**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**12

# Search results for: Conservation laws

##### 12 A Hybrid Artificial Intelligence and Two Dimensional Depth Averaged Numerical Model for Solving Shallow Water and Exner Equations Simultaneously

**Authors:**
S. Mehrab Amiri,
Nasser Talebbeydokhti

**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.

**Keywords:**
Artificial neural network,
morphodynamic model,
sediment continuity equation,
shallow water equations.

##### 11 Numerical Investigation of Multiphase Flow in Pipelines

**Authors:**
Gozel Judakova,
Markus Bause

**Abstract:**

**Keywords:**
Discontinuous Galerkin method,
Euler system,
inviscid two-fluid model,
streamline upwind Petrov-Galerkin
method,
two-phase flow.

##### 10 Multisymplectic Geometry and Noether Symmetries for the Field Theories and the Relativistic Mechanics

**Authors:**
H. Loumi-Fergane,
A. Belaidi

**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 q^{i}, the currents obtained naturally from the transformations are respectively the energy and the momentum of the system.

**Keywords:**
Field theories,
relativistic mechanics,
Lagrangian formalism,
multisymplectic geometry,
symmetries,
Noether theorem,
conservation laws.

##### 9 A Numerical Method for Diffusion and Cahn-Hilliard Equations on Evolving Spherical Surfaces

**Authors:**
Jyh-Yang Wu,
Sheng-Gwo Chen

**Abstract:**

**Keywords:**
Conservation laws,
diffusion equations,
Cahn-Hilliard Equations,
evolving surfaces.

##### 8 Application of Novel Conserving Immersed Boundary Method to Moving Boundary Problem

**Authors:**
S. N. Hosseini,
S. M. H. Karimian

**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.

**Keywords:**
Immersed Boundary Method,
conservation of mass and momentum laws,
moving boundary,
boundary condition.

##### 7 Symmetries, Conservation Laws and Reduction of Wave and Gordon-type Equations on Riemannian Manifolds

**Authors:**
Sameerah Jamal,
Abdul Hamid Kara,
Ashfaque H. Bokhari

**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.

**Keywords:**
Bianchi metric,
conservation laws,
Milne metric,
symmetries.

##### 6 A Robust TVD-WENO Scheme for Conservation Laws

**Authors:**
A. Abdalla,
A. Kaltayev

**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.

**Keywords:**
WENO scheme,
TVD schemes,
smoothness indicators,
multi-resolution.

##### 5 Current Distribution and Cathode Flooding Prediction in a PEM Fuel Cell

**Authors:**
A. Jamekhorshid,
G. Karimi,
I. Noshadi,
A. Jahangiri

**Abstract:**

**Keywords:**
Current distribution,
Flooding,
Hydrogen energysystem,
PEM fuel cell.

##### 4 On the Mechanism Broadening of Optical Spectrum of a Solvated Electron in Ammonia

**Authors:**
V.K. Mukhomorov

**Abstract:**

**Keywords:**
Canonical transformations,
solvated electron,
width
of the optical spectrum.

##### 3 Traffic Flow on Road Junctions

**Authors:**
Wah Wah Aung,
Cho Cho San

**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.

**Keywords:**
boundary conditions,
conservation laws,
finite difference Schemes,
traffic flow.

##### 2 Physical Conserved Quantities for the Axisymmetric Liquid, Free and Wall Jets

**Authors:**
Rehana Naz,
D. P. Mason,
Fazal Mahomed

**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.

**Keywords:**
Axisymmetric jet,
liquid jet,
free jet,
wall jet,
conservation laws,
conserved quantity.

##### 1 A Conservative Multi-block Algorithm for Two-dimensional Numerical Model

**Authors:**
Yaoxin Zhang,
Yafei Jia,
Sam S.Y. Wang

**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.

**Keywords:**
Multi-block algorithm,
conservation,
interpolation,
numerical model,
flow simulation.