Pub Date : 2020-01-01DOI: 10.2495/cmem-v8-n1-27-35
P. Vorobieff, P. Wayne, S. Lingampally, G. Vigil, Josh Ludwigsen, D. Freelong, C. Truman, G. Jacobs
Falling particle curtains are important in many engineering applications, including receivers for concentrating solar power facilities. During the formation of such a curtain, we observe a multiphase analog of Rayleigh–Taylor instability (RTI). It was originally described in 2011 for a situation when air sparsely seeded with glycol droplets was placed above a volume of unseeded air, producing an unstably stratified average density distribution that was characterized by an effective Atwood number 0.03. In that case, the evolution of the instability was indistinguishable from single-phase RTI with the same Atwood number, as the presence of the droplets largely acted as an additional contribution to the mean density of the gaseous medium. Here, we present experiments where the volume (and mass) fraction of the seeding particles in gas is considerably higher, and the gravity-driven flow is dominated by the particle movement. In this case, the evolution of the observed instability appears significantly different.
{"title":"Formation of a falling particle curtain","authors":"P. Vorobieff, P. Wayne, S. Lingampally, G. Vigil, Josh Ludwigsen, D. Freelong, C. Truman, G. Jacobs","doi":"10.2495/cmem-v8-n1-27-35","DOIUrl":"https://doi.org/10.2495/cmem-v8-n1-27-35","url":null,"abstract":"Falling particle curtains are important in many engineering applications, including receivers for concentrating solar power facilities. During the formation of such a curtain, we observe a multiphase analog of Rayleigh–Taylor instability (RTI). It was originally described in 2011 for a situation when air sparsely seeded with glycol droplets was placed above a volume of unseeded air, producing an unstably stratified average density distribution that was characterized by an effective Atwood number 0.03. In that case, the evolution of the instability was indistinguishable from single-phase RTI with the same Atwood number, as the presence of the droplets largely acted as an additional contribution to the mean density of the gaseous medium. Here, we present experiments where the volume (and mass) fraction of the seeding particles in gas is considerably higher, and the gravity-driven flow is dominated by the particle movement. In this case, the evolution of the observed instability appears significantly different.","PeriodicalId":22520,"journal":{"name":"THE INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS AND EXPERIMENTAL MEASUREMENTS","volume":"118 1","pages":"27-35"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84948249","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 : 2020-01-01DOI: 10.2495/CMEM-V8-N1-70-90
F. Nieto, A. J. Álvarez, S. Hernández, Antía Troche
A piece of software that acts as a Graphical User Interface (GUI) for the setup of computational fluid dynamics (CFD) models that are solved by means of the open source code OpenFOAM, is presented. The software is extensively described, with emphasis in the generation of block structured meshes using hexahedral elements. This computer program has been developed aiming at being applied in wind engineering problems of interest in civil engineering, such as the computation of force coefficients, flutter derivatives and vortex-induced vibrations. It has been devised to deal efficiently with rectangular cylinders and streamlined box decks. This software demands limited intervention from the user, and its core routines can be embedded in automated design processes such as parametric or optimal design problems in wind engineering. Two application examples have been considered: static and forced oscillation simulations of both, a side ratio 2:1 rectangular cylinder and a streamlined box deck. It has been found that this software is an efficient tool for the setup of URANS simulations in OpenFOAM, while the numerical results obtained for the studied aerodynamic and aeroelastic phenomena show good agreement with wind tunnel data, and their level of accuracy is equivalent to other CFD-based simulations.
{"title":"Semi-automated setup of CFD simulations of rectangular cylinders and streamlined box decks","authors":"F. Nieto, A. J. Álvarez, S. Hernández, Antía Troche","doi":"10.2495/CMEM-V8-N1-70-90","DOIUrl":"https://doi.org/10.2495/CMEM-V8-N1-70-90","url":null,"abstract":"A piece of software that acts as a Graphical User Interface (GUI) for the setup of computational fluid dynamics (CFD) models that are solved by means of the open source code OpenFOAM, is presented. The software is extensively described, with emphasis in the generation of block structured meshes using hexahedral elements. This computer program has been developed aiming at being applied in wind engineering problems of interest in civil engineering, such as the computation of force coefficients, flutter derivatives and vortex-induced vibrations. It has been devised to deal efficiently with rectangular cylinders and streamlined box decks. This software demands limited intervention from the user, and its core routines can be embedded in automated design processes such as parametric or optimal design problems in wind engineering. Two application examples have been considered: static and forced oscillation simulations of both, a side ratio 2:1 rectangular cylinder and a streamlined box deck. It has been found that this software is an efficient tool for the setup of URANS simulations in OpenFOAM, while the numerical results obtained for the studied aerodynamic and aeroelastic phenomena show good agreement with wind tunnel data, and their level of accuracy is equivalent to other CFD-based simulations.","PeriodicalId":22520,"journal":{"name":"THE INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS AND EXPERIMENTAL MEASUREMENTS","volume":"15 1","pages":"70-90"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85884839","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 : 2020-01-01DOI: 10.2495/cmem-v8-n1-61-69
F. Concli, C. Gorla
Mud pumps, like those used in the field of oil well drilling, are typically of the reciprocating type and are designed to circulate drilling fluid under high pressure down the drill string and back up the annulus. automatic valves must be applied to the fluid end in order to grant the desired pumping effect. from the engineering point of view, the design of the valve geometry must ensure that the phenomenon of cavitation does not occur and that, during the pumping action, the stiffness of the reaction coil spring is able to avoid reaching the condition of end stroke of the valve. Cavitation consists in the development of vapour cavities in the liquid phase. Inside the cavities, the pressure is relatively low. When subjected to higher pressure, the voids implode and generate an intense shock waves that promote the wear for the components (i.e. valve, valve seat, etc.). a deep understanding of the fluid behaviour is crucial for an effective design. Transient CfD simulations of the valve opening have been performed using a non-Newtonian fluid model able to describe the drilling muds. after a deep literature review, the Herschel-Bulkley model was selected as the most suitable for emulating the drilling mud. With the abovementioned approach, the reaction spring and design the valve seat to avoid premature wear phenomena were properly designed. The simulations have been also done considering a Newtonian fluid behaviour, in order to better understand the importance of considering the non-Newton behaviour for an effective design.
{"title":"non-newtonian cfd modelling of a valve for mud pumps","authors":"F. Concli, C. Gorla","doi":"10.2495/cmem-v8-n1-61-69","DOIUrl":"https://doi.org/10.2495/cmem-v8-n1-61-69","url":null,"abstract":"Mud pumps, like those used in the field of oil well drilling, are typically of the reciprocating type and are designed to circulate drilling fluid under high pressure down the drill string and back up the annulus. automatic valves must be applied to the fluid end in order to grant the desired pumping effect. from the engineering point of view, the design of the valve geometry must ensure that the phenomenon of cavitation does not occur and that, during the pumping action, the stiffness of the reaction coil spring is able to avoid reaching the condition of end stroke of the valve. Cavitation consists in the development of vapour cavities in the liquid phase. Inside the cavities, the pressure is relatively low. When subjected to higher pressure, the voids implode and generate an intense shock waves that promote the wear for the components (i.e. valve, valve seat, etc.). a deep understanding of the fluid behaviour is crucial for an effective design. Transient CfD simulations of the valve opening have been performed using a non-Newtonian fluid model able to describe the drilling muds. after a deep literature review, the Herschel-Bulkley model was selected as the most suitable for emulating the drilling mud. With the abovementioned approach, the reaction spring and design the valve seat to avoid premature wear phenomena were properly designed. The simulations have been also done considering a Newtonian fluid behaviour, in order to better understand the importance of considering the non-Newton behaviour for an effective design.","PeriodicalId":22520,"journal":{"name":"THE INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS AND EXPERIMENTAL MEASUREMENTS","volume":"43 1","pages":"61-69"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77730088","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}
Experimental studies using an X-ray tomography system were performed on a 4-inch horizontal section of the multiphase flow loop at NEl for gas–water and gas–oil–water flows. Values of liquid holdup and water liquid ratio are reported alongside analysis of the phase linear fraction through the crosssection of the pipe. The X-ray system revealed areas of gas entrainment and separation of oil and water which are not evident from high-speed video footage. The flow pattern of the tests was stratified-wavy, and computational fluid dynamics (CfD) analysis was performed using the volume of fluid (VOf) method. The prediction of liquid holdup and gas distribution through the pipe height as determined by CfD, correlated well with that determined by X-ray tomography. however, the results suggest that a transient VOf with a high-order mesh resolution is required to account for gas entrainment. This study shows that an X-ray system can be utilised to provide quantifiable validation data which are of value to multiphase models in CfD and provide insight that is not apparent during high-speed video analysis. The data generated from this system will be of considerable value to multiphase flow specialists and instrumentation developers.
{"title":"X-Ray tomography reconstruction of multiphase flows and the verification of CFD","authors":"S. Black, M. Laing","doi":"10.2495/CMEM-V8-N1-1-12","DOIUrl":"https://doi.org/10.2495/CMEM-V8-N1-1-12","url":null,"abstract":"Experimental studies using an X-ray tomography system were performed on a 4-inch horizontal section of the multiphase flow loop at NEl for gas–water and gas–oil–water flows. Values of liquid holdup and water liquid ratio are reported alongside analysis of the phase linear fraction through the crosssection of the pipe. The X-ray system revealed areas of gas entrainment and separation of oil and water which are not evident from high-speed video footage. The flow pattern of the tests was stratified-wavy, and computational fluid dynamics (CfD) analysis was performed using the volume of fluid (VOf) method. The prediction of liquid holdup and gas distribution through the pipe height as determined by CfD, correlated well with that determined by X-ray tomography. however, the results suggest that a transient VOf with a high-order mesh resolution is required to account for gas entrainment. This study shows that an X-ray system can be utilised to provide quantifiable validation data which are of value to multiphase models in CfD and provide insight that is not apparent during high-speed video analysis. The data generated from this system will be of considerable value to multiphase flow specialists and instrumentation developers.","PeriodicalId":22520,"journal":{"name":"THE INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS AND EXPERIMENTAL MEASUREMENTS","volume":"62 1","pages":"1-12"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78687432","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 : 2018-01-01DOI: 10.2495/CMEM-V6-N6-1087-1096
J. Ravnik, J. Tibaut
In this paper, we derive a boundary-domain integral formulation for the vorticity transport equation under the assumption that the viscosity of the fluid, through which the vorticity is transported by diffusion and convection, is spatially changing. The vorticity transport equation is a second order partial differential equation of a diffusion-convection type. The final boundary-domain integral representation of the vorticity transport equation is discretized using a domain decomposition approach, where a system of linear equations is set-up for each sub-domain, while subdomains are joint by compatibility conditions. The validity of the method is checked using several analytical examples. Convergence properties are studied yielding that the proposed discretization technique is second order accurate for constant and variable viscosity cases.
{"title":"Boundary-domain integral method for vorticity transport equation with variable viscosity","authors":"J. Ravnik, J. Tibaut","doi":"10.2495/CMEM-V6-N6-1087-1096","DOIUrl":"https://doi.org/10.2495/CMEM-V6-N6-1087-1096","url":null,"abstract":"In this paper, we derive a boundary-domain integral formulation for the vorticity transport equation under the assumption that the viscosity of the fluid, through which the vorticity is transported by diffusion and convection, is spatially changing. The vorticity transport equation is a second order partial differential equation of a diffusion-convection type. The final boundary-domain integral representation of the vorticity transport equation is discretized using a domain decomposition approach, where a system of linear equations is set-up for each sub-domain, while subdomains are joint by compatibility conditions. The validity of the method is checked using several analytical examples. Convergence properties are studied yielding that the proposed discretization technique is second order accurate for constant and variable viscosity cases.","PeriodicalId":22520,"journal":{"name":"THE INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS AND EXPERIMENTAL MEASUREMENTS","volume":"81 1","pages":"1087-1096"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73360452","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 : 2018-01-01DOI: 10.2495/CMEM-V6-N6-1108-1119
L. Godinho, P. Amado-Mendes, Pedro Alves-Costa, C. Albino
Phononic crystals have been extensively studied, and their capacity to attenuate the propagation of sound waves at specific frequency bands is well known and documented in the literature. However, few studies exist concerning the behaviour of such structures in the context of elastic media, with the purpose of attenuating the transmission of vibrations. Applying this concept can be quite interesting, and may allow new vibration control devices to be developed, tailored at specific applications. As an example, buried periodic structures may be used to control elastic wave propagation in the ground, and thus to help reducing the vibrations that can reach sensible structures. In this work, the authors make use of a 2.5D numerical model based on the Method of Fundamental Solutions (MFS) to analyse this complex problem, considering the case of arrays of elastic inclusions buried in a homogeneous medium, fully considering the complete elastodynamic interaction between the inclusions and the host medium. Due to the geometric periodicity of the analysed problem, the numerical formulation can be simplified, particularly in what concerns the calculation of the system matrix, and significant computational gains can be obtained. The results of a numerical study concerning the behaviour of a sequence of embedded inclusions within an elastic material, when subject to the incidence of waves with different frequencies, is here presented, and the interpretation of the involved phenomena is described in order to clarify the main wave propagation features in the presence of multiple elastic inclusions. The computed results are promising, clearly revealing the existence of band gaps where large attenuation occurs, although limitations related to the existence of guided waves traveling along the inclusions are also identified.
{"title":"MFS analysis of the vibration filtering effect of periodic structures in elastic media","authors":"L. Godinho, P. Amado-Mendes, Pedro Alves-Costa, C. Albino","doi":"10.2495/CMEM-V6-N6-1108-1119","DOIUrl":"https://doi.org/10.2495/CMEM-V6-N6-1108-1119","url":null,"abstract":"Phononic crystals have been extensively studied, and their capacity to attenuate the propagation of sound waves at specific frequency bands is well known and documented in the literature. However, few studies exist concerning the behaviour of such structures in the context of elastic media, with the purpose of attenuating the transmission of vibrations. Applying this concept can be quite interesting, and may allow new vibration control devices to be developed, tailored at specific applications. As an example, buried periodic structures may be used to control elastic wave propagation in the ground, and thus to help reducing the vibrations that can reach sensible structures. In this work, the authors make use of a 2.5D numerical model based on the Method of Fundamental Solutions (MFS) to analyse this complex problem, considering the case of arrays of elastic inclusions buried in a homogeneous medium, fully considering the complete elastodynamic interaction between the inclusions and the host medium. Due to the geometric periodicity of the analysed problem, the numerical formulation can be simplified, particularly in what concerns the calculation of the system matrix, and significant computational gains can be obtained. The results of a numerical study concerning the behaviour of a sequence of embedded inclusions within an elastic material, when subject to the incidence of waves with different frequencies, is here presented, and the interpretation of the involved phenomena is described in order to clarify the main wave propagation features in the presence of multiple elastic inclusions. The computed results are promising, clearly revealing the existence of band gaps where large attenuation occurs, although limitations related to the existence of guided waves traveling along the inclusions are also identified.","PeriodicalId":22520,"journal":{"name":"THE INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS AND EXPERIMENTAL MEASUREMENTS","volume":"15 1","pages":"1108-1119"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80573849","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 : 2018-01-01DOI: 10.2495/CMEM-V6-N6-1033-1042
K. Matsushima, H. Isakari, Toru Takahashi, Toshiro Matsumoto
This paper presents a numerical method for topology optimisation for two-dimensional elastodynamics based on the level set method and the boundary element method (BEM) accelerated by the H-matrix method and its application to identifications of defects in an infinite elastic medium. Gradient-based topology optimisation methods require design sensitivity, which is obtained by solving some boundary value problems. The BEM is employed for this sensitivity analysis because the BEM can deal with infinite domains rigorously without any approximation. However, the computational cost in the BEM is expensive, and this is a serious drawback since we need to repeat sensitivity analysis even for a single optimisation process. In this study, the H-matrix method is used as an acceleration method of the BEM for the reduction of the computational cost of the sensitivity analysis. Also proposed is a method to improve the efficiency of the H-matrix method by exploiting a property of the kernel function of the elastodynamic fundamental solution. Some numerical examples are demonstrated, and the effectiveness of the proposed method is confirmed.
{"title":"An application of topology optimisation to defect identification in two-dimensional elastodynamics with the BEM and H-matrixmethod","authors":"K. Matsushima, H. Isakari, Toru Takahashi, Toshiro Matsumoto","doi":"10.2495/CMEM-V6-N6-1033-1042","DOIUrl":"https://doi.org/10.2495/CMEM-V6-N6-1033-1042","url":null,"abstract":"This paper presents a numerical method for topology optimisation for two-dimensional elastodynamics based on the level set method and the boundary element method (BEM) accelerated by the H-matrix method and its application to identifications of defects in an infinite elastic medium. Gradient-based topology optimisation methods require design sensitivity, which is obtained by solving some boundary value problems. The BEM is employed for this sensitivity analysis because the BEM can deal with infinite domains rigorously without any approximation. However, the computational cost in the BEM is expensive, and this is a serious drawback since we need to repeat sensitivity analysis even for a single optimisation process. In this study, the H-matrix method is used as an acceleration method of the BEM for the reduction of the computational cost of the sensitivity analysis. Also proposed is a method to improve the efficiency of the H-matrix method by exploiting a property of the kernel function of the elastodynamic fundamental solution. Some numerical examples are demonstrated, and the effectiveness of the proposed method is confirmed.","PeriodicalId":22520,"journal":{"name":"THE INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS AND EXPERIMENTAL MEASUREMENTS","volume":"61 1","pages":"1033-1042"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90897683","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 : 2018-01-01DOI: 10.2495/CMEM-V6-N6-1097-1107
J. Tibaut, L. Skerget, J. Ravnik
In this paper, we present a fast boundary element method (BEM) algorithm for the solution of the velocity-vorticity formulation of the Navier-Stokes equations. The Navier-Stokes equations govern incompressible fluid flow, which is inherently nonlinear and when discretizised by BEM requires the discretization of the domain and calculation of domain integrals. The computational demands of such method scale with O(N2), where N is the number of boundary nodes. To accelerate the solution process and reduce the computational demand, we present two different approaches, the subdomain method and an approximation procedure with hierarchical structure. Several approximation techniques exist, such as multipole approximation methods FMM (fast multiple method), SVD (singular value decomposition method), wavelet transform method and a cross approximation method. In this paper, we present the cross approximation method in combination with the hierarchical H-structure. The cross approximation method can reduce the computational demands from O(N2) to O(N log N). There are many forms of the cross approximation, like the algebraic cross approximation and the hybrid cross approximation. Here, we applied the algebraic cross approximation form. The main advantage is that we did not need to evaluate the integral and then to change it with a degenerate kernel function. The cross approximation algorithm was used to solve the kinematics equation for unknown boundary vorticity values. Results show that an increasing of the compression rate has a negative influence on the solution accuracy. On the other hand, the solution accuracy increases with computational grid density. Tests were performed using the 3D lid-driven cavity test case with Reynolds numbers up to 1000. Solution accuracy was similar for all Reynolds numbers considered. In conclusion, the tests showed that our implementation of the algebraic cross approximation for the acceleration of the solution of the kinematics equation can be applied to decrease the computational demands and to accelerate the BEM.
{"title":"Acceleration Of Bem With The Cross Approximation For Determination Of Boundary Vorticity","authors":"J. Tibaut, L. Skerget, J. Ravnik","doi":"10.2495/CMEM-V6-N6-1097-1107","DOIUrl":"https://doi.org/10.2495/CMEM-V6-N6-1097-1107","url":null,"abstract":"In this paper, we present a fast boundary element method (BEM) algorithm for the solution of the velocity-vorticity formulation of the Navier-Stokes equations. The Navier-Stokes equations govern incompressible fluid flow, which is inherently nonlinear and when discretizised by BEM requires the discretization of the domain and calculation of domain integrals. The computational demands of such method scale with O(N2), where N is the number of boundary nodes. To accelerate the solution process and reduce the computational demand, we present two different approaches, the subdomain method and an approximation procedure with hierarchical structure. Several approximation techniques exist, such as multipole approximation methods FMM (fast multiple method), SVD (singular value decomposition method), wavelet transform method and a cross approximation method. In this paper, we present the cross approximation method in combination with the hierarchical H-structure. The cross approximation method can reduce the computational demands from O(N2) to O(N log N). There are many forms of the cross approximation, like the algebraic cross approximation and the hybrid cross approximation. Here, we applied the algebraic cross approximation form. The main advantage is that we did not need to evaluate the integral and then to change it with a degenerate kernel function. The cross approximation algorithm was used to solve the kinematics equation for unknown boundary vorticity values. Results show that an increasing of the compression rate has a negative influence on the solution accuracy. On the other hand, the solution accuracy increases with computational grid density. Tests were performed using the 3D lid-driven cavity test case with Reynolds numbers up to 1000. Solution accuracy was similar for all Reynolds numbers considered. In conclusion, the tests showed that our implementation of the algebraic cross approximation for the acceleration of the solution of the kinematics equation can be applied to decrease the computational demands and to accelerate the BEM.","PeriodicalId":22520,"journal":{"name":"THE INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS AND EXPERIMENTAL MEASUREMENTS","volume":"14 1","pages":"1097-1107"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85875906","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 : 2018-01-01DOI: 10.2495/cmem-v6-n6-1161-1172
V. Sládek, L. Sátor, J. Sládek
It is well known that the original 3D elasticity problem in plate structures subjected to transversal loading can be converted to a 2D problem. In addition to in-plane displacements, we need to introduce the deflection and/or rotation field variables in the plate mid-plane, in order to describe displacements and deformations within the plate structure. Thus, one can develop unified formulation for bending and inplane deformation modes within the classical Kirchhoff-Love theory for bending of thin elastic plates and the shear deformation plate theories (the first order – FSDPT, and the third order TSDPT). In this paper, we extend the derivation of the 2D formulation for coupled problems of thermoelasticity in plate structures. Three material coefficients play the role in stationary problems, namely the Young modulus, coefficient of linear thermal extension and the heat conduction coefficient. The influence of continuous gradation of these coefficients on the response of the plate subjected to thermal loadings is investigated in numerical simulations. The element-free strong formulation with using meshless approximations for spatial variation of field variables is developed.
{"title":"Thermoelastic Analysis Of Bending Problems In Fgm Plates","authors":"V. Sládek, L. Sátor, J. Sládek","doi":"10.2495/cmem-v6-n6-1161-1172","DOIUrl":"https://doi.org/10.2495/cmem-v6-n6-1161-1172","url":null,"abstract":"It is well known that the original 3D elasticity problem in plate structures subjected to transversal loading can be converted to a 2D problem. In addition to in-plane displacements, we need to introduce the deflection and/or rotation field variables in the plate mid-plane, in order to describe displacements and deformations within the plate structure. Thus, one can develop unified formulation for bending and inplane deformation modes within the classical Kirchhoff-Love theory for bending of thin elastic plates and the shear deformation plate theories (the first order – FSDPT, and the third order TSDPT). In this paper, we extend the derivation of the 2D formulation for coupled problems of thermoelasticity in plate structures. Three material coefficients play the role in stationary problems, namely the Young modulus, coefficient of linear thermal extension and the heat conduction coefficient. The influence of continuous gradation of these coefficients on the response of the plate subjected to thermal loadings is investigated in numerical simulations. The element-free strong formulation with using meshless approximations for spatial variation of field variables is developed.","PeriodicalId":22520,"journal":{"name":"THE INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS AND EXPERIMENTAL MEASUREMENTS","volume":"251 1","pages":"1161-1172"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76321114","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 : 2018-01-01DOI: 10.2495/CMEM-V6-N6-1000-1007
M. Jankowska, A. Karageorghis, Chingshyang Chen
We apply the Kansa–radial basis function (RBF) collocation method to two– dimensional nonlinear boundary value problems. The system of nonlinear equations resulting from the Kansa–RBF discretiza- tion is solved by directly applying a standard nonlinear solver. In a natural way, the value of the shape parameter in the RBFs employed in the approximation is included in the unknowns to be determined. The numerical results of some examples are presented and analysed.
{"title":"Kansa RBF method for nonlinear problems","authors":"M. Jankowska, A. Karageorghis, Chingshyang Chen","doi":"10.2495/CMEM-V6-N6-1000-1007","DOIUrl":"https://doi.org/10.2495/CMEM-V6-N6-1000-1007","url":null,"abstract":"We apply the Kansa–radial basis function (RBF) collocation method to two– dimensional nonlinear boundary value problems. The system of nonlinear equations resulting from the Kansa–RBF discretiza- tion is solved by directly applying a standard nonlinear solver. In a natural way, the value of the shape parameter in the RBFs employed in the approximation is included in the unknowns to be determined. The numerical results of some examples are presented and analysed.","PeriodicalId":22520,"journal":{"name":"THE INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS AND EXPERIMENTAL MEASUREMENTS","volume":"1 1","pages":"1000-1007"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76694130","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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