This paper proposes a new two-step non-oscillatory shape-preserving positive definite finite difference advection transport scheme, which merges the advantages of small dispersion error in the simple first-order upst... This paper proposes a new two-step non-oscillatory shape-preserving positive definite finite difference advection transport scheme, which merges the advantages of small dispersion error in the simple first-order upstream scheme and small dissipation error in the simple second-order Lax-Wendroff scheme and is completely different from most of present positive definite advection schemes which are based on revising the upstream scheme results. The proposed scheme is much less time consuming than present shape-preserving or non-oscillatory advection transport schemes and produces results which are comparable to the results obtained from the present more complicated schemes. Elementary tests are also presented to examine the behavior of the scheme.展开更多
We extend the traditional kinetic scheme for ideal gases to the Euler equations with the equation of state for a multi-component stiffened gas. Based on a careful analysis of the oscillation mechanism of the tradition...We extend the traditional kinetic scheme for ideal gases to the Euler equations with the equation of state for a multi-component stiffened gas. Based on a careful analysis of the oscillation mechanism of the traditional kinetic scheme across contact discontinuities, we propose a new non-oscillatory kinetic （NOK） scheme for multi-component stiffened gases. The basic idea in the construction is to use a flux splitting technique to construct numerical fluxes which do not depend on the concrete form of the equilibrium state. The new scheme can not only can avoid spurious oscillations of the pressure and velocity near a material interface which are observed in the traditional kinetic schemes such as the kinetic flux vector splitting （KFVS） and BGK schemes, but also can deal with the stiffened gas equation of state. Moreover, we also carry out a careful analysis on the consistency condition, truncation error and positivity of the NOK scheme. A number of 1D and 2D numerical tests are presented which demonstrate the accuracy and robustness of the new scheme in the simulation of problems with smooth, weak and strong shock wave regions.展开更多
In this paper, we first establish the equivalence of the oscillation of the difference equations with several delays of the form:and the second-order difference equations without delay of the form:where {pj(n)} is a s...In this paper, we first establish the equivalence of the oscillation of the difference equations with several delays of the form:and the second-order difference equations without delay of the form:where {pj(n)} is a sequence of nonnegative real numbers and {ki}i=1m is a set of positive integers. Then we get some 'sharp' conditions for oscillation and non-oscillation of the first equation.展开更多
Some oscillation and non-oscillation criteria for second-order quasi-linear difference equations are given. The results in Zhang and Zhou [4] are improved.
Using the associated quadratic functional of the Hamiltonian system, we obtain the non-oscillation of all the prepared solutions for the Hamiltonian system at a finite point.
A one-dimensional monotone interpolation method based on interface reconstruction with partial volumes in the slope-space utilizing the Hermite cubic-spline, is proposed. The new method is only quartic, however is C2 ...A one-dimensional monotone interpolation method based on interface reconstruction with partial volumes in the slope-space utilizing the Hermite cubic-spline, is proposed. The new method is only quartic, however is C2 and unconditionally monotone. A set of control points is employed to constrain the curvature of the interpolation function and to eliminate possible nonphysical oscillations in the slope space. An extension of this method in two-dimensions is also discussed.展开更多
In this paper, we consider the following forced higher-order nonlinear neutral dynamic equation on time scales. By using Banach contraction principle, we obtain sufficient conditions for the existence of nonoscillator...In this paper, we consider the following forced higher-order nonlinear neutral dynamic equation on time scales. By using Banach contraction principle, we obtain sufficient conditions for the existence of nonoscillatory solutions for general and which means that we allow oscillatory and . We give some examples to illustrate the obtained results.展开更多
In this paper, we investigate a class of higher order delay differential equation x(n)(t)+p(t)x(t-t)=0 where is an even positive integer,p()C([to,=()]). We obtain a new oscillation condition for this class.
基金This work is supported by the Ntional Natural Science Foundation of China.
文摘 This paper proposes a new two-step non-oscillatory shape-preserving positive definite finite difference advection transport scheme, which merges the advantages of small dispersion error in the simple first-order upstream scheme and small dissipation error in the simple second-order Lax-Wendroff scheme and is completely different from most of present positive definite advection schemes which are based on revising the upstream scheme results. The proposed scheme is much less time consuming than present shape-preserving or non-oscillatory advection transport schemes and produces results which are comparable to the results obtained from the present more complicated schemes. Elementary tests are also presented to examine the behavior of the scheme.
文摘We extend the traditional kinetic scheme for ideal gases to the Euler equations with the equation of state for a multi-component stiffened gas. Based on a careful analysis of the oscillation mechanism of the traditional kinetic scheme across contact discontinuities, we propose a new non-oscillatory kinetic （NOK） scheme for multi-component stiffened gases. The basic idea in the construction is to use a flux splitting technique to construct numerical fluxes which do not depend on the concrete form of the equilibrium state. The new scheme can not only can avoid spurious oscillations of the pressure and velocity near a material interface which are observed in the traditional kinetic schemes such as the kinetic flux vector splitting （KFVS） and BGK schemes, but also can deal with the stiffened gas equation of state. Moreover, we also carry out a careful analysis on the consistency condition, truncation error and positivity of the NOK scheme. A number of 1D and 2D numerical tests are presented which demonstrate the accuracy and robustness of the new scheme in the simulation of problems with smooth, weak and strong shock wave regions.
基金Research supported Dy Distinguished Expert Science Foundation of Naval Aeronautical Engineering Institute
文摘In this paper, we first establish the equivalence of the oscillation of the difference equations with several delays of the form:and the second-order difference equations without delay of the form:where {pj(n)} is a sequence of nonnegative real numbers and {ki}i=1m is a set of positive integers. Then we get some 'sharp' conditions for oscillation and non-oscillation of the first equation.
基金This work is supported by the Distinguished Expert Science Foundation of Naval Aeronautical Engineering Institute.
文摘Some oscillation and non-oscillation criteria for second-order quasi-linear difference equations are given. The results in Zhang and Zhou [4] are improved.
基金This research was partially supported by the NSF of China (Grant 10471077)China Postdoctoral Science foundation (Grant 20040350596).
文摘Using the associated quadratic functional of the Hamiltonian system, we obtain the non-oscillation of all the prepared solutions for the Hamiltonian system at a finite point.
文摘A one-dimensional monotone interpolation method based on interface reconstruction with partial volumes in the slope-space utilizing the Hermite cubic-spline, is proposed. The new method is only quartic, however is C2 and unconditionally monotone. A set of control points is employed to constrain the curvature of the interpolation function and to eliminate possible nonphysical oscillations in the slope space. An extension of this method in two-dimensions is also discussed.
文摘In this paper, we consider the following forced higher-order nonlinear neutral dynamic equation on time scales. By using Banach contraction principle, we obtain sufficient conditions for the existence of nonoscillatory solutions for general and which means that we allow oscillatory and . We give some examples to illustrate the obtained results.
文摘In this paper, we investigate a class of higher order delay differential equation x(n)(t)+p(t)x(t-t)=0 where is an even positive integer,p()C([to,=()]). We obtain a new oscillation condition for this class.
