A two-dimensional adaptive spectral element method

1997 ◽  
Author(s):  
C. Mavriplis ◽  
L.-C. Hsu ◽  
C. Mavriplis ◽  
L.-C. Hsu
Keyword(s):  
Spectral Element Method ◽  
Spectral Element ◽  
Two Dimensional ◽  
Element Method

The Least Squares Spectral Element Method for the Navier-Stokes and Cahn-Hilliard Equations

2015 ◽  
Author(s):  
Keunsoo Park ◽  
Carlos A. Dorao ◽  
Ezequiel M. Chiapero ◽  
Maria Fernandino
Keyword(s):  
Least Squares ◽  
Spectral Element Method ◽  
Element Model ◽  
Spectral Element ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Order Continuity ◽  
Manufactured Solution ◽  
The Finite Element Model ◽  
Element Method

The least squares spectral element method (LS-SEM) offers many advantages in the implementation of the finite element model compared with the traditional weak Galerkin method. In this article, the LS-SEM is used to solve the Navier-Stokes (NS) and the Cahn-Hilliard (CH) equations. The NS equation is solved with both C0 and C1 basis functions and their performance is compared in terms of accuracy. A two-dimensional steady-state solver is verified with the case of Kovasznay flow and validated for the cavity flow, and a two-dimensional unsteady solver is verified by a transient manufactured solution case. The phenomenon of phase separation in binary system is described by the CH equation. Due to the fourth-order characteristics of the CH equation, only a high order continuity approximation is used by employing C1 basis function for both space and time domain. The obtained solutions are in accordance with previous results from the literature and show the fundamental characteristics of the NS and CH equations. The results in this study give the possibility of developing a solver for the coupled NS and CH equations.

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