We present a general strategy for developing structure and property preserving numerical algorithms for thermodynamically consistent models of incompressible multiphase polymer solutions with a variable mobility. We first present a formalism to derive thermodynamically consistent, incompressible, multiphase polymer models. Then, we develop the general strategy, known as the supplementary variable method, to devise thermodynamically consistent numerical approximations to the models. We illustrate the numerical strategy using newly developed models of incompressible diblock copolymer solutions coupled with an electric and a magnetic field, respectively. Mesh refinement is conducted to verify convergence rates of the developed schemes. Some numerical examples are given to exhibit underlying dynamics absent from and driven by the external fields, respectively, highlighting differences between models with the variable and constant mobilities.

我们提出了发展具有可变迁移率的不可压缩多相聚合物溶液的热力学一致性模型的结构和性能保留数值算法的一般策略。我们首先提出一种形式主义，以得出热力学上一致的，不可压缩的多相聚合物模型。然后，我们开发了称为补充变量方法的通用策略，以为模型设计热力学一致的数值逼近。我们举例说明了使用新开发的不可压缩的二嵌段共聚物溶液分别与电场和磁场耦合的模型的数值策略。进行网格细化以验证所开发方案的收敛速度。给出了一些数值示例，以展示外部场缺乏和受外部场驱动的潜在动力学，