Abstract: As is known, the role of the energy-momentum pseudotensors of the gravitational field is to extend the conservation law to the gravitational interaction by taking into account the energy and momentum of the gravitational field. We calculated the contribution of the Einstein pseudotensor to the total mass of a stationary material body and its gravitational field. It turned out that this contribution is positive, despite the fact that the mass-energy of a stationary gravitational field is negative. We concluded that the pseudotensor incorrectly describes the energy of the gravitational field. Nevertheless, this pseudotensor has been used in a large number of scientific works for 100 years. We explain this by the fact that the covariant component of the pseudotensor was regarded as the mass-energy. Besides, we prove the advantage of the covariant energy-momentum conservation law for matter in the Minkowski space-time.
Abstract: Modeling sediment transport processes by means of numerical approach often poses severe challenges. In this way, a number of techniques have been suggested to solve flow and sediment equations in decoupled, semi-coupled or fully coupled forms. Furthermore, in order to capture flow discontinuities, a number of techniques, like artificial viscosity and shock fitting, have been proposed for solving these equations which are mostly required careful calibration processes. In this research, a numerical scheme for solving shallow water and Exner equations in fully coupled form is presented. First-Order Centered scheme is applied for producing required numerical fluxes and the reconstruction process is carried out toward using Monotonic Upstream Scheme for Conservation Laws to achieve a high order scheme. In order to satisfy C-property of the scheme in presence of bed topography, Surface Gradient Method is proposed. Combining the presented scheme with fourth order Runge-Kutta algorithm for time integration yields a competent numerical scheme. In addition, to handle non-prismatic channels problems, Cartesian Cut Cell Method is employed. A trained Multi-Layer Perceptron Artificial Neural Network which is of Feed Forward Back Propagation (FFBP) type estimates sediment flow discharge in the model rather than usual empirical formulas. Hydrodynamic part of the model is tested for showing its capability in simulation of flow discontinuities, transcritical flows, wetting/drying conditions and non-prismatic channel flows. In this end, dam-break flow onto a locally non-prismatic converging-diverging channel with initially dry bed conditions is modeled. The morphodynamic part of the model is verified simulating dam break on a dry movable bed and bed level variations in an alluvial junction. The results show that the model is capable in capturing the flow discontinuities, solving wetting/drying problems even in non-prismatic channels and presenting proper results for movable bed situations. It can also be deducted that applying Artificial Neural Network, instead of common empirical formulas for estimating sediment flow discharge, leads to more accurate results.
Abstract: The problem of symmetries in field theory has been analyzed using geometric frameworks, such as the multisymplectic models by using in particular the multivector field formalism. In this paper, we expand the vector fields associated to infinitesimal symmetries which give rise to invariant quantities as Noether currents for classical field theories and relativistic mechanic using the multisymplectic geometry where the Poincaré-Cartan form has thus been greatly simplified using the Second Order Partial Differential Equation (SOPDE) for multi-vector fields verifying Euler equations. These symmetries have been classified naturally according to the construction of the fiber bundle used. In this work, unlike other works using the analytical method, our geometric model has allowed us firstly to distinguish the angular moments of the gauge field obtained during different transformations while these moments are gathered in a single expression and are obtained during a rotation in the Minkowsky space. Secondly, no conditions are imposed on the Lagrangian of the mechanics with respect to its dependence in time and in qi, the currents obtained naturally from the transformations are respectively the energy and the momentum of the system.
Abstract: We present and analyze reliable numerical techniques
for simulating complex flow and transport phenomena related to
natural gas transportation in pipelines. Such kind of problems
are of high interest in the field of petroleum and environmental
engineering. Modeling and understanding natural gas flow and
transformation processes during transportation is important for the
sake of physical realism and the design and operation of pipeline
systems. In our approach a two fluid flow model based on a system
of coupled hyperbolic conservation laws is considered for describing
natural gas flow undergoing hydratization. The accurate numerical
approximation of two-phase gas flow remains subject of strong
interest in the scientific community. Such hyperbolic problems are
characterized by solutions with steep gradients or discontinuities, and
their approximation by standard finite element techniques typically
gives rise to spurious oscillations and numerical artefacts. Recently,
stabilized and discontinuous Galerkin finite element techniques
have attracted researchers’ interest. They are highly adapted to the
hyperbolic nature of our two-phase flow model. In the presentation
a streamline upwind Petrov-Galerkin approach and a discontinuous
Galerkin finite element method for the numerical approximation of
our flow model of two coupled systems of Euler equations are
presented. Then the efficiency and reliability of stabilized continuous
and discontinous finite element methods for the approximation is
carefully analyzed and the potential of the either classes of numerical
schemes is investigated. In particular, standard benchmark problems
of two-phase flow like the shock tube problem are used for the
comparative numerical study.
Abstract: In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.
Abstract: This study is used as a definition method to the value
and function in manufacturing sector. In concurrence of discussion
about present condition of modeling method, until now definition of
1D-CAE is ambiguity and not conceptual. Across all the physic fields,
those methods are defined with the formulation of differential
algebraic equation which only applied time derivation and simulation.
At the same time, we propose semi-acausal modeling concept and
differential algebraic equation method as a newly modeling method
which the efficiency has been verified through the comparison of
numerical analysis result between the semi-acausal modeling
calculation and FEM theory calculation.
Abstract: The paper deals with a mathematical model for fluid dynamic flows on road networks which is based on conservation laws. This nonlinear framework is based on the conservation of cars. We focus on traffic circle, which is a finite number of roads that meet at some junctions. The traffic circle with junctions having either one incoming and two outgoing or two incoming and one outgoing roads. We describe the numerical schemes with the particular boundary conditions used to produce approximated solutions of the problem.
Abstract: A well balanced numerical scheme based on
stationary waves for shallow water flows with arbitrary topography
has been introduced by Thanh et al. [18]. The scheme was
constructed so that it maintains equilibrium states and tests indicate
that it is stable and fast. Applying the well-balanced scheme for the
one-dimensional shallow water equations, we study the early shock
waves propagation towards the Phuket coast in Southern Thailand
during a hypothetical tsunami. The initial tsunami wave is generated
in the deep ocean with the strength that of Indonesian tsunami of
2004.
Abstract: Equations on curved manifolds display interesting properties in a number of ways. In particular, the symmetries and, therefore, the conservation laws reduce depending on how curved the manifold is. Of particular interest are the wave and Gordon-type equations; we study the symmetry properties and conservation laws of these equations on the Milne and Bianchi type III metrics. Properties of reduction procedures via symmetries, variational structures and conservation laws are more involved than on the well known flat (Minkowski) manifold.
Abstract: Non-uniform current distribution in polymer
electrolyte membrane fuel cells results in local over-heating,
accelerated ageing, and lower power output than expected. This
issue is very critical when fuel cell experiences water flooding. In
this work, the performance of a PEM fuel cell is investigated under
cathode flooding conditions. Two-dimensional partially flooded
GDL models based on the conservation laws and electrochemical
relations are proposed to study local current density distributions
along flow fields over a wide range of cell operating conditions.
The model results show a direct association between cathode inlet
humidity increases and that of average current density but the
system becomes more sensitive to flooding. The anode inlet
relative humidity shows a similar effect. Operating the cell at
higher temperatures would lead to higher average current densities
and the chance of system being flooded is reduced. In addition,
higher cathode stoichiometries prevent system flooding but the
average current density remains almost constant. The higher anode
stoichiometry leads to higher average current density and higher
sensitivity to cathode flooding.
Abstract: A new conserving approach in the context of Immersed Boundary Method (IBM) is presented to simulate one dimensional, incompressible flow in a moving boundary problem. The method employs control volume scheme to simulate the flow field. The concept of ghost node is used at the boundaries to conserve the mass and momentum equations. The Present method implements the conservation laws in all cells including boundary control volumes. Application of the method is studied in a test case with moving boundary. Comparison between the results of this new method and a sharp interface (Image Point Method) IBM algorithm shows a well distinguished improvement in both pressure and velocity fields of the present method. Fluctuations in pressure field are fully resolved in this proposed method. This approach expands the IBM capability to simulate flow field for variety of problems by implementing conservation laws in a fully Cartesian grid compared to other conserving methods.
Abstract: A systematic way to derive the conserved quantities for the axisymmetric liquid jet, free jet and wall jet using conservation laws is presented. The flow in axisymmetric jets is governed by Prandtl-s momentum boundary layer equation and the continuity equation. The multiplier approach is used to construct a basis of conserved vectors for the system of two partial differential equations for the two velocity components. The basis consists of two conserved vectors. By integrating the corresponding conservation laws across the jet and imposing the boundary conditions, conserved quantities are derived for the axisymmetric liquid and free jet. The multiplier approach applied to the third-order partial differential equation for the stream function yields two local conserved vectors one of which is a non-local conserved vector for the system. One of the conserved vectors gives the conserved quantity for the axisymmetric free jet but the conserved quantity for the wall jet is not obtained from the second conserved vector. The conserved quantity for the axisymmetric wall jet is derived from a non-local conserved vector of the third-order partial differential equation for the stream function. This non-local conserved vector for the third-order partial differential equation for the stream function is obtained by using the stream function as multiplier.
Abstract: The solvated electron is self-trapped (polaron) owing
to strong interaction with the quantum polarization field. If the
electron and quantum field are strongly coupled then the collective
localized state of the field and quasi-particle is formed. In such a
formation the electron motion is rather intricate. On the one hand the
electron oscillated within a rather deep polarization potential well
and undergoes the optical transitions, and on the other, it moves
together with the center of inertia of the system and participates in
the thermal random walk. The problem is to separate these motions
correctly, rigorously taking into account the conservation laws. This
can be conveniently done using Bogolyubov-Tyablikov method of
canonical transformation to the collective coordinates. This
transformation removes the translational degeneracy and allows one
to develop the successive approximation algorithm for the energy and
wave function while simultaneously fulfilling the law of conservation
of total momentum of the system. The resulting equations determine
the electron transitions and depend explicitly on the translational
velocity of the quasi-particle as whole. The frequency of optical
transition is calculated for the solvated electron in ammonia, and an
estimate is made for the thermal-induced spectral bandwidth.
Abstract: A multi-block algorithm and its implementation in two-dimensional finite element numerical model CCHE2D are presented. In addition to a conventional Lagrangian Interpolation Method (LIM), a novel interpolation method, called Consistent Interpolation Method (CIM), is proposed for more accurate information transfer across the interfaces. The consistent interpolation solves the governing equations over the auxiliary elements constructed around the interpolation nodes using the same numerical scheme used for the internal computational nodes. With the CIM, the momentum conservation can be maintained as well as the mass conservation. An imbalance correction scheme is used to enforce the conservation laws (mass and momentum) across the interfaces. Comparisons of the LIM and the CIM are made using several flow simulation examples. It is shown that the proposed CIM is physically more accurate and produces satisfactory results efficiently.
Abstract: The ultimate goal of this article is to develop a robust and accurate numerical method for solving hyperbolic conservation laws in one and two dimensions. A hybrid numerical method, coupling a cheap fourth order total variation diminishing (TVD) scheme [1] for smooth region and a Robust seventh-order weighted non-oscillatory (WENO) scheme [2] near discontinuities, is considered. High order multi-resolution analysis is used to detect the high gradients regions of the numerical solution in order to capture the shocks with the WENO scheme, while the smooth regions are computed with fourth order total variation diminishing (TVD). For time integration, we use the third order TVD Runge-Kutta scheme. The accuracy of the resulting hybrid high order scheme is comparable with these of WENO, but with significant decrease of the CPU cost. Numerical demonstrates that the proposed scheme is comparable to the high order WENO scheme and superior to the fourth order TVD scheme. Our scheme has the added advantage of simplicity and computational efficiency. Numerical tests are presented which show the robustness and effectiveness of the proposed scheme.