A hybrid vertex-centered finite volume/element method for viscous incompressible flows on non-staggered unstructured meshes

This paper proposes a hybrid vertex-centered fi- nite volume/finite element method for solution of the two di- mensional （2D） incompressible Navier-Stokes equations on unstructured grids. An incremental pressure fractional step method is adopted to handle the velocity-pressure coupling. The velocity and the pressure are collocated at the node of the vertex-centered control volume which is formed by join- ing the centroid of cells sharing the common vertex. For the temporal integration of the momentum equations, an im- plicit second-order scheme is utilized to enhance the com- putational stability and eliminate the time step limit due to the diffusion term. The momentum equations are discretized by the vertex-centered finite volume method （FVM） and the pressure Poisson equation is solved by the Galerkin finite el- ement method （FEM）. The momentum interpolation is used to damp out the spurious pressure wiggles. The test case with analytical solutions demonstrates second-order accuracy of the current hybrid scheme in time and space for both veloc- ity and pressure. The classic test cases, the lid-driven cavity flow, the skew cavity flow and the backward-facing step flow, show that numerical results are in good agreement with the published benchmark solutions.

A Compact Difference Scheme for Multi-point Boundary Value Problems of Heat Equations

In this paper,a compact difference scheme is established for the heat equations with multi-point boundary value conditions.The truncation error of the difference scheme is O(τ2+h^4),where t and h are the temporal step size and the spatial step size.A prior estimate of the difference solution in a weighted norm is obtained.The unique solvability,stability and convergence of the difference scheme are proved by the energy method.The theoretical statements for the solution of the difference scheme are supported by numerical examples.

Finite Element Simulation of the Polymeric Liquid Flow in Coat-hanger Die

A three - dimenslonal finite element model is developed to deal with the polymeric liquid flow in coat - hanger die. This model is used to predict the flow behavior of the 2％ CMC/watsr solution in the coat - hanger die with linearly taper manifolds and its validity is experimentally verified quantitatively and qualitatively by using Laser Doppler Velocimetry and Particle Image Velocimetry respectively.

Construction of n-sided polygonal spline element using area coordinates and B-net method

In general, triangular and quadrilateral elements are commonly applied in two-dimensional finite element methods. If they are used to compute polycrystalline materials, the cost of computation can be quite significant. Polygonal elements can do well in simulation of the materials behavior and provide greater flexibility for the meshing of complex geometries. Hence, the study on the polygonal element is a very useful and necessary part in the finite element method. In this paper, an n-sided polygonal element based on quadratic spline interpolant, denoted by PS2 element, is presented using the triangular area coordinates and the B-net method. The PS2 element is conforming and can exactly model the quadratic field. It is valid for both convex and non-convex polygonal element, and insensitive to mesh distortions. In addition, no mapping or coordinate transformation is required and thus no Jacobian matrix and its inverse are evaluated. Some appropriate examples are employed to evaluate the performance of the proposed element.

An explicit finite volume element method for solving characteristic level set equation on triangular grids

Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow phenomena.This paper presents a characteristic level set equation which is derived from the two-dimensional level set equation by using the characteristic-based scheme.An explicit finite volume element method is developed to discretize the equation on triangular grids.Several examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time.The proposed level set method is also coupled with the Navier-Stokes equations for two-phase immiscible incompressible flow analysis with surface tension.The Rayleigh-Taylor instability problem is used to test and evaluate the effectiveness of the proposed scheme.

Two 8-node quadrilateral spline elements by B-net method

Isoparametric quadrilateral elements are widely used in the finite element method, but the accuracy of the isoparametric quadrilateral elements will drop obviously deteriorate due to mesh distortions. Spline functions have some properties of simplicity and conformality. Two 8-node quadrilateral elements have been developed using the trian- gular area coordinates and the B-net method, which can ex- actly model the quadratic field for both convex and concave quadrangles. Some appropriate examples are employed to evaluate the performance of the proposed elements. The nu- merical results show that the two spline elements can obtain solutions which are highly accurate and insensitive to mesh distortions.

Pseudo-beam method for compressive buckling characteristics analysis of space inflatable load-carrying structures

This paper extends Le van＇s work to the case of nonlinear problem and the complicated configuration. The wrinkling stress distribution and the pressure effects are also included in our analysis. Pseudo-beam method is presented based on the inflatable beam theory to model the inflatable structures as a set of inflatable beam elements with a prestressed state. In this method, the discretized nonlinear equations are given based upon the virtual work principle with a 3-node Timoshenko＇s beam model. Finite element simulation is performed by using a 3-node BEAM189 element incorporating ANSYS nonlinear program. The pressure effect is equivalent included in our method by modifying beam element cross-section parameters related to pressure. A benchmark example, the bending case of an inflatable cantilever beam, is performed to verify the accuracy of our proposed method. The comparisons reveal that the numerical results obtained with our method are close to open published analytical and membrane finite element results. The method is then used to evaluate the whole buckling and the loadcarrying characteristics of an inflatable support frame subjected to a compression force. The wrinkling stress and region characteristics are also shown in the end. This method gives better convergence characteristics, and requires much less computation time. It is very effective to deal with the whole load-carrying ability analytical problems for large scale inflatable structures with complex configuration.

Parametric study on single shot peening by dimensional analysis method incorporated with finite element method

Shot peening is a widely used surface treatment method by generating compressive residual stress near the surface of metallic materials to increase fatigue life and re- sistance to corrosion fatigue, cracking, etc. Compressive re- sidual stress and dent profile are important factors to eval- uate the effectiveness of shot peening process. In this pa- per, the influence of dimensionless parameters on maximum compressive residual stress and maximum depth of the dent were investigated. Firstly, dimensionless relations of pro- cessing parameters that affect the maximum compressive residual stress and the maximum depth of the dent were de- duced by dimensional analysis method. Secondly, the in- fluence of each dimensionless parameter on dimensionless variables was investigated by the finite element method. Fur- thermore, related empirical formulas were given for each di- mensionless parameter based on the simulation results. Fi- nally, comparison was made and good agreement was found between the simulation results and the empirical formula, which shows that a useful approach is provided in this pa- per for analyzing the influence of each individual parameter.

Three-dimensional hydrodynamic model of Xiamen waters

A semi-implicit and Eulerian - Lagrangian finite difference method for three-dimensionalshallow flow has been extended to a more complete system of equations incorporating second-moment turbulence closure model and transport equations of salinity and temperature. The simulation for flooding and drying of mudflats has been improved. The model is applied to Xiamen waters. Based on extensive survey data, water level elevation, temperature and salinity field along the eastern open boundary and at the Jiulong River inlets and runoffs are analyzed, specified and calibrated. The computed results show good agreement with the measured data, reproduce flooding, emergence of large and complex mudflat region.

Theoretical analysis of the sound absorption characteristics of periodically stiffened micro-perforated plates

The vibro-acoustic responses and sound absorption characteristics of two kinds of periodically stiffened micro-perforated plates are analyzed theoretically. The connected periodical structures of the stiffened plates can be ribs or block-like structures. Based on fundamental acoustic formulas of the micro-perforated plate of Maa and Takahashi, semi-analytical models of the vibrating stiffened plates are developed in this paper. Approaches like the space harmonic method, Fourier transforms and finite element method （FEM） are adopted to investigate both kinds of the stiffened plates. In the present work, the vibro-acoustic responses of micro-perforated stiffened plates in the wavenumber space are expressed as functions of plate displacement amplitudes. After approximate numerical solutions of the amplitudes, the vibration equations and sound absorption coefficients of the two kinds of stiffened plates in the physical space are then derived by employing the Fourier inverse transform. In numerical examples, the effects of some physical parameters, such as the perforation ratio, incident angles and periodical distances etc., on the sound absorption performance are examined. The proposed approaches are also validated by comparing the present results with solutions of Takahashi and previous studies of stiffened plates. Numerical results indicate that the flexural vibration of the plate has a signif- icant effect on the sound absorption coefficient in the water but has little influence in the air.

CFD simulation of an industrial hydrocyclone with Eulerian-Eulerian approach: A case study

In the present study, a three-dimensional computational fluid dynamics simulation together with experimental field measurements was applied to optimize the performance of an industrial hydrocyclone at Sarcheshmeh copper complex. In the simulation, the Eulerian–Eulerian approach was used for solid and liquid phases, the latter being water. In this approach, nine continuous phases were considered for the solid particles with different sizes and one continuous phase for water. The continuity and momentum equations with inclusion of buoyancy and drag forces were solved by the finite volume method. The k–e RNG turbulence model was used for modeling of turbulency. There was a good agreement between the simulation results and the experimental data. After validation of the model accuracy, the effect of inlet solid percentage, pulp inlet velocity, rod inserting in the middle of the hydrocyclone and apex diameter on hydrocyclone performance was investigated. The results showed that by decreasing the inlet solid percentage and increasing the pulp inlet velocity, the efficiency of hydrocyclone increased. Decreasing the apex diameter caused an increase in the hydrocyclone efficiency.

NUMERICAL SIMULATION OF STRESS-STRAIN DISTRIBUTIONS FOR WELD METAL SOLIDIFICATION CRACKING IN STAINLESS STEEL

This paper analyzed the characteristics of welding solidification crack of stainless steels,and clearly re- vealed the the of the deformation in the molten - the pool and the solidification shrinkage on the stress - strain fields in the trail of molten - weld pool.Moreover, rheologic properties of the alloys in solid - liquid zone were also obtained by measuring the hading and unloading deform curves of the steels.As a result, a numerical model for simulation of stress - strain distributions of welding solidifi- cation crack was developed. On the basis of the model,the thesis simulated the driving force of solidifi- cation crack of stainless steels, that is, stress - strain fields in the trail of molten-weld pool with fi- nite element method.

A Three-dimensional Forecasting Model for Oil Spill

A 3-D forecasting model for oil-spill is developed using the finite difference method to numerically solve the shallow water equation. The instantaneous flow distribution in the studied area is calculated and the trajectory of the oil-slick centroid is predicted by means of Lagrange’s method. The computed results agree with the observed data well, this shows that this 3-D forecasting model has high accuracy.

Finite element analysis of chip formation and residual stresses induced by sequential cutting in side milling with microns to sub- micron uncut chip thickness and finite cutting edge radius

In this paper, the effect of four sequential cuts in side milling of Ti6Al4V on chip formation and residual stresses （RS） are investigated using finite element method （FEM）. While the open literature is limited mainly to the studies of orthogonal sequential cutting with the constant uncut chip thickness greater than 0.01 mm, it is suggested herein to investigate not only the variable uncut chip thickness which characterises the down milling process, but also the uncut chip thickness in the sub-micron range using a finite cutting edge radius. For the resulting ductile machining regime, the characteristics of the chip mor- phology, the force profiles, the plastic deformation and temperature distributions have been analyzed. Furthermore, this study revealed that the RS should be extracted toward the area where the insert exits the workpiece in the FE simulation of the down-milling process. The simulation of a number of sequential cuts due to the consecutive engagements of the insert is required in order to capture the gradual accumulation of the RS before reaching an asymptotic convergence of the RS profile. The predicted RS are in reasonable agreement with the experimental results.

h-P Finite Element Approximation for Full-Potential Electronic Structure Calculations

The(continuous) finite element approximations of different orders for the computation of the solution to electronic structures were proposed in some papers and the performance of these approaches is becoming appreciable and is now well understood.In this publication,the author proposes to extend this discretization for full-potential electronic structure calculations by combining the refinement of the finite element mesh,where the solution is most singular with the increase of the degree of the polynomial approximations in the regions where the solution is mostly regular.This combination of increase of approximation properties,done in an a priori or a posteriori manner,is well-known to generally produce an optimal exponential type convergence rate with respect to the number of degrees of freedom even when the solution is singular.The analysis performed here sustains this property in the case of Hartree-Fock and Kohn-Sham problems.

DISTURBED SPARSE LINEAR EQUATIONS OVER THE 0-1 FINITE FIELD

In this paper, disturbed sparse linear equations over the 0-1 finite field are considered. Due to the special structure of the problem, the standard alternating coordinate method can be implemented in such a way to yield a fast and efficient algorithm. Our alternating coordinate algorithm makes use of the sparsity of the coefficient matrix and the current residuals of the equations. Some hybrid techniques such as random restarts and genetic crossovers are also applied to improve our algorithm.

Compliance-based testing method for fatigue crack propagation rates of mixed-modeⅠ-Ⅱcracks

Mixed-mode I-II crack-based fatigue crack propagation(FCPⅠ-Ⅱ)usually occurs in engineering structures;however,no theoretical formula or effective compliance test methods have been established for FCPI-IIto date.For mixed-mode I-II flawed components,based on the principle of mean-value energy equivalence,we propose a theoretical method to describe the relationship between material elastic parameters,geometrical dimensions,load(or displacement),and energy.Based on the maximum circumferential stress criterion,we propose a uniform compliance model for compact tensile shear(CTS)specimens with horizontal cracks deflecting and propagating(flat-folding propagation)under different loading angles,geometries,and materials.Along with an innovative design of the fixture of CTS specimens used for FCPI-IItests,we develop a new compliancebased testing method for FCPⅠ-Ⅱ.For the 30Cr2Ni4MoV rotor steel,the FCP rates of modeⅠ,modeⅡ,and mixed-modeⅠ-Ⅱcracks were obtained via FCP tests using compact tension,Arcan,and CTS specimens,respectively.The obtained da/d N versusΔJ curves of the FCP rates are close.The loading angleαand dimensionless initial crack length a0/W demonstrated negligible effects on the FCP rates.Hence,the FCP rates of mode I crack can be used to predict the residual life of structural crack propagation.

Modeling of fluid dynamics interacting with ductile fraction propagation in high pressure pipeline

This paper presents a computational model for the fluid dynamics in a fractured ductile pipe under high pressure. The pressure profile in front of the crack tip, which is the driving source of crack propagation, is computed using a nonlinear wave equation. The solution is coupled with a one dimensional choked flow analysis behind the crack. The simulation utilizes a high order optimized prefactored compact-finite volume method in space, and low dispersion and dissipation Runge-Kutta in time. As the pipe fractures the rapid depressurization take place inside the pipe and the propagation of the crack-induced waves strongly influences the outflow dynamics. Consistent with the experimental observation, the model predicts the expansion wave inside the pipe, and the reflection and outflow of the wave. The model also helps characterize the propagation of the crack dynamics and fluid flows around the tip of the crack.