Spherulites are growth patterns of average spherical form which may occur in the polycrystallization of binary mixtures due to misoriented angles at low grain boundaries. The dynamic growth of spherulites can be described by a phase field model where the underlying free energy depends on two phase field variables, namely the local degree of crystallinity and the orientation angle. For the solution of the phase field model we suggest a splitting scheme based on an implicit discretization in time which decouples the model and at each time step requires the successive solution of an evolutionary inclusion in the orientation angle and an evolutionary equation in the local degree of crystallinity. The discretization in space is done by piecewise linear Lagrangian finite elements. The fully discretized splitting scheme amounts to the solution of two systems of nonlinear algebraic equations. For the numerical solution we suggest a predictor-corrector continuation method with the discrete time as a parameter featuring constant continuation as a predictor and a semismooth Newton method for the first system and the classical Newton method for the second system as a corrector. This allows an adaptive choice of the time steps. Numerical results are given for the formation of a Category 1 spherulite.

球晶是平均球形形式的生长模式，由于低晶界处的取向错误，可能会在二元混合物的多晶化过程中出现。球晶的动态生长可以通过相场模型来描述，其中潜在的自由能取决于两个相场变量，即局部结晶度和取向角。对于相场模型的求解，我们建议一种基于时间隐式离散化的拆分方案，该方案将模型解耦，并且在每个时间步都需要依次求解取向角中的演化包含项和局部角处的演化方程。结晶度。空间的离散化是通过分段线性拉格朗日有限元完成的。完全离散的分裂方案等于两个非线性代数方程组的解。对于数值解，我们建议以离散时间为参数的预测器-校正器连续方法，其特征为恒定连续作为预测器，对于第一个系统，半光滑牛顿法，对于第二个系统，使用经典牛顿法作为校正器。这允许对时间步长进行自适应选择。给出了形成1类球晶的数值结果。这允许对时间步长进行自适应选择。给出了形成1类球晶的数值结果。这允许对时间步长进行自适应选择。给出了形成1类球晶的数值结果。