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.

Modal analysis of the flux reconstruction (FR) formulation is performed to obtain the semi-discrete and fully-discrete dispersion relations, using which, the wave properties of physical as well as spurious modes are characterized. The effect of polynomial order, correction function and solution points on the dispersion, dissipation and relative energies of the modes are investigated. Using this...

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.

This paper is devoted with numerical solution of the system fractional differential equations (FDEs) which are generated by optimization problem using the Chebyshev collocation method. The fractional derivatives are presented in terms of Caputo sense. The application of the proposed method to the generated system of FDEs leads to algebraic system which can be solved by the Newton iteration meth...

In this paper, we price American options using the radial basis function (RBF) interpolation method. Two processes for the volatility are assumed: local volatility and stochastic volatility. In particular, we focus on the constant elasticity of variance (CEV) model (Cox and Ross (1976)) and the Heston model (Heston (1993)). Several experiments are performed to evaluate the pricing accuracy and ...

Abstract. A numerical method is presented for the treatment of one-dimensional compressible flames. The method consists of a conservative front tracking algorithm for use near the flame and a high-order finite difference scheme for capturing the hvdrodynamics throughout the rest of the domain. The results presented show that the method effectively models the interaction of gas dynamics with bot...

Models for multiphase-multicomponent flow in porous media are described in systems of PDEs. Solving them using finite difference discretization method can be of three ways; explicit, semi-implicit, and fully implicit. In this study, we present the implementation of an adaptive Newton-Raphson method in the context of IMPECS (Implicit Pressures Explicit Concentrations and Saturations) method of s...