DISCRETIZAÇÃO MATEMÁTICA DAS EQUAÇÕES NECESSÁRIAS PARA MODELAGEM DE FLUIDO COMPRESSÍVEL BIDIMENSIONAL COM CVFEM

Resumo

The present work provides in details the discretization of a set of mathematical equations
required to model a two‐dimensional compressible fluid flow. The hypothesis of not viscous flow is
considered in this work for effect of simplifying the equations, thus the compressible flow of the fluid
can be described by the Euler equations. The control volume based finite element method – CVFEM
was chosen to describe the differential equations of conservation. The numerical method uses
unstructured mesh (based on triangular elements) to discretize the geometric domain and the polygonal
control volumes for discretization of conservation equations. For that purposed, it was opted for the
segregated solution of the momentum and mass conservation equations, by the use of primitive variables
(velocity, pression and temperature) and co-located (integration of the momentum and mass
conservation equations is done above the same control volume for pressure and velocity). A
computational code programmed in MATLAB software language was developed to realize the
numerical simulations of compressible flows, two-dimensional (planar or axisymmetric) and transients.
The case of a subsonic / supersonic flow through a Channel with a Circular Arc Bump and the case of
the supersonic flow through the convergent-divergent channel were used to verify the developed code.
At the end of the work are presented results obtained by means of a numerical solution and these results
are compared to results available in literature, to ascertain that the computational code developed works
as it was expected.