scholarly journals A Mixed Volume Element With Characteristic Mixed Volume Element for Contamination Transport Problem

2020 ◽  
Vol 12 (5) ◽  
pp. 1
Author(s):  
Yirang Yuan ◽  
Changfeng Li ◽  
Huailing Song ◽  
Tongjun Sun
Keyword(s):  
Mixed Volume ◽  
Volume Element ◽  
Transport Problem ◽  
Numerical Dispersion ◽  
Computational Accuracy ◽  
Surface Absorption ◽  
Computational Stability ◽  
Darcy Velocity ◽  
L2 Norm ◽  
Contamination Transport

Nonlinear systems of convection-dominated diffusion equations are used as the mathematical model of contamination transport problem which is an important topic in environ mental protection science. An elliptic equation defines the pressure, a convection-diffusion equation expresses the concentration of contamination, and an ordinary differential equation interprets the surface absorption concentration. The transport pressure appears in the equation of the concentration which determines the Darcy velocity and also controls the physical process. The method of conservative mixed volume element is used to solve the flow equation which improves the computational accuracy of Darcy velocity by one order. We use the mixed volume element with the characteristic to approximate the concentration. This method of characteristic not only preserves the strong computational stability at sharp front, but also eliminates numerical dispersion and nonphysical oscillation. In the present scheme, we could adopt a large step without losing accuracy. The diffusion is approximated by the mixed volume element. The concentration and its adjoint vector function are obtained simultaneously, and the locally conservative law is preserved. An optimal second order estimates in l2-norm is derived.

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.

A Comparison between Moving Least-Square Method and Natural Neighbour Interpolation

2013 ◽  
Vol 739 ◽  
pp. 653-656
Author(s):  
Zhi Feng Nie ◽  
Xing Long Li ◽  
Heng Heng Wu
Keyword(s):  
Computational Efficiency ◽  
Matrix Multiplication ◽  
Least Square Method ◽  
Matrix Inversion ◽  
Least Square ◽  
Shape Functions ◽  
Computational Accuracy ◽  
Computational Stability ◽  
Moving Least Square ◽  
Order Continuous

The construction procedures of shape functions in the moving least-square method (MLS) are complicated, in which many matrix multiplication and matrix inversion are included, so that the computational efficiency is low. Moreover, the choices of some parameters are influenced by the artificial factors, and the computational stability is poor. However, the construction procedures of shape functions in natural neighbour interpolation (NNI) are based on Voronoi diagram and its dual Delaunay triangulation, computational results are only related with the locations of the discretized nodes, and the computational stability is good. In order to study the differences in the computational accuracy, the computational efficiency, and the adaptability to the fitted objects between MLS-based shape functions andC1natural neighbour interpolant, the two higher-order continuous shape functions are introduced in surface fitting.

Numerical Study on Hydraulic Performances of Pump as Turbine With Forward-Curved Blades

2014 ◽  
Author(s):  
Tao Wang ◽  
Fanyu Kong ◽  
Sunsheng Yang ◽  
Yanxia Fu
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Numerical Simulations ◽  
Turbulence Model ◽  
Numerical Study ◽  
Internal Flow ◽  
Hydraulic Turbine ◽  
Experimental Results ◽  
Computational Accuracy ◽  
Computational Stability

A reserved running centrifugal pump can work as a hydraulic turbine with its wide application in industrial energy recovery and the development of micro-hydraulic power. In order to improve the efficiency from the point of turbine working condition, the impeller with forward-curved blades was designed and the hydraulic performances were further analyzed based on the commercial software ANSYS CFX 12.0 in this study. Moreover, to improve the computational accuracy of numerical simulations on turbines, the grid number, the turbulence model, the circumferential flow distribution in the clearance between the volute and the impeller as well as the grid distribution in the boundary layer were considered. According grid independency analysis, the 1.2 million grids’ number was assumed for numerical simulations. Considering the consuming time and computational stability, as well as the accuracy of the CFD calculation, the k–ε turbulence model was chosen for further calculations. The shaft power and the efficiency of the turbine were more close to the experimental data as the whole computational flow domain in the clearance between the volute and the impeller was connected on the impeller domain. Compared with the performance curves with or without grids in the boundary layer, the boundary layer with grids used in the PAT during numerical simulations was more close to the experimental one. Compared with the experimental data, the H-Q curves of the hydraulic performances of the turbine with forward-curved blades predicted by CFD were positioned under the experimental one. With respect to the efficiency of the turbine, the various ranges of the efficiency is less than 5%, even there is some deviations between the CFD and experimental results. Therefore, the good agreement of the hydraulic performances between CFD and experimental results in present study indicates that the proposed numerical methods can adequately capture the internal flow in a hydraulic turbine with forward-curved blades, and can also provide a reliable reference for the design of hydraulic turbines.

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