Special meshes for finite differences approximations to an advection-diffusion equation with parabolic layers

Journal Article · Wed Mar 01 04:00:00 EST 1995 · Journal of Computational Physics

DOI:https://doi.org/10.1006/jcph.1995.1043· OSTI ID:91146

Hegarty, A F ^[1]; Miller, J J.H. ^[2]; O`Riordan, E ^[3]

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1. Univ. of Limerick (Ireland)
2. Trinity College, Dublin (Ireland)
3. Regional Technical College, Dublin (Ireland); and others

In this paper a model problem for fluid flow at high Reynolds number is examined. Parabolic boundary layers are present because part of the boundary of the domain is a characteristic of the reduced differential equation. For such problems it is shown, by numerical example, the upwind finite difference schemes on uniform meshes are not {epsilon}-uniformly convergent in the discrete L{infinity} norm, where {epsilon}-uniformly convergent method is constructed for a singularly perturbed elliptic equation, whose solution contains parabolic boundary layers for small values of the singular perturbation parameter {epsilon}. This method makes use of a special piecewise uniform mesh. Numerical results are given that validate the theoretical results, obtained earlier by the last author, for such special mesh methods. 27 refs., 5 figs., 4 tabs.

• OSTI ID: 91146
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 1 Vol. 117; ISSN 0021-9991; ISSN JCTPAH
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
99 GENERAL AND MISCELLANEOUS
ADVECTION
COMPUTERIZED SIMULATION
FINITE DIFFERENCE METHOD
FLUID FLOW
MESH GENERATION
NAVIER-STOKES EQUATIONS
NUMERICAL SOLUTION
OPTIMIZATION