3D Unsteady Convection-Diffusion-Reaction via GFEM Solver

2015 ◽  
Vol 751 ◽  
pp. 313-318
Author(s):  
Estaner Claro Romão ◽  
Luiz Felipe Mendes de Moura
Keyword(s):  
Numerical Simulation ◽  
Exact Solution ◽  
Galerkin Method ◽  
Diffusion Reaction ◽  
Convection Diffusion ◽  
Temporal Discretization ◽  
Physical Problems ◽  
Important Study ◽  
Initial Idea ◽  
The Galerkin Method

In this paper, an important study on the application of the α family of temporal discretization is presented. For spatial discretization the Galerkin Method (GFEM) was used. With the variation of the α coefficient in temporal discretization and through one numerical applications with exact solution, it will be possible to have an initial idea on how each one of the two suggested methods behaves. It is expected that this study can be able to advance several other studies within the domain of numerical simulation of physical problems. It is important to note that for all applications we will use a mesh that is considered gross, with the purpose of presenting a method that is robust, precise and mainly computationally economic.

3D Unsteady Convection Problems via LSFEM Solver

2015 ◽  
Vol 751 ◽  
pp. 319-324
Author(s):  
Estaner Claro Romão ◽  
Luiz Felipe Mendes de Moura
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Finite Element ◽  
Least Squares ◽  
Spatial Discretization ◽  
Temporal Discretization ◽  
Physical Problems ◽  
Important Study ◽  
Element Method

In this paper, an important study on the application of the α family of temporal discretization is presented. For spatial discretization, the Least Squares Finite Element Method (LSFEM) is used. It is expected that this study can be able to advance several other studies within the domain of numerical simulation of physical problems. It is important to note that for all applications we will use a mesh that is considered gross, with the purpose of presenting a method that is robust, precise and mainly computationally economic.

The Galerkin method applied to convective instability problems

1968 ◽  
Vol 33 (1) ◽  
pp. 201-208 ◽  
Author(s):  
Bruce A. Finlayson
Keyword(s):  
Exact Solution ◽  
Time Dependence ◽  
Galerkin Method ◽  
Convective Instability ◽  
Fluid Layer ◽  
Oscillatory Instability ◽  
Rotating Fluid ◽  
Exponential Time ◽  
The Stability ◽  
The Galerkin Method

The Galerkin method is applied in a new way to problems of stationary and oscillatory convective instability. By retaining the time derivatives in the equations rather than assuming an exponential time-dependence, the exact solution is approximated by the solution to a set of ordinary differential equations in time. Computations are simplified because the stability of this set of equations can be determined without finding the detailed solution. Furthermore, both stationary and oscillatory instability can be studied by means of the same trial functions. Previous studies which have treated only stationary instability by the Galerkin method can now be extended easily to include oscillatory instability. The method is illustrated for convective instability of a rotating fluid layer transferring heat.

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