Double reduction of partial differential equations with applications to laminar jets and wakes
Date
2016
Authors
Kokela, Lady Nomvula
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Abstract
Invariant solutions for two-dimensional free and wall jets are derived by consid-
ering the Lie point symmetry associated with the appropriate conserved vectors
of Prandtl's boundary layer equations for the jets. For the two-dimensional
jets we also consider the comparison, advantages and disadvantages between
the standard method that uses a linear combination of all the Lie point symme-
tries of Prandtl's boundary layer equations to generate the invariant solution
with the new method explored in this paper which uses the Lie point sym-
metry associated with a conserved vector to generate the invariant solution.
Invariant solutions for two-dimensional classical and self-propelled wakes are
also derived by considering the Lie point symmetry associated with the appro-
priate conserved vectors of Prandtl's boundary layer equations for the wakes.
We also consider and discuss the standard method that uses a linear combi-
nation of all the Lie point symmetry of Prandtl's boundary layer equations to
generate the invariant solutions for the classical and self-propelled wakes.
Description
A dissertation submitted to the Faculty of Science, School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. Johannesburg, 2015.