A ROBUST HIGH-ORDER COMPACT METHOD FOR THE THREE DIMENSIONAL NONLINEAR BIHARMONIC EQUATIONS
A ROBUST HIGH-ORDER COMPACT METHOD FOR THE THREE DIMENSIONAL NONLINEAR BIHARMONIC EQUATIONS
复制标题
DOI：
10.1142/s0219876213500655
复制
发表时间：
2014-08
影响因子：
1.7
通讯作者：
S. Zhai;Xinlong Feng;Yinnian He
中科院分区：
文献类型：
--
作者：
S. Zhai;Xinlong Feng;Yinnian He
In this paper, a new family of fourth-order compact finite difference schemes are considered using coupled approach for numerical solutions of the three-dimensional (3D) linear biharmonic problems. A new fourth-order accurate algorithm is developed through the different composition of these schemes for 3D nonlinear biharmonic equations. And an optimal combination is found in numerical experiments. The main advantage of this algorithm is that it avoids the difficulties of constructing high order compact difference schemes for 3D nonlinear biharmonic equations. The numerical solutions of unknown variable and its first derivative and Laplacian are obtained. Finally, numerical experiments are conducted to show the solution accuracy and verify the validity of our new method, including the steady Navier–Stokes equation and Cahn–Hilliard equation.
