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Positive Definite Advection Transport Algorithm for Conservation Law Equations on Nonuniform Irregular Grids
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-04-10
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
The multidimensional positive definite advection transport algorithm (MPDATA) is an important numerical method for the computation of atmospheric dynamics.
MPDATA is second-order accurate, positive definite, conservative, and computationally efficient.
However, the method is problematic in which it results in a loss of precision when computing a nonuniform irregular grid.
Furthermore, research revealed two reasons for this problem.
On the one hand, numerical discretization of boundary derivatives of the finite-volume method is incompatible with nonuniform meshes (or grids); on the other hand, the up-wind scheme of staggered grids is not applicable to the calculation of irregular grids.
We overcome these two problems by using the multipoint Taylor expansion method to obtain a boundary derivative numerical approximation scheme that does not depend on the grid structure.
Furthermore, combined with the well-balance central-upwind scheme, a positive definite advection scheme for irregular meshes is proposed.
Then, the positivity of the new numerical scheme is analyzed.
Finally, the result of this study is verified by numerical simulation.
American Psychological Association (APA)
Yuan, Xinpeng& Xiong, Chunguang. 2020. Positive Definite Advection Transport Algorithm for Conservation Law Equations on Nonuniform Irregular Grids. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-15.
https://search.emarefa.net/detail/BIM-1195823
Modern Language Association (MLA)
Yuan, Xinpeng& Xiong, Chunguang. Positive Definite Advection Transport Algorithm for Conservation Law Equations on Nonuniform Irregular Grids. Mathematical Problems in Engineering No. 2020 (2020), pp.1-15.
https://search.emarefa.net/detail/BIM-1195823
American Medical Association (AMA)
Yuan, Xinpeng& Xiong, Chunguang. Positive Definite Advection Transport Algorithm for Conservation Law Equations on Nonuniform Irregular Grids. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-15.
https://search.emarefa.net/detail/BIM-1195823
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1195823