this paper introduces a mesh generating algorithm for solving the traffic flow equation as a conservation law equation. the idea behind the new method is to use the characteristic curves and moving non-oscillatory finite volume method. in addition, when characteristic curves intersect, the proposed scheme uses shock speed equation in order to improve computational efficiency. we also compare...

In this paper, a moving mesh technique and a non-standard finite difference method are combined, and a moving mesh non-standard finite difference (MMNSFD) method is developed to solve an initial boundary value problem involving a quartic nonlinearity that arises in heat transfer with thermal radiation. In this method, the moving spatial grid is obtained by a simple geometric adaptive algorithm ...

In this paper, symmetric water entry of twin wedges is investigated for deadrise angle of 30 degree. Three numerical simulation of a symmetric impact, considering rigid body dynamic equations of motion in two-phase flow is presented. The two-phase flow around the wedges is solved by Finite Element based on Finite Volume method (FEM-FVM) which is used in conjunction with Volume of Fluid (VOF) sc...

We establish the global existence of L∞ solutions for a model of polytropic gas flow with diffusive entropy. The result is obtained by showing the convergence of a class of finite difference schemes, which includes the Lax– Friedrichs and Godunov schemes. Such convergence is achieved by proving the estimates required for the application of the compensated compactness theory.

We develop a new efficient second-order finite difference scheme for two-dimensional problem of contaminant in groundwater flow. Theoretical analysis shows that the scheme is second-order convergence in the L2 norm and is unconditionally stable. Numerical results demonstrate that the error measures of the second-order scheme are several times smaller than those of the standard implicit finite d...

We investigate the connections between several recent methods for the discretization of anisotropic heterogeneous diffusion operators on general grids. We prove that the Mimetic Finite Difference scheme, the Hybrid Finite Volume scheme and the Mixed Finite Volume scheme are in fact identical up to some slight generalizations. As a consequence, some of the mathematical results obtained for each ...

This paper deals with the development of a computer model for flood routing in narrow rivers. Equations describing the propagation of a flood wave in a channel-flood plain system are presented and solved using an implicit finite difference scheme. Particular emphasis has been given to the treatment of the friction term in the governing equation of motion.

In this article a modification of the Chebyshev collocation method is applied to the solution of space fractional differential equations.The fractional derivative is considered in the Caputo sense.The finite difference scheme and Chebyshev collocation method are used .The numerical results obtained by this way have been compared with other methods.The results show the reliability and efficiency...

The surface diffusion flow is a moving boundary problem that has a gradient flow structure, and this gradient flow structure suggests an implicit finite-differences approach to compute numerical solutions. The resulting numerical scheme allows to compute the flow for any smooth orientable immersed initial surface. We provide an analytical proof of this gradient structure, and construct a discre...