Abstract
A high-accuracy numerical method based on a sixth-order combined compact difference scheme and the method of lines approach is proposed for the advection–diffusion transport equation with variable parameters. In this approach, the partial differential equation representing the advection-diffusion equation is converted into many ordinary differential equations. These time-dependent ordinary differential equations are then solved using an explicit fourth order Runge–Kutta method. Three test problems are studied to demonstrate the accuracy of the present methods. Numerical solutions obtained by the proposed method are compared with the analytical solutions and the available numerical solutions given in the literature. In addition to requiring less CPU time, the proposed method produces more accurate and more stable results than the numerical methods given in the literature.
Highlights
Advection-Diffusion Equation withThe transport of solutes by water takes place in a large variety of environmental, agricultural, and industrial conditions
The partial differential equation (PDE) spatial derivatives can be approximated using finite difference, finite element, finite volume, weighted residual method, and spectral method [44]. We propose another variation of the method of lines (MOL)
A combined compact finite difference scheme based on the method of lines is proposed for the numerical solution of the solute transport equation with variable parameters
Summary
The transport of solutes by water takes place in a large variety of environmental, agricultural, and industrial conditions. Solved the same equation with a uniform pulse type input condition and the initial solute concentration that decreased with distance In both studies, numerical solutions were obtained using the first-order explicit time integration approach and results were compared with analytical solutions reported in the literature. Gharehbaghi [40] used the differential quadrature method to obtain the numerical solution of the ADE with variable parameters in the semi-infinite domain. The explicit fourth order Runge–Kutta method (ERK4) is used as the numerical integration routine in the MOL approach
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