B-SPLINE PATCHES AND TRANSFINITE INTERPOLATION METHOD FOR PDE CONTROLLED SIMULATION

This paper is to discuss an approach which combines B-spline patches and transfinite interpolation to establish a linear algebraic system for solving partial differential equations and modify the WEB-spline method developed by Klaus Hollig to derive this new idea. First of all, the authors replace the R-function method with transfinite interpolation to build a function which vanishes on boundaries. Secondly, the authors simulate the partial differential equation by directly applying differential opera- tors to basis functions, which is similar to the RBF method rather than Hollig＇s method. These new strategies then make the constructing of bases and the linear system much more straightforward. And as the interpolation is brought in, the design of schemes for solving practical PDEs can be more flexi- ble. This new method is easy to carry out and suitable for simulations in the fields such as graphics to achieve rapid rendering. Especially when the specified much faster than WEB-spline method. precision is not very high, this method performs

On the Transfinite interpolation and Approximation by a Class of Periodic Bivariate Cubic Splines on Type-Ⅱ Triangulation

In this paper, we discuss the transfinite interpolation and approxiulation by a class of periodic bivariate cubic Splines on type-Ⅱ triangulated partition △（2）mn. the existence, uniqueness and the expression of interpolation periodic bivariate splines are given. And at last, we estimate their approximation order.

An Efficient Dynamic Mesh Generation Method for Complex Multi-Block Structured Grid

Aiming at a complex multi-block structured grid,an efficient dynamic mesh generation method is presented in this paper,which is based on radial basis functions(RBFs)and transfinite interpolation(TFI).When the object is moving,the multi-block structured grid would be changed.The fast mesh deformation is critical for numerical simulation.In this work,the dynamic mesh deformation is completed in two steps.At first,we select all block vertexes with known deformation as center points,and apply RBFs interpolation to get the grid deformation on block edges.Then,an arc-lengthbased TFI is employed to efficiently calculate the grid deformation on block faces and inside each block.The present approach can be well applied to both two-dimensional(2D)and three-dimensional(3D)problems.Numerical results show that the dynamic meshes for all test cases can be generated in an accurate and efficient manner.

A compressing and saving method for structured grid data based on block construction

The increasing grid data in CFD simulation has brought some new difficulties and challenges,such as high storage cost,low transmission efficiency.In order to overcome these problems,a novel method for compressing and saving the structured grid are proposed.In the present method,the geometric coordinates of the six logical domains of one grid block is saved instead of all grid vertex coordinates to reduce the size of the structured grid file when the grid is compressed.And all grid vertex coordinates are recovered from the compressed data with the use of the transfinite interpolation algorithm when the grid is decompressed.Firstly,single-block grid cases with different edge vertexes are tested to investigate the compression effect.The test results show that a higher compression ratio will be obtained on a larger grid.Secondly,further theoretical analysis is carried out to investigate the effects of parameters on grid compression.The analysis on single-block grid compression shows that the compression ratio is proportionate to the cubic root of the number of total vertexes.The highest compression ratio of single-block grid is obtained when the numbers of vertexes in three logical directions are equal.The analysis on multi-block grid compression shows that a higher compression ratio will be obtained when a larger difference of total vertexes number exists among the grid blocks.Finally,multi-blockgrids of two industrial aircraft configurations are compressed to validate the method.The compression results demonstrate that the present method has an excellent ability on structured grid compression.For a million-vertex structured grid,more than 80 percent disk space can be saved after compression.

A new grid deformation technology with high quality and robustness based on quaternion

Quality and robustness of grid deformation is of the most importance in the field of aircraft design, and grid in high quality is essential for improving the precision of numerical simulation. In order to maintain the orthogonality of deformed grid, the displacement of grid points is divided into rotational and translational parts in this paper, and inverse distance weighted interpolation is used to transfer the changing location from boundary grid to the spatial grid. Moreover, the deformation of rotational part is implemented in combination with the exponential space mapping that improves the certainty and stability of quaternion interpolation. Furthermore, the new grid deformation technique named ‘‘layering blend deformation＇＇ is built based on the basic quaternion technique, which combines the layering arithmetic with transfinite interpolation（TFI） technique. Then the proposed technique is applied in the movement of airfoil, parametric modeling, and the deformation of complex configuration, in which the robustness of grid quality is tested. The results show that the new method has the capacity to deal with the problems with large deformation, and the ‘‘layering blend deformation＇＇ improves the efficiency and quality of the basic quaternion deformation method significantly.