Search results for: discontinuous finite volume method

Authors: Raphael de Oliveira Garcia, Samuel Rocha de Oliveira

Abstract:

We have developed a new computer program in Fortran 90, in order to obtain numerical solutions of a system of Relativistic Magnetohydrodynamics partial differential equations with predetermined gravitation (GRMHD), capable of simulating the formation of relativistic jets from the accretion disk of matter up to his ejection. Initially we carried out a study on numerical methods of unidimensional Finite Volume, namely Lax-Friedrichs, Lax-Wendroff, Nessyahu-Tadmor method and Godunov methods dependent on Riemann problems, applied to equations Euler in order to verify their main features and make comparisons among those methods. It was then implemented the method of Finite Volume Centered of Nessyahu-Tadmor, a numerical schemes that has a formulation free and without dimensional separation of Riemann problem solvers, even in two or more spatial dimensions, at this point, already applied in equations GRMHD. Finally, the Nessyahu-Tadmor method was possible to obtain stable numerical solutions - without spurious oscillations or excessive dissipation - from the magnetized accretion disk process in rotation with respect to a central black hole (BH) Schwarzschild and immersed in a magnetosphere, for the ejection of matter in the form of jet over a distance of fourteen times the radius of the BH, a record in terms of astrophysical simulation of this kind. Also in our simulations, we managed to get substructures jets. A great advantage obtained was that, with the our code, we got simulate GRMHD equations in a simple personal computer.

Keywords: finite volume methods, central schemes, fortran 90, relativistic astrophysics, jet

Procedia PDF Downloads 416

Authors: Y. Long, L. Liu, K. V. Branin

Abstract:

One challenge faced by procurement decision-maker during the acquisition process is how to compare similar products from different suppliers and allocate orders among different products or services. This work focuses on allocating orders among multiple suppliers considering rebate. The objective function is to minimize the total acquisition cost including purchasing cost and rebate benefit. Rebate benefit is complex and difficult to estimate at the ordering step. Rebate rules vary for different suppliers and usually change over time. In this work, we developed a system to collect the rebate policies, standardized the rebate policies and developed two-stage optimization models for ordering allocation. Rebate policy with multi-tiers is considered in modeling. The discontinuous cost function of rebate benefit is formulated for different scenarios. A piecewise linear function is used to approximate the discontinuous cost function of rebate benefit. And a Mixed Integer Programing (MIP) model is built for order allocation problem with multi-tier rebate. A case study is presented and it shows that our optimization model can reduce the total acquisition cost by considering rebate rules.

Keywords: discontinuous cost function, mixed integer programming, optimization, procurement, rebate

Procedia PDF Downloads 231

Authors: Carlos Caro, Ernest Bladé, Pedro Acosta, Camilo Lesmes

Abstract:

The drying-wet process is one of the topics to be more careful in distributed hydrological modeling using finite volume schemes as a means of solving the equations of Saint Venant. In a hydrologic and hydraulic computer model, surface flow phenomena depend mainly on the different flow accumulation and subsequent runoff generation. These accumulations are generated by routing, cell by cell, from the heights of water, which begin to appear due to the rain at each instant of time. Determine when it is considered a dry cell and when considered wet to include in the full calculation is an issue that directly affects the quantification of direct runoff or generation of flow at the end of a zone of contribution by accumulations flow generated from cells or finite volume.

Keywords: hydrology, transport processes, hydrological modelling, finite volume schemes

Procedia PDF Downloads 358

Authors: Reza Mollapourasl, Majid Haghi

Abstract:

In this study, we develop local meshfree methods known as radial basis function-generated finite difference (RBF-FD) method and Hermite finite difference (RBF-HFD) method to design stencil weights and spatial discretization for Helmholtz equation. The convergence and stability of schemes are investigated numerically in three dimensions with irregular shaped domain. These localized meshless methods incorporate the advantages of the RBF method, finite difference and Hermite finite difference methods to handle the ill-conditioning issue that often destroys the convergence rate of global RBF methods. Moreover, numerical illustrations show that the proposed localized RBF type methods are efficient and applicable for problems with complex geometries. The convergence and accuracy of both schemes are compared by solving a test problem.

Keywords: radial basis functions, Hermite finite difference, Helmholtz equation, stability

Procedia PDF Downloads 65

Authors: Hassan Parandvar, Mehrdad Farid

Abstract:

In this paper, a finite element modeling is presented for large amplitude vibration of functionally graded material (FGM) plates subjected to combined random pressure and thermal load. The material properties of the plates are assumed to vary continuously in the thickness direction by a simple power law distribution in terms of the volume fractions of the constituents. The material properties depend on the temperature whose distribution along the thickness can be expressed explicitly. The von Karman large deflection strain displacement and extended Hamilton's principle are used to obtain the governing system of equations of motion in structural node degrees of freedom (DOF) using finite element method. Three-node triangular Mindlin plate element with shear correction factor is used. The nonlinear equations of motion in structural degrees of freedom are reduced by using modal reduction method. The reduced equations of motion are solved numerically by 4th order Runge-Kutta scheme. In this study, the random pressure is generated using Monte Carlo method. The modeling is verified and the nonlinear dynamic response of FGM plates is studied for various values of volume fraction and sound pressure level under different thermal loads. Snap-through type behavior of FGM plates is studied too.

Keywords: nonlinear vibration, finite element method, functionally graded material (FGM) plates, snap-through, random vibration, thermal effect

Procedia PDF Downloads 231

Authors: Haijie Li, Xuping Zhang

Abstract:

This paper presents a computationally efficient method for the modeling of robot manipulators with flexible links and joints. This approach combines the Discrete Time Transfer Matrix Method with the Finite Segment Method, in which the flexible links are discretized by a number of rigid segments connected by torsion springs; and the flexibility of joints are modeled by torsion springs. The proposed method avoids the global dynamics and has the advantage of modeling non-uniform manipulators. Experiments and simulations of a single-link flexible manipulator are conducted for verifying the proposed methodologies. The simulations of a three-link robot arm with links and joints flexibility are also performed.

Keywords: flexible manipulator, transfer matrix method, linearization, finite segment method

Procedia PDF Downloads 402

Authors: Gaspar J. Machado, Stéphane Clain, Raphael Loubère

Abstract:

The goal of the present work is to numerically study steady-state nonlinear hyperbolic equations in the context of the finite volume framework. We will consider the unidimensional Burgers' equation as the reference case for the scalar situation and the unidimensional Euler equations for the vectorial situation. We consider two approaches to solve the nonlinear equations: a time marching algorithm and a direct steady-state approach. We first develop the necessary and sufficient conditions to obtain the existence and unicity of the solution. We treat regular examples and solutions with a steady shock and to provide very-high-order finite volume approximations we implement a method based on the MOOD technology (Multi-dimensional Optimal Order Detection). The main ingredient consists in using an 'a posteriori' limiting strategy to eliminate non physical oscillations deriving from the Gibbs phenomenon while keeping a high accuracy for the smooth part.

Keywords: Euler equations, finite volume, MOOD, steady-state

Procedia PDF Downloads 244

Authors: Ying Yi Wu

Abstract:

In this paper, we present a proof of the fact that a finite morphism is proper. We show that a finite morphism is universally closed and of finite type, which are the conditions for properness. Our proof is based on the theory of schemes and involves the use of the projection formula and the base change theorem. We first show that a finite morphism is of finite type and then proceed to show that it is universally closed. We use the fact that a finite morphism is also an affine morphism, which allows us to use the theory of coherent sheaves and their modules. We then show that the map induced by a finite morphism is flat and that the module it induces is of finite type. We use these facts to show that a finite morphism is universally closed. Our proof is constructive, and we provide details for each step of the argument.

Keywords: finite, morphism, schemes, projection.

Procedia PDF Downloads 72

Authors: Ramzi B. Albadarneh

Abstract:

In this paper, we use the new definition of fractional derivative called conformable fractional derivative to derive some finite difference formulas and its error terms which are used to solve fractional differential equations and fractional partial differential equations, also to derive fractional Euler method and its error terms which can be applied to solve fractional differential equations. To provide the contribution of our work some applications on finite difference formulas and Euler Method are given.

Keywords: conformable fractional derivative, finite difference formula, fractional derivative, finite difference formula

Procedia PDF Downloads 407

Authors: N. Fusun Oyman Serteller

Abstract:

In this paper, the techniques to solve time dependent electromagnetic wave propagation equations based on the Finite Difference Method (FDM) are proposed by comparing the results with Finite Element Method (FEM) in 2D while discussing some special simulation examples.  Here, 2D dynamical wave equations for lossy media, even with a constant source, are discussed for establishing symbolic manipulation of wave propagation problems. The main objective of this contribution is to introduce a comparative study of two suitable numerical methods and to show that both methods can be applied effectively and efficiently to all types of wave propagation problems, both linear and nonlinear cases, by using symbolic computation. However, the results show that the FDM is more appropriate for solving the nonlinear cases in the symbolic solution. Furthermore, some specific complex domain examples of the comparison of electromagnetic waves equations are considered. Calculations are performed through Mathematica software by making some useful contribution to the programme and leveraging symbolic evaluations of FEM and FDM.

Keywords: finite difference method, finite element method, linear-nonlinear PDEs, symbolic computation, wave propagation equations

Procedia PDF Downloads 111

Authors: Abu Afree Andalib, Rafiur Rahman, Md Mezbah Uddin

Abstract:

The main objective of this work is to anatomize on the various parameters of AGM 88 missile anatomized using FSI module in Ansys. Computational fluid dynamics is used for the study of fluid flow pattern and fluidic phenomenon such as drag, pressure force, energy dissipation and shockwave distribution in water. Using finite element analysis module of Ansys, structural parameters such as stress and stress density, localization point, deflection, force propagation is determined. Separate analysis on structural parameters is done on Abacus. State of the art coupling module is used for FSI analysis. Fine mesh is considered in every case for better result during simulation according to computational machine power. The result of the above-mentioned parameters is analyzed and compared for two phases using graphical representation. The result of Ansys and Abaqus are also showed. Computational Fluid Dynamics and Finite Element analyses and subsequently the Fluid-Structure Interaction (FSI) technique is being considered. Finite volume method and finite element method are being considered for modelling fluid flow and structural parameters analysis. Feasible boundary conditions are also utilized in the research. Significant change in the interaction and interference pattern while the impact was found. Theoretically as well as according to simulation angled condition was found with higher impact.

Keywords: FSI (Fluid Surface Interaction), impact, missile, high viscous fluid, CFD (Computational Fluid Dynamics), FEM (Finite Element Analysis), FVM (Finite Volume Method), fluid flow, fluid pattern, structural analysis, AGM-88, Ansys, Abaqus, meshing, k-omega, turbulence model

Procedia PDF Downloads 437

Authors: Wissem Tighidet, Faïçal Naït Bouda, Moussa Allouche

Abstract:

The numerical study of the Fluid-Structure Interaction (FSI) in a partially filled flexible tank submitted to a horizontal harmonic excitation motion. It is investigated by using two-way Fluid-Structure Interaction (FSI) in a flexible tank by Coupling between the Transient Structural (Mechanical) and Fluid Flow (Fluent) in ANSYS-Workbench Student version. The Arbitrary Lagrangian-Eulerian (ALE) formulation is adopted to solve with the finite volume method, the Navier-Stokes equations in two phases in a moving domain. The Volume of Fluid (VOF) method is applied to track the free surface. However, the equations of the dynamics of the structure are solved with the finite element method assuming a linear elastic behavior. To conclude, the Fluid-Structure Interaction (IFS) has a vital role in the analysis of the dynamic behavior of the rectangular tank. The results indicate that the flexibility of the tank walls has a significant impact on the amplitude of tank sloshing and the deformation of the free surface as well as the effect of liquid sloshing on wall deformation.

Keywords: arbitrary lagrangian-eulerian, fluid-structure interaction, sloshing, volume of fluid

Procedia PDF Downloads 71

Authors: D. Remache, M. Semaan, C. Baron, M. Pithioux, P. Chabrand, J. M. Rossi, J. L. Milan

Abstract:

A good understanding of the mechanical properties of the bone implies a better understanding of its various diseases, such as osteoporosis. Berkovich nanoindentation tests were performed on the human cortical bone to extract its orthotropic parameters. The nanoindentation experiments were then simulated by the finite element method. Different configurations of interactions between the tip indenter and the bone were simulated. The orthotropic parameters of the material were identified by the inverse method for each configuration. The friction effect on the bone mechanical properties was then discussed. It was found that the inverse method using the finite element method is a very efficient method to predict the mechanical behavior of the bone.

Keywords: mechanical behavior of bone, nanoindentation, finite element analysis, inverse optimization approaches

Procedia PDF Downloads 354

Authors: Tawanda Mushiri, Charles Mbohwa

Abstract:

The performance of door assembly is very significant for the vehicle design. In the present paper, the finite element method is used in the development processes of the door assembly. The stiffness, strength, modal characteristic, and anti-extrusion of a newly developed passenger vehicle door assembly are calculated and evaluated by several finite element analysis commercial software. The structural problems discovered by FE analysis have been modified and finally achieved the expected door structure performance target of this new vehicle. The issue in focus is to predict the performance of the door assembly by powerful finite element analysis software, and optimize the structure to meet the design targets. It is observed that this method can be used to forecast the performance of vehicle door efficiently when it’s designed. In order to reduce lead time and cost in the product development of vehicles more development will be made virtually.

Keywords: vehicle door, structure, strength, stiffness, modal characteristic, anti-extrusion, Finite Element Method

Procedia PDF Downloads 392

Authors: Gyo Woo Lee, Man Young Kim

Abstract:

The blocked-off formulations for the analysis of radiative heat transfer are formulated and examined in order to find the solutions in a two-dimensional complex enclosure. The final discretization equations using the step scheme for spatial differencing practice are proposed with the additional source term to incorporate the blocked-off procedure. After introducing the implementation for inactive region into the general discretization equation, three different problems are examined to find the performance of the solution methods.

Keywords: radiative heat transfer, Finite Volume Method (FVM), blocked-off solution procedure, body-fitted coordinate

Procedia PDF Downloads 261

Authors: Partha P. Gopmandal, Somnath Bhattacharyya, Naren Bag

Abstract:

In this article, we have studied the effect of pH-regulated surface charge on the electroosmotic flow (EOF) through nanochannel filled with binary symmetric electrolyte solution. The channel wall possesses either an acidic or a basic functional group. Going beyond the widely employed Debye-Huckel linearization, we develop a mathematical model based on Nernst-Planck equation for the charged species, Poisson equation for the induced potential, Stokes equation for fluid flow. A finite volume based numerical algorithm is adopted to study the effect of key parameters on the EOF. We have computed the coupled governing equations through the finite volume method and our results found to be in good agreement with the analytical solution obtained from the corresponding linear model based on low surface charge condition or strong electrolyte solution. The influence of the surface charge density, reaction constant of the functional groups, bulk pH, and concentration of the electrolyte solution on the overall flow rate is studied extensively. We find the effect of surface charge diminishes with the increase in electrolyte concentration. In addition for strong electrolyte, the surface charge becomes independent of pH due to complete dissociation of the functional groups.

Keywords: electroosmosis, finite volume method, functional group, surface charge

Procedia PDF Downloads 377

Authors: C. Juntarasaid, T. Pulngern, S. Chucheepsakul

Abstract:

A formulation of postbuckling analysis of end supported rods under self-weight has been presented by the variational method. The variational formulation involving the strain energy due to bending and the potential energy of the self-weight, are expressed in terms of the intrinsic coordinates. The variational formulation is accomplished by introducing the Lagrange multiplier technique to impose the boundary conditions. The finite element method is used to derive a system of nonlinear equations resulting from the stationary of the total potential energy and then Newton-Raphson iterative procedure is applied to solve this system of equations. The numerical results demonstrate the postbluckled configurations of end supported rods under self-weight. This finite element method based on variational formulation expressed in term of intrinsic coordinate is highly recommended for postbuckling analysis of end-supported rods under self-weight.

Keywords: postbuckling, finite element method, variational method, intrinsic coordinate

Procedia PDF Downloads 116

Authors: Jesus Ruano, Asensi Oliva

Abstract:

The hydrodynamic field generated by a jet expansion is computed via three dimensional compressible Large Eddy Simulation (LES). Finite Volume Method (FVM) will be the discretization used during this simulation as well as hybrid schemes based on Kinetic Energy Preserving (KEP) schemes and up-winding Godunov based schemes with instabilities detectors. Velocity and pressure fields will be stored at different surfaces near the jet, but far enough to enclose all the fluctuations, in order to use them as input for the acoustic solver. The acoustic field is obtained in the far-field region at several locations by means of a hybrid method based on Ffowcs-Williams and Hawkings (FWH) equation. This equation will be formulated in the spectral domain, via Fourier Transform of the acoustic sources, which are modeled from the results of the initial simulation. The obtained results will allow the study of the broadband noise generated as well as sound directivities.

Keywords: far-field noise, Ffowcs-Williams and Hawkings, finite volume method, large eddy simulation, jet noise

Procedia PDF Downloads 273

Authors: Alia Alghosoun, Michael Herty, Mohammed Seaid

Abstract:

We present a new class of numerical techniques to solve shallow water flows over dry areas including run-up. Many recent investigations on wave run-up in coastal areas are based on the well-known shallow water equations. Numerical simulations have also performed to understand the effects of several factors on tsunami wave impact and run-up in the presence of coastal areas. In all these simulations the shallow water equations are solved in entire domain including dry areas and special treatments are used for numerical solution of singularities at these dry regions. In the present study we propose a new method to deal with these difficulties by reformulating the shallow water equations into a new system to be solved only in the wetted domain. The system is obtained by a change in the coordinates leading to a set of equations in a moving domain for which the wet/dry interface is the reconstructed using the wave speed. To solve the new system we present a finite volume method of Lax-Friedrich type along with a modified method of characteristics. The method is well-balanced and accurately resolves dam-break problems over dry areas.

Keywords: dam-break problems, finite volume method, run-up waves, shallow water flows, wet/dry interfaces

Procedia PDF Downloads 122

Authors: K. Noah, F.-S. Lien

Abstract:

In Computational Fluid Dynamics (CFD), there are a variety of numerical methods, of which some depend on macroscopic model representatives. These models can be solved by finite-volume, finite-element or finite-difference methods on a microscopic description. However, the lattice Boltzmann method (LBM) is considered to be a mesoscopic particle method, with its scale lying between the macroscopic and microscopic scales. The LBM works well for solving incompressible flow problems, but certain limitations arise from solving compressible flows, particularly at high Mach numbers. An improved lattice Boltzmann model for compressible flow problems is presented in this research study. A higher-order Taylor series expansion of the Maxwell equilibrium distribution function is used to overcome limitations in LBM when solving high-Mach-number flows. Large eddy simulation (LES) is implemented in LBM to simulate turbulent jet flows. The results have been validated with available experimental data for turbulent compressible free jet flow at subsonic speeds.

Keywords: compressible lattice Boltzmann method, multiple relaxation times, large eddy simulation, turbulent jet flows

Procedia PDF Downloads 245

Authors: K. P. Mredula, D. C. Vakaskar

Abstract:

The article traces developments and evolution of various algorithms developed for solving partial differential equations using the significant combination of wavelet with few already explored solution procedures. The approach depicts a study over a decade of traces and remarks on the modifications in implementing multi-resolution of wavelet, finite difference approach, finite element method and finite volume in dealing with a variety of partial differential equations in the areas like plasma physics, astrophysics, shallow water models, modified Burger equations used in optical fibers, biology, fluid dynamics, chemical kinetics etc.

Keywords: multi-resolution, Haar Wavelet, partial differential equation, numerical methods

Procedia PDF Downloads 263

Authors: Shidvash Vakilipour, Masoud Mohammadi, Rouzbeh Riazi, Scott Ormiston, Kimia Amiri, Sahar Barati

Abstract:

An essential component of a finite volume method (FVM) is the advection scheme that estimates values on the cell faces based on the calculated values on the nodes or cell centers. The most widely used advection schemes are upwind schemes. These schemes have been developed in FVM on different kinds of structured and unstructured grids. In this research, the physical influence scheme (PIS) is developed for a cell-centered FVM that uses an implicit coupled solver. Results are compared with the exponential differencing scheme (EDS) and the skew upwind differencing scheme (SUDS). Accuracy of these schemes is evaluated for a lid-driven cavity flow at Re = 1000, 3200, and 5000 and a backward-facing step flow at Re = 800. Simulations show considerable differences between the results of EDS scheme with benchmarks, especially for the lid-driven cavity flow at high Reynolds numbers. These differences occur due to false diffusion. Comparing SUDS and PIS schemes shows relatively close results for the backward-facing step flow and different results in lid-driven cavity flow. The poor results of SUDS in the lid-driven cavity flow can be related to its lack of sensitivity to the pressure difference between cell face and upwind points, which is critical for the prediction of such vortex dominant flows.

Keywords: cell-centered finite volume method, coupled solver, exponential differencing scheme (EDS), physical influence scheme (PIS), pressure weighted interpolation method (PWIM), skew upwind differencing scheme (SUDS)

Procedia PDF Downloads 248

Authors: Haoui Rabah

Abstract:

The aim of this work is to analyze a viscous flow around the axisymmetric blunt body taken into account the mesh size both in the free stream and into the boundary layer. The resolution of the Navier-Stokes equations is realized by using the finite volume method to determine the flow parameters and detached shock position. The numerical technique uses the Flux Vector Splitting method of Van Leer. Here, adequate time stepping parameter, CFL coefficient and mesh size level are selected to ensure numerical convergence. The effect of the mesh size is significant on the shear stress and velocity profile. The best solution is obtained with using a very fine grid. This study enabled us to confirm that the determination of boundary layer thickness can be obtained only if the size of the mesh is lower than a certain value limits given by our calculations.

Keywords: supersonic flow, viscous flow, finite volume, blunt body

Procedia PDF Downloads 578

Authors: Juan F. P. Ramírez, Jésica A. L. Isaza, Benjamín A. Rojano

Abstract:

This study proposes a novel use of a method to determine the mechanical properties of fruits by the use of the indentation tests. The method combines experimental results with a numerical finite elements model. The results presented correspond to a simplified numerical modeling of banana. The banana was assumed as one-layer material with an isotropic linear elastic mechanical behavior, the Young’s modulus found is 0.3Mpa. The method will be extended to multilayer models in further studies.

Keywords: finite element method, fruits, inverse analysis, mechanical properties

Procedia PDF Downloads 322

Authors: Bashar Albaalbaki, Roger E. Khayat

Abstract:

This work is a comparative study on the effect of Delaunay triangulation algorithms on discretization error for conduction-convection conservation problems. A structured triangulation and many unstructured Delaunay triangulations using three popular algorithms for node placement strategies are used. The numerical method employed is the vertex-centered finite volume method. It is found that when the computational domain can be meshed using a structured triangulation, the discretization error is lower for structured triangulations compared to unstructured ones for only low Peclet number values, i.e. when conduction is dominant. However, as the Peclet number is increased and convection becomes more significant, the unstructured triangulations reduce the discretization error. Also, no statistical correlation between triangulation angle extremums and the discretization error is found using 200 samples of randomly generated Delaunay and non-Delaunay triangulations. Thus, the angle extremums cannot be an indicator of the discretization error on their own and need to be combined with other triangulation quality measures, which is the subject of further studies.

Keywords: conduction-convection problems, Delaunay triangulation, discretization error, finite volume method

Procedia PDF Downloads 62

Authors: Sabrina Nouri, Abderahmane Ghezal, Said Abboudi, Pierre Spiteri

Abstract:

This paper deals with the numerical study of heat and mass transfer of laminar flow transition at low Prandtl numbers. The model includes the two-directional momentum, the energy and mass transfer equations. These equations are discretized by the finite volume method and solved by a self-made simpler like Fortran code. The effect of governing parameters, namely the Lewis and Prandtl numbers, on the transition of the flow and solute distribution is studied for positive and negative thermal and solutal buoyancy forces ratio. Nusselt and Sherwood numbers are derived for of Prandtl [10⁻²-10¹] and Lewis numbers [1-10⁴]. The results show unicell and multi-cell flow. Solute and flow boundary layers appear for low Prandtl number.

Keywords: natural convection, low Prandtl number, heat and mass transfer, finite volume method

Procedia PDF Downloads 172

Authors: Atousa Ataieyan, Salvador A. Gomez-Lopera, Gennaro Sepede

Abstract:

Today, due to the growing urban population and consequently, the increasing water demand in cities, the amount of contaminants entering the water resources is increasing. This can impose harmful effects on the quality of the downstream water. Therefore, predicting the concentration of discharged pollutants at different times and distances of the interested area is of high importance in order to carry out preventative and controlling measures, as well as to avoid consuming the contaminated water. In this paper, the concentration distribution of an injected conservative pollutant in a square reservoir containing four symmetric blocks and three sources using Finite Volume Method (FVM) is simulated. For this purpose, after estimating the flow velocity, classical Advection-Diffusion Equation (ADE) has been discretized over the studying domain by Backward Time- Backward Space (BTBS) scheme. Then, the discretized equations for each node have been derived according to the initial condition, boundary conditions and point contaminant sources. Finally, taking into account the appropriate time step and space step, a computational code was set up in MATLAB. Contaminant concentration was then obtained at different times and distances. Simulation results show how using BTBS differentiating scheme and FVM as a numerical method for solving the partial differential equation of transport is an appropriate approach in the case of two-dimensional contaminant transfer in an advective-diffusive flow.

Keywords: BTBS differentiating scheme, contaminant concentration, finite volume, mass transfer, water pollution

Procedia PDF Downloads 110

Authors: Utkan Caliskan

Abstract:

Two types of numerical codes based on finite volume method are developed in order to solve compressible Euler equations to simulate the flow through forward facing step channel. Both algorithms have AUSM+- up (Advection Upstream Splitting Method) scheme for flux splitting and two-stage Runge-Kutta scheme for time stepping. In this study, the flux calculations differentiate between the algorithm based on OpenFOAM mesh format which is called 'face-based' algorithm and the basic algorithm which is called 'element-based' algorithm. The face-based algorithm avoids redundant flux computations and also is more flexible with hybrid grids. Moreover, some of OpenFOAM’s preprocessing utilities can be used on the mesh. Parallelization of the face based algorithm for which atomic operations are needed due to the shared memory model, is also presented. For several mesh sizes, 2.13x speed up is obtained with face-based approach over the element-based approach.

Keywords: cell centered finite volume method, compressible Euler equations, OpenFOAM mesh format, OpenMP

Procedia PDF Downloads 288

Authors: Ionel D. Craiu, Mihai Nedelcu

Abstract:

Thin-walled cylinders are often used by the offshore industry as columns of floating installations. Based on observed strains, the inverse Finite Element Method (iFEM) may rebuild the deformation of structures. Structural Health Monitoring uses this approach extensively. However, the number of in-situ strain gauges is what determines how accurate it is, and for shell structures with complicated deformation, this number can easily become too high for practical use. Any thin-walled beam member's complicated deformation can be modeled by the Generalized Beam Theory (GBT) as a linear combination of pre-specified cross-section deformation modes. GBT uses bar finite elements as opposed to shell finite elements. This paper proposes an iFEM/GBT formulation for the shape sensing of thin-walled cylinders based on these benefits. This method significantly reduces the number of strain gauges compared to using the traditional inverse-shell finite elements. Using numerical simulations, dent damage detection is achieved by comparing the strain distributions of the undamaged and damaged members. The effect of noise on strain measurements is also investigated.

Keywords: damage detection, generalized beam theory, inverse finite element method, shape sensing

Procedia PDF Downloads 79

Authors: Jesus Ruano, Francesc Xavier Trias, Asensi Oliva

Abstract:

A three-dimensional incompressible Large Eddy Simulation (LES) is performed to compute the hydrodynamic field around a pair of tandem cylinders. Symmetry-preserving schemes will be used during this simulation in conjunction with Finite Volume Method (FVM) to obtain the hydrodynamic field around the selected geometry. A set of results consisting of pressure and velocity and the combination of them will be stored at different surfaces near the cylinders as the initial input for the second part of the study. A post-processing of the obtained results based on Ffowcs-Williams and Hawkings (FWH) equation with a Fourier Transform of the acoustic sources will be used to compute noise at several probes located far away from the region where the hydrodynamics are computed. Directivities as well as spectral profile of the obtained acoustic field will be analyzed.

Keywords: far-field noise, Ffowcs-Williams and Hawkings, finite volume method, large eddy simulation, long-span bodies

Procedia PDF Downloads 340