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A collocation method for convection dominated flows
Author(s) -
Chawla T. C.,
Leaf G.,
Minkowycz W. J.
Publication year - 1984
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650040305
Subject(s) - péclet number , discretization , collocation (remote sensing) , convection , flow (mathematics) , mechanics , collocation method , polygon mesh , field (mathematics) , mathematics , convection–diffusion equation , geometry , mathematical analysis , physics , geology , differential equation , ordinary differential equation , remote sensing , pure mathematics
A collocation method based on multiple regions with moving boundaries placed in a flow field in which convection effects dominate, is proposed. By making the moving boundaries of the regions coincide with moving sharp fronts present in the solution of convection dominated problems, and thereby allowing higher concentration of meshes to be placed about the fronts, the proposed method is able to achieve very high accuracy. By having a moving mesh, the Peclet number characterizing the flow field depends upon velocity relative to a moving mesh in a region. Consequently by choosing proper velocities of the moving boundaries, the value of this Peclet number can be made as small as desired. The traditional collocation method based on centred discretization, when applied to each region in the field, produces oscillation free solutions even when the values of Peclet number based on absolute velocity are extremely large. In view of these characteristics the method appears to be an excellent candidate for the solution of any two‐phase flow problem containing sharp fronts.