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Sheu, Tony W. H.; Fang, C. C.; Tsai, S. F.; Huang, Chung-Yuan

On an adaptive monotonic convection-diffusion flux discretization scheme. (English) Zbl 0964.76044

Comput. Methods Appl. Mech. Eng. 173, No. 1-2, 201-215 (1999).
From the summary: The paper concerns numerical investigation of a two-dimensional steady convection-diffusion scalar equation. Specific attention is given to resolving spurious oscillations in a confined region of high gradient. In smooth regions, a high-order accurate solution is desired, while in regions containing a sharp gradient, the strategy of applying a monotonic capturing scheme is preferred. We model fluxes by means of a finite element model which has spaces spanned by Legendre polynomials. The propensity to yield an irreducible diagonal-dominant stiffness matrix is an attribute of this finite element flux discretization scheme. By conducting a modified equation analysis, we confirm the consistency of the scheme. Both the stability and monotonicity of the solutions are also addressed. A guide for judging whether the stiffness matrix can yield a monotonic solution is rooted in the theory of the \(M\)-matrix. This monotonicity study provides us with greater numerical insight into the importance of the chosen Péclet number. Beyond its critical value, oscillatory solutions are present in the flow. This monotonic region is, however, fairly restricted.

Cited in 1 Document

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76R99 Diffusion and convection

Keywords:

\(M\)-matrix; two-dimensional steady convection-diffusion scalar equation; spurious oscillations; sharp gradient; monotonic capturing scheme; finite element model; Legendre polynomials; irreducible diagonal-dominant stiffness matrix; flux discretization scheme; stability; monotonicity; oscillatory solutions
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