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Wave equation model for solving advection–diffusion equation
Author(s) -
Wu Jiankang
Publication year - 1994
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620371603
Subject(s) - mathematics , numerical diffusion , advection , convection–diffusion equation , diffusion equation , numerical stability , wave equation , numerical analysis , mathematical analysis , physics , mechanics , economy , economics , thermodynamics , service (business)
This paper presents a Wave Equation Model (WEM) to solve advection dominant Advection–Diffusion (A–D) equation. It is known that the operator‐splitting approach is one of the effective methods to solve A–D equation. In the advection step the numerical solution of the advection equation is often troubled by numerical dispersion or numerical diffusion. Instead of directly solving the first‐order advection equation, the present wave equation model solves a second‐order equivalent wave equation whose solution is identical to that of the first‐order advection equation. Numerical examples of 1‐D and 2‐D with constant flow velocities and varying flow velocities are presented. The truncation error and stability condition of 1‐D wave equation model is given. The Fourier analysis of WEM is carried out. The numerical solutions are in good agreement with the exact solutions. The wave equation model introduces very little numerical oscillation. The numerical diffusion introduced by WEM is cancelled by inverse numerical diffusion introduced by WEM as well. It is found that the numerical solutions of WEM are not sensitive to Courant number under stability constraint. The computational cost is economical for practical applications.