A cell-based smoothed finite element method for incompressible turbulent flows

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mingyang Liu ◽  
Guangjun Gao ◽  
Huifen Zhu ◽  
Chen Jiang
Keyword(s):  
Boundary Layer ◽  
Finite Element Method ◽  
Finite Element ◽  
Turbulent Flows ◽  
New Combination ◽  
Wall Functions ◽  
Content Type ◽  
Numerical Examples ◽  
Smoothed Finite Element Method ◽  
Element Method

Purpose The purpose of this paper is to investigate the feasibility of solving turbulent flows based on smoothed finite element method (S-FEM). Then, the differences between S-FEM and finite element method (FEM) in dealing with turbulent flows are compared. Design/methodology/approach The stabilization scheme, the streamline-upwind/Petrov-Galerkin stabilization is coupled with stabilized pressure gradient projection in the fractional step framework. The Reynolds-averaged Navier-Stokes equations with standard k-epsilon model are selected to solve turbulent flows based on S-FEM and FEM. Standard wall functions are applied to predict boundary layer profiles. Findings This paper explores a completely new application of S-FEM on turbulent flows. The adopted stabilization scheme presents a good performance on stabilizing the flows, especially for very high Reynolds numbers flows. An advantage of S-FEM is found in applying wall functions comparing with FEM. The differences between S-FEM and FEM have been investigated. Research limitations/implications The research in this work is limited to the two-dimensional incompressible turbulent flow. Practical implications The verification and validation of a new combination are conducted by several numerical examples. The new combination could be used to deal with more complicated turbulent flows. Social implications The applications of the new combination to study basic and complex turbulent flow are also presented, which demonstrates its potential to solve more turbulent flows in nature and engineering. Originality/value This work carries out a great extension of S-FEM in simulations of fluid dynamics. The new combination is verified to be very effective in handling turbulent flows. The performances of S-FEM and FEM on turbulent flows were analyzed by several numerical examples. Superior results were found compared with existing results and experiments. Meanwhile, S-FEM has an advantage of accuracy in predicting boundary layer profile.

Use the Combination Finite Element Method to Solve the Crack Cylinder of the Torsion Problem

2011 ◽  
Vol 346 ◽  
pp. 751-756
Author(s):  
Xin Yan Tang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Results ◽  
New Combination ◽  
Torsion Problem ◽  
Ansys Software ◽  
Numerical Examples ◽  
Element Method

Based on Muskhelishvili’s theoretical expressions of the Saint-Venant’s problem, using the combination of Crack3D code and Ansys software, a new combination finite element method to calculate the Saint-Venant’s torsion problem including crack is proposed. In order to illustrate its application, the numerical examples for a torsion cylinder with crack are given and the numerical results are satisfactory.

Finite element modeling of nonlinear reaction–diffusion–advection systems of equations

2018 ◽  
Vol 28 (11) ◽  
pp. 2688-2715 ◽  
Author(s):  
Sanjay Komala Sheshachala ◽  
Ramon Codina
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Reaction Diffusion ◽  
Diffusion Reaction ◽  
Content Type ◽  
Numerical Examples ◽  
Stabilized Finite Element ◽  
Stabilized Finite Element Method ◽  
Nonlinear Reaction ◽  
Element Method

Purpose This paper aims to present a finite element formulation to approximate systems of reaction–diffusion–advection equations, focusing on cases with nonlinear reaction. The formulation is based on the orthogonal sub-grid scale approach, with some simplifications that allow one to stabilize only the convective term, which is the source of potential instabilities. The space approximation is combined with finite difference time integration and a Newton–Raphson linearization of the reactive term. Some numerical examples show the accuracy of the resulting formulation. Applications using classical nonlinear reaction models in population dynamics are also provided, showing the robustness of the approach proposed. Design/methodology/approach A stabilized finite element method for advection–diffusion–reaction equations to the problem on nonlinear reaction is adapted. The formulation designed has been implemented in a computer code. Numerical examples are run to show the accuracy and robustness of the formulation. Findings The stabilized finite element method from which the authors depart can be adapted to problems with nonlinear reaction. The resulting method is very robust and accurate. The framework developed is applicable to several problems of interest by themselves, such as the predator–prey model. Originality/value A stabilized finite element method to problems with nonlinear reaction has been extended. Original contributions are the design of the stabilization parameters and the linearization of the problem. The application examples, apart from demonstrating the validity of the numerical model, help to get insight in the system of nonlinear equations being solved.

A background cell-based numerical integration for B-spline wavelet on the interval finite element method

2019 ◽  
Vol 36 (2) ◽  
pp. 569-598 ◽  
Author(s):  
Shashank Vadlamani ◽  
Arun C.O.
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Quadrature Rule ◽  
Gauss Quadrature ◽  
Spline Wavelet ◽  
Content Type ◽  
B Spline ◽  
Numerical Examples ◽  
Wavelet Finite Element ◽  
Element Method

Purpose The purpose of this paper is to discuss about evaluating the integrals involving B-spline wavelet on the interval (BSWI), in wavelet finite element formulations, using Gauss Quadrature. Design/methodology/approach In the proposed scheme, background cells are placed over each BSWI element and Gauss quadrature rule is defined for each of these cells. The nodal discretization used for BSWI WFEM element is independent to the selection of number of background cells used for the integration process. During the analysis, background cells of various lengths are used for evaluating the integrals for various combination of order and resolution of BSWI scaling functions. Numerical examples based on one-dimensional (1D) and two-dimensional (2D) plane elasto-statics are solved. Problems on beams based on Euler Bernoulli and Timoshenko beam theory under different boundary conditions are also examined. The condition number and sparseness of the formulated stiffness matrices are analyzed. Findings It is found that to form a well-conditioned stiffness matrix, the support domain of every wavelet scaling function should possess sufficient number of integration points. The results are analyzed and validated against the existing analytical solutions. Numerical examples demonstrate that the accuracy of displacements and stresses is dependent on the size of the background cell and number of Gauss points considered per background cell during the analysis. Originality/value The current paper gives the details on implementation of Gauss Quadrature scheme, using a background cell-based approach, for evaluating the integrals involved in BSWI-based wavelet finite element method, which is missing in the existing literature.

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.

scholarly journals A Hybrid Smoothed Finite Element Method for Predicting the Sound Field in the Enclosure with High Wave Numbers

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Haitao Wang ◽  
Xiangyang Zeng ◽  
Ye Lei
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Sound Field ◽  
Numerical Dispersion ◽  
Computational Accuracy ◽  
Dispersion Error ◽  
High Wave ◽  
Wave Numbers ◽  
Smoothed Finite Element Method ◽  
Element Method

Wave-based methods for acoustic simulations within enclosures suffer the numerical dispersion and then usually have evident dispersion error for problems with high wave numbers. To improve the upper limit of calculating frequency for 3D problems, a hybrid smoothed finite element method (hybrid SFEM) is proposed in this paper. This method employs the smoothing technique to realize the reduction of the numerical dispersion. By constructing a type of mixed smoothing domain, the traditional node-based and face-based smoothing techniques are mixed in the hybrid SFEM to give a more accurate stiffness matrix, which is widely believed to be the ultimate cause for the numerical dispersion error. The numerical examples demonstrate that the hybrid SFEM has better accuracy than the standard FEM and traditional smoothed FEMs under the condition of the same basic elements. Moreover, the hybrid SFEM also has good performance on the computational efficiency. A convergence experiment shows that it costs less time than other comparison methods to achieve the same computational accuracy.

Smoothed finite element method for analysis of multi-layered systems – Applications in biomaterials

2016 ◽  
Vol 168 ◽  
pp. 16-29 ◽  
Author(s):  
Eric Li ◽  
Junning Chen ◽  
Zhongpu Zhang ◽  
Jianguang Fang ◽  
G.R. Liu ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Layered Systems ◽  
Smoothed Finite Element Method ◽  
Element Method
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