基于不可压缩Navier-Stokes方程流体/流体耦合问题高效解耦数值方法研究

Numerical simulation of coupled fluidf/fluid field is an important issue on fluid mechanics. However, there exists lots of difficulties in numerical analysis, such as the nonlinearity, the interaction of mutli-physical information, energy dissipation. Here, we pay more attention to the efficient numerical methods for the coupled fluid/fluid problems related to the Navier-Stokes equations. As for the coupled problems related to the incompressible flows, we design the efficient decoupling methods based on the interface equations and coupled boundary type. Especially, we design the efficient splitting methods for the coupled problems related to the time-dependent incompressible flows, which can be solved by noniterative method in individual domain. The nonlinear problems is solved by quasi-linear and Poisson equations per time step. Moreover, for the whole system, the large scale problems are solved with multi-step small scale computing. According to the relationship between the equations of the coupled problems, large time step algorithms are applied and multi-scale schemes are designed for the individual nonlinear physical field. Stabilization methods on the lowest order elements, multi-scale method, preconditioning approach are also applied for the nonlinear and large scale problems. Moreover, the efficient decoupling method are applied to develop some high-precision calculation scheme with non-increasing energy, mass conservation, good stability, and strong flexibility properties in order to maintain physical properties of the presented coupled problems, well explain in numerical analysis, provide the efficient numerical approaches to simulate multi-physical coupled problems and to develop the nonlinear scientific research, and apply to the fluid dynamics in the relevant industries.

基于不可压缩Navier-Stokes方程流体耦合问题数值模拟是流体力学研究的重要热点课题之一。本课题主要研究基于不可压缩流Navier-Stokes方程流体/流体耦合问题高效解耦数值方法，从数值角度分析非线性的复杂性、交界面多物理信息相互牵制、解耦时能量耗散以及不可压缩性等难点。我们根据模型的交界面方程和边界耦合方式设计高效解耦算法，在各自物理区域中求解各自问题；设计非稳态问题的非迭代解耦格式，非线性不可压缩流问题转化为拟线性问题和Poison问题的裂解格式，以及系统大时间步长与三线性项有关时空多尺度算法。结合高效稳定化方法、预条件处理、多重快速求解方法，运用多物理解耦思想设计高效稳定、保耗散结构、适应性强的耦合问题高精度计算格式。使得数值方法既能简单高效求解多物理场耦合问题，又能从数值方法角度进行科学解释，进而为非线性多物理流体力学耦合问题的理论探索和相关的应用提供新的研究途径。

基于不可压缩Navier-Stokes方程流体耦合问题数值模拟是流体力学研究的重要热点课题之一。本课题主要研究基于不可压缩流Navier-Stokes方程流体/流体耦合问题高效解耦数值方法，从数值角度分析非线性的复杂性、交界面多物理信息相互牵制、解耦时能量耗散以及不可压缩性等难点。我们根据模型的交界面方程和边界耦合方式设计高效解耦算法，在各自物理区域中求解各自问题；设计非稳态问题的非迭代解耦格式，非线性不可压缩流问题转化为拟线性问题和Poison问题的裂解格式，以及系统大时间步长与三线性项有关时空多尺度算法。结合高效稳定化方法、预条件处理、多重快速求解方法，运用多物理解耦思想设计高效稳定、保耗散结构、适应性强的耦合问题高精度计算格式。使得数值方法既能简单高效求解多物理场耦合问题，又能从数值方法角度进行科学解释，进而为非线性多物理流体力学耦合问题的理论探索和相关的应用提供新的研究途径。