Search results for: finite differences method

Authors: Martin Cermak, Stanislav Sysala

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In this paper we present the efficient parallel implementation of elastoplastic problems based on the TFETI (Total Finite Element Tearing and Interconnecting) domain decomposition method. This approach allow us to use parallel solution and compute this nonlinear problem on the supercomputers and decrease the solution time and compute problems with millions of DOFs. In our approach we consider an associated elastoplastic model with the von Mises plastic criterion and the combination of linear isotropic-kinematic hardening law. This model is discretized by the implicit Euler method in time and by the finite element method in space. We consider the system of nonlinear equations with a strongly semismooth and strongly monotone operator. The semismooth Newton method is applied to solve this nonlinear system. Corresponding linearized problems arising in the Newton iterations are solved in parallel by the above mentioned TFETI. The implementation of this problem is realized in our in-house MatSol packages developed in MATLAB.

Keywords: isotropic-kinematic hardening, TFETI, domain decomposition, parallel solution

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Authors: Mohammad Tahmasebipour, Hosein Salarpour

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Researchers suggest that variations in Poisson’s ratio affect the behavior of Timoshenko micro beam. Therefore, in this study, two epoxy Timoshenko micro beams with different dimensions were modeled using the finite element method considering all boundary conditions and initial conditions that govern the problem. The effect of Poisson’s ratio on the resonant frequency, maximum deflection, and maximum rotation of the micro beams was examined. The analyses suggest that an increased Poisson’s ratio reduces the maximum rotation and the maximum rotation and increases the resonant frequency. Results were consistent with those obtained using the couple stress, classical, and strain gradient elasticity theories.

Keywords: microbeam, microsensor, epoxy, poisson’s ratio, dynamic behavior, static behavior, finite element method

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Authors: Thana Ananacha

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This paper reports the numerical and experimental performances of Double Glass Wall are investigated. Two configurations were considered namely, the Double Clear Glass Wall (DCGW) and the Double Translucent Glass Wall (DTGW). The coupled governing equations as well as boundary conditions are solved using the finite element method (FEM) via COMSOLTM Multiphysics. Temperature profiles and flow field of the DCGW and DTGW are reported and discussed. Different constant heat fluxes were considered namely 400 and 800 W.m-2 the corresponding initial condition temperatures were to 30.5 and 38.5 ºC respectively. The results show that the simulation results are in agreement with the experimental data. Conclusively, the model considered in this study could reasonable be used simulate the thermal and ventilation performance of the DCGW and DTGW configurations.

Keywords: thermal simulation, Double Glass Wall, velocity field, finite element method (FEM)

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Authors: Zilong Peng, Jun Fan

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With the improvement of the living standards, the requirement on the acoustic comfort of the vehicle interior environment is becoming higher. The rain-the-roof producing interior noise is a common phenomenon for the vehicle, which usually discourages the conversation, especially for the heavy rain. This paper presents some numerical results about the rain-the-roof noise. The impact of each water drop is modeled as a short pulse, and the excitation locations on the roof are generated randomly. The vehicle body is simplified to a box closed with some certain-thickness shells. According to the main frequency components of the rain excitation, the analyzing frequency range is divided as low, high and middle frequency domains, which makes the vehicle body are modeled using finite element method (FEM), statistical energy analysis (SEA) and hybrid FE-SEA method, respectively. Furthermore, the effect of spatial distribution density and size of the rain on the sound pressure level are also discussed. These results may provide a guide for designing a more silent vehicle in the special weather.

Keywords: rain-the-roof noise, vehicle, finite element method, statistical energy analysis

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Authors: Nosakhare Enoma, Alphose Zingoni

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The requirements for various toroidal shell forms are increasing due to new applications, available storage space and the consideration of appearance. Because of the complexity of some of these structural forms, the finite element method is nowadays mainly used for their analysis, even for simple static studies. This paper presents an easy-to-use analytical algorithm for pressurized multi-segmented toroidal shells of revolution. The membrane solution, which acts as a particular solution of the bending-theory equations, is developed based on membrane theory of shells, and a general approach is formulated for quantifying discontinuity effects at the shell junctions using the well-known Geckeler’s approximation. On superimposing these effects, and applying the ensuing solution to the problem of the pressurized toroid with four segments, closed-form stress results are obtained for the entire toroid. A numerical example is carried out using the developed method. The analytical results obtained show excellent agreement with those from the finite element method, indicating that the proposed method can be also used for complementing and verifying FEM results, and providing insights on other related problems.

Keywords: bending theory of shells, membrane hypothesis, pressurized toroid, segmented toroidal vessel, shell analysis

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Authors: Nkwa Agbor Etobi Arreneke

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A well-designed earthing/grounding system will not only provide an effective path for direct dissipation of faulty currents into the earth/soil, but also ensure the safety of personnels withing and around its immediate surrounding perimeter is free from the possibility of fatal electric shock. In order to achieve the latter, it is of paramount importance to ensuring that both the step and touch potentials are kept within the allowable tolerance set by standards IEEE Std-80-2000. In this article, the step and touch potentials of an earthing system are simulated and conformity verified using the Finite Element Method (FEM), and has been found to be 242.4V and 194.80V respectively. The effect of injection current position is also analyzed to observe its effect on a person within or in contact with any active part of the earthing system of the substation. The values obtained closely matches those of other published works which made using different numerical methods and/or simulations Genetic Algorithm (GA). This current study is aimed at throwing more light to the dangers of step and touch potential of earthing systems of substation and electrical facilities as a whole, and the need for further in-dept analysis of these parameters. Observations made on this current paper shows that, the position of contact with an energize earthing system is of paramount important in determining its effect on living organisms in contact with any energized part of the earthing systems.

Keywords: earthing/grounding systems, finite element method (fem), ground/earth resistance, safety, touch and step potentials, generic algorithm

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Authors: Xuan Sun, Mingbo Tong

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To understand the factors which affect impact damage on composite structures, particularly the effects of impact position and ribs. In this paper, a finite element model (FEM) of low-velocity impact damage on the composite structure was established via the nonlinear finite element method, combined with the user-defined materials subroutine (VUMAT) of the ABAQUS software. The structural elements chosen for the investigation comprised a series of stiffened composite panels, representative of real aircraft structure. By impacting the panels at different positions relative to the ribs, the effect of relative position of ribs was found out. Then the simulation results and the experiments data were compared. Finally, the factors which affect impact damage on the structures were discussed. The paper was helpful for the design of stiffened composite structures.

Keywords: stiffened, low-velocity impact, Abaqus, impact energy

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Authors: Gozel Judakova, Markus Bause

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We present and analyze reliable numerical techniques for simulating complex flow and transport phenomena related to natural gas transportation in pipelines. Such kind of problems are of high interest in the field of petroleum and environmental engineering. Modeling and understanding natural gas flow and transformation processes during transportation is important for the sake of physical realism and the design and operation of pipeline systems. In our approach a two fluid flow model based on a system of coupled hyperbolic conservation laws is considered for describing natural gas flow undergoing hydratization. The accurate numerical approximation of two-phase gas flow remains subject of strong interest in the scientific community. Such hyperbolic problems are characterized by solutions with steep gradients or discontinuities, and their approximation by standard finite element techniques typically gives rise to spurious oscillations and numerical artefacts. Recently, stabilized and discontinuous Galerkin finite element techniques have attracted researchers’ interest. They are highly adapted to the hyperbolic nature of our two-phase flow model. In the presentation a streamline upwind Petrov-Galerkin approach and a discontinuous Galerkin finite element method for the numerical approximation of our flow model of two coupled systems of Euler equations are presented. Then the efficiency and reliability of stabilized continuous and discontinous finite element methods for the approximation is carefully analyzed and the potential of the either classes of numerical schemes is investigated. In particular, standard benchmark problems of two-phase flow like the shock tube problem are used for the comparative numerical study.

Keywords: discontinuous Galerkin method, Euler system, inviscid two-fluid model, streamline upwind Petrov-Galerkin method, twophase flow

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Authors: L. I. Izhar, T. Stathaki, K. Howell

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Analyzing and interpreting of thermograms have been increasingly employed in the diagnosis and monitoring of diseases thanks to its non-invasive, non-harmful nature and low cost. In this paper, a novel system is proposed to improve diagnosis and monitoring of morphoea skin disorder based on integration with the published lines of Blaschko. In the proposed system, image registration based on global and local registration methods are found inevitable. This paper presents a modified normalized gradient cross-correlation (NGC) method to reduce large geometrical differences between two multimodal images that are represented by smooth gray edge maps is proposed for the global registration approach. This method is improved further by incorporating an iterative-based normalized cross-correlation coefficient (NCC) method. It is found that by replacing the final registration part of the NGC method where translational differences are solved in the spatial Fourier domain with the NCC method performed in the spatial domain, the performance and robustness of the NGC method can be greatly improved. It is shown in this paper that the hybrid NGC method not only outperforms phase correlation (PC) method but also improved misregistration due to translation, suffered by the modified NGC method alone for thermograms with ill-defined jawline. This also demonstrates that by using the gradients of the gray edge maps and a hybrid technique, the performance of the PC based image registration method can be greatly improved.

Keywords: Blaschko’s lines, image registration, morphoea, thermal imaging

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Authors: Amir T. Payandeh Najafabadi

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This article considers the problem of evaluating infinite-time (or finite-time) ruin probability under a given compound Poisson surplus process by approximating the claim size distribution by a finite mixture exponential, say Hyperexponential, distribution. It restates the infinite-time (or finite-time) ruin probability as a solvable ordinary differential equation (or a partial differential equation). Application of our findings has been given through a simulation study.

Keywords: ruin probability, compound poisson processes, mixture exponential (hyperexponential) distribution, heavy-tailed distributions

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Authors: R. K. Apalowo, D. Chronopoulos, V. Thierry

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There exist a wide range of failure modes in composite structures due to the increased usage of the structures especially in aerospace industry. Moreover, temperature dependent wave response of composite and layered structures have been continuously studied, though still limited, in the last decade mainly due to the broad operating temperature range of aerospace structures. A wave finite element (WFE) and finite element (FE) based computational method is presented by which the temperature dependent wave dispersion characteristics and interaction phenomenon in composite structures can be predicted. Initially, the temperature dependent mechanical properties of the panel in the range of -100 ◦C to 150 ◦C are measured experimentally using the Thermal Mechanical Analysis (TMA). Temperature dependent wave dispersion characteristics of each waveguide of the structural system, which is discretized as a system of a number of waveguides coupled by a coupling element, is calculated using the WFE approach. The wave scattering properties, as a function of temperature, is determined by coupling the WFE wave characteristics models of the waveguides with the full FE modelling of the coupling element on which defect is included. Numerical case studies are exhibited for two waveguides coupled through a coupling element.

Keywords: finite element, temperature dependency, wave dispersion characteristics, wave finite element, wave scattering properties

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Authors: Lian Song, Shao-Bo Kang, Bo Yang

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Concrete filled steel tubular (CFST) structure has been widely used in construction practices due to its superior performances under various loading conditions. However, limited studies are available when this type of structure is subjected to impact or explosive loads. Current methods in relevant design codes are not specific for preventing progressive collapse of CFST structures. Therefore, it is necessary to carry out numerical simulations on CFST structure under impact loads. In this study, finite element analyses are conducted on the mechanical behaviour of composite frames which composed of CFST columns and steel beams subject to impact loading. In the model, CFST columns are simulated using finite element software ABAQUS. The model is verified by test results of solid and hollow CFST columns under lateral impacts, and reasonably good agreement is obtained through comparisons. Thereafter, a multi-scale finite element modelling technique is developed to evaluate the behaviour of a five-storey three-span planar composite frame. Alternate path method and direct simulation method are adopted to perform the dynamic response of the frame when a supporting column is removed suddenly. In the former method, the reason for column removal is not considered and only the remaining frame is simulated, whereas in the latter, a specific impact load is applied to the frame to take account of the column failure induced by vehicle impact. Comparisons are made between these two methods in terms of displacement history and internal force redistribution, and design recommendations are provided for the design of CFST structures under impact loads.

Keywords: planar composite frame, collapse analysis, impact loading, direct simulation method, alternate path method

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Authors: Shreya Thusoo, Karan Modi, Ankit Kumar Jha, Rajesh Kumar

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Since the evolution of computational tools and simulation software, there has been considerable increase in research on Soil Structure Interaction (SSI) to decrease the computational time and increase accuracy in the results. To aid the designer with a proper understanding of the response of structure in different soil types, the presented paper compares the deformation, shear stress, acceleration and other parameters of multi-storey building for a specific input ground motion using Response-spectrum Analysis (RSA) method. The response of all the models of different heights have been compared in different soil types. Finite Element Simulation software, ANSYS, has been used for all the computational purposes. Overall, higher response is observed with SSI, while it increases with decreasing stiffness of soil.

Keywords: soil-structure interaction, response spectrum, analysis, finite element method, multi-storey buildings

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

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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

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Authors: Boukelkoul Lahcen

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The cumulative costs for O&M may represent as much as 65%-90% of the turbine's investment cost. Nowadays the cost effectiveness concept becomes a decision-making and technology evaluation metric. The cost of energy metric accounts for the effect replacement cost and unscheduled maintenance cost parameters. One key of the proposed approach is the idea of maintaining the WTs which can be captured via use of a finite state Markov chain. Such a model can be embedded within a probabilistic operation and maintenance simulation reflecting the action to be done. In this paper, an approach of estimating the cost of O&M is presented. The finite state Markov model is used for decision problems with number of determined periods (life cycle) to predict the cost according to various options of maintenance.

Keywords: cost, finite state, Markov model, operation and maintenance

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Authors: Utkan Caliskan

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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

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Authors: Mojtaba Ahmadabadi, Akbar Masoudi, Morteza Rezai

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In this paper, using the finite element method, the effect of soil and wall characteristics was investigated. Thirty and two different models were studied by different parameters. These studies could calculate displacement at any height of the wall for frictional-cohesive soils. The main purpose of this research is to determine the most effective soil characteristics in reducing the wall displacement. Comparing different models showed that the overall increase in internal friction angle, angle of friction between soil and wall and modulus of elasticity reduce the replacement of the wall. In addition, increase in special weight of soil will increase the wall displacement. Based on results, it can be said that all wall displacements were overturning and in the backfill, soil was bulging. Results show that the highest impact is seen in reducing wall displacement, internal friction angle, and the angle friction between soil and wall. One of the advantages of this study is taking into account all the parameters of the soil and walls replacement distribution in wall and backfill soil. In this paper, using the finite element method and considering all parameters of the soil, we investigated the impact of soil parameter in wall displacement. The aim of this study is to provide the best conditions in reducing the wall displacement and displacement wall and soil distribution.

Keywords: retaining wall, fem, soil and wall interaction, angle of internal friction of the soil, wall displacement

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Authors: H. C. Nguyen

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This contribution considers seismic effects on the stability of slope and footing resting on a slope. The seismic force is simply treated as static inertial force through the values of acceleration factor. All domains are assumed to be plasticity deformations approximated using node-based smoothed finite element method (NS-FEM). The failure mechanism and safety factor were then explored using numerical procedure based on upper bound approach in which optimization problem was formed as second order cone programming (SOCP). The data obtained confirm that upper bound procedure using NS-FEM and SOCP can give stable and rapid convergence results of seismic stability factors.

Keywords: upper bound analysis, safety factor, slope stability, footing resting on slope

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Authors: Mehdi Ghatei, Masoomeh Lorestani

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Upstream Tailings Storage Facilities (TSFs) may experience slope instabilities due to soil liquefaction, especially in regions known to be seismically active. In this study, liquefaction susceptibility of an upstream-raised TSF in Western Australia was assessed using two different approaches. The first approach assessed liquefaction susceptibility using Cone Penetration Tests with pore pressure measurement (CPTu) as described by the National Centre for Earthquake Engineering Research (NCEER). This assessment was based on the four CPTu tests that were conducted on the perimeter embankment of the TSF. The second approach used the Finite Element (FE) method with application of an equivalent linear model to predict the undrained cyclic behavior, the pore water pressure and the liquefaction of the materials. The tailings parameters were estimated from the CPTu profiles and from the laboratory tests. The cyclic parameters were estimated from the literature where test results of similar material were available. The results showed that there was a good agreement, in the liquefaction susceptibility of the tailings material, between the NCEER and FE methods with equivalent linear model.

Keywords: liquefaction , CPTU, NCEER, finite element method, equivalent linear model

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Authors: Yee-Ting Lee, Jyun-Rong Zhuang, Wen-Hsin Hsieh, An-Shik Yang

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Additive manufacturing (AM) is increasingly crucial in biomedical and aerospace industries. As a recently developed AM technique, selective laser melting (SLM) has become a commercial method for various manufacturing processes. However, the molten pool configuration during SLM of metal powders is a decisive issue for the product quality. It is very important to investigate the heat transfer characteristics during the laser heating process. In this work, the finite element method (FEM) software ANSYS^® (work bench module 16.0) was used to predict the unsteady temperature distribution for resolving molten pool dimensions with consideration of temperature-dependent thermal physical properties of TiAl6V4 at different laser powers and scanning speeds. The simulated results of the temperature distributions illustrated that the ratio of laser power to scanning speed can greatly influence the size of molten pool of titanium alloy powder for SLM development.

Keywords: additive manufacturing, finite element method, molten pool dimensions, selective laser melting

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Authors: Muna Tabuni

Abstract:

The paper contains an investigation on the special properties of the zeros of the analytic representations of finite quantum systems. These zeros and their paths completely define the finite quantum system. The present paper studies the construction of the analytic representation from its zeros. The analytic functions of finite quantum systems are introduced. The zeros of the analytic theta functions and their paths have been studied. The analytic function f(z) have exactly d zeros. The analytic function has been constructed from its zeros.

Keywords: construction, analytic, representation, zeros

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Authors: Manikanta Prasad Banda, Che Hua Yang

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Anti-symmetric wave propagation along the particle motion of the wedge waves is known as anti-symmetric flexural (ASF) modes which travel along the wedge tips of the mid-plane apex with a small truncation. This paper investigates the characteristics of the ASF modes propagation with the wedge tip crack. The simulation and experimental results obtained by a three-dimensional (3-D) finite element model explained the contact acoustic non-linear (CAN) behavior in explicit dynamics in ABAQUS and the ultrasonic non-destructive testing (NDT) method is used for defect detection. The effect of various parameters on its high and low-level conversion modes are known for complex reflections and transmissions involved with direct reflections and transmissions. The results are used to predict the location of crack through complex transmission and reflection coefficients.

Keywords: ASF mode, crack detection, finite elements method, laser ultrasound technique, wedge waves

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Authors: Mohamed Hafid, Marcel Lacroix

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This study presents a simple inverse heat transfer procedure for predicting the wall erosion and the time-varying thickness of the protective bank that covers the inside surface of the refractory brick wall of a melting furnace. The direct problem is solved by using the Finite-Volume model. The melting/solidification process is modeled using the enthalpy method. The inverse procedure rests on the Levenberg-Marquardt method combined with the Broyden method. The effect of the location of the temperature sensors and of the measurement noise on the inverse predictions is investigated. Recommendations are made concerning the location of the temperature sensor.

Keywords: melting furnace, inverse heat transfer, enthalpy method, levenberg–marquardt method

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Authors: Kamel Al-Khaled

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In this paper, numerical solutions for the nonlinear coupled Korteweg-de Vries, (abbreviated as KdV) equations are calculated by Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. First, discretizing time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a $\theta-$weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method.

Keywords: Nonlinear coupled KdV equations, Soliton solutions, Sinc-collocation method, Sinc functions

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Authors: Raphael Zanella

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This works deals with the finite element approximation of axisymmetric problems. The weak formulation of the heat equation under the axisymmetry assumption is established for continuous finite elements. The weak formulation is implemented in a C++ solver with implicit march-in-time. The code is verified by space and time convergence tests using a manufactured solution. The solving of an example problem with an axisymmetric formulation is compared to that with a full-3D formulation. Both formulations lead to the same result, but the code based on the axisymmetric formulation is much faster due to the lower number of degrees of freedom. This confirms the correctness of our approach and the interest in using an axisymmetric formulation when it is possible.

Keywords: axisymmetric problem, continuous finite elements, heat equation, weak formulation

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Authors: C. F. Kumru, C. Kocatepe, O. Arikan

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In this study, electric field distribution analyses for three pylon models are carried out by a Finite Element Method (FEM) based software. Analyses are performed in both stationary and time domains to observe instantaneous values along with the effective ones. Considering the results of the study, different line geometries is considerably affecting the magnitude and distribution of electric field although the line voltages are the same. Furthermore, it is observed that maximum values of instantaneous electric field obtained in time domain analysis are quite higher than the effective ones in stationary mode. In consequence, electric field distribution analyses should be individually made for each different line model and the limit exposure values or distances to residential buildings should be defined according to the results obtained.

Keywords: electric field, energy transmission line, finite element method, pylon

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Authors: Masoud Mahdavi

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During an earthquake, the structure is subjected to seismic loads that cause tension in the members of the building. The use of energy dissipation elements in the structure reduces the percentage of seismic forces on the main members of the building (especially the columns). Steel plate shear wall, as one of the most widely used types of energy dissipation element, has evolved today, and regular drilling of its inner plate is one of the common cases. In the present study, using a finite element method, the shear wall of the steel plate is designed as a floor (with dimensions of 447 × 6/246 cm) with Abacus software and in three different modes on which a cyclic load has been applied. The steel shear wall has a horizontal element (beam) with a reduced beam section (RBS). The hole in the interior plate of the models is created in such a way that it has the process of increasing the area, which makes the effect of increasing the surface area of the hole on the seismic performance of the steel shear wall completely clear. In the end, it was found that with increasing the opening level in the steel shear wall (with reduced cross-section beam), total displacement and plastic strain indicators increased, structural capacity and total energy indicators decreased and the Mises Monson stress index did not change much.

Keywords: steel plate shear wall with opening, cyclic loading, reduced cross-section beam, finite element method, Abaqus software

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Authors: Nakache Radouane, M. Boukelloul, M. Fredj

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Method room and pillar sizes are key factors for safe mining and their recovery in open-stop mining. This method is advantageous due to its simplicity and requirement of little information to be used. It is probably the most representative method among the total load approach methods although it also remains a safe design method. Using a finite element software (PLAXIS 3D), analyses were carried out with an elasto-plastic model and comparisons were made with methods based on the total load approach. The results were presented as the optimization for improving the ore recovery rate while maintaining a safe working environment.

Keywords: room and pillar, mining, total load approach, elasto-plastic

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Authors: Haoui Rabah

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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

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Authors: Edip Kemal, Sheshov Vlatko, Bojadjieva Julijana, Bogdanovic ALeksandra, Gjorgjeska Irena

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The wave propagation phenomenon in porous domains is of great importance in the field of geotechnical earthquake engineering. In these kinds of problems, the elastic waves propagate from the interior to the exterior domain and require special treatment at the computational level since apart from displacement in the solid-state there is a p-wave that takes place in the pore water phase. In this paper, a study on the implementation of multiphase finite elements is presented. The proposed algorithm is implemented in the ANSYS finite element software and tested on one-dimensional wave propagation considering both pore pressure wave propagation and displacement fields. In the simulation of porous media such as soils, the behavior is governed largely by the interaction of the solid skeleton with water and/or air in the pores. Therefore, coupled problems of fluid flow and deformation of the solid skeleton are considered in a detailed way.

Keywords: wave propagation, multiphase model, numerical methods, finite element method

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