A Two-Dimensional Isoparametric Galerkin Finite Element for Acoustic-Flow Problems

1983 ◽  
Vol 105 (3) ◽  
pp. 385-391
Author(s):  
S.-F. Ling ◽  
J. F. Hamilton ◽  
J. J. Allen
Keyword(s):  
Finite Element ◽  
Simultaneous Equations ◽  
Two Dimensional ◽  
Duct Acoustics ◽  
Galerkin Finite Element ◽  
Acoustic Flow ◽  
Flow Problems ◽  
Isoparametric Finite Element ◽  
Complicated Geometry ◽  
Boundary Impedance

In duct acoustics, analytical solutions are difficult to obtain because of the presence of flow, boundary impedance, and complicated geometry. A Galerkin isoparametric finite element based on a domain equation which is uncoupled from the flow field is developed. Applying the method to duct acoustic problems results in a set of complex, unsymmetric, nondiagonal dominant simultaneous equations of high order. The Crout reduction scheme is modified to alleviate the computer storage difficulties in solving the numerical problem. The finite element is applied to the analysis of a semi-infinite duct with flow, and a convergent-divergent duct with flow.

Finite Element Analysis of Two-Dimensional Turbulent Asymmetric Near and Far Non-Periodic and Periodic Wakes by κ-ϵ Model of Turbulence

1993 ◽  
Author(s):  
Amlan Kusum Nayak ◽  
N. Venkatrayulu ◽  
D. Prithvi Raj
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Wake Flow ◽  
Two Dimensional ◽  
Galerkin Finite Element Method ◽  
Element Analysis ◽  
Galerkin Finite Element ◽  
Flow Problems ◽  
Newton Raphson ◽  
Good Agreement

Two dimensional time averaged, steady incompressible, adiabatic turbulent asymmetric near and far non-periodic and periodic wake flow problems are solved by Galerkin Finite Element Method. A primitive-variables formulation is adopted using Reynolds-averaged momentum equations, with standard k-ε turbulence model. Finite element equations are solved by Newton-Raphson technique with relaxation, using frontal solver. Periodic boundary condition is specified on the periodic lines of the cascade, and asymptotic boundary condition is specified at the exit. These boundary conditions are applied without much difficulty which are not so straight forward in finite volume (FV) method. The results show good agreement with FV prediction and experimental data.

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