Desenvolvimento de metodo implicito para simulador numerico tridimensional de escoamentos compressiveis inviscidos

AUTOR(ES)
DATA DE PUBLICAÇÃO

2004

RESUMO

The simulation of compressible flows considered inviscid is largely appliable to aeronautics. The development of such simulations using the Garlekin discontinuous method[7,12,16,20], wich presents the good characteristics of fine element and finite volume methods, benefitting from the polynomial interpolation within subdomains and discontinuous across interfaces among them, has been the focus of many current researches. In this work the author extends the functionalities of the PZ finite element environment[28], enabling it to model the Euler equations of gas dynamics with the discontinuous Galerkin method in three space dimensions. The flux evaluation across interfaces uses the first order Roe?s numerical flux. Artificial diffusive terms added to the formulation aatempt to stabilize spatial oscillations of the distribution of the solution within each subdomain. The time marcing scheme applied is the implicit first order Euler, solved by a Newton-Raphson method. The evaluation of the matrix tangent to the Euler residual required by the neton-Raphson method is challenging due to the complexity of the artificial diffusive and numerical flux terms, but feasible thanks to the automatic differentiation techniques. Given the quality of the consistently implicit time integrator. CFL evolution algorithms are developed and applied to reduce the simulation ti-ming. The proposed scheme validation as well as the result quality juclgements are obtained through the simulation of test problems proposed by the author. The result is a 2D and 3D robust simulator that off ers results consistent ivith those availabe in the bibliography. Outstanding qualities are presented by the CFL c.volution scheme. which reduces the num-ber of time marching iterations required to converge to steady-state solutions. An efficiency benchmark of the artificial cliff usive terms and the matricial development of such are also emphasized. This work evinces the qualities of the discontinuous Galerkin approximation method compared to analytical and finite volume simulation solutions and the qualities of the developed time integrator. guiding future developments and stating suggestions on pos-sible extensions focusing performance enhancement and additional features.

ASSUNTO(S)

metodo dos elementos finitos metodos de finite elements euler equations discontinuous galerkin cfd galerkin mecanica dos fluidos dinamica dos gases

ACESSO AO ARTIGO

Documentos Relacionados