Mathematical Model For Numerical Simulation Research Articles

Numerical Simulation of 2D Flows with Hydraulic Jump Using Shallow Water Equations

This paper is concerned with a mathematical model for numerical simulation of 2D flow accompanied with a hydraulic jump. The governing water equations are solved by the Mac Cormack’s predictor-corrector technique. The mathematical model is used to numerically predict 2D hydraulic jump in a rectangular open channel. The comparison and the analysis show that the proposed method is accurate, reliable and effective in simulation of hydraulic jump flows.

On the validation of DEM and FEM/DEM models in 2D and 3D

PurposeAs particulate systems evolve, sliding, rolling and collision contacts all produce forces that discrete element method (DEM) methods aim to predict. Verification of friction rarely takes high priority in validation studies even though friction plays a very important role in applications and in mathematical models for numerical simulation. The purpose of this paper is to address sliding friction in finite element method (FEM)/DEM and rolling friction in DEM.Design/methodology/approachAnalytical solutions for “block sliding” were used to verify the authors' tangential contact force implementation of 2D FEM/DEM. Inspired by the kinetic art work Liquid Reflections by Liliane Lijn, which consists of free balls responding within a rotating shallow dish, DEM was used to simulate rolling, sliding and state‐of‐rest of spherical particles relative to horizontal and inclined, concave and flat spinning platforms. Various material properties, initial and boundary conditions are set which produce different trajectory regimes.FindingsSimulation output is found to be in excellent agreement when compared with experimental results and analytical solutions.Originality/valueThe more widespread use of analytically solvable benchmark tests for DEM and FEM/DEM codes is recommended.

Numerical simulation of corona-induced vibration of high voltage conductor

When it rains, electric power transmission lines start vibrating due to corona effect. This type of vibration is known as “corona-induced vibration”. The aim of this paper is to elaborate a mathematical model for numerical simulation of the corona-induced vibration, with consideration of the influence of the magnitude and the polarity of the electric field on the conductor surface. Finite element method was employed to develop the numerical model, and the finite difference method was used for the time discretisation. The moment of application of the coronainduced force is evaluated using the resultant vertical force applied to a water drop, suspended under a high voltage conductor. Some experimental results of other authors are exploited to evaluate the precision of the simulation and the validation of numerical results.

The modeling of piezoelectrically excited waves in beams and layered substructures

Two mathematical models for numerical simulation of traveling waves excited in an elastic waveguide by a pair of piezoceramic actuators are considered. The first model uses a simplified approach by Bernoulli–Euler beam theory and a simple actuation model. The second approach involves a boundary-value problem for an elastic layer with flexible piezoceramic strips bonded ideally to its surface. The limits of the applicability of the simplified beam model are then estimated by a comparison of the results both of the beam model and the solution of the patch-layer contact problem. Numerical results illustrate the effect of the actuators properties and position on the wave characteristics.

Predicting heat conduction during solidification of a food inside a freezer due to natural convection

A new mathematical model for numerical simulation of two dimensional food freezing due to natural convection is presented. Fluid mechanics and heat transfer by natural convection between air and a solid food in a freezer are predicted along with the heat conduction inside a plate shaped food. The mathematical model used includes continuity, linear momentum and energy partial differential equations for air and the non-linear heat diffusion equation for the solidification of the water content in the food. Unsteady two dimensional results of the velocity and temperatures distributions in the air around the food obtained by using the finite volume method are presented. Experimental data of temperature variation in time for a slab shaped food inside a freezer are used to assess the accuracy of the mathematical model and the solution procedure. It is found that the use of this model, that does not require heat transfer coefficients, allows to simulate two dimensional freezing experiments in a slab shaped food by natural convection with maximum and mean deviations of 5.2% and 1.2%, respectively.

Numerical computation of the electromagnetic field in the electrodes of a three-phase arc furnace

In this paper we introduce and numerically solve a mathematical model for numerical simulation of electromagnetic field in a three-phase electric reduction furnace. The model allows us to compute the current distribution on a cross-section of the three electrodes. A combined boundary element/finite element method is used. Numerical results for real industrial furnaces are shown. As a by-product we compute the torque on the electrodes due to the Lorentz electromagnetic force. Copyright © 1999 John Wiley & Sons, Ltd.

Numerical simulation of seismic sloshing of LMR reactors

Numerical simulations of EPRI/CRIEPI sloshing experiments have been performed by Argonne National Laboratory using the ANL-developed FLUSTR computer code. The number of meshes used in the mathematical model for numerical simulation is rather small. Thus, the computing cost is relatively inexpensive. Results of numerical simulations of the sloshing responses of two test configurations (1 and 2) which were performed by CRIEPI are described in detail. Natural frequencies and sloshing wave heights and fluid pressures at locations of sensors are calculated. The predicted values are compared with the experimental data. In all comparisons, the agreement is very good. Thus, these computer codes can be used for numerical simulation of seismic sloshing.

Analysis of thermal impact in tidal rivers and estuaries

Abstract The paper presents a far field mathematical model for numerical simulation of transient one- or two-dimensional thermal distributions in regions with severe reversing flow conditions. The Eulerian formulation employs the integral form of the conservation principles for mass and thermal energy. The two-dimensional (2D) solution area is spanned by discrete elements of variable size and shape. The three-dimensional geometry of the flow region is accounted for by spatially integrating over the enclosure surfaces of the discrete element. The derivation of the two-dimensional depth-averaged temperature equations includes the contributions of the vertical variations of velocity and temperature. Surface heat transfer as well as turbulent effects are taken into account. Important mathematical and computational features of the model are summarized. There is a discussion of the four main algorithms, necessary to treat flow regions with complex shoreline geometries, viz. (i) specification of the boundary (ii) determination of all discrete element midpoints lying within the (possibly multiconnected) solution area (iii) construction of discrete elements of irregular geometry exactly matching the (curved) boundary, (iv) treatment of boundary conditions and numerical solution of the resulting mathematical system of weakly coupled, ordinary differential equations derived from the conservation principles. Preliminary results of a computer simulation are compared with the available data for a section of the Lower Elbe river. The calculation of the two-dimensional temperature distribution includes existing power plants and industrial sites. It is noted that the programs developed for this study are more widely applicable, potentially to solving the Poisson equation, in constructing the ion trajectories of an ion extraction system, or in calculating 1D and 2D flow fields.