Least-squares spectral element method for three dimensional Stokes equations

2016 ◽  
Vol 102 ◽  
pp. 31-54 ◽  
Author(s):  
Subhashree Mohapatra ◽  
Akhlaq Husain
Keyword(s):  
Least Squares ◽  
Spectral Element Method ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Spectral Element ◽  
Element Method

Three Dimensional Simulations of Convective Heat Transfer With Spectral Element Method

2017 ◽  
Author(s):  
Don Liu ◽  
Yong-Lai Zheng ◽  
Arden Moore
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Spectral Element Method ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Spectral Element ◽  
Viscous Heating ◽  
Thermal Buoyancy ◽  
Element Method

This paper presents new equations for simulating three-dimensional convective heat transfer using the complete viscous dissipation function in the energy equation to account for the viscous heating and incorporating the Boussinesq approximation for the thermal buoyancy term in the Navier-Stokes equations. In addition, new implementation of fourth order Stiffly Stable schemes were achieved and tested for time integration. In order to provide dual-level mesh refinement, for flexible spatial resolutions, a modal spectral element method was implemented in solving these equations in three dimensions. Simulation results demonstrate that these new equations and implementations are accurate enough for investigating convective heat transfer with viscous heating subject to complex thermal and flow boundary conditions in three dimensional irregular domains using the high order finite element method.

scholarly journals Wave Propagation Analysis in Composite Laminates Containing a Delamination Using a Three-Dimensional Spectral Element Method

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Fucai Li ◽  
Haikuo Peng ◽  
Xuewei Sun ◽  
Jinfu Wang ◽  
Guang Meng
Keyword(s):  
Wave Propagation ◽  
Lamb Wave ◽  
Composite Laminates ◽  
Composite Structures ◽  
Spectral Element Method ◽  
Three Dimensional ◽  
Spectral Element ◽  
Wave Mode ◽  
Diagonal Form ◽  
Element Method

A three-dimensional spectral element method (SEM) was developed for analysis of Lamb wave propagation in composite laminates containing a delamination. SEM is more efficient in simulating wave propagation in structures than conventional finite element method (FEM) because of its unique diagonal form of the mass matrix. Three types of composite laminates, namely, unidirectional-ply laminates, cross-ply laminates, and angle-ply laminates are modeled using three-dimensional spectral finite elements. Wave propagation characteristics in intact composite laminates are investigated, and the effectiveness of the method is validated by comparison of the simulation results with analytical solutions based on transfer matrix method. Different Lamb wave mode interactions with delamination are evaluated, and it is demonstrated that symmetric Lamb wave mode may be insensitive to delamination at certain interfaces of laminates while the antisymmetric mode is more suited for identification of delamination in composite structures.

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