CONSERVATIVE MULTIGRID METHODS FOR TERNARY CAHN-HILLIARD SYSTEMS ∗
CONSERVATIVE MULTIGRID METHODS FOR TERNARY CAHN-HILLIARD SYSTEMS ∗
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DOI：
10.4310/cms.2004.v2.n1.a4
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发表时间：
2004-03
影响因子：
1
通讯作者：
Junseok Kim;K. Kang;J. Lowengrub
中科院分区：
文献类型：
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作者：
Junseok Kim;K. Kang;J. Lowengrub
我们开发了一个保守的，二阶精确的全隐式离散的三元（三相）Cahn-Hilliard（CH）系统，有一个相关的离散能量泛函。这是我们对两相系统工作的扩展（13）。分析并证明了格式的收敛性。为了有效地解决离散系统的隐式时间水平，我们使用非线性多重网格方法。所得到的格式是有效的，鲁棒的，并且最多存在一阶时间步长的稳定性约束。我们证明了我们的计划数值收敛，我们提出了几个模拟的三元系统中的相变。
We develop a conservative, second order accurate fully implicit discretization of ternary (three-phase) Cahn-Hilliard (CH) systems that has an associated discrete energy functional. This is an extension of our work for two-phase systems (13). We analyze and prove convergence of the scheme. To efficiently solve the discrete system at the implicit time-level, we use a nonlinear multigrid method. The resulting scheme is efficient, robust and there is at most a 1 st order time step constraint for stability. We demonstrate convergence of our scheme numerically and we present several simulations of phase transitions in ternary systems.