Pub Date : 2020-11-23DOI: 10.13052/EJCM2642-2085.2912
Daniel Herrero Adan, R. Cardoso
Isotropic triangulation of NURBS surfaces provides high quality triangular meshes, where all triangles are equilateral. This isotropy increases representation quality and analysis accuracy. We introduce a new algorithm to generate quasi-isotropic triangulation on NURBS surfaces at once, with no prior meshing. The procedure consists of one front made of vertexes that advances in a divergence manner avoiding front collision. Vertexes are calculated by intersecting arcs whose radius is estimated by trapezoidal rule integration of directional derivatives. The parameter space is discretized in partitions such that the error of trapezoidal rule is controlled efficiently. A new space, called pattern space, is used to infer the direction of the arcs’ intersection. Derivatives, whose analytical computation is expensive, are estimated by NURBS surface fitting procedures, which increases the speed of the process. The resultant algorithm is robust and efficient. The mesh achieved possesses most of the triangles equilateral and with high uniformity of sizes. The performance is evaluated by measuring angles, vertex valences and size uniformity in different numerical examples.
{"title":"Quasi-Isotropic Initial Triangulation of NURBS Surfaces","authors":"Daniel Herrero Adan, R. Cardoso","doi":"10.13052/EJCM2642-2085.2912","DOIUrl":"https://doi.org/10.13052/EJCM2642-2085.2912","url":null,"abstract":"Isotropic triangulation of NURBS surfaces provides high quality triangular meshes, where all triangles are equilateral. This isotropy increases representation quality and analysis accuracy. We introduce a new algorithm to generate quasi-isotropic triangulation on NURBS surfaces at once, with no prior meshing. The procedure consists of one front made of vertexes that advances in a divergence manner avoiding front collision. Vertexes are calculated by intersecting arcs whose radius is estimated by trapezoidal rule integration of directional derivatives. The parameter space is discretized in partitions such that the error of trapezoidal rule is controlled efficiently. A new space, called pattern space, is used to infer the direction of the arcs’ intersection. Derivatives, whose analytical computation is expensive, are estimated by NURBS surface fitting procedures, which increases the speed of the process. The resultant algorithm is robust and efficient. The mesh achieved possesses most of the triangles equilateral and with high uniformity of sizes. The performance is evaluated by measuring angles, vertex valences and size uniformity in different numerical examples.","PeriodicalId":45463,"journal":{"name":"European Journal of Computational Mechanics","volume":"1 1","pages":"27–82-27–82"},"PeriodicalIF":1.2,"publicationDate":"2020-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43654178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-13DOI: 10.13052/ejcm2642-2085.2911
V. Ghazanfari, A. Salehi, A. Keshtkar, M. Shadman, M. H. Askari
The performance of a gas centrifuge that is used for isotopes separation is dependent on the gas flow inside it. In this study, for modeling the UF6 gas flow, an Implicit Coupled Density-Based (ICDB) solver, was developed in OpenFOAM. To validate the ICDB solver, the gas flow within the rotor in total reflux state was compared with the analytical solution obtained by Onsager model and the numerical solution obtained by the Fluent software. The results showed that the ICDB solver had acceptable accuracy and validity. Also the computational efficiency of Roe, AUSM (Advection Upstream Splitting Method) and AUSM+ up schemes were compared. The results showed AUSM+ up scheme is efficient. Then, the uranium isotopes separation in a gas centrifuge was simulated. It was revealed that all gas flow characteristics including velocity, pressure, temperature and axial mass flux, as well as uranium isotope separation parameters including separation power and separation coefficients could well be predicted.
{"title":"Modeling and Simulation of Flow and Uranium Isotopes Separation in Gas Centrifuges Using Implicit Coupled Density-Based Solver in OpenFOAM","authors":"V. Ghazanfari, A. Salehi, A. Keshtkar, M. Shadman, M. H. Askari","doi":"10.13052/ejcm2642-2085.2911","DOIUrl":"https://doi.org/10.13052/ejcm2642-2085.2911","url":null,"abstract":"The performance of a gas centrifuge that is used for isotopes separation is dependent on the gas flow inside it. In this study, for modeling the UF6 gas flow, an Implicit Coupled Density-Based (ICDB) solver, was developed in OpenFOAM. To validate the ICDB solver, the gas flow within the rotor in total reflux state was compared with the analytical solution obtained by Onsager model and the numerical solution obtained by the Fluent software. The results showed that the ICDB solver had acceptable accuracy and validity. Also the computational efficiency of Roe, AUSM (Advection Upstream Splitting Method) and AUSM+ up schemes were compared. The results showed AUSM+ up scheme is efficient. Then, the uranium isotopes separation in a gas centrifuge was simulated. It was revealed that all gas flow characteristics including velocity, pressure, temperature and axial mass flux, as well as uranium isotope separation parameters including separation power and separation coefficients could well be predicted.","PeriodicalId":45463,"journal":{"name":"European Journal of Computational Mechanics","volume":"1 1","pages":"1–26-1–26"},"PeriodicalIF":1.2,"publicationDate":"2020-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48236819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-16DOI: 10.13052/ejcm2642-2085.2863
M. Hassanzadeh
In the current paper, the general procedure of the first and second-order sensitivity analysis is presented using the extended complex variables method (ECVM). In the traditional complex variables method, only the imaginary step is used for sensitivity analysis. However, in the ECVM, both of the real and imaginary parts are employed to improve the efficiency of the method. To show this, the ECVM is applied to the steady state incompressible laminar flow around a cylinder. The governing Navier-Stokes equations are solved by the finite element method and then the ECVM is employed. The results are validated through comparing with those of obtained by an analytical as well as the finite difference methods and the convergence rate is investigated. It is illustrated that the first-order sensitivity analysis is not influenced by the change of the step length for both of the traditional and extended complex variables methods. However, it is shown that unlike the traditional complex variables method, the ECVM is less dependent on the step size for calculating the second-order sensitivity. This can be considered as an enhancement in the efficiency of this method. Hence, the ECVM is suggested as an appropriate technique for calculating simultaneously the first and second-order sensitivities with high accuracy as well as low computational cost. The proposed method is applicable to a wide range of problems having simple or complex parameters.
{"title":"Computation of Second-order Design Sensitivities for Steady State Incompressible Laminar Flows Using the Extended Complex Variables Method","authors":"M. Hassanzadeh","doi":"10.13052/ejcm2642-2085.2863","DOIUrl":"https://doi.org/10.13052/ejcm2642-2085.2863","url":null,"abstract":"In the current paper, the general procedure of the first and second-order sensitivity analysis is presented using the extended complex variables method (ECVM). In the traditional complex variables method, only the imaginary step is used for sensitivity analysis. However, in the ECVM, both of the real and imaginary parts are employed to improve the efficiency of the method. To show this, the ECVM is applied to the steady state incompressible laminar flow around a cylinder. The governing Navier-Stokes equations are solved by the finite element method and then the ECVM is employed. The results are validated through comparing with those of obtained by an analytical as well as the finite difference methods and the convergence rate is investigated. It is illustrated that the first-order sensitivity analysis is not influenced by the change of the step length for both of the traditional and extended complex variables methods. However, it is shown that unlike the traditional complex variables method, the ECVM is less dependent on the step size for calculating the second-order sensitivity. This can be considered as an enhancement in the efficiency of this method. Hence, the ECVM is suggested as an appropriate technique for calculating simultaneously the first and second-order sensitivities with high accuracy as well as low computational cost. The proposed method is applicable to a wide range of problems having simple or complex parameters.","PeriodicalId":45463,"journal":{"name":"European Journal of Computational Mechanics","volume":"1 1","pages":"605–634-605–634"},"PeriodicalIF":1.2,"publicationDate":"2020-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48970052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-03-11DOI: 10.13052/ejcm2642-2085.2862
Alaa A. Abdel Rahman, A. E. Nabawy, A. Abdelhaleem, S. Ali-Eldin
Suspension systems in running vehicles keep the occupants comfortable and isolated from road noise, disturbances, and vibrations and consequently prevent the vehicle from damage and wearing. To attain comfortable and vibration isolation conditions, both material flexibility and damping should be considered in the considered suspension model. This paper presents an incremental finite element model to study and analyze the dynamic behavior of double wishbone suspension systems considering both material flexibility and damping effects. The flexibility of the suspension links are modeled with plane frame element based on Timoshenko beam hypothesis (TBH). On the other hand, the flexibility of joints connecting the suspension links together and with the vehicle chassis is modeled with the revolute joint element. To incorporate the damping effect, viscoelastic, viscous and proportional damping are considered. An incremental viscoelastic constitutive relations, suitable for finite element implementation, are developed. The developed finite element equations of motion are solved using the Newmark technique. The developed procedure is verified by comparing the obtained results with that obtained by the developed analytical solution and an excellent agreement is found. The applicability and effectiveness of the developed procedure are demonstrated by conducting parametric studies to show the effects of the road irregularities profiles, the vehicle speed, and the material damping on the transverse deflection and the resultant stresses of suspension system. Results obtained are supportive in the mechanical design, manufacturing processes of such type of structural systems.
{"title":"Dynamic Finite Element Analysis of Flexible Double Wishbone Suspension Systems with Different Damping Mechanisms","authors":"Alaa A. Abdel Rahman, A. E. Nabawy, A. Abdelhaleem, S. Ali-Eldin","doi":"10.13052/ejcm2642-2085.2862","DOIUrl":"https://doi.org/10.13052/ejcm2642-2085.2862","url":null,"abstract":"Suspension systems in running vehicles keep the occupants comfortable and isolated from road noise, disturbances, and vibrations and consequently prevent the vehicle from damage and wearing. To attain comfortable and vibration isolation conditions, both material flexibility and damping should be considered in the considered suspension model. This paper presents an incremental finite element model to study and analyze the dynamic behavior of double wishbone suspension systems considering both material flexibility and damping effects. The flexibility of the suspension links are modeled with plane frame element based on Timoshenko beam hypothesis (TBH). On the other hand, the flexibility of joints connecting the suspension links together and with the vehicle chassis is modeled with the revolute joint element. To incorporate the damping effect, viscoelastic, viscous and proportional damping are considered. An incremental viscoelastic constitutive relations, suitable for finite element implementation, are developed. The developed finite element equations of motion are solved using the Newmark technique. The developed procedure is verified by comparing the obtained results with that obtained by the developed analytical solution and an excellent agreement is found. The applicability and effectiveness of the developed procedure are demonstrated by conducting parametric studies to show the effects of the road irregularities profiles, the vehicle speed, and the material damping on the transverse deflection and the resultant stresses of suspension system. Results obtained are supportive in the mechanical design, manufacturing processes of such type of structural systems.","PeriodicalId":45463,"journal":{"name":"European Journal of Computational Mechanics","volume":"1 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2020-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43096028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-03-02DOI: 10.13052/ejcm2642-2085.2861
V. Ghazanfari, A. Salehi, A. Keshtkar, M. Shadman, M. H. Askari
In this work, we attempted to develop an Implicit Coupled Density-Based (ICDB) solver using LU-SGS algorithm based on the AUSM+ up scheme in OpenFOAM. Then sonicFoam solver was modified to include viscous dissipation in order to improve its capability to capture shock wave and aerothermal variables. The details of the ICDB solver as well as key implementation details of the viscous dissipation to energy equation were introduced. Finally, two benchmark tests of hypersonic airflow over a flat plate and a 2-D cylinder were simulated to show the accuracy of ICDB solver. To verify and validate the ICDB solver, the obtained results were compared with other published experimental data. It was revealed that ICDB solver has good agreement with the experimental data. So it can be used as reference in other studies. It was also observed that ICDB solver enjoy advantages such as high resolution for contact discontinuity and low computational time. Moreover, to investigate the performance of modified sonicFoam, a case study of airflow over the prism was considered. Then the results of the modified sonicFoam were compared with the ICDB, rhoCentralFoam and sonicFoam solvers. The results showed that the modified sonicFoam solver possesses higher accuracy and lower computational time in comparison with the sonicFoam and rhoCentralFoam solvers, respectively.
{"title":"Numerical Simulation Using a Modified Solver within OpenFOAM for Compressible Viscous Flows","authors":"V. Ghazanfari, A. Salehi, A. Keshtkar, M. Shadman, M. H. Askari","doi":"10.13052/ejcm2642-2085.2861","DOIUrl":"https://doi.org/10.13052/ejcm2642-2085.2861","url":null,"abstract":"In this work, we attempted to develop an Implicit Coupled Density-Based (ICDB) solver using LU-SGS algorithm based on the AUSM+ up scheme in OpenFOAM. Then sonicFoam solver was modified to include viscous dissipation in order to improve its capability to capture shock wave and aerothermal variables. The details of the ICDB solver as well as key implementation details of the viscous dissipation to energy equation were introduced. Finally, two benchmark tests of hypersonic airflow over a flat plate and a 2-D cylinder were simulated to show the accuracy of ICDB solver. To verify and validate the ICDB solver, the obtained results were compared with other published experimental data. It was revealed that ICDB solver has good agreement with the experimental data. So it can be used as reference in other studies. It was also observed that ICDB solver enjoy advantages such as high resolution for contact discontinuity and low computational time. Moreover, to investigate the performance of modified sonicFoam, a case study of airflow over the prism was considered. Then the results of the modified sonicFoam were compared with the ICDB, rhoCentralFoam and sonicFoam solvers. The results showed that the modified sonicFoam solver possesses higher accuracy and lower computational time in comparison with the sonicFoam and rhoCentralFoam solvers, respectively.","PeriodicalId":45463,"journal":{"name":"European Journal of Computational Mechanics","volume":"1 1","pages":"541–572-541–572"},"PeriodicalIF":1.2,"publicationDate":"2020-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43651806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-21DOI: 10.13052/ejcm2642-2085.2855
Ouafa Soualhi, M. Mandari, M. Rhoudaf
In this paper, we prove the convergence of a schema using stabilisation and hybrid interfaces of partial differential equations describing miscible displacement in porous media. This system is made of two coupled equations:an anisotropic diffusion equation on the pressure and a convection-diffusion dispersion equation on the concentration of invading fluid. The anisotropicdiffusion operators in both equations require special care while discretizing bya finite volume method SUSHI. Later, we present some numerical experiments.
{"title":"Numerical analysis of a SUSHI scheme for an elliptic-parabolic system modeling miscible fluid flows in porous media","authors":"Ouafa Soualhi, M. Mandari, M. Rhoudaf","doi":"10.13052/ejcm2642-2085.2855","DOIUrl":"https://doi.org/10.13052/ejcm2642-2085.2855","url":null,"abstract":"In this paper, we prove the convergence of a schema using stabilisation and hybrid interfaces of partial differential equations describing miscible displacement in porous media. This system is made of two coupled equations:an anisotropic diffusion equation on the pressure and a convection-diffusion dispersion equation on the concentration of invading fluid. The anisotropicdiffusion operators in both equations require special care while discretizing bya finite volume method SUSHI. Later, we present some numerical experiments.","PeriodicalId":45463,"journal":{"name":"European Journal of Computational Mechanics","volume":"1 1","pages":"499–540-499–540"},"PeriodicalIF":1.2,"publicationDate":"2020-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47894513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-14DOI: 10.13052/ejcm2642-2085.2853
M. Rezaiee-Pajand, R. Naserian, H. Afsharimoghadam
By applying the inner product of vectors, two objective functions are found. These vectors are taken from the structural equilibrium path. Via minimizing these functions, with respect to the load incremental parameter and the angle between particular vectors, two new constraint equalities are achieved. Since the scheme of authors is general, three more constraints are also reached. These formulations are similar to the previous presented nonlinear solvers, which confirm the legitimacy of new procedure. Afterward, several numerical tests are performed to prove the ability of the proposed techniques. Findings show that the new algorithms are capable in passing the load and displacement limit points of the various benchmark problems with severe nonlinear behaviors. Based on the number of increments and iterations and also the total analysis duration, the suggested methods have the maximum rapid convergence rate, in comparison to the normal plane, the updated normal plane and the cylindrical arc length strategies.
{"title":"Two Ways of Solving System of Nonlinear Structural Equations","authors":"M. Rezaiee-Pajand, R. Naserian, H. Afsharimoghadam","doi":"10.13052/ejcm2642-2085.2853","DOIUrl":"https://doi.org/10.13052/ejcm2642-2085.2853","url":null,"abstract":"By applying the inner product of vectors, two objective functions are found. These vectors are taken from the structural equilibrium path. Via minimizing these functions, with respect to the load incremental parameter and the angle between particular vectors, two new constraint equalities are achieved. Since the scheme of authors is general, three more constraints are also reached. These formulations are similar to the previous presented nonlinear solvers, which confirm the legitimacy of new procedure. Afterward, several numerical tests are performed to prove the ability of the proposed techniques. Findings show that the new algorithms are capable in passing the load and displacement limit points of the various benchmark problems with severe nonlinear behaviors. Based on the number of increments and iterations and also the total analysis duration, the suggested methods have the maximum rapid convergence rate, in comparison to the normal plane, the updated normal plane and the cylindrical arc length strategies.","PeriodicalId":45463,"journal":{"name":"European Journal of Computational Mechanics","volume":"1 1","pages":"433–466-433–466"},"PeriodicalIF":1.2,"publicationDate":"2020-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47050337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-14DOI: 10.13052/ejcm2642-2085.2854
L. Govindarao, J. Mohapatra
In this article, a singularly perturbed parabolic convection-diffusion equation on a rectangular domain is considered. The solution of the problem possesses regular boundary layer which appears in the spatial variable. To discretize the time derivative, we use two type of schemes, first the implicit Euler scheme and second the implicit trapezoidal scheme on a uniform mesh. For approximating the spatial derivatives, we use the monotone hybrid scheme, which is a combination of midpoint upwind scheme and central difference scheme with variable weights on Shishkin-type meshes (standard Shishkin mesh, Bakhvalov-Shishkin mesh and modified Bakhvalov-Shishkin mesh). We prove that both numerical schemes converge uniformly with respect to the perturbation parameter and are of second order accurate. Thomas algorithm is used to solve the tri-diagonal system. Finally, to support the theoretical results, we present a numerical experiment by using the proposed methods.
{"title":"A Second Order Weighted Numerical Scheme on Nonuniform Meshes for Convection Diffusion Parabolic Problems","authors":"L. Govindarao, J. Mohapatra","doi":"10.13052/ejcm2642-2085.2854","DOIUrl":"https://doi.org/10.13052/ejcm2642-2085.2854","url":null,"abstract":"In this article, a singularly perturbed parabolic convection-diffusion equation on a rectangular domain is considered. The solution of the problem possesses regular boundary layer which appears in the spatial variable. To discretize the time derivative, we use two type of schemes, first the implicit Euler scheme and second the implicit trapezoidal scheme on a uniform mesh. For approximating the spatial derivatives, we use the monotone hybrid scheme, which is a combination of midpoint upwind scheme and central difference scheme with variable weights on Shishkin-type meshes (standard Shishkin mesh, Bakhvalov-Shishkin mesh and modified Bakhvalov-Shishkin mesh). We prove that both numerical schemes converge uniformly with respect to the perturbation parameter and are of second order accurate. Thomas algorithm is used to solve the tri-diagonal system. Finally, to support the theoretical results, we present a numerical experiment by using the proposed methods.","PeriodicalId":45463,"journal":{"name":"European Journal of Computational Mechanics","volume":"1 1","pages":"467–498-467–498"},"PeriodicalIF":1.2,"publicationDate":"2020-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42865991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-18DOI: 10.13052/ejcm2642-2085.2851
M. Rezaiee-Pajand, A. Karimipour
The finite element method is a powerful tool for solving most of the structural problems. This technique has been used extensively, since the complexity of the elastic field equations does not allow the specialist to find analytical solutions, especially for the three-dimensional structures. It is well-known that the finite element formulation yields the approximate stress responses. To remedy this defect, the Airy stress function is utilized in this study. The stress function formulation leads to a valid solution since it satisfies equilibrium and compatibility equations simultaneously. Two cuboid isoparametric elements are formulated for solving three-dimensional elastic structures. To demonstrate the performance of the proposed technique, various benchmark problems are analyzed. The errors between the exact, displacement-based finite element and recommended scheme solution are also calculated. All the obtained outcomes show the good merit of the presented new elements.
{"title":"Stress Analysis by Two Cuboid Isoparametric Elements","authors":"M. Rezaiee-Pajand, A. Karimipour","doi":"10.13052/ejcm2642-2085.2851","DOIUrl":"https://doi.org/10.13052/ejcm2642-2085.2851","url":null,"abstract":"The finite element method is a powerful tool for solving most of the structural problems. This technique has been used extensively, since the complexity of the elastic field equations does not allow the specialist to find analytical solutions, especially for the three-dimensional structures. It is well-known that the finite element formulation yields the approximate stress responses. To remedy this defect, the Airy stress function is utilized in this study. The stress function formulation leads to a valid solution since it satisfies equilibrium and compatibility equations simultaneously. Two cuboid isoparametric elements are formulated for solving three-dimensional elastic structures. To demonstrate the performance of the proposed technique, various benchmark problems are analyzed. The errors between the exact, displacement-based finite element and recommended scheme solution are also calculated. All the obtained outcomes show the good merit of the presented new elements.","PeriodicalId":45463,"journal":{"name":"European Journal of Computational Mechanics","volume":"1 1","pages":"373–410-373–410"},"PeriodicalIF":1.2,"publicationDate":"2019-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42690337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-18DOI: 10.13052/ejcm2642-2085.2852
Merve Gürbüz, M. Tezer-Sezgin
The purpose of this paper is to study numerically the influence of the magnetic field, buoyancy force and viscous dissipation on the convective flow and temperature of the fluid in a square cavity, lid-driven cavity, and lid-driven cavity with an obstacle at the center. The continuity, momentum and energy equations are coupled including buoyancy and magnetic forces, and energy equation contains Joule heating and viscous dissipation. The equations are solved in terms of stream function, vorticity and temperature by using polynomial radial basis function (RBF) approximation for the inhomogeneity and particular solution. The numerical solutions are obtained for several values of Grashof number (Gr), Hartmann number (M) for fixed Prandtl number Pr = 0:71 and fixed Reynolds number Re = 100 with or without viscous dissipation. It is observed that in the absence of obstacle, viscous dissipation changes the symmetry of the isotherms, and the dominance of buoyancy force increases with an increase in Gr, whereas decreases when the intensity of magnetic field increases. The obstacle in the lid-driven cavity causes a secondary flow on its left part. The effect of moving lid is weakened on the flow and isotherms especially for large Gr when the cavity contains obstacle.
{"title":"Numerical Solution of MHD Incompressible Convection Flow in Channels","authors":"Merve Gürbüz, M. Tezer-Sezgin","doi":"10.13052/ejcm2642-2085.2852","DOIUrl":"https://doi.org/10.13052/ejcm2642-2085.2852","url":null,"abstract":"The purpose of this paper is to study numerically the influence of the magnetic field, buoyancy force and viscous dissipation on the convective flow and temperature of the fluid in a square cavity, lid-driven cavity, and lid-driven cavity with an obstacle at the center. The continuity, momentum and energy equations are coupled including buoyancy and magnetic forces, and energy equation contains Joule heating and viscous dissipation. The equations are solved in terms of stream function, vorticity and temperature by using polynomial radial basis function (RBF) approximation for the inhomogeneity and particular solution. The numerical solutions are obtained for several values of Grashof number (Gr), Hartmann number (M) for fixed Prandtl number Pr = 0:71 and fixed Reynolds number Re = 100 with or without viscous dissipation. It is observed that in the absence of obstacle, viscous dissipation changes the symmetry of the isotherms, and the dominance of buoyancy force increases with an increase in Gr, whereas decreases when the intensity of magnetic field increases. The obstacle in the lid-driven cavity causes a secondary flow on its left part. The effect of moving lid is weakened on the flow and isotherms especially for large Gr when the cavity contains obstacle.","PeriodicalId":45463,"journal":{"name":"European Journal of Computational Mechanics","volume":"1 1","pages":"411–432-411–432"},"PeriodicalIF":1.2,"publicationDate":"2019-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41478367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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