A new spectral integral equation method for solving two-dimensional unsteady advection-diffusion equations via Chebyshev polynomials. Issue 7 (12th August 2019)

• Record Type: Journal Article
• Authors: Hadadian Nejad Yousefi, Mohsen; Ghoreishi Najafabadi, Seyed Hossein; Tohidi, Emran
• Is Part Of: Engineering computations. Volume 36:Issue 7(2019)
• Page Start: 2327
• Page End: 2368
• Publication Date: 2019-08-12
• Subjects: Operational matrices -- Integral equations -- Chebyshev polynomials -- Advection-diffusion equation -- Dirichlet boundary conditions -- Spectral methods; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-02-2018-0063
• Languages: English
• ISSNs: 0264-4401

Abstract

Abstract : Purpose: The purpose of this paper is to develop an efficient and reliable spectral integral equation method for solving two-dimensional unsteady advection-diffusion equations. Design/methodology/approach: In this study, the considered two-dimensional unsteady advection-diffusion equations are transformed into the equivalent partial integro-differential equations via integrating from the considered unsteady advection-diffusion equation. After this stage, by using Chebyshev polynomials of the first kind and the operational matrix of integration, the integral equation would be transformed into the system of linear algebraic equations. Robustness and efficiency of the proposed method were illustrated by six numerical simulations experimentally. The numerical results confirm that the method is efficient, highly accurate, fast and stable for solving two-dimensional unsteady advection-diffusion equations. Findings: The proposed method can solve the equations with discontinuity near the boundaries, the advection-dominated equations and the equations in irregular domains. One of the numerical test problems designed specially to evaluate the performance of the proposed method for discontinuity near boundaries. Originality/value: This study extends the intention of one dimensional Chebyshev approximate approaches (Yuksel and Sezer, 2013; Yuksel et al., 2015) for two-dimensional unsteady advection-diffusion problems and the basic intention of our suggested method is quite different from the approaches for hyperbolic problems (Bulbul and Sezer, 2011).