Simulations of transport in one dimension
This is an incremental application of an existing numerical method to specific transport problems, offering no major breakthroughs.
The study solves one-dimensional advection-dispersion equations using a differential quadrature method based on sine cardinal functions, achieving accurate simulations of pure advection and fade-out problems with errors measured by discrete maximum norm.
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.