グリッドレス法による 2 階微分の評価とその精度(流体工学, 流体機械)

抄録

Two gridless type methods for evaluating the second derivatives are presented. In the first method, the second derivatives are evaluated with evaluating the first derivatives of the derivatives. On the other hand, Laplace operators as well as the second derivatives are directly evaluated in the second method. The methods can be applied to numerical solutions of any partial differential equations on Cartesian grids, structured grids, and unstructured grids. In this paper, the methods are applied to Poisson equations. Numerical solutions are obtained and compared with analytic solutions on several levels of point density so that grid convergence studies of L₂ errors are carried out. The second order accuracy is confirmed for both the gridless methods, while the directly evaluating method of the Laplace operator is more effective than the successive evaluating method.