An Efficient High-Order Method for Fluid-Structure Interactions

本计画针对三维Navier-Stokes方程与三维非线性弹性动力学方程耦合以达到高阶精度的数学、算法与计算问题。流体和结构之间的传输条件将与建议的配方，这使得流体和结构的子问题，以独立和并行计算，大大方便了大规模并行计算机上的解决方案，这样的系统将被严格执行。弹性动力学方程和Navier-Stokes方程采用相同的高阶基函数求解，大大简化了流体和结构之间的传输条件的实现。流固耦合问题在自然和人工环境中无处不在，是许多工程、物理和生物应用的基础。 风吹落树叶和钟声，飓风冲破堤坝摧毁社区或整个城市，正常或患病动脉中的血液循环为动脉瘤或动脉粥样硬化斑块的形成提供了有利条件，这些都是直接的例子。拟议的研究将能够精确计算流体-结构相互作用。这将带来前所未有的预测能力，并深刻影响许多科学学科。

This project addresses mathematical, algorithmic, and computational issues for coupling the three-dimensional Navier-Stokes equations and the three-dimensional nonlinear elastodynamic equations to achieve high-order accuracy. The transmission conditions between the fluid and structure will be enforced exactly with the proposed formulation, which allows for the fluid and structure sub-problems to be computed independently and in parallel, greatly facilitating the solution of such systems on massively parallel computers. The elastodynamic equations and the Navier-Stokes equations are solved employing identical set of high-order basis functions, substantially simplifying the implementation of transmission conditions between the fluid and the structure. Scalable algorithms for efficient computations of large-scale fluid-structure problems are proposed and investigated.Fluid-structure interaction is omnipresent in natural and man-made environments, and underlies many engineering, physical and biological applications. Wind rustling leaves and ringing chimes, hurricanes breaching levees and destroying a community or an entire city, circulating blood in normal or diseased arteries inducing favorable conditions for the formation of aneurysms or atherosclerotic plaques, are several immediate examples. The proposed research will enable accurate computations of fluid-structure interactions. This will bring about unprecedented predictive capabilities and profoundly impact many scientific disciplines.