Abstract
We extend the explicit hybrid numerical method for solving the Allen–Cahn (AC) equation to the scheme for the nonlocal AC equation with isotropically symmetric interfacial energy. The proposed method combines the previous explicit hybrid method with a space-time dependent Lagrange multiplier which enforces conservation of mass. We perform numerical tests for the area-preserving mean curvature flow, which is the basic property of the nonlocal AC equation. The numerical results show good agreement with the theoretical solutions. Furthermore, to demonstrate the usefulness of the proposed method, we perform a cell growth simulation in a complex domain. Because the proposed numerical scheme is explicit, it is remarkably simple to implement the numerical solution algorithm on complex discrete domains.
Highlights
The phase-field model is one of the representatives of the interface capturing approach and has been widely investigated in order to interpret the interfacial dynamics [1]
We present the explicit hybrid numerical solution algorithm for solving the nonlocal AC equation, which is an extension of the algorithm for the AC equation [4]
We proposed the explicit hybrid numerical method for the nonlocal AC equation with isotropically symmetric interfacial energy in this paper
Summary
The phase-field model is one of the representatives of the interface capturing approach and has been widely investigated in order to interpret the interfacial dynamics [1]. The AC equation is not conservative, and Brassel and Bretin [10] proposed the nonlocal AC equation with the time-dependent Lagrange multiplier which preserves the shape of interface in local coordinates unlike the multiplier presented earlier in [11]. This equation has both nonlocal and local effects, even though the mass conservation property can be achieved in the local AC equation; we adopt the nonlocal
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