A ROBUST HIGH-ORDER COMPACT METHOD FOR THE THREE DIMENSIONAL NONLINEAR BIHARMONIC EQUATIONS

Abstract

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.