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This paper presents the numerical model of the measuring stand - the wind tunnel, in which is fixed the cylinder with cooling inlet oscillating stream. The aim of this work is the juxtaposition and comparison of characteristic values concerning the oscillating turbulent flow around cylinder, obtained from the experiment conducted in the wind tunnel at the Institute of Thermal Machinery, Czestochowa University of Technology with the data obtained as a result of numerical modeling of unsteady flow phenomena with heat transfer processes. Model discussed in this paper was created using a commercial program ANSYS FLUENT, that is used for mathematical modeling of flow and heat transfer processes. The expected outcome of this study is that it is possible in a way that doesn’t require large expenditures of time, numerical modeling a similar stand, which greatly facilitated by further research into the very large issue of unsteady flows.

Reliable modeling of multiphase pipe flows demand the development of fast and robust numerical techniques. The presented in this paper study proposes a multi-fluid model and its implementation using the Jacobian-Free Newton-Krylov (JFNK) method. The fully implicit formulation framework described in this paper will enable to efficiently solve governing fluid flow equations. A reduction of a multi-fluid model in zones of phase disappearance based on the phase state distribution over the cells is considered within the numerical method where the single phase cells and multiphase cells are distinguished by solving reduced set of governing equations for single phase cells. Current algorithm for slug flows simulations and further perspectives are proposed and discussed in this paper.

This paper presents the numerical method applied to predict the performance and wave wash of the river craft. In recent years fast ferries have been introduced on many ferry routes all over the world. Mainly when operating in shallow waters and near the coast, the waves generated by these crafts give escalate to clash with recreational use of beaches and coastal waters. The performance of HSC vehicle in these areas and the potential coastal erosion caused by a changed wave impact has been a subject of concern. In this paper, a finite volume method (FVM) and RANS approach was applied to investigate the wave wash, resistance, trim, and pressure acted on the craft. Actually a dynamic mesh with two degrees of freedom was used and the results were compared with a markedly proper experimental results and the competency of applied method was proved.

The aim of this paper is to develop numerical methods for solving systems of integral equations with cardinal splines. The unknown functions are expressed as a linear combination of horizontal translations of certain cardinal spline functions with small compact supports. Then a simple system of equations on the coefficients is obtained for the system of integral equations. It is relatively straight forward to solve the system of unknowns and an approximation of the original solution with high accuracy is achieved. Several cardinal splines are used in the paper to enhance the accuracy. The sufficient condition for the existence of the inverse matrix is examined and the convergence rate is investigated. Examples are given to demonstrate the benefits of the methods.

Landslide due to rainfall has been and continues to be one of the most important concerns of geotechnical engineering. The paper presents the variation of factor of safety of stone column-supported embankment constructed over soft soil due to change in water level for an incessant period of rainfall. A combined simulation-optimization based methodology has been proposed to predict the critical surface of failure of the embankment and to optimize the corresponding factor of safety under rainfall conditions using an evolutionary genetic algorithm NSGA-II (Non-Dominated Sorted Genetic Algorithm-II). It has been observed that the position of water table can be reliably estimated with varying periods of infiltration using developed numerical method. The parametric study is presented to study the optimum factor of safety of the embankment and its corresponding critical failure surface under the steady-state infiltration condition. Results show that in case of floating stone columns, period of infiltration has no effect on factor of safety. Even critical failure surfaces for a particular floating column length remain same irrespective of rainfall duration.

One-step block method for solving linear Volterra integro-differential equations (VIDEs) is presented in this paper. In VIDEs, the unknown function appears in the form of derivative and under the integral sign. The popular methods for solving VIDEs are the method of quadrature or quadrature method combined with numerical method. The proposed block method will solve the ordinary differential equations (ODEs) part and Newton-Cotes quadrature rule is applied to calculate the integral part of VIDEs. Numerical problems are presented to illustrate the performance of the proposed method.

This paper is focused on the numerical simulation of the interaction of an ultrasound wave and an air bubble surrounded by water. Our interest is to develop a fully compressible solver in the two phases and to account for surface tension effects. As the volume oscillation of the bubble occurs in a low Mach number regime, a specific attention must be paid to the effectiveness of the numerical method chosen to solve the compressible Euler equations. Several numerical methods are implemented and confronted on a benchmarck. This preliminary test highlights that the projection method is the most accurate one. Then a basic implementation of the surface tension leads to strong spurious currents and numerical instabilities. A specific velocity/pressure time splitting is thus proposed to overcome this issue. Numerical evidences of the efficiency of this new numerical scheme are provided with the numerical simulation of the interaction between a bubble and a wavefront. Indeed, both the accuracy and the stability of...

In real impact applications, an energy absorber rarely sustains dynamic loading either axial or oblique but a combination of both. Established studies have proved that thin-walled tube is an excellent energy absorber under dynamic loading. Furthermore, the introduction of foam filling successfully enhanced the energy absorption capacity of thin-walled tube. However, the understanding of its response under oblique loading has yet been fully explored. Moreover, emerging in automotive industry has lead to increase interests on lightweight materials such as aluminium alloy. As such, this paper presents the crushing behaviour of empty and foam-filled aluminium alloy (AA6061-T6) conical tubes under oblique impact loading using a validated nonlinear finite element (FE) code, LS-DYNA. The study aims to assess the effect of foam filling on the energy absorption of AA6061-T6 tubes for variations in filler density. In fact, to the best of our knowledge, this study is the first attempt to evaluate a response of empty...

We describe an improved damage function model for bread dough rheology. The model has relatively few parameters, all of which can easily be found from simple experiments. Small deformations in the linear region are described by a gel-like power-law memory function. A set of large non-reversing deformations - stress relaxation after a step of shear, steady shearing and elongation beginning from rest, and biaxial stretching, is used to test the model. With the introduction of a revised strain measure which includes a Mooney-Rivlin term, all of these motions can be well described by the damage function described in previous papers. For reversing step strains, larger amplitude oscillatory shearing and recoil reasonable predictions have been found. The numerical methods used are discussed and we give some examples.

The critical energy constant is of significant interest for the theoretical and numerical analysis of Boussinesq type equations. In the one-dimensional case this constant is evaluated exactly. In this paper we propose a method for numerical evaluation of this constant in the multi-dimensional cases by computing the ground state. Aspects of the numerical implementation are discussed and many numerical results are demonstrated.

This paper proposes a wavelet based numerical method for the solution of elastoplastic problem. The method is based on the Lagrange variational equation of elastic static and the Haar wavelet transform of the components of deformation field. Some examples of analysis of multilevel deformation are shown for the demonstration of the method’s capabilities. Some differences in the wavelet spectrums of multilevel inhomogeneous media are shown and discussed.

In the present paper the thermal fluid-structure-interaction is experimentally and numerically investigated. There-fore, the interaction phenomena is modeled by the Reynolds-averaged Navier-Stokes equations and the nonlinear Fourier heat conduction equation are used for the fluid and the solid phase, respectively. The simulation is performed using a partitioned approach using the finite volume method for the fluid domain, the finite element method for the solid domain and Runge-Kutta integration schemes for the time domain. Furthermore, as a basis for the understanding of thermal fluid-structure-interaction and also for the verification and validation of the applied continuum mechanical models and numerical methods, respectively, a fundamental wind tunnel experiment is presented.

This paper considers control systems with a finite number of control parameters, i.e. dynamical polysystems. It is assumed that control switchings can occur only at certain discrete times. Statistical methods in number theory are used to investigate the controllability of these systems. Existence of control switching times is established through analysis of Diophantine equations. The values of control switching times are found through suitable numerical methods. Certain assertions on the controllability of the polysystems of the class under consideration are proved. Some examples are considered.

This paper investigates the application of three form-finding methods for tensegrity structures made of cables and bars. The examined methods allow the determination of nodal positions and the prestress state which is essential for the mechanical properties of these kind of structures. The computational results are compared to measurements of the geometry and the prestress state obtained by experiments using laboratory tensegrity structures made of aluminium bars, steel cables as well as sophisticated connection and prestressing elements. This comparative study demonstrates the quality of the form-finding methods but also the demands on strategies considering additionally the mechanical behaviour of these structures and on improved assembly methods.

A method for determining the effective Rayleigh surface wave (RSW) velocity under the probe during a RSW imaging experiment was developed. The synthetic aperture routine can take in polycrystalline data with arbitrary c-axis orientation for each crystal and calculate the total effect that the crystals below the probe has on the response. It relies on calculation of RSW velocity in arbitrary directions for hexagonal crystals by applying numerical methods to the general theory described by several groups using the Stroh formalism. In this paper, the method will be summarized and example will be shown that demonstrate the feasibility of the routine for approximating scans over the surface of samples. Application of the method in the context of material characterization will be discussed.

The numerical solution of partial differential equations discretized along the space variables requires the employ of highly stable methods, due to their intrisic multiscale (thus stiff) nature. The purpose of this paper is then the introduction of some building blocks leading to an efficient and accurate treatment of such stiff problems through highly stable multivalue numerical methods. We present a strategy based on a suitable modification of collocation technique which avoids, unlike classical collocation based Runge-Kutta methods, the order reduction phenomenon. Some novel issues on the error analysis, in view of a combined variable stepsize-variable order implementation, are here presented.

This paper is devoted to the numerical simulation of stochastic system for inventory management products using controlled semi-Markov process. The results of a special software for the system’s research and finding the optimal control are presented.

In this paper, three numerical methods have been used to solve a 1-D Convection-Diffusion equation with specified initial and boundary conditions. The methods used are the third order upwind scheme [1], fourth order upwind scheme [1] and a Non-Standard Finite Difference (NSFD) scheme [4]. The problem we considered has steep boundary layers near x=1 [3] and this is a challenging test case as many schemes are plagued by nonphysical oscillation near steep boundaries. We compute the L2 and L∞ errors, dissipation and dispersion errors when the three numerical schemes are used and observe that the NSFD is much better than the other two schemes for both coarse and fine grids and also at low and high Reynolds numbers.

Concerning the environmental issue and the increase of fuel price, optimizing the fuel consumption has been recently an important subject in all industries. In marine industries one of the ways to decrease the energy consumption was by reducing the presence of cavitation on marine propeller blades. This will give a higher propulsive efficiency. This paper provides an investigation into the influence of the cavitation on a hydrodynamic performance around the propeller based on numerical method. Hydrofoil representing the blade form of propeller was of particular of interest. Two types of cavitation model were investigated with respect to the accuracy of the result and the effectiveness of the method. The results include the hydrodynamic characteristics of cavitation phenomenon like lift/drag variation with respect to the cavity extent. It was found that a high accuracy and low computational time is achieved when the cavitation model of Zwart-Gerber-Belamri is used. The interesting outcome of this study is ...

A computational experiment for simulating building performance needs basically three important input data sets, namely the material properties, environmental conditions and initial conditions. As the result of any prediction depends strongly on a considered geographical location, a database of locations and climatic data is required to support any reliable numerical simulation. In this paper, we present an online application for gathering, sharing and processing of climatic data from stations all around the world. An illustrative example confirms the necessity of such a software tool.

The paper focuses on numerical analysis of temperature field into a magneto-rheological break. The magneto-rheological fluid is used for a brake operated at different speeds. The magneto-rheological brake application was developed due to the magnetic control and fast response. The two dimensional axi-symmetric computational domain corresponds to the experimental magneto-rheological break. The numerical simulations have been performed for seven speed values with zero magnetic field. Firstly, the temperature map for magneto-rheological break is computed. Secondly, the temperature value obtained on the outside casing wall is validated against experimental data. Next, the maximum temperature value was identified based on numerical simulation in a point located into the magneto-rheological fluid. The numerical results will be used to improve the magneto-rheological break operation/design.

Guided waves are well suited for structural interrogation of continuously welded rail track, and are being exploited in a commercial monitoring system. This system relies on a pitch-catch mode of operation to reliably detect complete breaks in the rail. Efforts to extend this system to include a pulse-echo capability (for detecting damage before complete breaks occur) require numerical modelling to predict how propagating waves interact with damage. To this end, an efficient hybrid SAFE-FE numerical method, capable of predicting reflections from arbitrary discontinuities, has previously been implemented. In this paper, we attempt to validate the SAFE-FE method by comparison with both numerical and experimental results. A numerical comparison between the SAFE-FE method and a time domain analysis using the commercial finite element package ABAQUS Explicit is performed for two example problems. The ABAQUS Explicit time domain results are processed so that a comparison of power reflection coefficients is performed. In both instances, good agreement between the hybrid method and ABAQUS Explicit were observed. The experimental comparison involved the measurement of reflections from passive reflectors bonded to a rail in the field. These measurements were used to estimate the power transmission and reflection coefficients of the reflectors. A reasonable correlation was achieved for the power reflection coefficients, but the hybrid method was shown to somewhat over-predict the power transmission coefficients.

This work aims to present comparison of experimental measurements and numerical analysis with different turbulent models of a same issue, which is an air flowing in the pipeline with installed orifice plate. The paper contains experimental measurements and corresponding CFD calculations of the flowing air in the pipes with different geometry of used orifice plates.

This paper presents a numerical method that evolves an active contour toward the boundary of one connected image region. The numerical method implements a model which uses the solution of the Euler-Lagrange Differential Equation in order to minimize a “snake” functional. This functional is constructed as an integral of the so called internal and external energies. The internal energy is related to the moving contour. The external energy represents the image. The minimum of the functional falls on the boundaries of objects placed in the image. A half step numerical scheme implements the concepts. The contributions of the new model come from the use of the solution of the Poisson equation and development of a new penalty function to halt the contour on the object’s boundary. In order to make the contour move across homogeneous regions and enlarge the capture range, we solve the Poisson equation with Dirichlet boundary conditions and generate a gradient vector field of the image. The numerical method is implemented with MatLab and uses a stop condition based on the gradient. The advantages of the model are that it has a large capture range, is accurate in detecting the boundaries of image objects, and is capable of surpassing noise. A disadvantage is that the user has to select the right values of three parameters. Several experiments with synthetic, weapon, and medical images have been conducted to validate the model. Our work continues with the goal of cutting the curve in the event multiple objects have been enveloped.

In this paper, we investigate the possible use of control theory, particularly theory on optimal control to derive some numerical methods for unconstrained optimization problems. Based upon this control theory, we derive a Levenberg-Marquardt-like method that guarantees greatest descent in a particular search region. The implementation of this method in its original form requires inversion of a non-sparse matrix or equivalently solving a linear system in every iteration. Thus, an approximation of the proposed method via quasi-Newton update is constructed. Numerical results indicate that the new method is more effective and practical.

Electromagnetic wave resistivity (EWR) tools are used to provide real-time measurements of resistivity in the formation around the tool in Logging While Drilling (LWD). In this paper, the acquired resistivity information in the formation is analyzed to extract more information, including dipping angle and azimuth direction of the drill. A finite element (FM) model of EWR tool working in layered earth formations is established. Numerical analysis and FM simulations are employed to analyze the amplitude ratio and phase difference between the voltages measured at the two receivers of the EWR tool in deviated well drilling.

A new numerical method which is based on the coupling between localized multiscale method and meshless method with penalty is developed for 2D Burgers' equation. In this paper, penalty method is employed to enforce the essential boundary conditions due to the lack of the Kronecker delta property in meshless shape function. For the area involving high rate of velocity changes, solution needs to be refined and improved in order to properly capture the solution behaviour in the corresponding area. Here, the problem is decomposed into a coarse and a fine scale based on the variational formulation. In this work, multiscale method is adopted locally at the critical area with coarse scale and fine scales to represent global and local behaviour, respectively. Finally a 2D Burgers' problem with penalty is solved by using the localized multiscale meshless approximation and the results have been compared with normal meshless technique. The numerical results show that the former method obtains higher accuracy result compared with the latter method. Therefore, this localized multiscale meshless method with penalty is an attractive approach for solving more general problems which involve large deformation.

The main objective of this study is reduced the boundary-value problems of scattering and diffraction waves on plane-parallel structures to the singular or hypersingular integral equations. For these cases we use a method of the parametric representations of the integral and pseudo-differential operators. Numerical results of the model scattering problems on periodic and boundary gratings and also on the gratings above a flat screen reflector are presented in this paper.

In the paper, the problem of diffraction on thin ideally conductive screens is reduced to vector hypersingular integral equation with integral treated in the sense of finite Hadamard value. An numerical scheme to solve the equation is introduced. The scheme is based on piecewise approximation of unknown function. The advantage of the scheme is that integral of singular part is reduced to contour integral which can be analytically calculated so numerical calculation are significantly accelerated. Several examples of resulting numerical experiments are given in comparison with known theoretical and experimental data.

A BGK-type model is a simplified model to the Boltzmann equation where the complicated collision integral is approximated using a simple relaxation term. In this paper, a generalized BGK-type model is proposed by combining the original BGK, Shakhov and ellipsoidal statistical models. To verify the new model, theoretical and numerical analysis is performed. The Chapman-Enskog expansion shows that the generalized model can recover the Navier-Stokes-Fourier and Burnett equations by choosing properly the introduced parameters. In addition, the collision term of the model is evaluated for several designed relaxation problems. Results show that the new model can match the results of third-order moments obtained with DSMC method by adjusting the free parameters.

Aim of this paper is a discussion of certain transformations of matrices preserving either nonsingularity or trace or at last the point spectrum of the given real or complex matrix. Transformations of matrices discussed here are considered with respect to the possible applications of numerical methods, including the adaptation of obtained results for testing numerical algorithms, especially with regard to their numerical stability.

We present a conservative spectral method for the fully nonlinear Boltzmann collision operator based on the weighted convolution structure in Fourier space developed by Gamba and Tharkabhushnanam. This method can simulate a broad class of collisions, including both elastic and inelastic collisions as well as angularly dependent cross sections in which grazing collisions play a major role. The extension presented in this paper consists of factorizing the convolution weight on quadrature points by exploiting the symmetric nature of the particle interaction law, which reduces the computational cost and memory requirements of the method to O(M2N4logN) from the O(N6) complexity of the original spectral method, where N is the number of velocity grid points in each velocity dimension and M is the number of quadrature points in the factorization, which can be taken to be much smaller than N. We present preliminary numerical results.

In this paper we present a new search direction known as the CG-BFGS method, which uses the search direction of the conjugate gradient method approach in the quasi-Newton methods. The new algorithm is compared with the quasi-Newton methods in terms of the number of iterations and CPU-time. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is used as an updating formula for the approximation of the Hessian for both methods. Our numerical analysis provides strong evidence that our CG-BFGS method is more efficient than the ordinary BFGS method. Besides, we also prove that the new algorithm is globally convergent.

The paper addresses the topic of the numerical analysis up to collapse of masonry vaults. At this aim, an advanced numerical model is utilized, which requires the discretization of the structure by means of three dimensional six-noded wedge finite elements rigid and infinitely resistant and interfaces exhibiting a non linear behavior with softening. The incremental problem is solved by means of a robust quadratic programming procedure and interfaces mechanical properties are estimated by means of a consolidated homogenization strategy. Failure mechanisms and collapse loads are evaluated numerically for a case study in Italy (a masonry cross vault subjected to increasing vertical live loads up to collapse), varying mechanical properties of the vault and considering the stabilizing role played by the backfill. In light of the results obtained, limitations and possibilities of the widely diffusedtraditional approaches based on the subdivision of the vault into a series of arches are addressed.

In the rarefied gas dynamics, the DSMC method is one of the most popular numerical tools. It performs satisfactorily in simulating hypersonic flows surrounding re-entry vehicles and micro-/nano- flows. However, the computational cost is expensive, especially when Kn → 0. Even for flows in the near-continuum regime, pure DSMC simulations require a number of computational efforts for most cases. Albeit several DSMC/NS hybrid methods are proposed to deal with this, those methods still suffer from the boundary treatment, which may cause nonphysical solutions. Filbet and Jin [1] proposed a framework of new numerical methods of Boltzmann equation, called asymptotic preserving schemes, whose computational costs are affordable as Kn → 0. Recently, Ren et al. [2] realized the AP schemes with Monte Carlo methods (AP-DSMC), which have better performance than counterpart methods. In this paper, AP-DSMC is applied in simulating nonequilibrium hypersonic flows. Several numerical results are computed and analyzed to stu...

Circulatory system in human body is built up by network of blood vessels which includes numerous bifurcations. This study presents the influences of bifurcation geometry under the effects of gravity and an irregular stenosis. Along the studied vessel, blood is treated as an incompressible Newtonian fluid. In this paper, an unsteady two-dimensional nonlinear model is developed, where significant gravity term are added to the governing equations. The selected numerical method for the problem is the Marker and Cell (MAC) method based on finite difference approximations. The governing equations are discretized to uniform staggered grids before developing the algorithm in Matlab software. Furthermore, successive-over-relaxation (S.O.R.) method is used to solve the Poisson equation of pressure. Then, pressure-velocity corrector is implied to improve accuracy of the results obtained. The results are presented graphically.

A numerical study for hyperbolic equations having singular source terms is presented. Singular in the sense that within the spatial domain the source is defined by a Dirac delta function. Solutions of such problems will have discontinuities which forms an obstacle for standard numerical methods. In this paper, a fifth order flux implicit WENO method with non-uniform meshes is studied for approximate solutions of hyperbolic equations having singular source terms. Numerical examples are provided.

In this paper we propose a fast explicit positivity preserving finite difference scheme for finding an accurate solution of the famous Black-Scholes partial differential equation. We apply a non-traditional approximation of the spacial derivatives using values at different time levels. We explore the convergence, consistency and positivity of the iteration matrix of the obtained numerical method for the Black-Scholes equation with non-constant coefficients. The main advantages of the constructed method are monotonicity and positivity preserving properties of the numerical solution that in addition satisfies a discrete maximum principle. The latter is an important property for obtaining a smooth numerical solution in case of convection-diffusion equations with discontinuous initial conditions such as pricing digital or discrete options. The presented explicit method is characterized by a fast computational speed, it has a straightforward implementation and is very efficient for low volatility option valuation problems.

In this paper, we employ a new approximate analytical method called the optimal homotopy asymptotic method (OHAM) to solve steady state heat transfer problem in slabs. The heat transfer problem is modeled using nonlinear two-point boundary value problem. Using OHAM, we obtained the approximate analytical solution for dimensionless temperature with different values of a parameter e. Further, the OHAM results for dimensionless temperature have been presented graphically and in tabular form. Comparison has been provided with existing results from the use of homotopy perturbation method, perturbation method and numerical method. For numerical results, we used Runge-Kutta Fehlberg fourth-fifth order method. It was found that OHAM produces better approximate analytical solutions than those which are obtained by homotopy perturbation and perturbation methods, in the sense of closer agreement with results obtained from the use of Runge-Kutta Fehlberg fourth-fifth order method.

Numerical simulations of rarefied gas flows are generally made with DSMC methods. Up to a recent period, deterministic numerical methods based on a discretization of the Boltzmann equation were restricted to simple problems (1D, linearized flows, or simple geometries, for instance). In the last decade, several deterministic solvers have been developed in different teams to tackle more complex problems like 2D and 3D flows. Some of them are based on the full Boltzmann equation. Solving this equation numerically is still very challenging, and 3D solvers are still restricted to monoatomic gases, even if recent works have proved it was possible to simulate simple flows for polyatomic gases. Other solvers are based on simpler BGK like models: they allow for much more intensive simulations on 3D flows for realistic geometries, but treating complex gases requires extended BGK models that are still under development. In this paper, we discuss the main features of these existing solvers, and we focus on their strengths and inefficiencies. We will also review some recent results that show how these solvers can be improved: - higher accuracy (higher order finite volume methods, discontinuous Galerkin approaches) - lower memory and CPU costs with special velocity discretization (adaptive grids, spectral methods) - multi-scale simulations by using hybrid and asymptotic preserving schemes - efficient implementation on high performance computers (parallel computing, hybrid parallelization) Finally, we propose some perspectives to make these solvers more efficient and more popular.