三维势流场的比例边界有限元求解方法  

Computation of potential flow around three-dimensional obstacles by a scaled boundary finite-element method

作　　者：滕斌[1] 赵明[1] 何广华[1] 

机构地区：[1]大连理工大学海岸和近海工程国家重点实验室,辽宁大连116024

出　　处：《计算力学学报》2006年第3期301-306,共6页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(1037202050025924)资助项目

摘　　要：比例边界有限元法(SBFEM)是线性偏微分方程的一种新的数值求解方法。该方法只对计算域边界利用Galerkin方法进行数值离散,相对于有限元方法(FEM)减少了一个空间坐标的维数,而在减少的空间坐标方向利用解析方法进行求解;相对于边界元法(BEM),比例边界有限元方法不需要基本解,避免了奇异积分的计算,所以它结合了有限元和边界元方法的优点。本文建立了利用比例边界有限元法求解三维Laplace方程的数值模型并用于计算三维物体周围的水流场,将计算结果与解析解和边界元方法进行了对比,结果表明此方法可以很好地模拟水流场,且具有较高的计算精度。The scaled boundary finite-element method is a novel semi-analytical technique for solving the linear partial differential equation. The method discretizes the governing equation only on the boundary of the computational domain. Comparing with the finite-element method, the method reduces the spatial dimension by one, and the analytical procedure is applied at the reduced direction instead. Comparing with the boundary element method, the scaled boundary finite-element needs not the fundamental solution and thus no singular integrals must be evaluated. So the scaled boundary finite-element combines the advantages of the finite-element method and the boundary element method. A numerical model of the scaled boundary finite-element method is established to solve the three-dimensional Laplace equation in this paper, and further the flow around an obstacle is computed by this method. The numerical solutions are compared to the analytical ones and those from a boundary element method. The comparisons show that the present method can well simulate the flow field, and its accuracy is high.

关 键 词：比例边界有限元法 LAPLACE方程 势流 

分 类 号：O241[理学—计算数学]