Fourth-order compact finite difference method for solving two-dimensional convection–diffusion equation

Abstract

A fourth-order compact finite difference scheme of the two-dimensional convection-diffusion equation is proposed to solve groundwater pollution problems. A suitable scheme is constructed to simulate the law of movement of pollutants in the medium, which is spatially fourth-order accurate and temporally second-order accurate. The matrix form and solving methods for the linear system of equations are discussed. The theoretical analysis of unconditionally stable character of the scheme is verified by the Fourier amplification factor method. Numerical experiments are given to demonstrate the efficiency and accuracy of the scheme proposed, and these show excellent agreement with the exact solution.

Numerical Analysis of Time-Fractional Diffusion Equations via a Novel Approach

“…In heat engines, heat transfer, the primary source of entropy production is a mass transfer, the coupling between heat, entropy generation and chemical reaction, electrical conduction, as described in the seminal sequence of publications by Bejan et al [5,6]. Scholars have utilized different methods for the analysis of diffusion equations such as Chebyshev collocation technique [7], finite difference technique [8], finite volume element technique [9], variational iteration technique [10], two-step Adomian decomposition technique [11], finite volume technique [12], and Laplace transform [10].…”

Analytical and approximate solution of two-dimensional convection-diffusion problems

“…And some numerical solutions have been developed to solve these types of convection-diffusion problems. likes: Higher-Order ADI method [10] or rational high-order compact ADI method [11], the alternating direction implicit method [12], the finite element method [13], fourth-order compact finite difference method [14], decomposition Method [15], the finite difference method [16], restrictive taylors approximation [17], The fundamental solution [18], finite difference method [19], combined compact difference scheme and alternating direction implicit method [20], higher order compact schemes method [21], the finite volume method [22], the finite difference and legendre spectral method [23] and even the Monte *Corresponding Author Carlo method [24]. Keskin in [25] proposed the RDTM to solve various PDE and fractional nonlinear partial differential equations.…”

Space–Time Radial Basis Function–Based Meshless Approach for Solving Convection–Diffusion Equations

“…The convection-diffusion equation is extensively used in many contexts in scientific and engineering problems, such as those related to groundwater pollution [1], gas flow after-treatment systems [2], and methane reformation in catalytic reactors [3]. The convection-diffusion equation is a combination of diffusion and convection processes that are referred to as substance diffusion and concentration change, respectively.…”