Since the Industrial Revolution, humanity has been intensifying the burning of fossil fuels and as a consequence, the average temperature on Earth has been increasing. The 20th century was the warmest and future prosp...Since the Industrial Revolution, humanity has been intensifying the burning of fossil fuels and as a consequence, the average temperature on Earth has been increasing. The 20th century was the warmest and future prospects are not favorable, that is, even higher temperatures are expected. This demonstrates the importance of studies on the subject, mainly to predict possible environmental, social and economic consequences. The objective of this work was to identify the interference of the increase in ambient temperature in the dynamics of fluids, such as ocean waves advancing over the continent. For this, thermal energy was considered in the Saint-Venant equations and computational implementations were performed via Lax-Friedrichs and Adams-Moulton methods. The results indicated that, in fact, depending on the amount of thermal energy transferred to the fluid, the advance of water towards the continent can occur, even in places where such a phenomenon has never been observed.展开更多
Flow in tidal rivers periodically propagates upstream or downstream under tidal influence. Hydrodynamic models based on the Saint-Venant equations （the SVN model） are extensively used to model tidal rivers. A force-...Flow in tidal rivers periodically propagates upstream or downstream under tidal influence. Hydrodynamic models based on the Saint-Venant equations （the SVN model） are extensively used to model tidal rivers. A force-corrected term expressed as the combination of flow velocity and the change rate of the tidal fevel was developed to represent tidal effects in the SVN model. A momentum equation incorporating with the corrected term was derived based on Newton＇s second law. By combing the modified momentum equation with the continuity equation, an improved SVN model for tidal rivers （the ISVN model） was constructed. The simulation of a tidal reach of the Qiantang River shows that the ISVN model performs better than the SVN model. It indicates that the corrected force derived for tidal effects is reasonable; the ISVN model provides an appropriate enhancement of the SVN model for flow simulation of tidal rivers.展开更多
Using the single crack solution and the regular solution elf plane harmonic function, the problem of Saint-Venant bending of a cracked cylinder by a transverse force was reduced to solving two sets of integral equatio...Using the single crack solution and the regular solution elf plane harmonic function, the problem of Saint-Venant bending of a cracked cylinder by a transverse force was reduced to solving two sets of integral equations and its general solution was then obtained. Based on the obtained solution, a method to calculate the bending center and the stress intensity factors of the cracked cylinger whose cross-section is not thin-walled, but of small torsion rigidity is proposed. Some numerical examples are given.展开更多
In the paper, the solution of Saint-Venant problem is obtained through assumption of principal stress curves by means of the equilibrium equations which were deduced in paper [1]. The results show that the speed of sh...In the paper, the solution of Saint-Venant problem is obtained through assumption of principal stress curves by means of the equilibrium equations which were deduced in paper [1]. The results show that the speed of shear approaching to zero is a(3)/y(3) and axial stress approaching to constant is a(2)/y(2).展开更多
This paper investigates the torsion analysis of coated bars with a rectangular cross-section. Two opposite faces of a bar are coated by two isotropie layers with different materials of the original substrate that are ...This paper investigates the torsion analysis of coated bars with a rectangular cross-section. Two opposite faces of a bar are coated by two isotropie layers with different materials of the original substrate that are perfectly bonded to the bar. With the Saint- Venant torsion theory, the governing equation of the problem in terms of the warping function is established and solved using the finite Fourier cosine transform. The state of stress on the cross-section, warping of the cross-section, and torsional rigidity of the bar are evaluated. Effects of thickness of the coating layers and material properties on these quantities are investigated. A set of graphs are provided that can be used to determine the coating thicknesses and material properties so as to keep the maximum von Mises stress on the cross-section below an allowable value for effective use of the coating layer.展开更多
Into the frame of the French TANDEM project (Tsunamis in the Atlantic and the English ChaNnel: Definition of the Effects through numerical Modelling) Principia has been working on the development and qualification of ...Into the frame of the French TANDEM project (Tsunamis in the Atlantic and the English ChaNnel: Definition of the Effects through numerical Modelling) Principia has been working on the development and qualification of two in-house CFD software: the 2D EOLE-SV (Saint-Venant) model for simulation of large scale tsunami propagation from the source up to coastal scale and the 3D EOLE-NS (Navier-Stokes) model dedicated to tsunami coastal impact modelling. This paper presents a large range of test cases carried out into the frame of the project and dedicated to the validation of numerical codes in various tsunami wave conditions. The main aspects of phenomena such as wave generation, propagation and coastal impact are investigated on academic situations. A real case simulation is concerned as well, the devastating 2011 Tohoku event which is compared with in-situ data.展开更多
The overall objectives to support analytically the mathematical background of hydraulics, linking the Navier-Stokes with hydraulic formulas, which origin is experimental but have wide and varied application. This, lea...The overall objectives to support analytically the mathematical background of hydraulics, linking the Navier-Stokes with hydraulic formulas, which origin is experimental but have wide and varied application. This, leads us study the inverse problem of the coefficients of differential equations, such as equations of the porous medium, Saint-Venant, and Reynolds, and accordingly with the order of derivatives. The research led us to see that the classic version suffers from a parameter that reflects the fractal and non-local character of the viscous interaction. Motivated by the concept of spatial occupancy rate, the authors set forth Navier-Stokes＇s fractional equation and the authors obtain the fractional Saint-Venant. In particular, the hydraulic gradient, or friction, is conceived as a fractional derivative of velocity. The friction factor is described as a linear operator acting on speed, so that the information it contains is transferred to the order of the derivative, so that the same is linearly related to the exponent of the friction factor. It states Darcy＇s non-linear law. The authors take a previous result that describes the nonlinear flow law with a leading term that contains a hyper-geometric function, whose parameters depend on the exponent of the friction factor and the exponent of the hydraulic radius. It searches the various laws of flow according to the best known laws of hydraulic resistance, such as Chezy and Manning.展开更多
We develop a new moving-water equilibria preserving partial relaxation(PR)scheme for the two-dimensional(2-D)Saint-Venant systemof shallowwater equations.The new scheme is a 2-D generalization of the one-dimensional(1...We develop a new moving-water equilibria preserving partial relaxation(PR)scheme for the two-dimensional(2-D)Saint-Venant systemof shallowwater equations.The new scheme is a 2-D generalization of the one-dimensional(1-D)PR scheme recently proposed in[X.Liu,X.Chen,S.Jin,A.Kurganov,andH.Yu,SIAMJ.Sci.Comput.,42(2020),pp.A2206–A2229].Our scheme is based on the PR approximation,which is designed in two steps.First,the geometric source terms are incorporated into the discharge fluxes,which results in a hyperbolic system with global fluxes.Second,the discharge equations are relaxed so that the nonlinearity is moved into the stiff right-hand side of the four added auxiliary equation.The obtained PR system is then numerically integrated using a semi-discrete hybrid upwind/central-upwind finitevolume method combined with an efficient semi-implicit ODE solver.The new 2-D PR scheme inherits the main advantages of the 1-D PR scheme:(i)no special treatment of the geometric source terms is required,(ii)no nonlinear(cubic)equations should be solved to obtain the point values of the water depth out of the reconstructed equilibriumvariables.The performance of the proposed PR scheme is illustrated on a number of numerical examples,in which we demonstrate that the PR scheme not only capable of exactly preserving quasi 1-D moving-water steady states and accurately capturing their small perturbations,but can also handle genuinely 2-D steady states and their small perturbations in a non-oscillatory manner.展开更多
This paper is concerned with the decay of Saint-Venant end effects for plane deformations of piezoelectric （PE）-piezomagnetic （PM） sandwich structures, where a PM layer is located between two PE layers with the sa...This paper is concerned with the decay of Saint-Venant end effects for plane deformations of piezoelectric （PE）-piezomagnetic （PM） sandwich structures, where a PM layer is located between two PE layers with the same material properties or reversely. The end of the sandwich structure is subjected to a set of self-equilibrated magneto-electro-elastic loads. The upper and lower surfaces of the sandwich structure axe mechanically free, electrically open or shorted as well as magnetically open or shorted. Firstly the constitutive equations of PE mate- rials and PM materials for plane strain are given and normalized. Secondly, the simplified state space approach is employed to arrange the constitutive equations into differential equations in a matrix form. Finally, by using the transfer matrix method, the characteristic equations for eigen- values or decay rates axe derived. Based on the obtained characteristic equations, the decay rates for the PE-PM-PE and PM-PE-PM sandwich structures are calculated. The influences of the electromagnetic boundary conditions, material properties of PE layers and volume fraction on the decay rates are discussed in detail.展开更多
A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of SaintVenant equations in one-dimensional open channel flows. The method adopts a mass-conservative fi...A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of SaintVenant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.展开更多
The eigenvalue problem about a nonhomogeneous semi-infinite strip is investigated using the methodology proposed by Papkovich and Fadle for homogeneous plane problems. Two types of nonhomogeneity are considered： （i...The eigenvalue problem about a nonhomogeneous semi-infinite strip is investigated using the methodology proposed by Papkovich and Fadle for homogeneous plane problems. Two types of nonhomogeneity are considered： （i） the elastic modulus varying with the thickness coor- dinate x exponentially, （ii） it varying with the length coordinate y exponentially. The eigenvalues for the two cases are obtained numerically in plane strain and plane stress states, respectively. By considering the smallest positive eigenvalue, tile Saint-Venant Decay rates are estimated, which indicates material nonhomogeneity has a signifcant influence on the Saint-Venant end effect.展开更多
文摘Since the Industrial Revolution, humanity has been intensifying the burning of fossil fuels and as a consequence, the average temperature on Earth has been increasing. The 20th century was the warmest and future prospects are not favorable, that is, even higher temperatures are expected. This demonstrates the importance of studies on the subject, mainly to predict possible environmental, social and economic consequences. The objective of this work was to identify the interference of the increase in ambient temperature in the dynamics of fluids, such as ocean waves advancing over the continent. For this, thermal energy was considered in the Saint-Venant equations and computational implementations were performed via Lax-Friedrichs and Adams-Moulton methods. The results indicated that, in fact, depending on the amount of thermal energy transferred to the fluid, the advance of water towards the continent can occur, even in places where such a phenomenon has never been observed.
基金supported by the National Key Technologies R&D Program of China for the Eleventh Five-Year Plan Period (Grant No. 2008BAB29B08-02)the Program for the Ministry of Education and State Administration of Foreign Experts Affairs of China (Grant No. B08408)
文摘Flow in tidal rivers periodically propagates upstream or downstream under tidal influence. Hydrodynamic models based on the Saint-Venant equations （the SVN model） are extensively used to model tidal rivers. A force-corrected term expressed as the combination of flow velocity and the change rate of the tidal fevel was developed to represent tidal effects in the SVN model. A momentum equation incorporating with the corrected term was derived based on Newton＇s second law. By combing the modified momentum equation with the continuity equation, an improved SVN model for tidal rivers （the ISVN model） was constructed. The simulation of a tidal reach of the Qiantang River shows that the ISVN model performs better than the SVN model. It indicates that the corrected force derived for tidal effects is reasonable; the ISVN model provides an appropriate enhancement of the SVN model for flow simulation of tidal rivers.
文摘Using the single crack solution and the regular solution elf plane harmonic function, the problem of Saint-Venant bending of a cracked cylinder by a transverse force was reduced to solving two sets of integral equations and its general solution was then obtained. Based on the obtained solution, a method to calculate the bending center and the stress intensity factors of the cracked cylinger whose cross-section is not thin-walled, but of small torsion rigidity is proposed. Some numerical examples are given.
文摘In the paper, the solution of Saint-Venant problem is obtained through assumption of principal stress curves by means of the equilibrium equations which were deduced in paper [1]. The results show that the speed of shear approaching to zero is a(3)/y(3) and axial stress approaching to constant is a(2)/y(2).
文摘This paper investigates the torsion analysis of coated bars with a rectangular cross-section. Two opposite faces of a bar are coated by two isotropie layers with different materials of the original substrate that are perfectly bonded to the bar. With the Saint- Venant torsion theory, the governing equation of the problem in terms of the warping function is established and solved using the finite Fourier cosine transform. The state of stress on the cross-section, warping of the cross-section, and torsional rigidity of the bar are evaluated. Effects of thickness of the coating layers and material properties on these quantities are investigated. A set of graphs are provided that can be used to determine the coating thicknesses and material properties so as to keep the maximum von Mises stress on the cross-section below an allowable value for effective use of the coating layer.
文摘Into the frame of the French TANDEM project (Tsunamis in the Atlantic and the English ChaNnel: Definition of the Effects through numerical Modelling) Principia has been working on the development and qualification of two in-house CFD software: the 2D EOLE-SV (Saint-Venant) model for simulation of large scale tsunami propagation from the source up to coastal scale and the 3D EOLE-NS (Navier-Stokes) model dedicated to tsunami coastal impact modelling. This paper presents a large range of test cases carried out into the frame of the project and dedicated to the validation of numerical codes in various tsunami wave conditions. The main aspects of phenomena such as wave generation, propagation and coastal impact are investigated on academic situations. A real case simulation is concerned as well, the devastating 2011 Tohoku event which is compared with in-situ data.
文摘The overall objectives to support analytically the mathematical background of hydraulics, linking the Navier-Stokes with hydraulic formulas, which origin is experimental but have wide and varied application. This, leads us study the inverse problem of the coefficients of differential equations, such as equations of the porous medium, Saint-Venant, and Reynolds, and accordingly with the order of derivatives. The research led us to see that the classic version suffers from a parameter that reflects the fractal and non-local character of the viscous interaction. Motivated by the concept of spatial occupancy rate, the authors set forth Navier-Stokes＇s fractional equation and the authors obtain the fractional Saint-Venant. In particular, the hydraulic gradient, or friction, is conceived as a fractional derivative of velocity. The friction factor is described as a linear operator acting on speed, so that the information it contains is transferred to the order of the derivative, so that the same is linearly related to the exponent of the friction factor. It states Darcy＇s non-linear law. The authors take a previous result that describes the nonlinear flow law with a leading term that contains a hyper-geometric function, whose parameters depend on the exponent of the friction factor and the exponent of the hydraulic radius. It searches the various laws of flow according to the best known laws of hydraulic resistance, such as Chezy and Manning.
基金The work of A.Kurganov was supported in part by NSFC grants 12111530004 and 12171226by the fund of the Guangdong Provincial Key Laboratory of Computational Science and Material Design(No.2019B030301001).
文摘We develop a new moving-water equilibria preserving partial relaxation(PR)scheme for the two-dimensional(2-D)Saint-Venant systemof shallowwater equations.The new scheme is a 2-D generalization of the one-dimensional(1-D)PR scheme recently proposed in[X.Liu,X.Chen,S.Jin,A.Kurganov,andH.Yu,SIAMJ.Sci.Comput.,42(2020),pp.A2206–A2229].Our scheme is based on the PR approximation,which is designed in two steps.First,the geometric source terms are incorporated into the discharge fluxes,which results in a hyperbolic system with global fluxes.Second,the discharge equations are relaxed so that the nonlinearity is moved into the stiff right-hand side of the four added auxiliary equation.The obtained PR system is then numerically integrated using a semi-discrete hybrid upwind/central-upwind finitevolume method combined with an efficient semi-implicit ODE solver.The new 2-D PR scheme inherits the main advantages of the 1-D PR scheme:(i)no special treatment of the geometric source terms is required,(ii)no nonlinear(cubic)equations should be solved to obtain the point values of the water depth out of the reconstructed equilibriumvariables.The performance of the proposed PR scheme is illustrated on a number of numerical examples,in which we demonstrate that the PR scheme not only capable of exactly preserving quasi 1-D moving-water steady states and accurately capturing their small perturbations,but can also handle genuinely 2-D steady states and their small perturbations in a non-oscillatory manner.
基金Project supported by the National Natural Science Foundation of China (No. 10972147)
文摘This paper is concerned with the decay of Saint-Venant end effects for plane deformations of piezoelectric （PE）-piezomagnetic （PM） sandwich structures, where a PM layer is located between two PE layers with the same material properties or reversely. The end of the sandwich structure is subjected to a set of self-equilibrated magneto-electro-elastic loads. The upper and lower surfaces of the sandwich structure axe mechanically free, electrically open or shorted as well as magnetically open or shorted. Firstly the constitutive equations of PE mate- rials and PM materials for plane strain are given and normalized. Secondly, the simplified state space approach is employed to arrange the constitutive equations into differential equations in a matrix form. Finally, by using the transfer matrix method, the characteristic equations for eigen- values or decay rates axe derived. Based on the obtained characteristic equations, the decay rates for the PE-PM-PE and PM-PE-PM sandwich structures are calculated. The influences of the electromagnetic boundary conditions, material properties of PE layers and volume fraction on the decay rates are discussed in detail.
文摘A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of SaintVenant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.
基金Project supported by the National Natural Science Foundation of China(No.41072207)
文摘The eigenvalue problem about a nonhomogeneous semi-infinite strip is investigated using the methodology proposed by Papkovich and Fadle for homogeneous plane problems. Two types of nonhomogeneity are considered： （i） the elastic modulus varying with the thickness coor- dinate x exponentially, （ii） it varying with the length coordinate y exponentially. The eigenvalues for the two cases are obtained numerically in plane strain and plane stress states, respectively. By considering the smallest positive eigenvalue, tile Saint-Venant Decay rates are estimated, which indicates material nonhomogeneity has a signifcant influence on the Saint-Venant end effect.
