Search results for: numerical illustration

Authors: Lei Zhang, Jean-Michel Ghidaglia, Anela Kumbaro

Abstract:

This work focuses on numerical simulation of two-phase flows based on the bi-fluid six-equation model widely used in many industrial areas, such as nuclear power plant safety analysis. A pressure-based numerical method is adopted in our studies due to the fact that in two-phase flows, it is common to have a large range of Mach numbers because of the mixture of liquid and gas, and density-based solvers experience stiffness problems as well as a loss of accuracy when approaching the low Mach number limit. This work extends the semi-implicit pressure solver in the nuclear component CUPID code, where the governing equations are solved on unstructured grids with co-located variables to accommodate complicated geometries. A conservative version of the solver is developed in order to capture exactly the shock in one-phase flows, and is extended to two-phase situations. An inter-facial pressure term is added to the bi-fluid model to make the system hyperbolic and to establish a well-posed mathematical problem that will allow us to obtain convergent solutions with refined meshes. The ability of the numerical method to treat phase appearance and disappearance as well as the behavior of the scheme at low Mach numbers will be demonstrated through several numerical results. Finally, inter-facial mass and heat transfer models are included to deal with situations when mass and energy transfer between phases is important, and associated industrial numerical benchmarks with tabulated EOS (equations of state) for fluids are performed.

Keywords: two-phase flows, numerical simulation, bi-fluid model, unstructured grids, phase appearance and disappearance

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Authors: M. Li, V. D. Thi, M. Khelifa, M. El Ganaoui

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This study presents an overview of the work carried out by the use of wood waste as coarse aggregate in mortar. The paper describes experimental and numerical investigations carried on pervious concrete made of wood chips and also sheds lights on the mechanical properties of this new product. The properties of pervious wood-concrete such as strength, elastic modulus, and failure modes are compared and evaluated. The characterization procedure of the mechanical properties of wood waste ash are presented and discussed. The numerical and tested load–deflection response results are compared. It was observed that the numerical results are in good agreement with the experimental results.

Keywords: wood waste ash, characterization, mechanical properties, bending tests

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Authors: V. Geza, J. Vencels, G. Zageris, S. Pavlovs

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One of the most perspective methods to produce SoG-Si is refinement via metallurgical route. The most critical part of this route is refinement from boron and phosphorus. Therefore, a new approach could address this problem. We propose an approach of creating surface waves on silicon melt’s surface in order to enlarge its area and accelerate removal of boron via chemical reactions and evaporation of phosphorus. A two dimensional numerical model is created which includes coupling of electromagnetic and fluid dynamic simulations with free surface dynamics. First results show behaviour similar to experimental results from literature.

Keywords: numerical modelling, silicon refinement, surface waves, VOF method

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Authors: Salah Alrabeei, Mohammad Yousuf

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The goal of option pricing theory is to help the investors to manage their money, enhance returns and control their financial future by theoretically valuing their options. Modeling option pricing by Black-School models with jumps guarantees to consider the market movement. However, only numerical methods can solve this model. Furthermore, not all the numerical methods are efficient to solve these models because they have nonsmoothing payoffs or discontinuous derivatives at the exercise price. In this paper, the exponential time differencing (ETD) method is applied for solving partial integrodifferential equations arising in pricing European options under Merton’s and Kou’s jump-diffusion models. Fast Fourier Transform (FFT) algorithm is used as a matrix-vector multiplication solver, which reduces the complexity from O(M2) into O(M logM). A partial fraction form of Pad`e schemes is used to overcome the complexity of inverting polynomial of matrices. These two tools guarantee to get efficient and accurate numerical solutions. We construct a parallel and easy to implement a version of the numerical scheme. Numerical experiments are given to show how fast and accurate is our scheme.

Keywords: Integral differential equations, , L-stable methods, pricing European options, Jump–diffusion model

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Authors: Lin Lu, Qiang Li, Tao Cai, Pengjun Zhang

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In this study, a detailed analysis of trajectory stability and flow characteristics of a high-speed projectile during the water-entry and water-exit process has been investigated numerically. The Zwart-Gerber-Belamri (Z-G-B) cavitation model and the SST k-ω turbulence model based on the Reynolds Averaged Navier-Stokes (RANS) method are employed. The numerical methodology is validated by comparing the experimental photograph of cavitation shape and the experimental underwater velocity with the numerical simulation results. Based on the numerical methodology, the influences of rotational speed, water-entry and water-exit angle of the projectile on the trajectory stability and flow characteristics have been carried out in detail. The variation features of projectile trajectory and total resistance have been conducted, respectively. In addition, the cavitation characteristics of water-entry and water-exit have been presented and analyzed. Results show that it may not be applicable for the water-entry and water-exit to achieve the projectile stability through the rotation of projectile. Furthermore, there ought to be a critical water-entry angle for the water-entry stability of practical projectile. The impact of water-exit angle on the trajectory stability and cavity phenomenon is not as remarkable as that of the water-entry angle.

Keywords: cavitation characteristics, high-speed projectile, numerical predictions, trajectory stability, water-entry, water-exit

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Authors: Muhammad Umar Kiani, Waseem Sakawat

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This study presents the development of FEM code using Quadrilateral 4-Node (Q4) and Triangular 3-Node (T3) elements. Code is formulated using MATLAB language. Instead of using both elements in the same code, two separate codes are written. Quadrilateral element is difficult to handle directly, that is why natural coordinates (eta, ksi) are used. Due to this, Q4 code includes numerical integration (Gauss quadrature). In this case, complete numerical integration is performed using 2 points. On the other hand, T3 element can be modeled directly, by using direct stiffness approach. Axially loaded element, cantilever (special constraints) and Patch test cases were analyzed using both codes and the results were verified by using Ansys.

Keywords: FEM code, MATLAB, numerical integration, ANSYS

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Authors: Shubham Jaiswal

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During modeling of transport phenomena in porous media, many nonlinear partial differential equations (NPDEs) encountered which greatly described the convection, diffusion and reaction process. To solve such types of nonlinear problems, a reliable and efficient technique is needed. In this article, the numerical solution of NPDEs encountered in porous media is derived. Here Jacobi collocation method is used to solve the considered problems which convert the NPDEs in systems of nonlinear algebraic equations that can be solved using Newton-Raphson method. The numerical results of some illustrative examples are reported to show the efficiency and high accuracy of the proposed approach. The comparison of the numerical results with the existing analytical results already reported in the literature and the error analysis for each example exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.

Keywords: nonlinear porous media equation, shifted Jacobi polynomials, operational matrix, spectral collocation method

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Authors: Parisa Ahmadi Oliaei, Seyed Abolhassan Naeini

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The knowledge of soil–reinforcement interaction parameters is particularly important in the design of reinforced soil structures. The pull-out test is one of the most widely used tests in this regard. The results of tensile tests may be very sensitive to boundary conditions, and more research is needed for a better understanding of the Pull-out response of reinforcement, so numerical analysis using the finite element method can be a useful tool for the understanding of the Pull-out response of soil-geogrid interaction. The main objective of the present study is to compare the numerical and experimental results of Pull- out a test on geogrid-reinforced sandy soils interactions. Plaxis 2D finite element software is used for simulation. In the present study, the pull-out test modeling has been done on sandy soil. The effect of geogrid hardness was also investigated by considering two different types of geogrids. The numerical results curve had a good agreement with the pull-out laboratory results.

Keywords: plaxis, pull-out test, sand, soil- geogrid interaction

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Authors: M. Ziółkowska, J. T. Duda, J. Milewska-Duda

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This paper describes an approach to the adsorption phenomena modeling aimed at specifying the adsorption mechanisms on localized or nonlocalized adsorbent sites, when applied to the nanocarbons. The concept comes from the fundamental thermodynamic description of adsorption equilibrium and is based on numerical calculations of the hydrogen adsorbed particles volume on the surface of selected nanocarbons: single-walled nanotube and nanocone. This approach enables to obtain information on adsorption mechanism and then as a consequence to take appropriate mathematical adsorption model, thus allowing for a more reliable identification of the material porous structure. Theoretical basis of the approach is discussed and newly derived results of the numerical calculations are presented for the selected nanocarbons.

Keywords: adsorption, mathematical modeling, nanocarbons, numerical analysis

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Authors: Manoj Reghu, Prabhu Rajagopal, C. V. Krishnamurthy, Krishnan Balasubramaniam

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A thorough understanding of guided ultrasonic wave behavior in structures is essential for the application of existing Non Destructive Evaluation (NDE) technologies, as well as for the development of new methods. However, the analysis of guided wave phenomena is challenging because of their complex dispersive and multimodal nature. Although numerical solution procedures have proven to be very useful in this regard, the increasing complexity of features and defects to be considered, as well as the desire to improve the accuracy of inspection often imposes a large computational cost. Hybrid models that combine numerical solutions for wave scattering with faster alternative methods for wave propagation have long been considered as a solution to this problem. However usually such models require modification of the base code of the solution procedure. Here we aim to develop Generic Hybrid models that can be directly applied to any two different solution procedures. With this goal in mind, a Numerical Hybrid model and an Analytical-Numerical Hybrid model has been developed. The concept and implementation of these Hybrid models are discussed in this paper.

Keywords: guided ultrasonic waves, Finite Element Method (FEM), Hybrid model

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Authors: Yue-Tzu Yang, Shu-Ching Liao

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This study presents the numerical simulation of three-dimensional incompressible steady and laminar fluid flow and conjugate heat transfer of a trapezoidal microchannel heat sink using water as a cooling fluid in a silicon substrate. Navier-Stokes equations with conjugate energy equation are discretized by finite-volume method. We perform numerical computations for a range of 50 ≦ Re ≦ 600, 0.05W ≦ P ≦ 0.8W, 20W/cm2 ≦ ≦ 40W/cm2. The present study demonstrates the numerical optimization of a trapezoidal microchannel heat sink design using the response surface methodology (RSM) and the genetic algorithm method (GA). The results show that the average Nusselt number increases with an increase in the Reynolds number or pumping power, and the thermal resistance decreases as the pumping power increases. The thermal resistance of a trapezoidal microchannel is minimized for a constant heat flux and constant pumping power.

Keywords: microchannel heat sinks, conjugate heat transfer, optimization, genetic algorithm method

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Authors: Kerkouri Abdelkadir

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Numerical calculations of turbulent flows are one of the most prominent modern interests in various engineering applications. Due to the difficulty of predicting, following up and studying this flow for computational fluid dynamic (CFD), in this paper, we simulated numerical study of a flow past in a staggered tube bundle, using CFD Code ANSYS FLUENT with several models of turbulence following: k-ε, k-ω and SST approaches. The flow is modeled based on the experimental studies. The predictions of mean velocities are in very good agreement with detailed LDA (Laser Doppler Anemometry) measurements performed in 8 stations along the depth of the array. The sizes of the recirculation zones behind the cylinders are also predicted. The simulations are conducted for Reynolds numbers of 12858. The Reynolds number is set to depend experimental results.

Keywords: flow, tube bundle, ANSYS Fluent, CFD, turbulence, LDA, RANS (k-ε, k-ω, SST)

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Authors: Suba Periyal Subramaniam, Babette Scheres, Altomare Corrado, Holger Schuttrumpf

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Due to the climatic change and the usage of coastal areas, there is an increasing risk of dike failures along the coast worldwide. Wave run-up plays a key role in planning and design of a coastal structure. The coastal dike lines are bent either due to geological characteristics or due to influence of anthropogenic activities. The effect of the curvature of coastal dikes on wave run-up and overtopping is not yet investigated. The scope of this research is to find the effects of the dike curvature on wave run-up by employing numerical model studies for various dike opening angles. Numerical simulation is carried out using DualSPHysics, a meshless method, and OpenFOAM, a mesh-based method. The numerical results of the wave run-up on a curved dike and the wave transformation process for various opening angles, wave attacks, and wave parameters will be compared and discussed. This research aims to contribute a more precise analysis and understanding the influence of the curvature in the dike line and thus ensuring a higher level of protection in the future development of coastal structures.

Keywords: curved dikes, DualSPHysics, OpenFOAM, wave run-up

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Authors: A. M. Tahsini

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Computational study of two dimensional supersonic reacting hydrogen-air flows is performed to investigate the nitrogen effects on ignition delay time for premixed and diffusion flames. Chemical reaction is treated using detail kinetics and the advection upstream splitting method is used to calculate the numerical inviscid fluxes. The results show that only in the stoichiometric condition for both premixed and diffusion flames, there is monotone dependency of the ignition delay time to the nitrogen addition. In other situations, the optimal condition from ignition viewpoint should be found using numerical investigations.

Keywords: diffusion flame, ignition delay time, mixing layer, numerical simulation, premixed flame, supersonic flow

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Authors: K. S. Agrawal

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The performance of jet ejector was studied in detail by different authors. Several authors have studied mass transfer characteristics like interfacial area, mass transfer coefficients etc. In this paper, we have made an attempt to develop PDE model by considering bubble properties and apply Lattice-Boltzmann technique for PDE model. We may present the results for the interfacial area which we have obtained from our numerical simulation. Later the results are compared with previous work.

Keywords: jet ejector, mass transfer characteristics, numerical simulation, Lattice-Boltzmann technique

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Authors: Sidique Gawusu, Xiaobing Zhang

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Turbulence models play a significant role in all computational fluid dynamics based modelling approaches. There is, however, no general turbulence model suitable for all flow scenarios. Therefore, a successful numerical modelling approach is only achievable if a more appropriate closure model is used. This paper evaluates different turbulence models in numerical modelling of oil-water flow within the Eulerian-Eulerian approach. A comparison among the obtained numerical results and published benchmark data showed reasonable agreement. The domain was meshed using structured mesh, and grid test was performed to ascertain grid independence. The evaluation of the models was made through analysis of velocity and pressure profiles across the domain. The models were tested for their suitability to accurately obtain a scalable and precise numerical experience. As a result, it is found that all the models except Standard-ω provide comparable results. The study also revealed new insights on flow in porous media, specifically oil reservoirs.

Keywords: turbulence modelling, simulation, multi-phase flows, water-flooding, heavy oil

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Authors: A. Mostafa

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This paper presents a numerical study on determination of ballistic limit velocity (V₅₀) of stainless steel 304 (SS 304) used in manufacturing security screens. The simulated ballistic impact tests were conducted on clamped sheets with different thicknesses using ABAQUS/Explicit nonlinear finite element (FE) package. The ballistic limit velocity was determined using three approaches, namely: numerical tests based on material properties, FE calculated residual velocities and FE calculated residual energies. Johnson-Cook plasticity and failure criterion were utilized to simulate the dynamic behaviour of the SS 304 under various strain rates, while the well-known Lambert-Jonas equation was used for the data regression for the residual velocity and energy model. Good agreement between the investigated numerical methods was achieved. Additionally, the dependence of the ballistic limit velocity on the sheet thickness was observed. The proposed approaches present viable and cost-effective assessment methods of the ballistic performance of SS 304, which will support the development of robust security screen systems.

Keywords: ballistic velocity, stainless steel, numerical approaches, security screen

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Authors: R. Ziaie Moayed, B. Mohammadi-Haji

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Stone columns have been widely employing to improve the load-settlement characteristics of soft soils. The results of two small scale displacement control loading tests on stone columns were used in order to validate numerical finite element simulations. Additionally, a series of numerical calculations of static loading have been performed on strengthened raft footing to investigate the effects of using stone columns on bearing capacity of footings. The bearing capacity of single and group of stone columns under static loading compares with unimproved ground.

Keywords: circular raft footing, numerical analysis, validation, vertically encased stone column

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Authors: Clarinda Vitorino Nhangumbe, Ercília Sousa

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Weather derivatives are financial products used to cover non catastrophic weather events with a weather index as the underlying asset. The rainfall weather derivative pricing model is modeled based in the assumption that the rainfall dynamics follows Ornstein-Uhlenbeck process, and the partial differential equation approach is used to derive the convection-diffusion two dimensional time dependent partial differential equation, where the spatial variables are the rainfall index and rainfall depth. To compute the approximation solutions of the partial differential equation, the appropriate boundary conditions are suggested, and an explicit numerical method is proposed in order to deal efficiently with the different choices of the coefficients involved in the equation. Being an explicit numerical method, it will be conditionally stable, then the stability region of the numerical method and the order of convergence are discussed. The model is tested for real precipitation data.

Keywords: finite differences method, ornstein-uhlenbeck process, partial differential equations approach, rainfall derivatives

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Authors: Aliakbar Golshani, Seyyed Mehdi Poorhashemi, Mahsa Gharizadeh

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The under passing tunnels are strongly influenced by the soils around. There are some complexities in the specification of real soil behavior, owing to the fact that lots of uncertainties exist in soil properties, and additionally, inappropriate soil constitutive models. Such mentioned factors may cause incompatible settlements in numerical analysis with the obtained values in actual construction. This paper aims to report a case study on a specific tunnel constructed by NATM. The tunnel has a depth of 11.4 m, height of 12.2 m, and width of 14.4 m with 2.5 lanes. The numerical modeling was based on a 2D finite element program. The soil material behavior was modeled by hardening soil model. According to the field observations, the numerical estimated settlement at the ground surface was approximately four times more than the measured one, after the entire installation of the initial lining, indicating that some unknown factors affect the values. Consequently, the geotechnical parameters are accurately revised by a numerical back-analysis using laboratory and field test data and based on the obtained monitoring data. The obtained result confirms that typically, the soil parameters are conservatively low-estimated. And additionally, the constitutive models cannot be applied properly for all soil conditions.

Keywords: NATM tunnel, initial lining, laboratory test data, numerical back-analysis

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Authors: Gozde Inal Kiziltepe, Ozgun Uyanik

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There is growing evidence that socioeconomic (SES)-related differences in mathematical knowledge primarily start in early childhood period. Preschoolers from low-income families are likely to perform substantially worse in mathematical knowledge than their counterparts from middle and higher income families. The differences are seen on a wide range of recognizing written numerals, counting, adding and subtracting, and comparing numerical magnitudes. Early differences in numerical knowledge have a permanent effect childrens’ mathematical knowledge in other grades. In this respect, analyzing the effect of number board game on the number knowledge of 48-60 month-old children from disadvantaged low-income families constitutes the main objective of the study. Participants were the 71 preschoolers from a childcare center which served low-income urban families. Children were randomly assigned to the number board condition or to the color board condition. The number board condition included 35 children and the color board game condition included 36 children. Both board games were 50 cm long and 30 cm high; had ‘The Great Race’ written across the top; and included 11 horizontally arranged, different colored squares of equal sizes with the leftmost square labeled ‘Start’. The numerical board had the numbers 1–10 in the rightmost 10 squares; the color board had different colors in those squares. A rabbit or a bear token were presented to children for selecting, and on each trial spun a spinner to determine whether the token would move one or two spaces. The number condition spinner had a ‘1’ half and a ‘2’ half; the color condition spinner had colors that matched the colors of the squares on the board. Children met one-on-one with an experimenter for four 15- to 20-min sessions within a 2-week period. In the first and fourth sessions, children were administered identical pretest and posttest measures of numerical knowledge. All children were presented three numerical tasks and one subtest presented in the following order: counting, numerical magnitude comparison, numerical identification and Count Objects – Circle Number Probe subtest of Early Numeracy Assessment. In addition, same numerical tasks and subtest were given as a follow-up test four weeks after the post-test administration. Findings obtained from the study; showed that there was a meaningful difference between scores of children who played a color board game in favor of children who played number board game.

Keywords: low income, numerical board game, numerical knowledge, preschool education

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Authors: N. A. Mokhtar, A. G. Hussin, Y. Z. Zubairi

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This paper proposes a new simultaneous simple linear functional relationship model by assuming equal error variances. We derive the maximum likelihood estimate of the parameters in the simultaneous model and the covariance. We show by simulation study the small bias values of the parameters suggest the suitability of the estimation method. As an illustration, the proposed simultaneous model is applied to real data of the wind direction and wave direction measured by two different instruments.

Keywords: simultaneous linear functional relationship model, Fisher information matrix, parameter estimation, circular variables

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Authors: Hadi Farhadian, Homayoon Katibeh

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Groundwater inflow to the tunnels is one of the most important problems in tunneling operation. The objective of this study is the investigation of model dimension effects on tunnel inflow assessment in discontinuous rock masses using numerical modeling. In the numerical simulation, the model dimension has an important role in prediction of water inflow rate. When the model dimension is very small, due to low distance to the tunnel border, the model boundary conditions affect the estimated amount of groundwater flow into the tunnel and results show a very high inflow to tunnel. Hence, in this study, the two-dimensional universal distinct element code (UDEC) used and the impact of different model parameters, such as tunnel radius, joint spacing, horizontal and vertical model domain extent has been evaluated. Results show that the model domain extent is a function of the most significant parameters, which are tunnel radius and joint spacing.

Keywords: water inflow, tunnel, discontinues rock, numerical simulation

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Authors: Nassima Sotehi

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This article presents experimental and numerical results concerning the thermal properties of the porous materials used as heat insulator in the buildings sector. Initially, the thermal conductivity of three types of studied walls (classic concrete, concrete with cork aggregate and polystyrene concrete) was measured in experiments by the method of the boxes. Then a numerical modeling of the heat and mass transfers which occur within porous materials was applied to these walls. This work shows the influence of the presence of water in building materials on their thermophysical properties, as well as influence of the nature of materials and dosage of fibers introduced within these materials on the thermal and mass transfers.

Keywords: modeling, porous media, thermal materials, thermal properties

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Authors: Sara Bilal, Abdi Omar Shuriye, Raihan Othman

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Numerical Methods is a course that can be conducted using workshops and group discussion. This study has been implemented on undergraduate students of level two at the Faculty of Engineering, International Islamic University Malaysia. The Numerical Method course has been delivered to two Sections 1 and 2 with 44 and 22 students in each section, respectively. Systematic steps have been followed to apply the student centered learning approach in teaching Numerical Method course. Initially, the instructor has chosen the topic which was Euler’s Method to solve Ordinary Differential Equations (ODE) to be learned. The students were then divided into groups with five members in each group. Initial instructions have been given to the group members to prepare their subtopics before meeting members from other groups to discuss the subtopics in an expert group inside the classroom. For the time assigned for the classroom discussion, the setting of the classroom was rearranged to accommodate the student centered learning approach. Teacher strength was by monitoring the process of learning inside and outside the class. The students have been assessed during the migrating to the expert groups, recording of a video explanation outside the classroom and during the final examination. Euler’s Method to solve the ODE was set as part of Question 3(b) in the final exam. It is observed that none of the students from both sections obtained a zero grade in Q3(b), compared to Q3(a) and Q3(c). Also, for Section 1(44 students), 29 students obtained the full mark of 7/7, while only 10 obtained 7/7 for Q3(a) and no students obtained 6/6 for Q3(c). Finally, we can recommend that the Numerical Method course be moved toward more student-centered Learning classrooms where the students will be engaged in group discussion rather than having a teacher one man show.

Keywords: teacher centered learning, student centered learning, mathematic, numerical methods

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Authors: Bouziane Mohamed Tewfik

Abstract:

In order to improve the understanding of the influence of rainfall intensity on infiltration and deformation behaviour of unsaturated soil slopes, numerical 2D analyses are carried out by a three phase elasto-viscoplastic seepage-deformation coupled method. From the numerical results, it is shown that regardless of the saturated permeability of the soil slope, the increase in the pore water pressure (reduction in suction) during rainfall infiltration is localized close to the slope surface. In addition, the generation of the pore water pressure and the lateral displacement are mainly controlled by the ratio of the rainfall intensity to the saturated permeability of the soil.

Keywords: unsaturated soil, slope stability, rainfall infiltration, numerical analysis

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Authors: Palwinder Singh, Munish Sandhir, Tejinder Singh

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The ordinary differential equations (ODE) represent a natural framework for mathematical modeling of many real-life situations in the field of engineering, control systems, physics, chemistry and astronomy etc. Such type of differential equations can be solved by analytical methods or by numerical methods. If the solution is calculated using analytical methods, it is done through calculus theories, and thus requires a longer time to solve. In this paper, we compare the numerical accuracy of the solutions given by the three main types of one-step initial value solvers: Taylor’s Series Method, Euler’s Method and Runge-Kutta Fourth Order Method (RK4). The comparison of accuracy is obtained through comparing the solutions of ordinary differential equation given by these three methods. Furthermore, to verify the accuracy; we compare these numerical solutions with the exact solutions.

Keywords: Ordinary differential equations (ODE), Taylor’s Series Method, Euler’s Method, Runge-Kutta Fourth Order Method

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Authors: Amin Saeidi

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Using a representation-theoretic approach and considering G to be a finite primitive permutation group of degree n, our aim is to determine linear codes of length n that admit G as a permutation automorphism group. We can show that in some cases, every binary linear code admitting G as a permutation automorphism group is a submodule of a permutation module defined by a primitive action of G. As an illustration of the method, we consider the sporadic simple group M₁₁ and the unitary group U(3,3). We also construct some point- and block-primitive 1-designs from the supports of some codewords of the codes in the discussion.

Keywords: linear code, permutation representation, support design, simple group

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Authors: Claude Tadonki

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We address the issues related to the computation of the covariance matrix. This matrix is likely to be ill conditioned following its canonical expression, thus consequently raises serious numerical issues. The underlying linear system, which therefore should be solved by means of iterative approaches, becomes computationally challenging. A huge number of iterations is expected in order to reach an acceptable level of convergence, necessary to meet the required accuracy of the computation. In addition, this linear system needs to be solved at each iteration following the general form of the covariance matrix. Putting all together, its comes that we need to compute as fast as possible the associated matrix-vector product. This is our purpose in the work, where we consider and discuss skillful formulations of the problem, then propose a parallel implementation of the matrix-vector product involved. Numerical and performance oriented discussions are provided based on experimental evaluations.

Keywords: covariance-matrix, multicore, numerical computing, parallel computing

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Authors: Badr Alkahtani

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In this poster, numerical solutions of two-dimensional and three-dimensional lid driven cavity are presented by solving the steady Navier-Stokes equations at high Reynolds numbers where it becomes difficult. Lid driven cavity is where the a fluid contained in a cube and the upper wall is moving. In two dimensions, we use the streamfunction-vorticity formulation to solve the problem in a square domain. A numerical method is employed to discretize the problem in the x and y directions with a spectral collocation method. The problem is coded in the MATLAB programming environment. Solutions at high Reynolds numbers are obtained up to Re=20000 on a fine grid of 131 * 131. Also in this presentation, the numerical solutions for the three-dimensional lid-driven cavity problem are obtained by solving the velocity-vorticity formulation of the Navier-Stokes equations (which is the first time that this has been simulated with special boundary conditions) for various Reynolds numbers. A spectral collocation method is employed to discretize the y and z directions and a finite difference method is used to discretize the x direction. Numerical solutions are obtained for Reynolds number up to 200. , The work prepared here is to show the efficiency of methods used to simulate the physical problem where accurate simulations of lid driven cavity are obtained at high Reynolds number as mentioned above. The result for the two dimensional problem is far from the previous researcher result.

Keywords: lid driven cavity, navier-stokes, simulation, Reynolds number

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