Accurate Simulation of Contaminant Transport Using High-Order Compact Finite Difference Schemes

Accurate Simulation of Contaminant Transport Using High-Order Compact Finite Difference Schemes

Numerical simulation of advective-dispersive contaminant transport is carried out by using high-order compact finite difference schemes combined with second-order MacCormack and fourth-order Runge-Kutta schemes. Both of the two schemes have accuracy of sixth-order in space. A sixth-order MacCormack scheme is proposed for the first time within this study. For the aim of demonstrating efficiency ...

High Order Compact Finite Difference Schemes for Solving Bratu-Type Equations

In the present study, high order compact finite difference methods is used to solve one-dimensional Bratu-type equations numerically. The convergence analysis of the methods is discussed and it is shown that the theoretical order of the method is consistent with its numerical rate of convergence. The maximum absolute errors in the solution at grid points are calculated and it is shown that the ...

Derivation of high-order compact finite difference schemes for non-uniform grid using polynomial interpolation

In this paper simple polynomial interpolation is used to derive arbitrarily high-order compact schemes for the first derivative and tridiagonal compact schemes for the second derivative (consisting of three second derivative nodes in the interior and two on the boundary) on non-uniform grids. Boundary and near boundary schemes of the same order as the interior are also developed using polynomia...

High-Order Compact Finite Difference Methods

In this work we present a general approach for developing high-order compact differencing schemes by utilizing the governing differential equation to help approximate truncation error terms. As an illustrative application we consider the stream-function vorticity form of the Navier Stokes equations, and provide driven cavity results. Some extensions to treat non-constant metric coefficients res...

Computational Aero-Acoustic Using High-order Finite-Difference Schemes