Paper Info
Title
A Cell-Centered Nonlinear Finite Volume Scheme Preserving Fully Positivity for Diffusion Equation
Abstract
Abstract In the construction of existing nonlinear cell-centered finite volume schemes with monotonicity, it is required to assume that values of auxiliary unknowns are nonnegative. However, this assumption is not always satisfied, especially when accurate reconstruction of auxiliary unknowns is concerned on distorted meshes. In this paper we propose a new method to deal with this issue by introducing both edge unknowns and vertex unknowns as auxiliary unknowns. Edge unknowns are approximated by a convex combination of cell-centered unknowns and vertex unknowns by using the continuity of flux on cell edge. Vertex unknowns are approximated by a convex combination of cell-centered unknowns and edge unknowns. Our new method can assure that these weighted coefficients are nonnegative and the sum of these coefficients in each convex combination is one. The resulting scheme is a nonlinear monotone scheme with nonlinear coefficients depending on both edge unknowns and vertex unknowns, and a linear cell-centered finite volume scheme is formed at each nonlinear iteration by using the Picard linearized method. Numerical results show that our monotone scheme based on the new method of eliminating auxiliary unknowns is more accurate and robust than some existing monotone schemes.
Year
DOI
Venue
2016
10.1007/s10915-015-0148-7
Journal of Scientific Computing
Keywords
Field
DocType
Positivity,Finite volume scheme,Vertex unknowns,Edge unknowns
Monotonic function,Mathematical optimization,Polygon mesh,Nonlinear system,Vertex (geometry),Convex combination,Mathematical analysis,Finite volume method,Monotone polygon,Diffusion equation,Mathematics
Journal
Volume
Issue
ISSN
68
2
1573-7691
Citations 
PageRank 
References 
0
0.34
21
Authors
2
Name
Order
Citations
PageRank
Zhiqiang Sheng112914.39
Guangwei Yuan216523.06