The recent result of an orbit continuation algorithm has provided a rigorous method for long-term numerical integration of an orbit on the unstable manifold of a periodic solution.This algorithm is matrix-free and emp...The recent result of an orbit continuation algorithm has provided a rigorous method for long-term numerical integration of an orbit on the unstable manifold of a periodic solution.This algorithm is matrix-free and employs a combination of the Newton-Raphson method and the Krylov subspace method.Moreover,the algorithm adopts a multiple shooting method to address the problem of orbital instability due to long-term numerical integration.The algorithm is described through computing the extension of unstable manifold of a recomputed Nagata′s lowerbranch steady solution of plane Couette flow,which is an example of an exact coherent state that has recently been studied in subcritical transition to turbulence.展开更多
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
This paper presents a new mathematical model for the highly nonlinear problem of frictional con- tact. A programming model, multipole boundary element method (BEM), was developed for 3-D elastic con- tact with frict...This paper presents a new mathematical model for the highly nonlinear problem of frictional con- tact. A programming model, multipole boundary element method (BEM), was developed for 3-D elastic con- tact with friction to replace the Monte Carlo method. A numerical example shows that the optimization pro- gramming model for the point-to-surface contact with friction and the fast optimization generalized minimal residual algorithm (GMRES(m)) significantly improve the analysis of such problems relative to the conven- tional BEM.展开更多
In this paper, an unstructured, collocated finite volume method for solvingthe Navier-Stokes equations was developed by virtue of auxiliary points. The derivatives weredetermined by the Gauss theorem. The proposed met...In this paper, an unstructured, collocated finite volume method for solvingthe Navier-Stokes equations was developed by virtue of auxiliary points. The derivatives weredetermined by the Gauss theorem. The proposed method could provide control volumes with arbitrarygeometry and preserve the second-order accuracy even if highly distorted grids are used. Althougharbitrary number of cell faces can be used, the hybrid quadrilateral/triangular grids are moredesirable for the simplicity of implementation and applications to engineering problems. Thepressure-velocity coupling was treated using a SIMPLE-like algorithm. The Generalized MinimumResidual (GMRES) method with the Incomplete LU (ILU) preconditioner was used to solve linearequations. Four test cases were studied for validating the proposed method. In using this method,grid quality is not important. Thus, engineers can pay mostly attention to physical mechanism ofproblems. Turbulence models can be simply integrated and the method can be straightforwardlyextended to treat three-dimensional problems.展开更多
The velocity field in the Wu River at Chongqing was simulated using the shallow water equation implemented on clustered workstations. The parallel computing technique was used to increase the comput- ing power. The sh...The velocity field in the Wu River at Chongqing was simulated using the shallow water equation implemented on clustered workstations. The parallel computing technique was used to increase the comput- ing power. The shallow water equation was discretized to a linear system of equations with a direct parallel generalized minimum residual algorithm (GMRES) used to solve the linear system. Unlike other parallel GMRES methods, the direct GMRES method does not alter the sequential algorithm, but bases the paral- lelization on basic operations such as the matrix-vector product. The computed results agree well with ob- served results. The parallel computing technique significantly increases the solution speed for this large- scale problem.展开更多
文摘The recent result of an orbit continuation algorithm has provided a rigorous method for long-term numerical integration of an orbit on the unstable manifold of a periodic solution.This algorithm is matrix-free and employs a combination of the Newton-Raphson method and the Krylov subspace method.Moreover,the algorithm adopts a multiple shooting method to address the problem of orbital instability due to long-term numerical integration.The algorithm is described through computing the extension of unstable manifold of a recomputed Nagata′s lowerbranch steady solution of plane Couette flow,which is an example of an exact coherent state that has recently been studied in subcritical transition to turbulence.
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.
基金Supported by the National Natural Science Foundation of China(No. 50075075)
文摘This paper presents a new mathematical model for the highly nonlinear problem of frictional con- tact. A programming model, multipole boundary element method (BEM), was developed for 3-D elastic con- tact with friction to replace the Monte Carlo method. A numerical example shows that the optimization pro- gramming model for the point-to-surface contact with friction and the fast optimization generalized minimal residual algorithm (GMRES(m)) significantly improve the analysis of such problems relative to the conven- tional BEM.
文摘In this paper, an unstructured, collocated finite volume method for solvingthe Navier-Stokes equations was developed by virtue of auxiliary points. The derivatives weredetermined by the Gauss theorem. The proposed method could provide control volumes with arbitrarygeometry and preserve the second-order accuracy even if highly distorted grids are used. Althougharbitrary number of cell faces can be used, the hybrid quadrilateral/triangular grids are moredesirable for the simplicity of implementation and applications to engineering problems. Thepressure-velocity coupling was treated using a SIMPLE-like algorithm. The Generalized MinimumResidual (GMRES) method with the Incomplete LU (ILU) preconditioner was used to solve linearequations. Four test cases were studied for validating the proposed method. In using this method,grid quality is not important. Thus, engineers can pay mostly attention to physical mechanism ofproblems. Turbulence models can be simply integrated and the method can be straightforwardlyextended to treat three-dimensional problems.
基金Supported by the National Natural Science Foundation of China (Nos. 50379022 and 59979013)
文摘The velocity field in the Wu River at Chongqing was simulated using the shallow water equation implemented on clustered workstations. The parallel computing technique was used to increase the comput- ing power. The shallow water equation was discretized to a linear system of equations with a direct parallel generalized minimum residual algorithm (GMRES) used to solve the linear system. Unlike other parallel GMRES methods, the direct GMRES method does not alter the sequential algorithm, but bases the paral- lelization on basic operations such as the matrix-vector product. The computed results agree well with ob- served results. The parallel computing technique significantly increases the solution speed for this large- scale problem.
