THE MESHLESS VIRTUAL BOUNDARY METHOD AND ITS APPLICATIONS TO 2D ELASTICITY PROBLEMS

A novel numerical method for eliminating the singular integral and boundary effect is processed. In the proposed method, the virtual boundaries corresponding to the numbers of the true boundary arguments are chosen to be as simple as possible. An indirect radial basis function network （IRBFN） constructed by functions resulting from the indeterminate integral is used to construct the approaching virtual source functions distributed along the virtual boundaries. By using the linear superposition method, the governing equations presented in the boundaries integral equations （BIE） can be established while the fundamental solutions to the problems are introduced. The singular value decomposition （SVD） method is used to solve the governing equations since an optimal solution in the least squares sense to the system equations is available. In addition, no elements are required, and the boundary conditions can be imposed easily because of the Kronecker delta function properties of the approaching functions. Three classical 2D elasticity problems have been examined to verify the performance of the method proposed. The results show that this method has faster convergence and higher accuracy than the conventional boundary type numerical methods.

Optimum Tactics of Parallel Multi-Grid Algorithm with Virtual Boundary Forecast Method Running on a Local Network with the PVM Platform

In this paper, an optimum tactic of multi-grid parallel algorithmwith virtual boundary forecast method is disscussed, and a two-stage implementationis presented. The numerical results of solving a non-linear heat transfer equationshow that the optimum implementation is much better than the non-optimum one.

WAVE SUPERPOSITION METHOD BASED ON VIRTUAL SOURCE BOUNDARY WITH COMPLEX RADIUS VECTOR FOR SOLVING ACOUSTIC RADIATION PROBLEMS

By virtue of the comparability between the wave superposition method and the dynamic analysis of structures, a general format for overcoming the non-uniqueness of solution induced by the wave superposition method at the eigenfrequencies of the corresponding interior problems is proposed. By adding appropriate damp to the virtual source system of the wave superposition method, the unique solutions for all wave numbers can be ensured. Based on this thought, a novel method-wave superposition method with complex radius vector is constructed. Not only is the computational time of this method approximately equal to that of the standard wave superposition method, but also the accuracy is much higher compared with other correlative methods. Finally, by taking the pulsating sphere and oscillating sphere as examples, the results of calculation show that the present method can effectively overcome the non-uniqueness problem.

A Forced System of Two Cylinders with Various Spacings

The spectrum characteristics and wake structures for a circular cylinder oscillating in a wake are investigated by use of the currently modified virtual boundary method. A forced system of two cylinders with a small spacing (the downstream one is made to oscillate in the transverse direction) is studied and interesting flow characteristics are observed. A vortex switch and the change of vortex modes (between 2S mode and 2P mode) are observed in the “lock in' region. Vortex bands are formed and lost with the increasing excitation frequency. Information concerning saddle points in the flow field is obtained for different excitation frequencies. For a forced system of two cylinders with a large spacing, the upstream cylinder sheds vortexes because there is no downstream cylinder oscillating in the wake. No distinct “lock in' response is found for the downstream cylinder.

Three-Dimensional Instability of Flow Around Two Circular Cylinders in Tandem Arrangement

The spatial evolution of vortices and transition to three-dimensionality in the wake of two circular cylinders in tandem arrangement have been numerically studied. An improved virtual body method developed from the virtual boundary method is used here. A Reynolds number range between 220 and 270 has been considered, and the spacing between two cylinders is selected as L/D=3 and L/D=3.5. When L/D=3, the secondary vortices of Mode-A are seen to appear at Re=240 and persist over the range of the Reynolds number of 240～270. When L/D=3.5, the similar critical Reynolds number has been found at Re=250. No obvious discontinuity has been found in the Strouhal-Reynolds number relationship, and this is different from three-dimensional flow around a single cylinder at the critical Reynolds number. The spanwise wavelength is about four times the diameter of the cylinder, and it is the characteristic wavelength for Mode-A instability. This paper can give some foremost insight into the three-dimensional instability of flow by complicated geometrical configuration.

UNIFIED WAY FOR DEALING WITH THREE-DIMENSIONAL PROBLEMS OF SOLID ELASTICITY

Unified way for dealing with the problems of three dimensional solid, each type of plates and shells etc. was presented with the virtual boundary element least, squares method(VBEM). It proceeded from the differential equations of three-dimensional theory of elasticity and employs the Kelvin solution and the least squares method, It is advantageous to the establishment of the models of a software for general application to calculate each type of three-dimensional problems of elasticity. Owing to directly employing the Kelvin solution and not citing any hypothesis, the numerical results of the method should be better than any others. The merits of the method are highlighted in comparison with the direct formulation of boundary element method (BEM). It is shown that coefficient matrix is symmetric and the treatment of singular integration is rendered unnecessary in the presented method. The examples prove the efficiency and calculating precision of the method.

THREE-DIMENSIONAL FLOW AROUND TWO TANDEM CIRCULAR CYLINDERS WITH VARIOUS SPACING AT Re=220

The flow around two tandem circular cylinders was studied by a three-dimensional numerical simulation of the Navier-Stokes equations at Re=220 . The improved virtual boundary method was applied to model the no-slip boundary condition of the cylinders. The results show that as the spac ing ratio L/D≥4 , the three dimensionality occurs in the wake. When L/D≤3.5 the wake keeps a two-dimensional state at the Reynolds number Re=220 . The critical spacing for the appearance of three-dimensional instability obtained is at the range 3.5〈 L/D 〈 4, similar to the critical spacing found in two-dimensional case. Two sources of instability from upstream and downstream cylinder generate a complicat ed vortex structures in the wake, investigated by streamlines topology analysis in the streamwise plane. Many other interesting problems were also addressed in this paper.