高分子复杂流体相分离动力学的数值模拟

高分子材料的结构和性能与高分子体系的相行为及转变行为是密切相关的，而相分离是影响高分子材料结构、性能及其稳定性的决定性因素。本项目针对高分子复杂流体的相分离动力学模型，研究数值逼近中的高效高精度算法，时空离散分别采用自适应时间步长方法和高阶紧致差分格式。一方面运用算子分裂方法、浸入界面方法和解耦技巧等，提出若干能量非增、稳定性好、质量不变、大时间步长计算、适应性强的高精度全离散格式，并给出相应的数值分析。另一方面结合残量校正方法、多重网格方法和预条件处理技术等设计出强健的非线性迭代格式和求解器，降低求解离散系统的复杂度，并研制具备良好可移植性的并行计算程序，使其具有保耗散结构的性质，能在高性能计算机上实现长时间行为的模拟，从而得以分析高分子复杂流体的时空图样生成及其形态演化过程，更加深刻地理解相分离的本质，为非线性科学的研究和发展及计算流体力学在材料科学与工程技术中的应用提供新的研究途径。

)：Structure and properties of polymeric materials are closely related to phase behavior and phase transitions of polymeric systems, and the phase separation is the crucial factor controlling the stability, structure and properties of polymeric materials. In this project, we focus on devising the efficiently high precision algorithm for the phase separation dynamics of polymeric complex fluids. For time discretization and spatial discretization, the adaptive time-stepping method and higher-order compact difference scheme are used respectively. Firstly, by making use of operator splitting method, immersed interface method, decoupled technique etc., we develop some high precision full discretization schemes with non-increasing energy, mass conservation, good stability, large time-step size and strong flexibility properties and provide numerical analysis for these new schemes. Secondly, by using residual correction method, multigrid method and preconditioning technique, efficient iterative algorithms and fast solver are designed to reduce the computational cost for solving the discrete system. Finally, we design the parallel programs with dissipative structures in order to achieve long-time numerical simulation. Then spatial-temporal pattern formation and its morphology evolution of polymeric complex fluids can be analyzed and the essence of phase separation can be understood deeply. Furthermore, we provide the new research approaches to develop the nonlinear scientific research and apply to the computational fluid dynamics in the materials science and engineering technology.