Numerical approximations for a new [formula omitted]-gradient flow based Phase field crystal model with precise nonlocal mass conservation

Abstract

In this paper, we derive a new phase field crystal model based on the L2-gradient flow approach, where the total mass of atoms is conserved through a nonlocal Lagrange multiplier. We develop a second-order, unconditionally energy stable scheme by combining the IEQ approach with the stabilization technique, where two extra stabilization terms are added to enhance the stability and keep the required accuracy while using large time steps. The unconditional energy stability of the algorithm is proved rigorously. Through the comparisons with the classical H−1-gradient flow based phase field crystal model and several other type numerical schemes for simulating some benchmark numerical examples in 2D and 3D, we demonstrate the robustness of the new model, as well as the stability and the accuracy of the developed scheme, numerically.