In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discreti...In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ？ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ？ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.展开更多
In this paper, a Petrov-Galerkin scheme named the Runge-Kutta control volume （RKCV） discontinuous finite ele- ment method is constructed to solve the one-dimensional compressible Euler equations in the Lagrangian co...In this paper, a Petrov-Galerkin scheme named the Runge-Kutta control volume （RKCV） discontinuous finite ele- ment method is constructed to solve the one-dimensional compressible Euler equations in the Lagrangian coordinate. Its advantages include preservation of the local conservation and a high resolution. Compared with the Runge-Kutta discon- tinuous Galerkin （RKDG） method, the RKCV method is easier to implement. Moreover, the advantages of the RKCV and the Lagrangian methods are combined in the new method. Several numerical examples are given to illustrate the accuracy and the reliability of the algorithm.展开更多
A computational procedure is developed to solve the problems of coupled motion of a structure and a viscous incompressible fluid. In order to incorporate the effect of the moving surface of the structure as well as th...A computational procedure is developed to solve the problems of coupled motion of a structure and a viscous incompressible fluid. In order to incorporate the effect of the moving surface of the structure as well as the free surface motion, the arbitrary Lagrangian-Eulerian formulation is employed as the basis of the finite element spatial discretization. For numerical integration in time, the fraction,step method is used. This method is useful because one can use the same linear interpolation function for both velocity and pressure. The method is applied to the nonlinear interaction of a structure and a tuned liquid damper. All computations are performed with a personal computer.展开更多
A method for simulation of free surface problems is presented. Based on the viscous incompressible Navier-Stokes equations, space discretization of the flow is obtained by the least square finite element method. The t...A method for simulation of free surface problems is presented. Based on the viscous incompressible Navier-Stokes equations, space discretization of the flow is obtained by the least square finite element method. The time evolution is obtained by the finite difference method. Lagrangian description is used to track the free surface. The results are compared with the experimental dam break results, including water collapse in a 2D rectangular section and in a 3D cylinder section. A good agreement is achieved for the distance of surge front as well as the height of the residual column.展开更多
A large number of problems in engineering can be formulated as the optimization of certain functionals. In this paper, we present an algorithm that uses the augmented Lagrangian methods for finding numerical solutions...A large number of problems in engineering can be formulated as the optimization of certain functionals. In this paper, we present an algorithm that uses the augmented Lagrangian methods for finding numerical solutions to engineering problems. These engineering problems are described by differential equations with boundary values and are formulated as optimization of some functionals. The algorithm achieves its simplicity and versatility by choosing linear equality relations recursively for the augmented Lagrangian associated with an optimization problem. We demonstrate the formulation of an optimization functional for a 4th order nonlinear differential equation with boundary values. We also derive the associated augmented Lagrangian for this 4th order differential equation. Numerical test results are included that match up with well-established experimental outcomes. These numerical results indicate that the new algorithm is fully capable of producing accurate and stable solutions to differential equations.展开更多
研究了FLAC3D(fast lagrangian analysis of continua in 3 dimensions)的特点,并与有限单元法作了比较。FLAC3D方法以结点运动方程为支配方程,追踪了介质从受荷到达到平衡状态的过程,而有限元法是根据介质力学平衡方程直接求解,这是二...研究了FLAC3D(fast lagrangian analysis of continua in 3 dimensions)的特点,并与有限单元法作了比较。FLAC3D方法以结点运动方程为支配方程,追踪了介质从受荷到达到平衡状态的过程,而有限元法是根据介质力学平衡方程直接求解,这是二者主要区别。FLAC3D没有采用介质真实的阻尼特性和结点质量,给出的不是介质所经历的真实过程,不能正确反映过程的影响,因此给出的介质应力和变形计算结果的物理意义是不甚明确的。求解过程中的介质振动,是一种噪音,可引起弹塑性介质计算结果误差,而弹性介质的计算结果几乎不受影响。研究指出了FLAC3D方法的优缺点。还通过算例作了四个方面的研究:(1)Drucker-Prager屈服准则与Mohr-Coulomb屈服准则比较;(2)膨胀角取值对计算结果的影响;(3)大变形与小变形对计算结果的影响;(4)精度设置对计算结果的影响。研究表明,Drucker-Prager准则与Mohr-Coulomb准则结果差异颇大;膨胀角取值对结果的影响是敏感和显著的;一般情况下,取小变形模式是合适的,计算精度取10-5是足够的。展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11261035,11171038,and 10771019)the Science Reaearch Foundation of Institute of Higher Education of Inner Mongolia Autonomous Region,China (Grant No. NJZZ12198)the Natural Science Foundation of Inner Mongolia Autonomous Region,China (Grant No. 2012MS0102)
文摘In this paper,Runge-Kutta Discontinuous Galerkin（RKDG） finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ？ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ？ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11261035 and 11171038)the Science Research Foundation of the Institute of Higher Education of Inner Mongolia Autonomous Region, China (Grant No. NJZZ12198)the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 2012MS0102)
文摘In this paper, a Petrov-Galerkin scheme named the Runge-Kutta control volume （RKCV） discontinuous finite ele- ment method is constructed to solve the one-dimensional compressible Euler equations in the Lagrangian coordinate. Its advantages include preservation of the local conservation and a high resolution. Compared with the Runge-Kutta discon- tinuous Galerkin （RKDG） method, the RKCV method is easier to implement. Moreover, the advantages of the RKCV and the Lagrangian methods are combined in the new method. Several numerical examples are given to illustrate the accuracy and the reliability of the algorithm.
文摘A computational procedure is developed to solve the problems of coupled motion of a structure and a viscous incompressible fluid. In order to incorporate the effect of the moving surface of the structure as well as the free surface motion, the arbitrary Lagrangian-Eulerian formulation is employed as the basis of the finite element spatial discretization. For numerical integration in time, the fraction,step method is used. This method is useful because one can use the same linear interpolation function for both velocity and pressure. The method is applied to the nonlinear interaction of a structure and a tuned liquid damper. All computations are performed with a personal computer.
基金Project supported by the National Natural Science Foundation of China (Nos.10302013,10572022)
文摘A method for simulation of free surface problems is presented. Based on the viscous incompressible Navier-Stokes equations, space discretization of the flow is obtained by the least square finite element method. The time evolution is obtained by the finite difference method. Lagrangian description is used to track the free surface. The results are compared with the experimental dam break results, including water collapse in a 2D rectangular section and in a 3D cylinder section. A good agreement is achieved for the distance of surge front as well as the height of the residual column.
文摘A large number of problems in engineering can be formulated as the optimization of certain functionals. In this paper, we present an algorithm that uses the augmented Lagrangian methods for finding numerical solutions to engineering problems. These engineering problems are described by differential equations with boundary values and are formulated as optimization of some functionals. The algorithm achieves its simplicity and versatility by choosing linear equality relations recursively for the augmented Lagrangian associated with an optimization problem. We demonstrate the formulation of an optimization functional for a 4th order nonlinear differential equation with boundary values. We also derive the associated augmented Lagrangian for this 4th order differential equation. Numerical test results are included that match up with well-established experimental outcomes. These numerical results indicate that the new algorithm is fully capable of producing accurate and stable solutions to differential equations.
基金National Natural Science Foundation of China(11261035,11571002)Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(NJYT-15-A07)+3 种基金Natural Science Foundation of Inner Mongolia Autonomous Region,China(2015MS0108,2012MS0102)Science Research Foundation of Institute of Higher Education of Inner Mongolia Autonomous Region,China(NJZZ12198)Science and Technology Development Foundation of CAEP(2015B0101021)Defense Industrial Technology Development Program(B1520133015)
文摘研究了FLAC3D(fast lagrangian analysis of continua in 3 dimensions)的特点,并与有限单元法作了比较。FLAC3D方法以结点运动方程为支配方程,追踪了介质从受荷到达到平衡状态的过程,而有限元法是根据介质力学平衡方程直接求解,这是二者主要区别。FLAC3D没有采用介质真实的阻尼特性和结点质量,给出的不是介质所经历的真实过程,不能正确反映过程的影响,因此给出的介质应力和变形计算结果的物理意义是不甚明确的。求解过程中的介质振动,是一种噪音,可引起弹塑性介质计算结果误差,而弹性介质的计算结果几乎不受影响。研究指出了FLAC3D方法的优缺点。还通过算例作了四个方面的研究:(1)Drucker-Prager屈服准则与Mohr-Coulomb屈服准则比较;(2)膨胀角取值对计算结果的影响;(3)大变形与小变形对计算结果的影响;(4)精度设置对计算结果的影响。研究表明,Drucker-Prager准则与Mohr-Coulomb准则结果差异颇大;膨胀角取值对结果的影响是敏感和显著的;一般情况下,取小变形模式是合适的,计算精度取10-5是足够的。
