A multigrid solver for the steady incompressible Navier-Stokes equations on a curvilinear grid is constructed. The Cartesian velocity components are used in the discretization of the momentum equations. A staggered, g...
A multigrid solver for the steady incompressible Navier-Stokes equations on a curvilinear grid is constructed. The Cartesian velocity components are used in the discretization of the momentum equations. A staggered, geometrically symmetric distribution of velocity components is adopted which eliminates spurious pressure oscillations and facilitates the transformation between Cartesian and co-or contravariant velocity components. The SCGS (symmetrical collective Gauss-Seidel) relaxation scheme proposed by Vanka on a Cartesian grid is extended to this case to serve as the smoothing procedure of the multigrid solver, in both ''box'' and ''box-line'' versions. Due to the symmetric distribution of velocity components of this scheme, the convergence rate and numerical accuracy are not affected by grid orientation, in contrast to a scheme proposed in the literature in which difficulties arise when the grid lines turn 90-degrees from the Cartesian coordinates. Some preliminary numerical experiences with this scheme are presented. (C) 1994 Academic Press. Inc.
In this paper, we construct Poisson difference schemes of any order accuracy based on Pade approximation for linear Hamiltonian systems on Poisson manifolds with constant coefficients. For nonlinear Hamiltonian system...
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In this paper, we construct Poisson difference schemes of any order accuracy based on Pade approximation for linear Hamiltonian systems on Poisson manifolds with constant coefficients. For nonlinear Hamiltonian systems on Poisson manifolds, we point out that symplectic diagonal implicit Runge-Kutta methods are also Poisson schemes. The preservation of distinguished functions and quadratic first integrals of the original Hamiltonian systems of these schemes are also discussed.
In this paper, we apply the higher order self-adjoint schemes constructed in [1] to wave equation and heat equation to show these methods can also be used to solve partial differential equations to get higher order ac...
In this paper, we apply the higher order self-adjoint schemes constructed in [1] to wave equation and heat equation to show these methods can also be used to solve partial differential equations to get higher order accuracy in the time direction.
In this paper, we discuss the conditions for Euler midpoint rule to be volume-preserving and present explicit volume preserving schemes. Some numerical experiments are done to test these schemes.
In this paper, we discuss the conditions for Euler midpoint rule to be volume-preserving and present explicit volume preserving schemes. Some numerical experiments are done to test these schemes.
In this paper, we discuss the conditions for the Euler midpoint rule to be volume-preserving and present Euler type explicit volume-preserving schemes. Some numerical applications to the system defining rigid body mot...
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In this paper, we discuss the conditions for the Euler midpoint rule to be volume-preserving and present Euler type explicit volume-preserving schemes. Some numerical applications to the system defining rigid body motion and the ABC flow are also given.
We use formal power series to expand the method used by Yoshida in constructing explicit canonical higher order schemes for separable Hamiltonian systems and construct general higher order schemes for general dynamica...
We use formal power series to expand the method used by Yoshida in constructing explicit canonical higher order schemes for separable Hamiltonian systems and construct general higher order schemes for general dynamical systems.
The stability of a three-stage difference scheme constructed in [1] is discussed, with the construction process given out concisely at first. We also present some numerical examples to test our theoretical results.
The stability of a three-stage difference scheme constructed in [1] is discussed, with the construction process given out concisely at first. We also present some numerical examples to test our theoretical results.
The main purpose of this paper is to develop and simplify the general conditions for an s-stage explicit canonical difference scheme to be of qth order while the simplified order conditions for canonical RKN methods, ...
Hamiltonian systems are canonical systems on phase space endowed with symplectic structures. The dynamical evolutions, i.e., the phase flow of the Hamiltonian systems are symplectic transformations which are area-pres...
Hamiltonian systems are canonical systems on phase space endowed with symplectic structures. The dynamical evolutions, i.e., the phase flow of the Hamiltonian systems are symplectic transformations which are area-preserving. The importance of the Hamiltonian systems and their special property require the numerical algorithms for them should preserve as much as possible the relevant symplectic properties of the original systems. Feng Kang [1-3] proposed in 1984 a new approach to computing Hamiltonian systems from the view point of symplectic geometry. He systematically described the general method for constructing symplectic schemes with any order accuracy via generating functions. A generalization of the above theory and methods for canonical Hamiltonian equations in infinite dimension can be found in [4]. Using self-adjoint schemes, we can construct schemes of arbitrary even order [5]. These schemes can be applied to wave equation [6,7] and the stability of them can be seen in [7,8]. In this paper, we will use the hyperbolic functions sinh(x), cosh(x) and tanh(x) to construct symplectic schemes of arbitrary order for wave equations and stabilities of these constructed schemes are also discussed.
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