A multisympletic system for the symmetric regularized long wave (SRLW) equation is obtained with canconical momentum. The system satisfies the multisymplectic conservation law. A Fourier pseudo-spectral method which adapts to periodic boundary conditions in space is introduced. An Euler mid-point scheme in time and a Fourier pseudo-spactral method in space are used to the muhisymplectic formulation of the SRLW equation. It makes a multisymplectic Fourier pseudo-spectral scheme. Several discrete conservation laws of this scheme are proved; Numerical experiments are performed to simulate the single soliton solution. The chase, collision and separation of multi-soliton solutions are simulated.

Two influential traffic flow models formulated by Zhang H M and Wu Zheng are improved to include the lane-change problem,and the relations between the two models and the traditional speed-density hypothesis model are discussed.Runge-Kutta Discontinuous Galerkin Finite Element Method is generalized and applied to these three models for numerical solutions through which the traffic signal problem,lane-change problem and non-equilibrium traffic flow phenomena are well simulated.

By taking the numerical method and traffic phenomena into account, reasonable improvement is attained on the kinetics equation of the L-W theory. The comparison between what is deduced from the original model by means of characteristics and discontinuity analysis and what is shown by the numerical results of the improved model is made, which further reveals that the latter is the approximation of the former and that such results are convincing. Numerical examples include such problems as red-and-green and traffic accidents, which concern mixed density distribution from the minimum to the maximum, lane changing and a quick density increase or decrease on the boundary and which are also considered most challenging in the field.

It proposes a viewpoint that the finite element method (FEM) might be well used in traffic flow models, among which a newly developed dynamics model is elaborated. In the discussion, it is foreseen that the new model is fundamentally sound and has much advantage over some well known traditional ones. In the FEM solution, the weak form of the model is properly constructed by means of weight residual method and equations for weak solution are given. Finally, it achieves some favorable results in the numerical simulation and this, in a degree, makes the argument convincing.

A speedily developed numerical method called as finite volume method (FVM),which possesses both merits of finite difference method and finite element method,is devoloped.The construction of FVM for conservation laws is introduced.Especially,some efficient and successful schemes for solving the discontinuous problems are discussed in detail.Moreover,several numerical results of simulation of 2D dam break problem are given.Finally,a summary of advances in numerical applications and theoretical analysis of FVM is presented.

In the paper a new method for solving discontinuous problems——QRCM is proposed.The main difference between QRCM and RCM^[2] is that QRCM transforms the governing equation system (∂u)/(∂t)+A(u)(∂u)/(∂x)=H(u) (A) into mutually independent scalar equations utilizing quasi characterized method^[5] ωi(u)·du|_{(dx)/(dt)=λi}=ωi(u)·H(u)dt ωi(u)·((∂u)/(∂t)+λ₁(∂u)/(∂x)=ωi(u)·H(u) or ωi(u)·du|_{(dx)/(dt)=λi}=ωi(u)·H(u)dt (B) so that solving Riemann problems of (A) can be replaced by solving Rie-mann problem of each (B)'s scalar equation, where λi and ωi(u) are the eigenvalues and eigenvectors respectively of Jacobian mafrix A(u).The method keeps the main advantages of RCM.Especially, it is suitable for parallel computation.Finally,two test examples are computed,the numerical results are sati-sfctory compared with known results.

In this paper a simple and convenient approach for numerical simulaionapproach of Mach reflection——splitting quasicharacteristic method is proposedThe method is adaptable and flexiole, the construction of the schemes of this method is simple and various, the programming is quite easy, and the quantities of the arithmetic operation and the informations are not expensive compared with the others.For example of Mach reflect ion, in the paper,a plane shock wave past wedge is numerically simulated, The computting results show that the contour of Mach reflection and the basical characters of the flow field are satisfactory.

We consider the effect of the impinging of a plane wave on a surface of a stratified media at two different angles of incidence. The Goupillaud's equal-traveltime layer model and it's exact inverse formulas[1] are used, the time sequence of the video impedances can be computed.In order to compute the deepness distribution of the densities and velocities for the layered media, we propose in this paper "The contrast method of the layer-interfaces", by which, the computational experiments were made and the numerical results are satisfactory.