ADAPTIVE METHOD FOR THE SOLUTION OF 1D AND 2D ADVECTION-DIFFUSION EQUATIONS USED IN ENVIRONMENTAL ENGINEERING - Publication - MOST Wiedzy

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ADAPTIVE METHOD FOR THE SOLUTION OF 1D AND 2D ADVECTION-DIFFUSION EQUATIONS USED IN ENVIRONMENTAL ENGINEERING

Abstract

The paper concerns the numerical solution of one-dimensional (1D) and two-dimensional (2D) advection-diffusion equations. For the numerical solution of the 1D advection-diffusion equation a method, originally proposed for solution of the 1D pure advection equation, has been developed. A modified equation analysis carried out for the proposed method allowed increasing of the resulting solution accuracy and consequently, to reduce the numerical dissipation and dispersion. This is achieved by proper choice of the involved weighting parameter being a function of the Courant number and the diffusive number. The method is adaptive because for uniform grid point and for uniform flow velocity the weighting parameter takes constant value whereas, for non-uniform grid and for varying flow velocity its value varies in the region of solution. For solution of the 2D transport equation the dimensional decomposition in the form of Strang splitting technique is used. Consequently, this equation is reduced to a series of the 1D equations with regard to x and y directions which next are solved using afore mentioned method. The results of computational experiments compared with the exact solutions confirmed that the proposed approaches ensure high solution accuracy of the transport equations.

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DOI:
Digital Object Identifier (open in new tab) 10.2166/hydro.2021.062
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Category:
Articles
Type:
artykuły w czasopismach
Published in:
JOURNAL OF HYDROINFORMATICS no. 23, pages 1290 - 1311,
ISSN: 1464-7141
Language:
English
Publication year:
2021
Bibliographic description:
Szymkiewicz R., Gąsiorowski D.: ADAPTIVE METHOD FOR THE SOLUTION OF 1D AND 2D ADVECTION-DIFFUSION EQUATIONS USED IN ENVIRONMENTAL ENGINEERING// JOURNAL OF HYDROINFORMATICS -Vol. 23,iss. 6 (2021), s.1290-1311
DOI:
Digital Object Identifier (open in new tab) 10.2166/hydro.2021.062
Verified by:
Gdańsk University of Technology

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