Flow Balancing in Modeling of Multi-Phase Flow using Non-Conformal Finite Element Meshes

2021 ◽  
Vol 12 (9) ◽  
pp. 450-458
Author(s):  
M. G. Persova ◽  
◽  
Yu. G. Soloveichik ◽  
A. M. Grif ◽  
◽  
...  
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Phase Transfer ◽  
High Viscosity ◽  
Complex Model ◽  
Real Field ◽  
Approximation Accuracy ◽  
Computational Costs ◽  
Order Of Magnitude ◽  
Finite Element Meshes

The method of balancing numerical finite element flows in modeling a process of multiphase flow using non-conformal hexagonal meshes is considered. Studies have been carried out for a simple reservoir configuration and on a more complex model of a real field of high-viscosity oil in the Tatarstan. The research results showed that the balancing method allows one to obtain a conservative solution when using non-conformal finite element meshes with sufficiently large cells. At the same time, this method is completely free of problems associated with grid orientation, even for complex models containing zones with highly variable permeability. The proposed algorithm for the adaptive choice of parameters allows to do the factorization of the SLAE matrix at sufficiently small number of time steps; therefore, the computational costs of the flow balancing procedure are an order of magnitude less than the costs associated with calculating the pressure field and phase transfer. The used non-conformal finite element meshes with an arbitrary number of docked hexagons can significantly reduce the number of degrees of freedom when modeling multiphase flows in reservoirs with much small local heterogeneity and in the presence of several perforated zones. As a result, computational costs are reduced by almost an order of magnitude, and, at the same time, the required approximation accuracy is maintained. With an increase in the scale of the model and the number of operating wells, this advantage increases even more.

A Reduced Full-System Finite Element Approach to the Solution of EHL Problems: Line Contacts

2010 ◽  
Author(s):  
W. Habchi ◽  
J. Issa
Keyword(s):  
Finite Element ◽  
Linear Elasticity ◽  
Degrees Of Freedom ◽  
Contact Problems ◽  
Full System ◽  
Acceptable Solution ◽  
Line Contacts ◽  
Order Of Magnitude ◽  
Element Approach ◽  
Basis Method

This paper presents a reduced full-system finite element solution of isothermal elastohydrodynamic (EHD) line contact problems. The proposed model is based on a full-system finite element resolution of the EHL equations: Reynolds, linear elasticity and load balance. A reduced model is proposed for the linear elasticity problem. For this, three different techniques are tested: the classical “Modal reduction” and “Ritz-vector” methods and a novel “EHL-basis” method. The reduction order in the first two appears to be insufficient and a large number of degrees of freedom is required in order to attain an acceptable solution. On the other hand, the “EHL-basis” method shows up to be much more efficient, requiring only a few degrees of freedom to compose the elastic deformation of the solid components. In addition, a comparison with the full model shows an order of magnitude cpu time gain with errors of the order of only 1‰ for the central and minimum film thicknesses.

scholarly journals A Simplified Matrix Analysis Approach to Multi Storey Buildings Involving a Friction Damper

2021 ◽  
Vol 29 (3) ◽  
pp. 1-8
Author(s):  
Kamyar Gharra ◽  
Karen Khanlari ◽  
Jafar Asgari ◽  
Mohammad
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Matrix Analysis ◽  
Friction Damper ◽  
Analysis Algorithm ◽  
Computational Costs ◽  
Dynamic Forces ◽  
Damped Systems ◽  
Element Method

Abstract Damping through friction tends to be one of the most efficient methods to suppress damage to structures from earthquakes. Realizing robust structures is therefore highly dependent on designing for the dynamic forces of friction- damped structures and exploring their reliability against natural disasters. This paper presents a simplified matrix analysis algorithm for multi-storey friction- damped buildings. We have analyzed the behavior of friction- damped systems more accurately by modeling the master-slave degree of freedom of the joints. First, the formulation of the problem is discussed, and a condensed general equation is derived. Then, an end- to- end solution is proposed to find the responses of structures. The displacement response of each storey has been carried out in both condensed and non-condensed general equations, and the results clearly show the accuracy of the proposed method. The numerical analysis and the results of the simulation of various friction- damped structures depicts the proposed approach consists with the commercial finite element method and is applicable for the analysis various types of structures. It is noted that the acceleration and displacement responses of the structures investigated under the proposed method and the traditional finite element method are so consistent that only a 1.5% difference is observed. Moreover, as a result of the proper allocation of degrees of freedom during the analysis, this method yields a reduction in computational costs especially in large buildings.

scholarly journals A Simplified Matrix Analysis Approach to Multi-story Buildings Involving a Friction Damper

2021 ◽  
Author(s):  
Kamyar Gharra ◽  
Karen Khanlari ◽  
Jafar Asgari Marnani
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Matrix Analysis ◽  
Friction Damper ◽  
Analysis Algorithm ◽  
Computational Costs ◽  
Dynamic Forces ◽  
Damped Systems ◽  
Element Method

Damping through friction tends to be one of the most efficient methods to suppress damage to structures from earthquakes. Realizing robust structures is therefore highly dependent on designing for the dynamic forces of friction-damped structures and exploring their reliability against natural disasters. This paper presents a simplified matrix analysis algorithm for multi-story friction- damped buildings. The behavior of friction-damped systems has analyzed more accurately by modeling the master-slave degree of freedom of the joints. First, the formulation of the problem is discussed, and a condensed general equation is derived. Then, an end-to-end solution is proposed to find the responses of structures. The displacement response of each story has been carried out in both condensed and non-condensed general equations, and the results clearly show the accuracy of the proposed method. The numerical analysis and the results of the simulation of various friction-damped structures depicts the proposed approach consists with the commercial finite element method and is applicable for the analysis various types of structures. It is noted that the acceleration and displacement responses of the structures investigated under the proposed method and the traditional finite element method are so consistent that only a 1.5% difference is observed. Moreover, as a result of the proper allocation of degrees of freedom during the analysis, this method yields a reduction in computational costs especially in large buildings.

Simplified FEM Model of Paper Machine Roll for Multibody Rolling Contact Analyses

2001 ◽  
Author(s):  
Veli-Matti Järvenpää ◽  
Erno K. Keskinen
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Element Model ◽  
Rolling Contact ◽  
Fe Model ◽  
Test Model ◽  
Paper Machine ◽  
Element Analysis ◽  
Computational Costs

Abstract In this paper a finite element model of a rotating paper machine roll for nip unit rolling contact analyses is discussed. This work presented here is based on the earlier work of the authors presented in [1] and [2]. The major motivations for developing a tailored FE-model including the large spin rotation are firstly to include the complex vibration phenomena as the shell vibrations of the roll structure in the analyses and secondly to reduce the computational costs of the numerical simulations due to the large number of degrees of freedom. The approach used is the use of the modal analysis i.e. to express the dynamics of the roll in terms of the lowest eigenmodes. The equations of motion are at first written in the rotating coordinates and then in addition to this the equations are expressed by using the modal coordinates. Numerical tests executed show that this modeling technique reduces computational costs significantly. Furthermore, use of the (semidefinite) eigenmode basis maintains the vibration characteristics of the roll structure. For verification purposes a test model was constructed and these simulation results were compared to the standard geometrically non-linear finite element analysis.

Non-Iterative Mode Shape Expansion for Beam Structures Based on Coordinate Decomposition

2013 ◽  
Vol 284-287 ◽  
pp. 503-507
Author(s):  
Fu Shun Liu ◽  
Wen Wen Chen ◽  
Chun Fu Peng ◽  
Wei Li
Keyword(s):  
Finite Element ◽  
Mode Shape ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Expansion Method ◽  
Element Model ◽  
Numerical Studies ◽  
Order Of Magnitude ◽  
Convergence Performance ◽  
Weighting Coefficients

The direct mode shape expansion method is an iterative technique, then one can conclude that the convergence performance maybe challenged when applied to three-dimensional structures. In addition, mode shape values at different DOFs (degrees-of-freedom) sometimes are not in a same order of magnitude, which will produce much error for the estimation of small values of unmeasured mode components. Thus, this paper proposed a non-iterative mode shape expansion method based on coordinate decomposition and neglecting modelling errors between the finite element model and the experimental structure. The advantage of coordinate decomposition is that the unmeasured components of mode shape values could be estimated with different weighting coefficients, even in a physical meaningful interval. Numerical studies in this paper are conducted for a 30-DOF (degree-of-freedom) cantilever beam with multiple damaged elements, as the measured modes are synthesized from finite element models. The results show that the approach can estimate unmeasured mode shape values at translational and rotational DOFs in x, y and z directions with different weighting coefficients, respectively; and better mode shape expansion results can be obtained when proper constraints are employed.

scholarly journals An Introduction to the Analysis and Implementation of Sparse Grid Finite Element Methods

2017 ◽  
Vol 17 (2) ◽  
pp. 299-322 ◽  
Author(s):  
Stephen Russell ◽  
Niall Madden
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Degrees Of Freedom ◽  
Grid Method ◽  
Sparse Grid ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Computational Costs ◽  
Matlab Code ◽  
Sparse Grid Method

AbstractOur goal is to present an elementary approach to the analysis and programming of sparse grid finite element methods. This family of schemes can compute accurate solutions to partial differential equations, but using far fewer degrees of freedom than their classical counterparts. After a brief discussion of the classical Galerkin finite element method with bilinear elements, we give a short analysis of what is probably the simplest sparse grid method: the two-scale technique of Lin et al. [14]. We then demonstrate how to extend this to a multiscale sparse grid method which, up to choice of basis, is equivalent to the hierarchical approach, as described by, e.g., Bungartz and Griebel [4]. However, by presenting it as an extension of the two-scale method, we can give an elementary treatment of its analysis and implementation. For each method considered, we provide MATLAB code, and a comparison of accuracy and computational costs.

The Influence of Loading Position in A Priori High Stress Detection using Mode Superposition

2020 ◽  
Vol 1 (1) ◽  
pp. 93-102
Author(s):  
Carsten Strzalka ◽  
◽  
Manfred Zehn ◽  
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
A Priori ◽  
High Stress ◽  
Von Mises Stress ◽  
Detailed Knowledge ◽  
Variable Loading ◽  
Numerical Effort ◽  
Von Mises

For the analysis of structural components, the finite element method (FEM) has become the most widely applied tool for numerical stress- and subsequent durability analyses. In industrial application advanced FE-models result in high numbers of degrees of freedom, making dynamic analyses time-consuming and expensive. As detailed finite element models are necessary for accurate stress results, the resulting data and connected numerical effort from dynamic stress analysis can be high. For the reduction of that effort, sophisticated methods have been developed to limit numerical calculations and processing of data to only small fractions of the global model. Therefore, detailed knowledge of the position of a component’s highly stressed areas is of great advantage for any present or subsequent analysis steps. In this paper an efficient method for the a priori detection of highly stressed areas of force-excited components is presented, based on modal stress superposition. As the component’s dynamic response and corresponding stress is always a function of its excitation, special attention is paid to the influence of the loading position. Based on the frequency domain solution of the modally decoupled equations of motion, a coefficient for a priori weighted superposition of modal von Mises stress fields is developed and validated on a simply supported cantilever beam structure with variable loading positions. The proposed approach is then applied to a simplified industrial model of a twist beam rear axle.

scholarly journals A Finite Element Approach to the Analysis of Rotating Bladed-Disk Assemblies Coupled With Flexible Shaft

1994 ◽  
Author(s):  
Wen Zhang ◽  
Wenliang Wang ◽  
Hao Wang ◽  
Jiong Tang
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Coupled System ◽  
Equation Of Motion ◽  
Coupled Systems ◽  
The Finite Element Method ◽  
Bladed Disk ◽  
Modal Synthesis ◽  
Element Approach ◽  
Final Equation

A method for dynamic analysis of flexible bladed-disk/shaft coupled systems is presented in this paper. Being independant substructures first, the rigid-disk/shaft and each of the bladed-disk assemblies are analyzed separately in a centrifugal force field by means of the finite element method. Then through a modal synthesis approach the equation of motion for the integral system is derived. In the vibration analysis of the rotating bladed-disk substructure, the geometrically nonlinear deformation is taken into account and the rotationally periodic symmetry is utilized to condense the degrees of freedom into one sector. The final equation of motion for the coupled system involves the degrees of freedom of the shaft and those of only one sector of each of the bladed-disks, thereby reducing the computer storage. Some computational and experimental results are given.

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