known problem of a nondispersive discontinuity, the second-order nature of the dielectric function now gives rise to two shifted frequencies. As a consequence, whereas in the nondispersive scenario the continuity of the electric displacement D and the magnetic induction B suffices to find the amplitude of the new forward and backward wave, we now need two extra temporal boundary conditions. That is, two forward and two backward plane waves are now instantaneously generated in response to a forward-only plane wave. We also include a transmission-line equivalent with lumped circuit elements that describes the dispersive time-discontinuous scenario under consideration.

Zoning strategy of zonal modeling for thermally stratified large spaces

Large space buildings play a significant role in modern society because of their environmental advantages and market value. While the zonal model is promising for the efficient and rapid evaluation of the stratified thermal environment, there is a lack of a reasonable and convenient zoning strategy with the advent of modern computing. This paper presents a universal and practical zonal model, in which a simplified momentum equation is applied to consider air momentum preservation, transformation, and dissipation. Hence, the zoning structure is generalized and flexible. Moreover, limiting the dimensionless temperature constraint between adjacent zones establishes the connection between thermal nonuniformity and zoning results automatically. Simultaneously, the dimension and number of zones should be restricted within reasonable ranges to satisfy the characteristics of zonal simulation and reach the criteria of convergence. To further explore and validate the zonal model, a reduced-scale experimental model was constructed to replicate the thermal stratification in a mechanically ventilated large space by considering many crucial realistic factors. A particle image velocimetry (PIV) measurement was then conducted to visualize the airflow pattern and support the partition of zones. The results showed that the zonal simulation with adaptive zoning method can realize a similar accuracy with fewer zones and exhibit a better tolerance for zoning results compared to the conventional empirical zoning method. Furthermore, a case study of an atrium was performed to demonstrate the practicality and efficiency of the method for long-term dynamic simulations of complex thermal environments and building energy use.

A generalized high-order momentum preserving (HOMP) method in the one-fluid model for incompressible two phase flows with high density ratio

Numerical methods for the simulation of two-phase flows based on the common one-fluid model suffer from important transfer of momentum between the two-phases when the density ratio becomes important, such as with common air and water. This problem has been addressed from various numerical frameworks. It principally arises from the hypothesis that the momentum equation can be simplified by subtracting the continuity equation to it. While this approach is correct in a continuous point of view, it however brings numerical errors at the discrete level, from both spatial and temporal points of view, errors that can highly deteriorate the fluids dynamic. Moreover, we have found this problem to be more and more present as the grid is refined. To correct this problem, we propose a High-Order Momentum Preserving (HOMP) method that is, additionally, independent on the interface representation (may it be level set, volume of fluid, etc.). Furthermore, HOMP can be easily implemented in an existing finite volume code. We show that this method permits to efficiently suppress dreadful momentum transfers at the interface on demonstrating examples. We also present how it enhances the quality of two-phase flows computation through the simulation of the dynamic of a breaking wave and the impact of a droplet in a liquid pool.

Elements of bases of mechanics of wood-polymer composites

s. Disclosed is a solution of a particular case of a problem of polycomponent motion within a poly speed model, which is reduced to setting conditions of joint motion of components and determining intercomponent thermal-force interaction. The study of construction of the basis of mechanics of wood-polymer composites from phenomenological positions of mechanics of heterogeneous media is presented by construction of equations of laws of mass and momentum preservation for two component media and their closure by a viscous-elastic-plastic rheological model of the composite material for development of the basis of mechanics of wood-polymer composites from phenomenological positions of mechanics of heterogeneous media, Contributing to improvement of production of structured composite for FDM - printing technologies due to production of composites on the basis of thermopolymers with filling of them with ground wood. Raw materials can be wastes of logging and wood processing industries, the product is a composite with high filling of wood with a wide field of application in different sectors of national economy and industry. The equations are closed by a viscous-elastic-plastic rheological model of the composite material and by matching the equations of inseparability and the displacement strain vector.

Application of MEG in Increasing External Quantum Efficiency Over 100%

This review paper focuses on increasing the efficiency of Solar cell using Quantum Dot. The principle idea is using MEG (Multiple exciton Generation). MEG is more efficient in quantum confined nanostructures than in bulk semiconductors because the momentum preservation prerequisite is relaxed. Even the carrier-carrier interactions are huge due to strong confinement. The carrier multiplication decoupling from the effective band gap allows amplified photo-voltage for corresponding carrier multiplication. Along with this, it was also found that external quantum efficiency (EQE) would reach almost 100%, sometimes even exceeding it, for energy which is greater than twice the band gap energy. This is due to the fact that high energy photons have the ability to produce more than one photo carrier pair. MEG is definitely a promising route to increasing solar cell efficiency. If a threshold of twice the band gap energy could be realized for impact ionization in a colloid Quantum Dot cell, the theoretical maximum possible conversion efficiency would shift to above 60%. The goal is to capture maximum energy incident on a given plane and targeting highyield transportation of the resultant photo generated charge.

Action principles for quantum automata and Lorentz invariance of discrete time quantum walks

A discrete action principle for general quantum automata is proposed. This action principle is particularized to Discrete Time Quantum Walks (DTQWs) and then extended into an energy and momentum preserving, manifestly covariant formulation. Space–time coordinates are introduced as new variables of the action and their equations of motion enforce energy and momentum conservation. This guarantees that the proposed action can be used to build future, DTQW-based self-consistent models of spinors interacting with gauge fields. A discrete stress–energy tensor for the DTQW is also obtained. The manifest covariance of the formulation highlights the special role played by the grid reference frame in the DTQW dynamics. The main discussion is complemented by three appendices.

Cosserat Rods with Projective Dynamics

AbstractWe present a novel method to simulate Cosserat rods with Projective Dynamics (PD). The proposed method is both numerically robust and accurate with respect to the underlying physics, making it suitable for a variety of applications in computer graphics and related disciplines. Cosserat theory assigns an orientation frame to each point and is thus able to realistically simulate stretching and shearing effects, in addition to bending and twisting. Within the PD framework, it is possible to obtain accurate simulations given the implicit integration over time and its decoupling of the local‐global solve. In the proposed method, we start from the continuous formulation of the Cosserat theory and derive the constraints for the PD solver. We extend the standard definition of PD and add body orientations as system variables. Thus, we include the preservation of angular momentum, so that twisting and bending can be accurately simulated. Our formulation allows the simulation of different bending behaviors with respect to a user‐defined Young's modulus, the radius of the rod's cross‐section, and material density. We show how different material specifications in our simulations converge within a few iterations to a reference solution, generated with a high‐precision finite element method. Furthermore, we demonstrate mesh independence of our formulation: Refining the simulation mesh still results in the same characteristic motion, which is in contrast to previous position based methods.

A variationally consistent Streamline Upwind Petrov–Galerkin Smooth Particle Hydrodynamics algorithm for large strain solid dynamics

This paper presents a new Smooth Particle Hydrodynamics (SPH) computational framework for explicit fast solid dynamics. The proposed methodology explores the use of the Streamline Upwind Petrov–Galerkin (SUPG) stabilisation methodology as an alternative to the Jameson–Schmidt–Turkel (JST) stabilisation recently presented by the authors in Lee et al. (2016) in the context of a conservation law formulation of fast solid dynamics. The work introduced in this paper puts forward three advantageous features over the recent JST-SPH framework. First, the variationally consistent nature of the SUPG stabilisation allows for the introduction of a locally preserving angular momentum procedure which can be solved in a monolithic manner in conjunction with the rest of the system equations. This differs from the JST-SPH framework, where an a posteriori projection procedure was required to ensure global angular momentum preservation. Second, evaluation of expensive harmonic and bi-harmonic operators, necessary for the JST stabilisation, is circumvented in the new SUPG-SPH framework. Third, the SUPG-SPH framework is more accurate (for the same number of degrees of freedom) than its JST-SPH counterpart and its accuracy is comparable to that of the robust (but computationally more demanding) Petrov–Galerkin Finite Element Method (PG-FEM) technique explored by the authors in Lee et al. (2014), Gil et al. (2014,2016), Bonet et al. (2015), as shown in the numerical examples included. A series of numerical examples are analysed in order to benchmark and assess the robustness and effectiveness of the proposed algorithm. The resulting SUPG-SPH framework is therefore accurate, robust and computationally efficient, three key desired features that will allow the authors in forthcoming publications to explore its applicability in large scale simulations.

A new approach for studying the operation of a secondary sedimentation tank

A new theory regarding the behavior of activated sludge in a sedimentation tank has been developed, based on the principles of momentum preservation in suspended sludge, the ratio between drag and gravity, and the potential energy of the sludge blanket. Field tests enabled the determination of new criteria for the functioning of secondary sedimentation tanks complying with this new theory.

Optical and spin polarization dynamics in GaSe nanoslabs

We report nearly complete preservation of "spin memory" between optical absorption and photoluminescence (PL) in nanometer slabs of GaSe pumped with up to 0.2 eV excess energy. At cryogenic temperatures, the initial degree of circular polarization ($\rho_0$) of PL approaches unity, with the major fraction of the spin polarization decaying with a time constant $>$500 ps in sub-100-nm GaSe nanoslabs. Even at room temperature, $\rho_0$ as large as 0.7 is observed, while pumping 1 eV above the band edge yields $\rho_0$ = 0.15. Angular momentum preservation for both electrons and holes is due to the separation of the non-degenerate conduction and valence bands from other bands. In contrast to valley polarization in atomically thin transition metal dichalcogenides, here optical spin polarization is preserved in nanoslabs of 100 layers or more of GaSe.

High order variational integrators in the optimal control of mechanical systems

In recent years, much effort in designing numerical methods for the simulation and optimization of mechanical systems has been put into schemes which are structure preserving. One particular class are variational integrators which are momentum preserving and symplectic. In this article, we develop two high order variational integrators which distinguish themselves in the dimension of the underling space of approximation and we investigate their application to finite-dimensional optimal control problems posed with mechanical systems. The convergence of state and control variables of the approximated problem is shown. Furthermore, by analyzing the adjoint systems of the optimal control problem and its discretized counterpart, we prove that, for these particular integrators, dualization and discretization commute.