三维势流场的比例边界有限元求解方法

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。

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

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.