On the basis of the quasi-steady assumption, the traditional quasi-steady friction model in liquid transients is proposed and its numerical solution with the method of characteristics is obtained.

By using the method of characteristics the global existence of C 1 solution to the IBVP with the dissipative boundary and the non-characteristics is proved,and it is also proved that there is no vacuum state as t>0,if there is no vacuum state in the initial time.

Mixed finite element method , characteristic method and discontinuous Galerkin methods are combined to one dimensional KdV equations. The characteristic mixed discontinuous finite element scheme and the modified method of characteristics with adjusted advection (MMOCAA) are given. Namely, the characteristic method in time and discontinuous finite element method in space are used.

In this paper, we employ a mixed finite element method to approximate the pressure and the Darcy velocity, and a Galerkin finite element method combined with the MMOC (modified method of characteristics) to approximate the concentration.

Based on the network modeling and sensitivity analysis of transmission lines with the method of characteristics, an optimization design method in time domain is developed for the interconnections in nonlinear high-speed circuits.

As the development of the computer science, a lot of methods have been used to solve the shallow water equations numerically. The most significant four methods of them are: Finite Difference Method (FDM), Method of Characteristics (MOC), Finite Element Method (FEM) and Finite Volume Method (FVM).

A novel numerical method for the time-domain electromagnetic problems, named method of characteristics, is presented and used to solve the above problem. The results obtained are in accordance with that by the method of FD-TD and that reported by literature.

The method of characteristics on one-dimensional wave equations of 1 inear viscoelastic materials is used in the curve match of high strain dynamic testing on pile.

The concentration equation is treated by an implicit finite difference method that applies a form of the method of characteristics to the transport terms.

A class of biquadratic interpolation is introduced for the method of characteristics.

The validity of the simplifications made is well confirmed by comparison with calculation, using the method of characteristics, and with experiment.

The determination of the extremal nozzle contour for gas flow without foreign particles has been carried out in several studies [1-6], based on the calculation of the flow field using the method of characteristics.

The method of integral relations [1] and the method of characteristics are used to construct a scheme for the numerical solution of the problem of the interaction of a supersonic underexpanded jet with an obstacle.

In previous investigations on the methods of computing the change of river bed due to sedimentation, the bed and water surface configurations were computed separately and the conventional back water equations were used. Since the bed changing process and the flow unsteadiness are two co-existing and mutually interfering phenomena, the assumptions necessarily introduced error. A method of computation was suggested in this paper, which takes care of the unsteady effects of the flow. For channels of constant width...

In previous investigations on the methods of computing the change of river bed due to sedimentation, the bed and water surface configurations were computed separately and the conventional back water equations were used. Since the bed changing process and the flow unsteadiness are two co-existing and mutually interfering phenomena, the assumptions necessarily introduced error. A method of computation was suggested in this paper, which takes care of the unsteady effects of the flow. For channels of constant width and flow carrying essentially suspended load, equations of continuity[Eq.(3) to(5)] and one-dimensional equation of motion[Eq.(6)] were presented. After the elimination of c through the use of Velikanoff's equation of silt transportation, a system of 3 equations for 3 unknowns u, h, z were obtained[Eq.(9)]. 4 additional systems of equations[Eqs.(10),(11),(12),(13)] based on different assumptions were also given, making up 5 cases. It may be mentioned that only Eqs.(12) and(13) have been used in previous investigations. All 5 sets of differential equations can be solved by the method of characteristics, the characteristic equations being Eqs.(20),(21);(24),(25);(26),(27);(28),(29);(30),(31) respectively. The values λ=dx/dt are given by the intersections of the curves F_1, G_1; F_2, G_2; F_3, G_3; F_4, G_4; F_5, G_5, as shown in Fig. 2. It can be seen that due to the simplifying assumptions made, the 4th and the 5th sets of equations have only 2 and 1 group of characteristic curves respectively. The authors recommend the use of Eqs.(24) and(25) in actual computation. In Fig. 4 curves were drawn for rapid determination of the λ's. It can be seen that for values of the parameters Ku/pω and u~2/gh usually encountered in sedimentation problems the three roots are all real. Illustrative example was given. In Appendix Ⅰ, the transportation of sediments by surges was discussed, further clarifying the physical meaning of the λ's. Equations for channels of variable width were presented in Appendix Ⅱ, and a method of solution was suggested, thus paving the way to practical application.

In the present paper the method of characteristics is used for calculating one-dimensional problems in water shock tubes. Numerical computations have been carried out for both the free boundary condition and the pressure-fixed (constant pressure) condition. In the free boundary problem, we have investigated the fracture and flying-off of the water. In the constant pressure boundary problem, we have examined the formation, development, and disappearance of the cavity of the water. Besides, the second accerelation...

In the present paper the method of characteristics is used for calculating one-dimensional problems in water shock tubes. Numerical computations have been carried out for both the free boundary condition and the pressure-fixed (constant pressure) condition. In the free boundary problem, we have investigated the fracture and flying-off of the water. In the constant pressure boundary problem, we have examined the formation, development, and disappearance of the cavity of the water. Besides, the second accerelation phenomenon similar to that of a plate under exploding load has been studied.

Based upon basic aerothermodynamics equations for flow in turbomachinery setted up by Prof. Wu, computing supersonic flow past inlet of cascade section on an arbitrary stream filament of revolution was programmed with method of characteristics. The effeets of the variations of the distance between two neighbouring S1 surfaces and the radius were taken into account. In the program, the coefficients used in the calculation are the average values between the two connecting points, obtained after iteration....

Based upon basic aerothermodynamics equations for flow in turbomachinery setted up by Prof. Wu, computing supersonic flow past inlet of cascade section on an arbitrary stream filament of revolution was programmed with method of characteristics. The effeets of the variations of the distance between two neighbouring S1 surfaces and the radius were taken into account. In the program, the coefficients used in the calculation are the average values between the two connecting points, obtained after iteration. This convergence rate is fast, and normally three or more cycles of iteration are sufficient for engineering requirement.For simplicity, the shape of the bow wave was taken from that given by W. Moeekel, since it had shown to be ture for supersonic flow of the Mach Number range encountered in the transonic compressor. The supersonic flow field was calculated using preceding equations, till next blade was reached. The values of Mach Number and angle of inlet flow for next blade were determined by interpolation which was made on the two-dimensional neighboring three points. Then, the calculation was extended along the circumferential direction several pitches, with preceding procedure, until the solution of one pitch length. respected itself. The uniform condition far upstream was determined by the use of the set of the equations of continuity, momentum and energy.The relation between variation of inlet flow angle and inlet Mach Number can be obtained. The value of inlet flow angle obtained is then the one corresponding to the unique-incidence for the incoming Mach Number. There were many logical comparision in the program, so that all procedure of calculation can be in progress automatically. The accuracy of the obtained results is high relatively.