In this paper, Radial point collocation method （RPCM）, a kind of meshfree method, is applied to solve convectiondiffusion problem. The main feature of this approach is to use the interpolation schemes in local suppo...In this paper, Radial point collocation method （RPCM）, a kind of meshfree method, is applied to solve convectiondiffusion problem. The main feature of this approach is to use the interpolation schemes in local supported domains based on radial basis functions. As a result, this method is local and hence the system matrix is banded which is very attractive for practical engineering problems. In the numerical examination, RPCM is applied to solve non-linear convection-diffusion 2D Burgers equations. The results obtained by RPCM demonstrate the accuracy and efficiency of the proposed method for solving transient fluid dynamic problems. A fictitious point scheme is adopted to improve the solution accuracy while Neumann boundary conditions exist. The meshfree feature of the nresent method is verv attractive in solving comnutational fluid nroblems.展开更多
One of major difficulties in the implementation of meshfree methods using the mov- ing least square （MLS） approximation, such as element-free Galerkin method （EFG）, is the im- position of essential boundary condit...One of major difficulties in the implementation of meshfree methods using the mov- ing least square （MLS） approximation, such as element-free Galerkin method （EFG）, is the im- position of essential boundary conditions as the approximations do not pass through the nodal parameter values. Another class of meshfree methods based on the radial basis point interpola- tion can satisfy the essential boundary conditions exactly since its approximation function passes through each node in an influence domain and thus its shape functions possess the properties of delta function. In this paper, a coupled element-free Galerkin（EFG）-radial point interpola- tion method （RPIM） is proposed to enhance their advantages and avoid their disadvantages. Discretized equations of equilibrium are obtained in the RPIM region and the EFG region, respectively. Then a collocation approach is introduced to couple the RPIM and the EFG method. This method satisfies the linear consistency exactly and can maintain the stiffness matrix symmetric. Numerical tests show that this method gives reasonably accurate results consistent with the theory.展开更多
基金Project (No. 10572128) supported by the National Natural ScienceFoundation of China
文摘In this paper, Radial point collocation method （RPCM）, a kind of meshfree method, is applied to solve convectiondiffusion problem. The main feature of this approach is to use the interpolation schemes in local supported domains based on radial basis functions. As a result, this method is local and hence the system matrix is banded which is very attractive for practical engineering problems. In the numerical examination, RPCM is applied to solve non-linear convection-diffusion 2D Burgers equations. The results obtained by RPCM demonstrate the accuracy and efficiency of the proposed method for solving transient fluid dynamic problems. A fictitious point scheme is adopted to improve the solution accuracy while Neumann boundary conditions exist. The meshfree feature of the nresent method is verv attractive in solving comnutational fluid nroblems.
基金supported by the National Natural Science Foundation of China (No. 11172192)the College Postgraduate Research and Innovation Project of Jiangsu Province (No. CX10B 029Z)the Nominated Excellent Thesis for PHD Candidates Program of Soochow University (No. 23320957)
文摘One of major difficulties in the implementation of meshfree methods using the mov- ing least square （MLS） approximation, such as element-free Galerkin method （EFG）, is the im- position of essential boundary conditions as the approximations do not pass through the nodal parameter values. Another class of meshfree methods based on the radial basis point interpola- tion can satisfy the essential boundary conditions exactly since its approximation function passes through each node in an influence domain and thus its shape functions possess the properties of delta function. In this paper, a coupled element-free Galerkin（EFG）-radial point interpola- tion method （RPIM） is proposed to enhance their advantages and avoid their disadvantages. Discretized equations of equilibrium are obtained in the RPIM region and the EFG region, respectively. Then a collocation approach is introduced to couple the RPIM and the EFG method. This method satisfies the linear consistency exactly and can maintain the stiffness matrix symmetric. Numerical tests show that this method gives reasonably accurate results consistent with the theory.
