It is important to simulate a groundwater transport process, e.g., pollutant migration, through the vadose zone and subsequent mixing within the saturated zone to assess potential impacts of contaminants in the subsurface in preliminary stages. It is challenging to simulate heterogeneous soil characteristics and non-uniform initial contaminant concentration. This paper proposes a vertically het...

The results of computations with eight explicit finite difference schemes on a suite of one-dimensional and two-dimensional test problems for the Euler equations are presented in various formats. Both dimensionally split and two-dimensional schemes are represented, as are central and upwind-biased methods, and all are at least second-order accurate.

A finite difference method is developed for solving symmetric positive differential equations in the sense of Friedrichs. The method is applicable to partial differential equations of mixed type with more general boundary conditions. The method is shown to have a convergence rate of 0(hxl2), h being the size of mesh grid. Some numerical results are presented for a model problem of forward-backw...

Direct sinrelations of smalland finite-amplitude disturbances in spatially periodic plane Poiseuille flow were performed. The ability of three high-order finite difference methods to predict the proper behavior of the disturbances was under investigation. The proposed procedure allowed to conclude about the spatial resolution and time-step required bv those schemes to produce numerically accura...

In this paper, a finite difference method for initial-boundary value problem of nonlinear Regularized-Long-Wave equation was considered. A energy conservative finite difference scheme of three levels was proposed, convergence and stability of difference solution was proved, if picking suitably,the accuracy of the new scheme is higher than others, so the method is efficient and reliable.

Vorticity-stream function method and MAC algorithm are adopted to systemically compare the finite volume method (FVM) and finite difference method (FDM) in this paper. Two typical problems—lid-driven flow and natural convection flow in a square cavity—are taken as examples to compare and analyze the calculation performances of FVM and FDMwith variant mesh densities, discrete forms, and treatmen...

We present sharp bounds on the supremum norm of DjSh for j ≥ 2, where D is the differential operator and S the Stein operator for the standard normal distribution. The same method is used to give analogous bounds for the exponential, Poisson and geometric distributions, with D replaced by the forward difference operator in the discrete case. We also discuss applications of these bounds to the c...

This paper presents a comprehensive analysis of numerical dispersion of the recently developed unconditionally stable three-dimensional finite-difference time-domain (FDTD) method where the alternatingdirection-implicit technique is applied. The dispersion relation is derived analytically and the effects of spatial and temporal steps on the numerical dispersion are investigated. It is found tha...

We have focused our attention on the development and use of the finite-difference time-domain (FDTD) method. This time-domain technique, which is flexible, robust, and simple to implement, has previously been used by the electromagnetics community to solve a wide range of problems. However, the FDTD method has not been widely used by the acoustics community and its ability to accurately solve m...

We present algorithms to count paths and cycles of a given length in a directed graph. The algorithms have time complexity O(2 n poly n) and space complexity O(poly n).