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A Petrov‐Galerkin method for the numerical solution of the Bradshaw‐Ferriss‐Atwell turbulence model
Author(s) -
Stewart I. B.,
Unsworth K.
Publication year - 1988
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.1650080502
Subject(s) - petrov–galerkin method , discretization , mathematics , galerkin method , simple (philosophy) , numerical analysis , mathematical analysis , eigenvalues and eigenvectors , finite element method , physics , philosophy , epistemology , quantum mechanics , thermodynamics
The Bradshaw‐Ferriss‐Atwell model for 2D constant property turbulent boundary layers is shown to be ill‐posed with respect to numerical solution. It is shown that a simple modification to the model equations results in a well‐posed system which is hyperbolic in nature. For this modified system a numerical algorithm is constructed by discretizing in space using the Petrov‐Galerkin technique (of which the standard Galerkin method is a special case) and stepping in the timelike direction with the trapezoidal (Crank‐Nicolson) rule. The algorithm is applied to a selection of test problems. It is found that the solutions produced by the standard Galerkin method exhibit oscillations. It is further shown that these oscillations may be eliminated by employing the Petrov‐Galerkin method with the free parameters set to simple functions of the eigenvalues of the modified system.