Simulations of transport in one dimension

TL;DR

This paper presents a numerical approach using differential quadrature with sine cardinal functions to solve 1D advection-dispersion problems, demonstrating accuracy and efficiency through various time integration methods.

Contribution

It introduces a differential quadrature method based on sine cardinal functions for 1D transport problems, with comprehensive comparison of multiple time integration techniques.

Findings

Accurate simulation of pure advection and fade out problems.

Comparison shows the proposed method's effectiveness over earlier approaches.

Errors are minimized using various time integration schemes.

Abstract

In this study, two initial boundary value problems for one dimensional advection-dispersion equation are solved by differential quadrature method based on sine cardinal functions. Pure advection problem modeling transport of conservative pollutants and fade out problem are simulated successfully by the proposed method. The time integration of the space discretized system is accomplished by using various single step and multi step methods covering forward, modified and improved Euler methods, Runge-Kutta, explicit Adams-Bashforth and implicit Adams-Moulton predictor-corrector methods of different orders. The errors between analytical and numerical solutions for both cases are measured by the use of discrete maximum norm. The numerical results are compared with some earlier results obtained by various methods.