This paper presents an investigation into the effect of surface asperities on the over-rolling of bearing surfaces in transient elastohydrodynamic lubrication(EHL) line contact. The governing equations are discretized...This paper presents an investigation into the effect of surface asperities on the over-rolling of bearing surfaces in transient elastohydrodynamic lubrication(EHL) line contact. The governing equations are discretized by the finite difference method. The resulting nonlinear system of algebraic equations is solved by the Jacobian-free Newtongeneralized minimal residual(GMRES) from the Krylov subspace method(KSM). The acceleration of the GMRES iteration is accomplished by a wavelet-based preconditioner.The profiles of the lubricant pressure and film thickness are obtained at each time step when the indented surface moves through the contact region. The prediction of pressure as a function of time provides an insight into the understanding of fatigue life of bearings.The analysis confirms the need for the time-dependent approach of EHL problems with surface asperities. This method requires less storage and yields an accurate solution with much coarser grids. It is stable, efficient, allows a larger time step, and covers a wide range of parameters of interest.展开更多
三维全堆芯pin-by-pin中子输运模型的高效加速方法是核反应堆高精度计算的重点和难点。本文有效融合课题组开发的并行多维离散纵坐标(S_(N))中子输运程序comeSn和Jacobian-Free Newton Krylov(JFNK)通用求解框架comeJFNK的高效并行特性...三维全堆芯pin-by-pin中子输运模型的高效加速方法是核反应堆高精度计算的重点和难点。本文有效融合课题组开发的并行多维离散纵坐标(S_(N))中子输运程序comeSn和Jacobian-Free Newton Krylov(JFNK)通用求解框架comeJFNK的高效并行特性、鲁棒性和强收敛性,开发了一套三维稳态及瞬态中子输运模型的JFNK并行求解程序comeSn_JFNK。为了提高计算效率,选择中子标通量密度(而非中子角通量密度)作为JFNK全局求解变量,并利用基于空间区域并行的KBA输运扫描方法和物理预处理方法,分别构建了稳态及瞬态模型的JFNK统一残差计算模型。计算结果表明,comeSn_JFNK相比于comeSn,计算效率具有显著优势,对于三维pin-by-pin稳态KAIST-3A算例,加速比为10倍以上;对于栅元均匀化的二维七群瞬态C5G7-TD2系列基准算例,加速比约为30倍。展开更多
There is a growing trend within energy and environmental simulation to consider tightly coupled solutions to multiphysics problems.This can be seen in nuclear reactor analysis where analysts are interested in coupled ...There is a growing trend within energy and environmental simulation to consider tightly coupled solutions to multiphysics problems.This can be seen in nuclear reactor analysis where analysts are interested in coupled flow,heat transfer and neutronics,and in nuclear fuel performance simulation where analysts are interested in thermomechanics with contact coupled to species transport and chemistry.In energy and environmental applications,energy extraction involves geomechanics,flow through porous media and fractured formations,adding heat transport for enhanced oil recovery and geothermal applications,and adding reactive transport in the case of applications modeling the underground flow of contaminants.These more ambitious simulations usually motivate some level of parallel computing.Many of the physics coupling efforts to date utilize simple code coupling or first-order operator splitting,often referred to as loose coupling.While these approaches can produce answers,they usually leave questions of accuracy and stability unanswered.Additionally,the different physics often reside on distinct meshes and data are coupled via simple interpolation,again leaving open questions of stability and accuracy.∗Corresponding author.Email addresses:Derek.Gaston@inl.gov(D.Gaston),This paper is the first part of a two part sequence on multiphysics algorithms and software.Part I examines the importance of accurate time and space integration and that the degree of coupling used for the solution should match the requirements of the simulation.It then discusses the preconditioned Jacobian-free Newton Krylov solution algorithm that is used for both multiphysics and multiscale solutions.Part II[1]presents the software framework;the Multiphysics Object Oriented Simulation Environment(MOOSE)and discusses applications based on it.展开更多
This paper is the second part of a two part sequence on multiphysics algorithms and software.The first[1]focused on the algorithms;this part treats the multiphysics software framework and applications based on it.Tigh...This paper is the second part of a two part sequence on multiphysics algorithms and software.The first[1]focused on the algorithms;this part treats the multiphysics software framework and applications based on it.Tight coupling is typically designed into the analysis application at inception,as such an application is strongly tied to a composite nonlinear solver that arrives at the final solution by treating all equations simultaneously.The applicationmust also take care tominimize both time and space error between the physics,particularly if more than one mesh representation is needed in the solution process.This paper presents an application framework that was specifically designed to support tightly coupled multiphysics analysis.The Multiphysics Object Oriented Simulation Environment(MOOSE)is based on the Jacobian-freeNewton-Krylov(JFNK)method combined with physics-based preconditioning to provide the underlying mathematical structure for applications.The report concludes with the presentation of a host of nuclear,energy,and environmental applications that demonstrate the efficacy of the approach and the utility of a well-designed multiphysics framework.展开更多
In this article we propose a higher-order space-time conservative method for hyperbolic systems with stiff and non stiff source terms as well as relaxation systems.We call the scheme a slope propagation(SP)method.It i...In this article we propose a higher-order space-time conservative method for hyperbolic systems with stiff and non stiff source terms as well as relaxation systems.We call the scheme a slope propagation(SP)method.It is an extension of our scheme derived for homogeneous hyperbolic systems[1].In the present inhomogeneous systems the relaxation time may vary from order of one to a very small value.These small values make the relaxation term stronger and highly stiff.In such situations underresolved numerical schemes may produce spurious numerical results.However,our present scheme has the capability to correctly capture the behavior of the physical phenomena with high order accuracy even if the initial layer and the small relaxation time are not numerically resolved.The scheme treats the space and time in a unified manner.The flow variables and their slopes are the basic unknowns in the scheme.The source term is treated by its volumetric integration over the space-time control volume and is a direct part of the overall space-time flux balance.We use two approaches for the slope calculations of the flow variables,the first one results directly from the flux balance over the control volumes,while in the second one we use a finite difference approach.The main features of the scheme are its simplicity,its Jacobian-free and Riemann solver-free recipe,as well as its efficiency and high of order accuracy.In particular we show that the scheme has a discrete analog of the continuous asymptotic limit.We have implemented our scheme for various test models available in the literature such as the Broadwell model,the extended thermodynamics equations,the shallow water equations,traffic flow and the Euler equations with heat transfer.The numerical results validate the accuracy,versatility and robustness of the present scheme.展开更多
基金financial support from the Indian National Science Academy,New Delhi,IndiaBiluru Gurubasava Mahaswamiji Institute of Technology for the encouragement and support。
文摘This paper presents an investigation into the effect of surface asperities on the over-rolling of bearing surfaces in transient elastohydrodynamic lubrication(EHL) line contact. The governing equations are discretized by the finite difference method. The resulting nonlinear system of algebraic equations is solved by the Jacobian-free Newtongeneralized minimal residual(GMRES) from the Krylov subspace method(KSM). The acceleration of the GMRES iteration is accomplished by a wavelet-based preconditioner.The profiles of the lubricant pressure and film thickness are obtained at each time step when the indented surface moves through the contact region. The prediction of pressure as a function of time provides an insight into the understanding of fatigue life of bearings.The analysis confirms the need for the time-dependent approach of EHL problems with surface asperities. This method requires less storage and yields an accurate solution with much coarser grids. It is stable, efficient, allows a larger time step, and covers a wide range of parameters of interest.
文摘三维全堆芯pin-by-pin中子输运模型的高效加速方法是核反应堆高精度计算的重点和难点。本文有效融合课题组开发的并行多维离散纵坐标(S_(N))中子输运程序comeSn和Jacobian-Free Newton Krylov(JFNK)通用求解框架comeJFNK的高效并行特性、鲁棒性和强收敛性,开发了一套三维稳态及瞬态中子输运模型的JFNK并行求解程序comeSn_JFNK。为了提高计算效率,选择中子标通量密度(而非中子角通量密度)作为JFNK全局求解变量,并利用基于空间区域并行的KBA输运扫描方法和物理预处理方法,分别构建了稳态及瞬态模型的JFNK统一残差计算模型。计算结果表明,comeSn_JFNK相比于comeSn,计算效率具有显著优势,对于三维pin-by-pin稳态KAIST-3A算例,加速比为10倍以上;对于栅元均匀化的二维七群瞬态C5G7-TD2系列基准算例,加速比约为30倍。
基金Supported by National Natural Science Foundation of China(11171039,11171038,11271054)National Basic Research Program of China(2011CB309702,2011CB309703)+1 种基金Science Foundation of CAEP(2012B0202026,2010A0202010)Foundation of National Key Laborotory of Science and Technology on Computation Physics and Defence Industrial Technology Development Program(B1520110011)
文摘There is a growing trend within energy and environmental simulation to consider tightly coupled solutions to multiphysics problems.This can be seen in nuclear reactor analysis where analysts are interested in coupled flow,heat transfer and neutronics,and in nuclear fuel performance simulation where analysts are interested in thermomechanics with contact coupled to species transport and chemistry.In energy and environmental applications,energy extraction involves geomechanics,flow through porous media and fractured formations,adding heat transport for enhanced oil recovery and geothermal applications,and adding reactive transport in the case of applications modeling the underground flow of contaminants.These more ambitious simulations usually motivate some level of parallel computing.Many of the physics coupling efforts to date utilize simple code coupling or first-order operator splitting,often referred to as loose coupling.While these approaches can produce answers,they usually leave questions of accuracy and stability unanswered.Additionally,the different physics often reside on distinct meshes and data are coupled via simple interpolation,again leaving open questions of stability and accuracy.∗Corresponding author.Email addresses:Derek.Gaston@inl.gov(D.Gaston),This paper is the first part of a two part sequence on multiphysics algorithms and software.Part I examines the importance of accurate time and space integration and that the degree of coupling used for the solution should match the requirements of the simulation.It then discusses the preconditioned Jacobian-free Newton Krylov solution algorithm that is used for both multiphysics and multiscale solutions.Part II[1]presents the software framework;the Multiphysics Object Oriented Simulation Environment(MOOSE)and discusses applications based on it.
文摘This paper is the second part of a two part sequence on multiphysics algorithms and software.The first[1]focused on the algorithms;this part treats the multiphysics software framework and applications based on it.Tight coupling is typically designed into the analysis application at inception,as such an application is strongly tied to a composite nonlinear solver that arrives at the final solution by treating all equations simultaneously.The applicationmust also take care tominimize both time and space error between the physics,particularly if more than one mesh representation is needed in the solution process.This paper presents an application framework that was specifically designed to support tightly coupled multiphysics analysis.The Multiphysics Object Oriented Simulation Environment(MOOSE)is based on the Jacobian-freeNewton-Krylov(JFNK)method combined with physics-based preconditioning to provide the underlying mathematical structure for applications.The report concludes with the presentation of a host of nuclear,energy,and environmental applications that demonstrate the efficacy of the approach and the utility of a well-designed multiphysics framework.
文摘In this article we propose a higher-order space-time conservative method for hyperbolic systems with stiff and non stiff source terms as well as relaxation systems.We call the scheme a slope propagation(SP)method.It is an extension of our scheme derived for homogeneous hyperbolic systems[1].In the present inhomogeneous systems the relaxation time may vary from order of one to a very small value.These small values make the relaxation term stronger and highly stiff.In such situations underresolved numerical schemes may produce spurious numerical results.However,our present scheme has the capability to correctly capture the behavior of the physical phenomena with high order accuracy even if the initial layer and the small relaxation time are not numerically resolved.The scheme treats the space and time in a unified manner.The flow variables and their slopes are the basic unknowns in the scheme.The source term is treated by its volumetric integration over the space-time control volume and is a direct part of the overall space-time flux balance.We use two approaches for the slope calculations of the flow variables,the first one results directly from the flux balance over the control volumes,while in the second one we use a finite difference approach.The main features of the scheme are its simplicity,its Jacobian-free and Riemann solver-free recipe,as well as its efficiency and high of order accuracy.In particular we show that the scheme has a discrete analog of the continuous asymptotic limit.We have implemented our scheme for various test models available in the literature such as the Broadwell model,the extended thermodynamics equations,the shallow water equations,traffic flow and the Euler equations with heat transfer.The numerical results validate the accuracy,versatility and robustness of the present scheme.
