Fast numerical methods for large-scale multiphysics problems

在这个项目中要考虑的第一类问题是线性和非线性流体-结构相互作用问题。它们出现在从飞机设计到人体动脉、心脏和气道肺泡流动模拟的整个应用范围内。其目的是探索一种新的方法来解决这些问题，据我们所知，迄今为止还没有使用。这种方法的关键思想是重新制定，流体和结构问题的一个新的变量，应力张量。此外，通过使用适当的分裂方法，3D时间离散方程组可以简化为一组更简单，更容易解决的低维问题。 因此，由此产生的数值算法将显着更快，更容易在并行计算机上实现。这种新的流体-结构相互作用问题的设置的另一个非常令人愉快的结果是，由于在这两个域中，它只使用应力作为变量，它不需要显式跟踪的结构域的形状，通常是相当有问题的原始变量中的现有方法。

The first type of problems to be considered in this project are linear and nonlinear fluid-structure interaction problems. They appear in a whole range of applications starting from aircraft design, to simulation of flows in human arteries, heart, and the alveoli of the airways. The intention is to explore a new approach to such problems that, to our knowledge, has not been used so far. The key idea of this approach is to reformulate both, the fluid and the structure problems in terms of a new variable, the stress tensor. Further, by using a proper splitting approach, the 3D time-discrete system of equations can be reduced to a set of much simpler, lower-dimensional problems that can be resolved much easier. So, the resulting numerical algorithm will be significantly faster and easier to implement on parallel computers. Another very pleasant outcome of this new setting of fluid-structure interaction problems is that since in both domains it uses only the stress as a variable, it does not require explicit tracking of the shape of the structure domain that is usually quite problematic in the existing methods in primitive variables.