Numerical simulation of the three dimensional AllenCahn equation by the high-order compact ADI method
In this paper, a new linearized high-order compact difference method is presented for numerical simulation of three dimensional (3D) AllenCahn equation with three kinds of boundary conditions. The method, which is based on the CrankNicholson/AdamsBashforth scheme combined with the DouglasGunn ADI method, is second order accurate in time and fourth order accurate in space and energy degradation. The main advantages of this method is that the nonlinear penalty term f(u) f ( u ) is linear and an extra stabilizing term is added to alleviate the stability constraint while maintaining accuracy and simplicity. Numerical experiments are given to demonstrate the validity and applicability of the new method.
adi method three kinds of boundary conditions energy degradation 3d allencahn equation linear difference scheme