The modified characteristics finite element method for time-dependent Darcy-Brinkman problem

2018 ◽  
Vol 36 (1) ◽  
pp. 356-376 ◽  
Author(s):  
Cheng Liao ◽  
Pengzhan Huang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Double Diffusion ◽  
Diffusion Problem ◽  
Content Type ◽  
Characteristics Method ◽  
Complicated Model ◽  
Velocity Pressure ◽  
First Time ◽  
Element Method

Purpose This study aims to capture the effective behavior of double-diffusion problem, which arises from the combined heat and mass transfer in porous medium and develop the modified characteristics finite element method. Design/methodology/approach The proposed finite element method deals with the nonlinear term temporal term by modified characteristics method. Then, the authors compute the velocity, pressure, temperature and concentration using the decoupled technique. Finally, to show the efficiency of the method, the authors give some numerical examples. Findings From the numerical results, one can see that the method has a good accuracy, which shows that the method can simulate this Darcy–Brinkman problem well. Originality/value The originality lies in the fact that the proposed scheme is the first time for solving the Darcy–Brinkman problem, which is a more complicated model, and includes the velocity, pressure, temperature and concentration.

scholarly journals A posteriori error estimates for a multi-scale finite-element method

2021 ◽  
Vol 40 (4) ◽  
Author(s):  
Khallih Ahmed Blal ◽  
Brahim Allam ◽  
Zoubida Mghazli
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
A Posteriori Error Estimates ◽  
Numerical Test ◽  
Posteriori Error ◽  
Diffusion Problem ◽  
A Posteriori ◽  
Essential Information ◽  
Multi Scale ◽  
Element Method

AbstractWe are interested in the discretization of a diffusion problem with highly oscillating coefficient, by a multi-scale finite-element method (MsFEM). The objective of this method is to capture the multi-scale structure of the solution via local basis functions which contain the essential information on small scales. In this paper, we perform an a posteriori analysis of this discretization. The main result consists of building error indicators with respect to both small and large meshes used in this method. We present a numerical test in which the experiments are in good coherency with the results of analysis.

Parallel finite-element method using domain decomposition and Parareal for transient motor starting analysis

2019 ◽  
Vol 38 (5) ◽  
pp. 1507-1520 ◽  
Author(s):  
Yasuhito Takahashi ◽  
Koji Fujiwara ◽  
Takeshi Iwashita ◽  
Hiroshi Nakashima
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Parallel Computing ◽  
Domain Decomposition ◽  
Parallel Computation ◽  
Domain Decomposition Method ◽  
Space Time ◽  
Content Type ◽  
Parallel Performance ◽  
Element Method

Purpose This paper aims to propose a parallel-in-space-time finite-element method (FEM) for transient motor starting analyses. Although the domain decomposition method (DDM) is suitable for solving large-scale problems and the parallel-in-time (PinT) integration method such as Parareal and time domain parallel FEM (TDPFEM) is effective for problems with a large number of time steps, their parallel performances get saturated as the number of processes increases. To overcome the difficulty, the hybrid approach in which both the DDM and PinT integration methods are used is investigated in a highly parallel computing environment. Design/methodology/approach First, the parallel performances of the DDM, Parareal and TDPFEM were compared because the scalability of these methods in highly parallel computation has not been deeply discussed. Then, the combination of the DDM and Parareal was investigated as a parallel-in-space-time FEM. The effectiveness of the developed method was demonstrated in transient starting analyses of induction motors. Findings The combination of Parareal with the DDM can improve the parallel performance in the case where the parallel performance of the DDM, TDPFEM or Parareal is saturated in highly parallel computation. In the case where the number of unknowns is large and the number of available processes is limited, the use of DDM is the most effective from the standpoint of computational cost. Originality/value This paper newly develops the parallel-in-space-time FEM and demonstrates its effectiveness in nonlinear magnetoquasistatic field analyses of electric machines. This finding is significantly important because a new direction of parallel computing techniques and great potential for its further development are clarified.

Semi-analytical finite element method for simulating chemical dissolution-front instability problems in fluid-saturated porous media

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Chongbin Zhao ◽  
B.E. Hobbs ◽  
Alison Ord
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Porous Media ◽  
Chemical Dissolution ◽  
Saturated Porous Media ◽  
Content Type ◽  
Front Instability ◽  
Fluid Saturated Porous Media ◽  
Dissolution Front ◽  
Element Method

PurposeThe objective of this paper is to develop a semi-analytical finite element method for solving chemical dissolution-front instability problems in fluid-saturated porous media.Design/methodology/approachThe porosity, horizontal and vertical components of the pore-fluid velocity and solute concentration are selected as four fundamental unknown variables for describing chemical dissolution-front instability problems in fluid-saturated porous media. To avoid the use of numerical integration, analytical solutions for the property matrices of a rectangular element are precisely derived in a purely mathematical manner. This means that the proposed finite element method is a kind of semi-analytical method. The column pivot element solver is used to solve the resulting finite element equations of the chemical dissolution-front instability problem.FindingsThe direct use of horizontal and vertical components of the pore-fluid velocity as fundamental unknown variables can improve the accuracy of the related numerical solution. The column pivot element solver is useful for solving the finite element equations of a chemical dissolution-front instability problem. The proposed semi-analytical finite element method can produce highly accurate numerical solutions for simulating chemical dissolution-front instability problems in fluid-saturated porous media.Originality/valueAnalytical solutions for the property matrices of a rectangular element are precisely derived for solving chemical dissolution-front instability problems in fluid-saturated porous media. The proposed semi-analytical finite element method provides a useful way for understanding the underlying dynamic mechanisms of the washing land method involved in the contaminated land remediation.

Stress, strain and displacement analysis of geodetic and conventional fuselage structure for future passenger aircraft

2019 ◽  
Vol 91 (6) ◽  
pp. 814-819
Author(s):  
Zdobyslaw Jan Goraj ◽  
Mariusz Kowalski ◽  
Bartlomiej Goliszek
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Weight Reduction ◽  
Composite Structures ◽  
Lattice Structure ◽  
Small Displacement ◽  
Structure Stability ◽  
Outer Diameter ◽  
Content Type ◽  
Element Method

Purpose This paper aims to present the results of calculations that checked how the longerons and frames arrangement affects the stiffness of a conventional structure. The paper focuses only on first stage of research – analysis of small displacement. Main goal was to compare different structures under static loads. These results are also compared with the results obtained for a geodetic structure fuselage model of the same dimensions subjected to the same internal and external loads. Design/methodology/approach The finite element method analysis was carried out for a section of the fuselage with a diameter of 6.3 m and a length equal to 10 m. A conventional and lattice structure – known as geodetic – was used. Findings Finite element analyses of the fuselage model with conventional and geodetic structures showed that with comparable stiffness, the weight of the geodetic fuselage is almost 20 per cent lower than that of the conventional one. Research limitations/implications This analysis is limited to small displacements, as the linear version of finite element method was used. Research and articles planned for the future will focus on nonlinear finite element method (FEM) analysis such as buckling, structure stability and limit cycles. Practical implications The increasing maturity of composite structures manufacturing technology offers great opportunities for aircraft designers. The use of carbon fibers with advanced resin systems and application of the geodetic fuselage concept gives the opportunity to obtain advanced structures with excellent mechanical properties and low weight. Originality/value This paper presents very efficient method of assessing and comparison of the stiffness and weight of geodetic and conventional fuselage structure. Geodetic fuselage design in combination with advanced composite materials yields an additional fuselage weight reduction of approximately 10 per cent. The additional weight reduction is achieved by reducing the number of rivets needed for joining the elements. A fuselage with a geodetic structure compared to the classic fuselage with the same outer diameter has a larger inner diameter, which gives a larger usable space in the cabin. The approach applied in this paper consisting in analyzing of main parameters of geodetic structure (hoop ribs, helical ribs and angle between the helical ribs) on fuselage stiffness and weight is original.

A MSFEM to simulate the eddy current problem in laminated iron cores in 3D

2019 ◽  
Vol 38 (5) ◽  
pp. 1667-1682 ◽  
Author(s):  
Karl Hollaus
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Eddy Current ◽  
Eddy Currents ◽  
Three Dimensional ◽  
Harmonic Balance Method ◽  
Three Dimensions ◽  
Magnetic Vector Potential ◽  
Content Type ◽  
Element Method

Purpose The simulation of eddy currents in laminated iron cores by the finite element method (FEM) is of great interest in the design of electrical devices. Modeling each laminate by finite elements leads to extremely large nonlinear systems of equations impossible to solve with present computer resources reasonably. The purpose of this study is to show that the multiscale finite element method (MSFEM) overcomes this difficulty. Design/methodology/approach A new MSFEM approach for eddy currents of laminated nonlinear iron cores in three dimensions based on the magnetic vector potential is presented. How to construct the MSFEM approach in principal is shown. The MSFEM with the Biot–Savart field in the frequency domain, a higher-order approach, the time stepping method and with the harmonic balance method are introduced and studied. Findings Various simulations demonstrate the feasibility, efficiency and versatility of the new MSFEM. Originality/value The novel MSFEM solves true three-dimensional eddy current problems in laminated iron cores taking into account of the edge effect.

Dynamic tensile process of blended fabric using finite element method

2020 ◽  
Vol 32 (5) ◽  
pp. 707-724
Author(s):  
Xuzhong Su ◽  
Xinjin Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Experimental Testing ◽  
Woven Fabrics ◽  
Weft Yarn ◽  
Tensile Fracture ◽  
Content Type ◽  
Tensile Process ◽  
Simulation Results ◽  
Element Method

PurposeTensile property is one basic mechanics performance of the fabric. In general, not only the tensile values of the fabric are needed, but also the dynamic changing process under the tension is also needed. However, the dynamic tensile process cannot be included in the common testing methods by using the instruments after fabric weaving.Design/methodology/approachBy choosing the weft yarn and warp yarn in the fabric as the minimum modeling unit, 1:1 finite element model of the whole woven fabrics was built by using AutoCAD software according to the measured geometric parameters of the fabrics and mechanical parameters of yarns. Then, the fabric dynamic tensile process was simulated by using the ANSYS software. The stress–strain curve along the warp direction and shrinkage rate curve along the weft direction of the fabrics were simulated. Meanwhile, simulation results were verified by comparing to the testing results.FindingsIt is shown that there are four stages during the fabric tensile fracture process along the warp direction under the tension. The first stage is fabric elastic deformation. The second stage is fabric yield deformation, and the change rate of stress begins to slow down. The third stage is fiber breaking, and the change of stress fluctuates since the breaking time of the fibers is different. The fourth stage is fabric breaking.Originality/valueIn this paper, the dynamic tensile process of blended woven fabrics was studied by using finite element method. Although there are differences between the simulation results and experimental testing results, the overall tendency of simulation results is the same as the experimental testing results.

CONTINUOUS Q1–Q1 STOKES ELEMENTS STABILIZED WITH NON-CONFORMING NULL EDGE AVERAGE VELOCITY FUNCTIONS

2007 ◽  
Vol 17 (03) ◽  
pp. 439-459 ◽  
Author(s):  
LEOPOLDO P. FRANCA ◽  
SAULO P. OLIVEIRA ◽  
MARCUS SARKIS
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stokes Equations ◽  
Least Squares Method ◽  
Approximation Properties ◽  
Stabilized Finite Element ◽  
Stabilized Finite Element Method ◽  
Bubble Functions ◽  
Velocity Pressure ◽  
Element Method

We present a stabilized finite element method for Stokes equations with piecewise continuous bilinear approximations for both velocity and pressure variables. The velocity field is enriched with piecewise polynomial bubble functions with null average at element edges. These functions are statically condensed at the element level and therefore they can be viewed as a continuous Q1–Q1 stabilized finite element method. The enriched velocity-pressure pair satisfies optimal inf–sup conditions and approximation properties. Numerical experiments show that the proposed discretization outperforms the Galerkin least-squares method.

Development of SFEM-Pre: A Novel Preprocessor for Model Creation for the Smoothed Finite Element Method

2019 ◽  
Vol 17 (02) ◽  
pp. 1845002 ◽  
Author(s):  
J. F. Zhang ◽  
R. P. Niu ◽  
Y. F. Zhang ◽  
C. Q. Wang ◽  
M. Li ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Complex Geometry ◽  
Three Dimensional ◽  
Efficient Computation ◽  
Practical Engineering ◽  
Smoothed Finite Element Method ◽  
2D And 3D ◽  
First Time ◽  
Element Method

Smoothed finite element method (S-FEM) is a new general numerical method which has been applied to solve various practical engineering problems. It combines standard finite element method (FEM) and meshfree techniques based on the weaken-weak (W2) formulation. This project, for the first time, develops a preprocessor software package SFEM-Pre for creating types of two-dimensional (2D) and three-dimensional (3D) S-FEM models following strictly the S-FEM theory. Because the software architecture of our 3D processor is the same as our 2D preprocessor, we will mainly introduce the 2D preprocessor in terms of software design for easier description, but the examples will include both 2D and 3D cases to fully demonstrate and validate the whole preprocessor of S-FEM. Our 2D preprocessor package is equipped with a graphical user interface (GUI) for easy use, and with a connectivity database for efficient computation. Schemes are developed for not only automatically meshes the problem domains using our GUI, but also accepts various geometry files made available from some existing commercial software packages, such as ABAQUS®and HyperMesh®. In order to improve the efficiency of our preprocessor, a parallel triangulation mesh generator has also been developed based on the advancing front technique (AFT) to create triangular meshes for complex geometry, and at the same time to create six types of connectivity needed for various S-FEM models. In addition, a database is implemented in our code to record all these connectivity to avoid duplicated calculation. Finally, intensive numerical experiments are conducted to validate the efficiency, accuracy and stability of our preprocessor codes. It is shown that with our preprocessor, an S-FEM can be created automatically without much human intervention for geometry of arbitrary complexity.

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