Moving Least-Squares Aided Finite Element method (MLS-FEM): a Powerful Means to Consider Simultaneously Velocity and Pressure Discontinuities of Multi-Phase Flow Fields

2021 ◽  
pp. 105255
Author(s):  
Mehdi Mostafaiyan ◽  
Sven Wießner ◽  
Gert Heinrich
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Least Squares ◽  
Flow Fields ◽  
Moving Least Squares ◽  
Phase Flow ◽  
Powerful Means ◽  
Multi Phase Flow ◽  
Multi Phase ◽  
Element Method

Moving least-squares finite element method

2007 ◽  
Vol 221 (9) ◽  
pp. 1019-1036 ◽  
Author(s):  
M Musivand-Arzanfudi ◽  
H Hosseini-Toudeshky
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Least Squares ◽  
Three Dimensional ◽  
Meshless Methods ◽  
Computational Method ◽  
Computational Time ◽  
Moving Least Squares ◽  
Shape Functions ◽  
Element Method

A new computational method here called moving least-squares finite element method (MLSFEM) is presented, in which the shape functions of the parametric elements are constructed using moving least-squares approximation. While preserving some excellent characteristics of the meshless methods such as elimination of the volumetric locking in near-incompressible materials and giving accurate strains and stresses near the boundaries of the problem, the computational time is decreased by constructing the meshless shape functions in the stage of creating parametric elements and then utilizing them for any new problem. Moreover, it is not necessary to have knowledge about the full details of the shape function generation method in future uses. The MLSFEM also eliminates another drawback of meshless methods associated with the lack of accordance between the integration cells and the problem boundaries. The method is described for two-dimensional problems, but it is extendable for three-dimensional problems too. The MLSFEM does not require the complex mesh generation. Excellent results can be obtained even using a simple mesh. A technique is also presented for isoparametric mapping which enables best possible mapping via a constrained optimization criterion. Several numerical examples are analysed to show the efficiency and convergence of the method.

Applying the Galerkin Least Squares Finite Element Method for Solving Stirred Tank Velocity Fields

2002 ◽  
Author(s):  
Kevin J. Bittorf
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Least Squares ◽  
Three Dimensional ◽  
Flow Fields ◽  
Stirred Tank ◽  
Pharmaceutical Chemical ◽  
Cfd Validation ◽  
Stirred Tank Reactors ◽  
Element Method

The Galerkin Least Squares finite element solver, in conjunction with the Spalart-Allmaras turbulence closure model, is used to solve the RANS based equations for flow fields in stirred tank reactors. This GLS finite element method is well established in the aerospace industry and presently is being validated for flow fields used in industrial processes that are commonly found in the pharmaceutical, chemical, food, and personal products industries. The CFD results, computed in the commercial package ORCA, compared well with experimental data attained for the dominating macro flow structures in an axial and radial impeller stirred tanks. The CFD quantitatively predicts the two and three-dimensional wall jet structures that govern the bulk flow in a stirred tank and are responsible for blending, solid suspension, and macro-flow. This area of experimentation provides an initial basis for CFD validation for bulk flows in stirred tank reactors.

Application of local least squares finite element method (LLSFEM) in the interface capturing of two-phase flow systems

2018 ◽  
Vol 174 ◽  
pp. 110-121 ◽  
Author(s):  
Mehdi Mostafaiyan ◽  
Sven Wießner ◽  
Gert Heinrich ◽  
Mahdi Salami Hosseini ◽  
Jan Domurath ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Least Squares ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase ◽  
Interface Capturing ◽  
Flow Systems ◽  
Element Method
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