To develop an efficient and robust aerodynamic analysis method for numerical optimization designs of wing and complex configuration, a combination of matrix preconditioning and multigrid method is presented and invest...To develop an efficient and robust aerodynamic analysis method for numerical optimization designs of wing and complex configuration, a combination of matrix preconditioning and multigrid method is presented and investigated. The time derivatives of three-dimensional Navier-Stokes equations are preconditioned by Choi-Merkle preconditioning matrix that is originally designed for two-dimensional low Mach number viscous flows. An extension to three-dimensional viscous flow is implemented, and a method improving the convergence for transonic flow is proposed. The space discretizaition is performed by employing a finite-volume cell-centered scheme and using a central difference. The time marching is based on an explicit Rtmge-Kutta scheme proposed by Jameson. An efficient FAS multigrid method is used to accelerate the convergence to steady-state solutions. Viscous flows over ONERA M6 wing and M100 wing are numerically simulated with Mach numbers ranging from 0.010 to 0.839. The inviscid flow over the DLR-F4 wing-body configuration is also calculated to preliminarily examine the performance of the presented method for complex configuration. The computed results are compared with the experimental data and good agreement is achieved. It is shown that the presented method is efficient and robust for both compressible and incompressible flows and is very attractive for aerodynamic optimization designs of wing and complex configuration.展开更多
A hybrid grid generation technique and a multigrid/parallel algorithm are presented in this paper for turbulence flow simulations over three-dimensional （3D） complex geometries. The hybrid grid generation technique ...A hybrid grid generation technique and a multigrid/parallel algorithm are presented in this paper for turbulence flow simulations over three-dimensional （3D） complex geometries. The hybrid grid generation technique is based on an agglomeration method of anisotropic tetrahedrons. Firstly, the complex computational domain is covered by pure tetrahedral grids, in which anisotropic tetrahedrons are adopted to discrete the boundary layer and isotropic tetrahedrons in the outer field. Then, the anisotropic tetrahedrons in the boundary layer are agglomerated to generate prismatic grids. The agglomeration method can improve the grid quality in boundary layer and reduce the grid quantity to enhance the numerical accuracy and efficiency. In order to accelerate the convergence history, a multigrid/parallel algorithm is developed also based on anisotropic agglomeration approach. The numerical results demonstrate the excellent accelerating capability of this multigrid method.展开更多
Based on the fact that 3-D model discretization by artificial could not always be successfully implemented especially for large-scaled problems when high accuracy and efficiency were required, a new adaptive multigrid...Based on the fact that 3-D model discretization by artificial could not always be successfully implemented especially for large-scaled problems when high accuracy and efficiency were required, a new adaptive multigrid finite element method was proposed. In this algorithm, a-posteriori error estimator was employed to generate adaptively refined mesh on a given initial mesh. On these iterative meshes, V-cycle based multigrid method was adopted to fast solve each linear equation with each initial iterative term interpolated from last mesh. With this error estimator, the unknowns were nearly optimally distributed on the final mesh which guaranteed the accuracy. The numerical results show that the multigrid solver is faster and more stable compared with ICCG solver. Meanwhile, the numerical results obtained from the final model discretization approximate the analytical solutions with maximal relative errors less than 1%, which remarkably validates this algorithm.展开更多
In order to solve the so-called ＂bull-eye＂ problem caused by using a simple bilinear interpolation as an observational mapping operator in the cost function in the multigrid three-dimensional variational （3DVAR） d...In order to solve the so-called ＂bull-eye＂ problem caused by using a simple bilinear interpolation as an observational mapping operator in the cost function in the multigrid three-dimensional variational （3DVAR） data assimilation scheme, a smoothing term, equivalent to a penalty term, is introduced into the cost function to serve as a means of troubleshooting. A theoretical analysis is first performed to figure out what on earth results in the issue of ＂bull-eye＂, and then the meaning of such smoothing term is elucidated and the uniqueness of solution of the multigrid 3DVAR with the smoothing term added is discussed through the theoretical deduction for one-dimensional （1D） case, and two idealized data assimilation experiments （one- and two-dimensional （2D） cases）. By exploring the relationship between the smoothing term and the recursive filter theoretically and practically, it is revealed why satisfied analysis results can be achieved by using such proposed solution for the issue of the multigrid 3DVAR.展开更多
We propose an efficient and robust algorithm to solve the steady Euler equa- tions on unstructured grids.The new algorithm is a Newton-iteration method in which each iteration step is a linear multigrid method using b...We propose an efficient and robust algorithm to solve the steady Euler equa- tions on unstructured grids.The new algorithm is a Newton-iteration method in which each iteration step is a linear multigrid method using block lower-upper symmetric Gauss-Seidel(LU-SGS)iteration as its smoother To regularize the Jacobian matrix of Newton-iteration,we adopted a local residual dependent regularization as the replace- ment of the standard time-stepping relaxation technique based on the local CFL number The proposed method can be extended to high order approximations and three spatial dimensions in a nature way.The solver was tested on a sequence of benchmark prob- lems on both quasi-uniform and local adaptive meshes.The numerical results illustrated the efficiency and robustness of our algorithm.展开更多
Assimilating satellite radiances into Numerical Weather Prediction(NWP) models has become an important approach to increase the accuracy of numerical weather forecasting. In this study, the assimilation technique sche...Assimilating satellite radiances into Numerical Weather Prediction(NWP) models has become an important approach to increase the accuracy of numerical weather forecasting. In this study, the assimilation technique scheme was employed in NOAA's STMAS(Space-Time Multiscale Analysis System) to assimilate AMSU-A radiances data.Channel selection sensitivity experiments were conducted on assimilated satellite data in the first place. Then, real case analysis of AMSU-A data assimilation was performed. The analysis results showed that, following assimilating of AMSU-A channels 5-11 in STMAS, the objective function quickly converged, and the channel vertical response was consistent with the AMSU-A weighting function distribution, which suggests that the channels can be used in the assimilation of satellite data in STMAS. With the case of the Typhoon Morakot in Taiwan Island in August 2009 as an example, experiments on assimilated and unassimilated AMSU-A radiances data were designed to analyze the impact of the assimilation of satellite data on STMAS. The results demonstrated that assimilation of AMSU-A data provided more accurate prediction of the precipitation region and intensity, and especially, it improved the 0-6h precipitation forecast significantly.展开更多
The internal turbulent flow in conical diffuser is a very complicated adverse pressure gradient flow.DLR k-ε turbulence model was adopted to study it.The every terms of the Laplace operator in DLR k-ε turbulence mod...The internal turbulent flow in conical diffuser is a very complicated adverse pressure gradient flow.DLR k-ε turbulence model was adopted to study it.The every terms of the Laplace operator in DLR k-ε turbulence model and pressure Poisson equation were discretized by upwind difference scheme.A new full implicit difference scheme of 5-point was constructed by using finite volume method and finite difference method.A large sparse matrix with five diagonals was formed and was stored by three arrays of one dimension in a compressed mode.General iterative methods do not work wel1 with large sparse matrix.With algebraic multigrid method(AMG),linear algebraic system of equations was solved and the precision was set at 10-6.The computation results were compared with the experimental results.The results show that the computation results have a good agreement with the experiment data.The precision of computational results and numerical simulation efficiency are greatly improved.展开更多
In this paper, standard and economical cascadic multigrid methods are considered for solving the algebraic systems resulting from the mortar finite element methods. Both cascadic multigrid methods do not need full ell...In this paper, standard and economical cascadic multigrid methods are considered for solving the algebraic systems resulting from the mortar finite element methods. Both cascadic multigrid methods do not need full elliptic regularity, so they can be used to tackle more general elliptic problems. Numerical experiments are reported to suonort our theorv.展开更多
China Ocean ReAnalysis(CORA) version 1.0 products for the period 2009-18 have been developed and validated.The model configuration and assimilation algorithm have both been updated compared to those of the 51-year(195...China Ocean ReAnalysis(CORA) version 1.0 products for the period 2009-18 have been developed and validated.The model configuration and assimilation algorithm have both been updated compared to those of the 51-year(1958-2008) products.The assimilated observations include temperature and salinity field data,satellite remote sensing sea surface temperature,and merged sea surface height(SSH) anomaly data.The validation includes the following three aspects:(1) Temperature,salinity,and SSH anomaly root-mean-square errors(RMSEs) are computed as a primary evaluation of the reanalysis quality.The 0-2000 m domain-averaged RMSEs of temperature and salinity are 0.61℃ and 0.08 psu,respectively.The SSH anomaly RMSE is less than 0.2 m in most regions.(2) The 35°N temperature section is used to evaluate the ability to reproduce the thermocline,mixing layer,and Yellow Sea cold water mass.In summer,the thermocline is reinforced,with the gradient changing from 3℃ in May to 10℃ in August.The mixing-layer depth reproduced by CORA is consistent with that computed from the observed climatology.The Yellow Sea cold water mass forms at a depth of 50 m.(3) The reanalysis current is examined against the tracks of some drifting buoys.The results show that the reanalysis current can capture the mesoscale eddies near the Kuroshio,which are similar to those described by the drifting buoys.Overall,the 2009-18 CORA reanalysis products are capable of reproducing major oceanic phenomena and processes in the coastal waters of China and adjacent seas.展开更多
A system of linear time-dependent hyperbolic partial differential equations in the form of the time-domain Maxwell′s equations is numerically solved using ageometric multigrid method.The multilevel method is an adapt...A system of linear time-dependent hyperbolic partial differential equations in the form of the time-domain Maxwell′s equations is numerically solved using ageometric multigrid method.The multilevel method is an adaptation of Ni′s cell-vertex based multigrid technique,originally proposed for accelerating steady state convergence of nonlinear time-dependent Euler equations of gas dynamics.We discuss issues pertaining to the application of the geometric multigrid method to a system of equations where the major issue is of accurately propagating linear waves over large distances leading to major constraints on the required grid resolution in terms of points-perwavelength.展开更多
A new forecasting system-the System of Multigrid Nonlinear Least-squares Four-dimensional Variational(NLS-4DVar)Data Assimilation for Numerical Weather Prediction(SNAP)-was established by building upon the multigrid N...A new forecasting system-the System of Multigrid Nonlinear Least-squares Four-dimensional Variational(NLS-4DVar)Data Assimilation for Numerical Weather Prediction(SNAP)-was established by building upon the multigrid NLS-4DVar data assimilation scheme,the operational Gridpoint Statistical Interpolation(GSI)−based data-processing and observation operators,and the widely used Weather Research and Forecasting numerical model.Drawing upon lessons learned from the superiority of the operational GSI analysis system,for its various observation operators and the ability to assimilate multiple-source observations,SNAP adopts GSI-based data-processing and observation operator modules to compute the observation innovations.The multigrid NLS-4DVar assimilation framework is used for the analysis,which can adequately correct errors from large to small scales and accelerate iteration solutions.The analysis variables are model state variables,rather than the control variables adopted in the conventional 4DVar system.Currently,we have achieved the assimilation of conventional observations,and we will continue to improve the assimilation of radar and satellite observations in the future.SNAP was evaluated by case evaluation experiments and one-week cycling assimilation experiments.In the case evaluation experiments,two six-hour time windows were established for assimilation experiments and precipitation forecasts were verified against hourly precipitation observations from more than 2400 national observation sites.This showed that SNAP can absorb observations and improve the initial field,thereby improving the precipitation forecast.In the one-week cycling assimilation experiments,six-hourly assimilation cycles were run in one week.SNAP produced slightly lower forecast RMSEs than the GSI 4DEnVar(Four-dimensional Ensemble Variational)as a whole and the threat scores of precipitation forecasts initialized from the analysis of SNAP were higher than those obtained from the analysis of GSI 4DEnVar.展开更多
Based on an asymptotic expansion of finite element, an extrapolation cascadic multigrid method （EXCMG） is proposed, in which the new extrapolation and quadratic interpolation are used to provide a better initial val...Based on an asymptotic expansion of finite element, an extrapolation cascadic multigrid method （EXCMG） is proposed, in which the new extrapolation and quadratic interpolation are used to provide a better initial value on refined grid. In the case of multiple grids, both superconvergence error in H^1-norm and the optimal error in l2-norm are analyzed. The numerical experiment shows the advantage of EXCMG in comparison with CMG.展开更多
In this paper,an efcient multigrid-DEIM semi-reduced-order model is developed to accelerate the simulation of unsteady single-phase compressible fow in porous media.The cornerstone of the proposed model is that the fu...In this paper,an efcient multigrid-DEIM semi-reduced-order model is developed to accelerate the simulation of unsteady single-phase compressible fow in porous media.The cornerstone of the proposed model is that the full approximate storage multigrid method is used to accelerate the solution of fow equation in original full-order space,and the discrete empirical interpolation method(DEIM)is applied to speed up the solution of Peng-Robinson equation of state in reduced-order subspace.The multigrid-DEIM semi-reduced-order model combines the computation both in full-order space and in reducedorder subspace,which not only preserves good prediction accuracy of full-order model,but also gains dramatic computational acceleration by multigrid and DEIM.Numerical performances including accuracy and acceleration of the proposed model are carefully evaluated by comparing with that of the standard semi-implicit method.In addition,the selection of interpolation points for constructing the low-dimensional subspace for solving the Peng-Robinson equation of state is demonstrated and carried out in detail.Comparison results indicate that the multigrid-DEIM semi-reduced-order model can speed up the simulation substantially at the same time preserve good computational accuracy with negligible errors.The general acceleration is up to 50-60 times faster than that of standard semi-implicit method in two-dimensional simulations,but the average relative errors of numerical results between these two methods only have the order of magnitude 10^(−4)-10^(−6)%.展开更多
Studies of problems involving physical anisotropy are applied in sciences and engineering,for instance,when the thermal conductivity depends on the direction.In this study,the multigrid method was used in order to acc...Studies of problems involving physical anisotropy are applied in sciences and engineering,for instance,when the thermal conductivity depends on the direction.In this study,the multigrid method was used in order to accelerate the convergence of the iterative methods used to solve this type of problem.The asymptotic convergence factor of the multigrid was determined empirically(computer aided)and also by employing local Fourier analysis(LFA).The mathematical model studied was the 2D anisotropic diffusion equation,in whichε>0 was the coefficient of a nisotropy.The equation was discretized by the Finite Difference Method(FDM)and Central Differencing Scheme(CDS).Correction Scheme(CS),pointwise Gauss-Seidel smoothers(Lexicographic and Red-Black ordering),and line Gauss-Seidel smoothers(Lexicographic and Zebra ordering)in x and y directions were used for building the multigrid.The best asymptotic convergence factor was obtained by the Gauss-Seidel method in the direction x for 0<ε<<1 and in the direction y forε>>1.In this sense,an xy-zebra-GS smoother was proposed,which proved to be efficient and robust for the different anisotropy coefficients.Moreover,the convergence factors calculated empirically and by LFA are in agreement.展开更多
In this paper image with horizontal motion blur, vertical motion blur and angled motion blur are considered. We construct several difference schemes to the highly nonlinear term △↓.（△↓u/√｜△↓｜^2＋β） of the ...In this paper image with horizontal motion blur, vertical motion blur and angled motion blur are considered. We construct several difference schemes to the highly nonlinear term △↓.（△↓u/√｜△↓｜^2＋β） of the total variation-based image motion deblurring problem. The large nonlinear system is linearized by fixed point iteration method. An algebraic multigrid method with Krylov subspace acceleration is used to solve the corresponding linear equations as in [7]. The algorithms can restore the image very well. We give some numerical experiments to demonstrate that our difference schemes are efficient and robust.展开更多
In this article algebraic multigrid as preconditioners are designed, with biorthogonal wavelets, as intergrid operators for the Krylov subspace iterative methods. Construction of hierarchy of matrices in algebraic mul...In this article algebraic multigrid as preconditioners are designed, with biorthogonal wavelets, as intergrid operators for the Krylov subspace iterative methods. Construction of hierarchy of matrices in algebraic multigrid context is based on lowpass filter version of Wavelet Transform. The robustness and efficiency of this new approach is tested by applying it to large sparse, unsymmetric and ill-conditioned matrices from Tim Davis collection of sparse matrices. Proposed preconditioners have potential in reducing cputime, operator complexity and storage space of algebraic multigrid V-cycle and meet the desired accuracy of solution compared with that of orthogonal wavelets.展开更多
This paper proposes a new method for data assimilation of the surface radial current observed by High Frequency ground wave radar and optimization of the bottom friction coefficient.In this method,the shallow water wa...This paper proposes a new method for data assimilation of the surface radial current observed by High Frequency ground wave radar and optimization of the bottom friction coefficient.In this method,the shallow water wave equation is introduced into the cost function of the multigrid three-dimensional variation data assimilation method as the weak constraint term,the surface current and the bottom friction coefficient are defined as the analytical variables,and the high spatiotemporal resolution surface radial flow observed by the high-frequency ground wave radar is used to optimize the surface current and bottom friction coefficient.This method can effectively consider the spatiotemporal correlation of radar data and extract multiscale information from surface radial flow data from long waves to short waves.Introducing the shallow water wave equation into the cost function as a weak constraint condition can adjust both the momentum and mass fields simultaneously to obtain more reasonable analysis information.The optimized bottom friction coefficient is introduced into the regional ocean numerical model to carry out numerical experiments.The test results show that the bottom friction coefficient obtained by this method can effectively improve the accuracy of the numerical simulation of sea surface height in the offshore area and reduce the simulation error.展开更多
This paper introduces two kinds of methods with high accuracy for fi-nite element probability computing method,by which the function value on one or afew nodes can be calculated without forming the total stiffness mat...This paper introduces two kinds of methods with high accuracy for fi-nite element probability computing method,by which the function value on one or afew nodes can be calculated without forming the total stiffness matrix.展开更多
Panel methods for the calculation of wavemaking resistance result in a linear equation system for the unknown singularities.The coefficient matrix is full but not well conditioned.In this paper an incomplete LU decomp...Panel methods for the calculation of wavemaking resistance result in a linear equation system for the unknown singularities.The coefficient matrix is full but not well conditioned.In this paper an incomplete LU decomposition (ILU) method and a combined multigrid ILU method are used to solve the linear system.Systematic computations using the ILU method have shown that the CPU time can be reduced to 30% to 40% of that using an incomplete Gaussian elimination method. In the proposed multigrid ILU method an averaged restriction and a piecewise constant prolongation are used.The construction of the coefficient matrix at coarse levels is based on geometrical considerations.It turns out that the condition of the relative consistency is fulfilled.Comparison computations have shown that nearly the same results were obtained.However,due to additional CPU time needed for the execution of the matrix vector products in the restriction and the prolongation proceses of the multigrid method,a further reduction of the total CPU time could not be reailized.展开更多
文摘To develop an efficient and robust aerodynamic analysis method for numerical optimization designs of wing and complex configuration, a combination of matrix preconditioning and multigrid method is presented and investigated. The time derivatives of three-dimensional Navier-Stokes equations are preconditioned by Choi-Merkle preconditioning matrix that is originally designed for two-dimensional low Mach number viscous flows. An extension to three-dimensional viscous flow is implemented, and a method improving the convergence for transonic flow is proposed. The space discretizaition is performed by employing a finite-volume cell-centered scheme and using a central difference. The time marching is based on an explicit Rtmge-Kutta scheme proposed by Jameson. An efficient FAS multigrid method is used to accelerate the convergence to steady-state solutions. Viscous flows over ONERA M6 wing and M100 wing are numerically simulated with Mach numbers ranging from 0.010 to 0.839. The inviscid flow over the DLR-F4 wing-body configuration is also calculated to preliminarily examine the performance of the presented method for complex configuration. The computed results are compared with the experimental data and good agreement is achieved. It is shown that the presented method is efficient and robust for both compressible and incompressible flows and is very attractive for aerodynamic optimization designs of wing and complex configuration.
基金supported partially by National Basic Research Program of China (Grant No. 2009CB723800)National Natural Science Foundation of China (Grant Nos: 91016001 and 10872023)
文摘A hybrid grid generation technique and a multigrid/parallel algorithm are presented in this paper for turbulence flow simulations over three-dimensional （3D） complex geometries. The hybrid grid generation technique is based on an agglomeration method of anisotropic tetrahedrons. Firstly, the complex computational domain is covered by pure tetrahedral grids, in which anisotropic tetrahedrons are adopted to discrete the boundary layer and isotropic tetrahedrons in the outer field. Then, the anisotropic tetrahedrons in the boundary layer are agglomerated to generate prismatic grids. The agglomeration method can improve the grid quality in boundary layer and reduce the grid quantity to enhance the numerical accuracy and efficiency. In order to accelerate the convergence history, a multigrid/parallel algorithm is developed also based on anisotropic agglomeration approach. The numerical results demonstrate the excellent accelerating capability of this multigrid method.
基金Projects(2006AA06Z105, 2007AA06Z134) supported by the National High-Tech Research and Development Program of ChinaProjects(2007, 2008) supported by China Scholarship Council (CSC)
文摘Based on the fact that 3-D model discretization by artificial could not always be successfully implemented especially for large-scaled problems when high accuracy and efficiency were required, a new adaptive multigrid finite element method was proposed. In this algorithm, a-posteriori error estimator was employed to generate adaptively refined mesh on a given initial mesh. On these iterative meshes, V-cycle based multigrid method was adopted to fast solve each linear equation with each initial iterative term interpolated from last mesh. With this error estimator, the unknowns were nearly optimally distributed on the final mesh which guaranteed the accuracy. The numerical results show that the multigrid solver is faster and more stable compared with ICCG solver. Meanwhile, the numerical results obtained from the final model discretization approximate the analytical solutions with maximal relative errors less than 1%, which remarkably validates this algorithm.
基金The National Basic Research Program of China under contract No. 2013CB430304the National High-Tech R&D Program of China under contract No. 2013AA09A505the National Natural Science Foundation of China under contract Nos 41030854,40906015,40906016,41106005 and 41176003
文摘In order to solve the so-called ＂bull-eye＂ problem caused by using a simple bilinear interpolation as an observational mapping operator in the cost function in the multigrid three-dimensional variational （3DVAR） data assimilation scheme, a smoothing term, equivalent to a penalty term, is introduced into the cost function to serve as a means of troubleshooting. A theoretical analysis is first performed to figure out what on earth results in the issue of ＂bull-eye＂, and then the meaning of such smoothing term is elucidated and the uniqueness of solution of the multigrid 3DVAR with the smoothing term added is discussed through the theoretical deduction for one-dimensional （1D） case, and two idealized data assimilation experiments （one- and two-dimensional （2D） cases）. By exploring the relationship between the smoothing term and the recursive filter theoretically and practically, it is revealed why satisfied analysis results can be achieved by using such proposed solution for the issue of the multigrid 3DVAR.
文摘We propose an efficient and robust algorithm to solve the steady Euler equa- tions on unstructured grids.The new algorithm is a Newton-iteration method in which each iteration step is a linear multigrid method using block lower-upper symmetric Gauss-Seidel(LU-SGS)iteration as its smoother To regularize the Jacobian matrix of Newton-iteration,we adopted a local residual dependent regularization as the replace- ment of the standard time-stepping relaxation technique based on the local CFL number The proposed method can be extended to high order approximations and three spatial dimensions in a nature way.The solver was tested on a sequence of benchmark prob- lems on both quasi-uniform and local adaptive meshes.The numerical results illustrated the efficiency and robustness of our algorithm.
基金National Natural Science Foundation of China(41375027,41130960,41275114,41275039)Public Benefit Research Foundation of China Meteorological Administration(GYHY201406001,GYHY201106044)+1 种基金"863"Program(2012AA120903)National Key Research and Development Program of China(2016YFB0502501)
文摘Assimilating satellite radiances into Numerical Weather Prediction(NWP) models has become an important approach to increase the accuracy of numerical weather forecasting. In this study, the assimilation technique scheme was employed in NOAA's STMAS(Space-Time Multiscale Analysis System) to assimilate AMSU-A radiances data.Channel selection sensitivity experiments were conducted on assimilated satellite data in the first place. Then, real case analysis of AMSU-A data assimilation was performed. The analysis results showed that, following assimilating of AMSU-A channels 5-11 in STMAS, the objective function quickly converged, and the channel vertical response was consistent with the AMSU-A weighting function distribution, which suggests that the channels can be used in the assimilation of satellite data in STMAS. With the case of the Typhoon Morakot in Taiwan Island in August 2009 as an example, experiments on assimilated and unassimilated AMSU-A radiances data were designed to analyze the impact of the assimilation of satellite data on STMAS. The results demonstrated that assimilation of AMSU-A data provided more accurate prediction of the precipitation region and intensity, and especially, it improved the 0-6h precipitation forecast significantly.
基金Projects(59375211,10771178,10676031) supported by the National Natural Science Foundation of ChinaProject(07A068) supported by the Key Project of Hunan Education CommissionProject(2005CB321702) supported by the National Key Basic Research Program of China
文摘The internal turbulent flow in conical diffuser is a very complicated adverse pressure gradient flow.DLR k-ε turbulence model was adopted to study it.The every terms of the Laplace operator in DLR k-ε turbulence model and pressure Poisson equation were discretized by upwind difference scheme.A new full implicit difference scheme of 5-point was constructed by using finite volume method and finite difference method.A large sparse matrix with five diagonals was formed and was stored by three arrays of one dimension in a compressed mode.General iterative methods do not work wel1 with large sparse matrix.With algebraic multigrid method(AMG),linear algebraic system of equations was solved and the precision was set at 10-6.The computation results were compared with the experimental results.The results show that the computation results have a good agreement with the experiment data.The precision of computational results and numerical simulation efficiency are greatly improved.
基金supported by the National Basic Research Program of China under the grant 2005CB321701the National Science Foundation(NSF) of China(10731060)111 project(B08018)
文摘In this paper, standard and economical cascadic multigrid methods are considered for solving the algebraic systems resulting from the mortar finite element methods. Both cascadic multigrid methods do not need full elliptic regularity, so they can be used to tackle more general elliptic problems. Numerical experiments are reported to suonort our theorv.
基金supported by grants from the National Key Research and Development Program of China [grant numbers 2016YFC1401800,2017YFC1404103,2016YFC1401701,and 2019YFC1510000]the National Natural Science Foundation of China [grant number 41976019]the Tianjin Natural Science Foundation [grant number 18JCQNJC01200]。
文摘China Ocean ReAnalysis(CORA) version 1.0 products for the period 2009-18 have been developed and validated.The model configuration and assimilation algorithm have both been updated compared to those of the 51-year(1958-2008) products.The assimilated observations include temperature and salinity field data,satellite remote sensing sea surface temperature,and merged sea surface height(SSH) anomaly data.The validation includes the following three aspects:(1) Temperature,salinity,and SSH anomaly root-mean-square errors(RMSEs) are computed as a primary evaluation of the reanalysis quality.The 0-2000 m domain-averaged RMSEs of temperature and salinity are 0.61℃ and 0.08 psu,respectively.The SSH anomaly RMSE is less than 0.2 m in most regions.(2) The 35°N temperature section is used to evaluate the ability to reproduce the thermocline,mixing layer,and Yellow Sea cold water mass.In summer,the thermocline is reinforced,with the gradient changing from 3℃ in May to 10℃ in August.The mixing-layer depth reproduced by CORA is consistent with that computed from the observed climatology.The Yellow Sea cold water mass forms at a depth of 50 m.(3) The reanalysis current is examined against the tracks of some drifting buoys.The results show that the reanalysis current can capture the mesoscale eddies near the Kuroshio,which are similar to those described by the drifting buoys.Overall,the 2009-18 CORA reanalysis products are capable of reproducing major oceanic phenomena and processes in the coastal waters of China and adjacent seas.
文摘A system of linear time-dependent hyperbolic partial differential equations in the form of the time-domain Maxwell′s equations is numerically solved using ageometric multigrid method.The multilevel method is an adaptation of Ni′s cell-vertex based multigrid technique,originally proposed for accelerating steady state convergence of nonlinear time-dependent Euler equations of gas dynamics.We discuss issues pertaining to the application of the geometric multigrid method to a system of equations where the major issue is of accurately propagating linear waves over large distances leading to major constraints on the required grid resolution in terms of points-perwavelength.
基金the National Key Research and Development Program of China(Grant No.2016YFA0600203)the National Natural Science Foundation of China(Grant No.41575100)+1 种基金the Key Research Program of Frontier Sciences,Chinese Academy of Sciences(Grant No.QYZDY-SSW-DQC012)the CMA Special Public Welfare Research Fund(Grant No.GYHY201506002).
文摘A new forecasting system-the System of Multigrid Nonlinear Least-squares Four-dimensional Variational(NLS-4DVar)Data Assimilation for Numerical Weather Prediction(SNAP)-was established by building upon the multigrid NLS-4DVar data assimilation scheme,the operational Gridpoint Statistical Interpolation(GSI)−based data-processing and observation operators,and the widely used Weather Research and Forecasting numerical model.Drawing upon lessons learned from the superiority of the operational GSI analysis system,for its various observation operators and the ability to assimilate multiple-source observations,SNAP adopts GSI-based data-processing and observation operator modules to compute the observation innovations.The multigrid NLS-4DVar assimilation framework is used for the analysis,which can adequately correct errors from large to small scales and accelerate iteration solutions.The analysis variables are model state variables,rather than the control variables adopted in the conventional 4DVar system.Currently,we have achieved the assimilation of conventional observations,and we will continue to improve the assimilation of radar and satellite observations in the future.SNAP was evaluated by case evaluation experiments and one-week cycling assimilation experiments.In the case evaluation experiments,two six-hour time windows were established for assimilation experiments and precipitation forecasts were verified against hourly precipitation observations from more than 2400 national observation sites.This showed that SNAP can absorb observations and improve the initial field,thereby improving the precipitation forecast.In the one-week cycling assimilation experiments,six-hourly assimilation cycles were run in one week.SNAP produced slightly lower forecast RMSEs than the GSI 4DEnVar(Four-dimensional Ensemble Variational)as a whole and the threat scores of precipitation forecasts initialized from the analysis of SNAP were higher than those obtained from the analysis of GSI 4DEnVar.
基金Supported by National Natural Science Foundation of China (10771063)the Doctor Programme of the National Education Committee (20050542006)
文摘Based on an asymptotic expansion of finite element, an extrapolation cascadic multigrid method （EXCMG） is proposed, in which the new extrapolation and quadratic interpolation are used to provide a better initial value on refined grid. In the case of multiple grids, both superconvergence error in H^1-norm and the optimal error in l2-norm are analyzed. The numerical experiment shows the advantage of EXCMG in comparison with CMG.
基金This study is supported by the National Natural Science Foundation of China(Nos.51904031,51936001)the Beijing Natural Science Foundation(No.3204038)the Jointly Projects of Beijing Natural Science Foundation and Beijing Municipal Education Commission(No.KZ201810017023).
文摘In this paper,an efcient multigrid-DEIM semi-reduced-order model is developed to accelerate the simulation of unsteady single-phase compressible fow in porous media.The cornerstone of the proposed model is that the full approximate storage multigrid method is used to accelerate the solution of fow equation in original full-order space,and the discrete empirical interpolation method(DEIM)is applied to speed up the solution of Peng-Robinson equation of state in reduced-order subspace.The multigrid-DEIM semi-reduced-order model combines the computation both in full-order space and in reducedorder subspace,which not only preserves good prediction accuracy of full-order model,but also gains dramatic computational acceleration by multigrid and DEIM.Numerical performances including accuracy and acceleration of the proposed model are carefully evaluated by comparing with that of the standard semi-implicit method.In addition,the selection of interpolation points for constructing the low-dimensional subspace for solving the Peng-Robinson equation of state is demonstrated and carried out in detail.Comparison results indicate that the multigrid-DEIM semi-reduced-order model can speed up the simulation substantially at the same time preserve good computational accuracy with negligible errors.The general acceleration is up to 50-60 times faster than that of standard semi-implicit method in two-dimensional simulations,but the average relative errors of numerical results between these two methods only have the order of magnitude 10^(−4)-10^(−6)%.
文摘Studies of problems involving physical anisotropy are applied in sciences and engineering,for instance,when the thermal conductivity depends on the direction.In this study,the multigrid method was used in order to accelerate the convergence of the iterative methods used to solve this type of problem.The asymptotic convergence factor of the multigrid was determined empirically(computer aided)and also by employing local Fourier analysis(LFA).The mathematical model studied was the 2D anisotropic diffusion equation,in whichε>0 was the coefficient of a nisotropy.The equation was discretized by the Finite Difference Method(FDM)and Central Differencing Scheme(CDS).Correction Scheme(CS),pointwise Gauss-Seidel smoothers(Lexicographic and Red-Black ordering),and line Gauss-Seidel smoothers(Lexicographic and Zebra ordering)in x and y directions were used for building the multigrid.The best asymptotic convergence factor was obtained by the Gauss-Seidel method in the direction x for 0<ε<<1 and in the direction y forε>>1.In this sense,an xy-zebra-GS smoother was proposed,which proved to be efficient and robust for the different anisotropy coefficients.Moreover,the convergence factors calculated empirically and by LFA are in agreement.
文摘In this paper image with horizontal motion blur, vertical motion blur and angled motion blur are considered. We construct several difference schemes to the highly nonlinear term △↓.（△↓u/√｜△↓｜^2＋β） of the total variation-based image motion deblurring problem. The large nonlinear system is linearized by fixed point iteration method. An algebraic multigrid method with Krylov subspace acceleration is used to solve the corresponding linear equations as in [7]. The algorithms can restore the image very well. We give some numerical experiments to demonstrate that our difference schemes are efficient and robust.
文摘In this article algebraic multigrid as preconditioners are designed, with biorthogonal wavelets, as intergrid operators for the Krylov subspace iterative methods. Construction of hierarchy of matrices in algebraic multigrid context is based on lowpass filter version of Wavelet Transform. The robustness and efficiency of this new approach is tested by applying it to large sparse, unsymmetric and ill-conditioned matrices from Tim Davis collection of sparse matrices. Proposed preconditioners have potential in reducing cputime, operator complexity and storage space of algebraic multigrid V-cycle and meet the desired accuracy of solution compared with that of orthogonal wavelets.
基金supported by the National Natural Science Foundation of China (Nos. 41506039, 41776004, 41775100 and 41606039)the National Key Research and Development Program of China (No. 2016YFC1401800)+1 种基金the Fundamental Research Funds for the Central Universities (No. 2016B12514)the National Programme on Global Change and Air-Sea Interaction of China (No. GASI-IPO VAI-04)
文摘This paper proposes a new method for data assimilation of the surface radial current observed by High Frequency ground wave radar and optimization of the bottom friction coefficient.In this method,the shallow water wave equation is introduced into the cost function of the multigrid three-dimensional variation data assimilation method as the weak constraint term,the surface current and the bottom friction coefficient are defined as the analytical variables,and the high spatiotemporal resolution surface radial flow observed by the high-frequency ground wave radar is used to optimize the surface current and bottom friction coefficient.This method can effectively consider the spatiotemporal correlation of radar data and extract multiscale information from surface radial flow data from long waves to short waves.Introducing the shallow water wave equation into the cost function as a weak constraint condition can adjust both the momentum and mass fields simultaneously to obtain more reasonable analysis information.The optimized bottom friction coefficient is introduced into the regional ocean numerical model to carry out numerical experiments.The test results show that the bottom friction coefficient obtained by this method can effectively improve the accuracy of the numerical simulation of sea surface height in the offshore area and reduce the simulation error.
基金the National Natural Scinence Foundation of China
文摘This paper introduces two kinds of methods with high accuracy for fi-nite element probability computing method,by which the function value on one or afew nodes can be calculated without forming the total stiffness matrix.
文摘Panel methods for the calculation of wavemaking resistance result in a linear equation system for the unknown singularities.The coefficient matrix is full but not well conditioned.In this paper an incomplete LU decomposition (ILU) method and a combined multigrid ILU method are used to solve the linear system.Systematic computations using the ILU method have shown that the CPU time can be reduced to 30% to 40% of that using an incomplete Gaussian elimination method. In the proposed multigrid ILU method an averaged restriction and a piecewise constant prolongation are used.The construction of the coefficient matrix at coarse levels is based on geometrical considerations.It turns out that the condition of the relative consistency is fulfilled.Comparison computations have shown that nearly the same results were obtained.However,due to additional CPU time needed for the execution of the matrix vector products in the restriction and the prolongation proceses of the multigrid method,a further reduction of the total CPU time could not be reailized.
