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An efficient semi‐implicit temporal scheme for boundary‐layer vertical diffusion
Author(s) -
Rokhzadi Arman,
Mohammadian Abdolmajid
Publication year - 2019
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.3455
Subject(s) - diffusion , nonlinear system , stability (learning theory) , scheme (mathematics) , diagonal , mathematics , term (time) , boundary layer , boundary (topology) , computer science , mathematical analysis , mechanics , geometry , thermodynamics , physics , quantum mechanics , machine learning
Time integration of the boundary‐layer vertical diffusion equation has been investigated. The nonlinearity associated with the diffusion coefficient makes the implicit approach impractical, while the use of an explicit scheme limits the stable time‐step sizes and consequently would be inefficient. By using a diagonally implicit Runge–Kutta scheme, a new approach has been proposed in which the diffusion coefficients at each internal stage are calculated by a weight‐averaged combination of solutions. Using the weight coefficient α offers more robust calculations due to involving implicit solutions and, as shown, it could improve the accuracy due to more engaging the explicit solutions. It has been found that the proposed semi‐implicit method is more accurate and computationally less expensive than the implicit scheme. Moreover, in terms of stability and accuracy improvement, the advantage of the proposed DIRK scheme, compared to the scheme proposed by Diamantakis et al . ([Diamantakis, M., 2006]), has been revealed, particularly for a highly nonlinear diffusion term.