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

Abstract

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 and high-order accuracy of the current methods, some numerical experiments have been done. The schemes are implemented to solve two test problems with known exact solutions. It has been exhibited that the methods are capable of succeeding high accuracy and efficiency with minimal computational effort, by comparisons of the computed results with exact solutions.

Yarı-Lagrangian bir şema yaklaşımına dayalı adveksiyon-difüzyon denkleminin bir sayısal çözümü

“…Eq. (5) shows that the concentration value of the advection process is not changed, see Figure 1. Also, the solution of the advection process with MOC-CS is independent of time.…”

“…(2) accurately. Some of these methods are classical finite difference method [2], high-order finite element method [3], high-order finite difference methods [4,5], green element method [6], cubic and extended B-spline collocation methods [7][8][9], cubic, quartic and quintic B-spline differential quadrature methods [10,11], method of characteristics unified with splines [12][13][14], cubic trigonometric B-spline approach [15], Taylor collocation and Taylor-Galerkin methods [16], Lattice Boltzmann method [17]. Moreover, non-linear advection-diffusion equation is studied in [18].…”

Sixth-Order Combined Compact Finite Difference Scheme for the Numerical Solution of One-Dimensional Advection-Diffusion Equation with Variable Parameters

“…A variety of numerical methods have been proposed for solving ADE, such as the method of characteristics [3][4][5][6][7][8][9], the finite difference method [10][11][12][13][14][15][16][17][18][19], the finite element method [20][21][22][23], the differential quadrature method [24,25], the Lattice Boltzman method [26], and the meshless method [27][28][29][30]. In these studies, solutions of the ADE with constant parameters have been obtained.…”

Numerical Solution of Advection-Diffusion Equation Using Operator Splitting Method

“…Gurarslan et al [11] have produced numerical solutions to a onedimensional advection-diffusion equation using a Runge-Kutta scheme of fourth-order and a compact finite difference scheme of sixth-order in space. In the study by Gurarslan [12], numerical simulations of the advection-dispersion equation were performed with high-order compact finite difference schemes. Compact finite difference schemes were used in conjunction with MacCormack and Runge-Kutta schemes to obtain solutions with the accuracy of sixthorder.…”