A 5D concept for space-time optimal control problems with application to simplified Carreau flow
S. Beuchler, B. Endtmayer, U. Langer, A. Schafelner, T. Wick
这项工作提出了一个5D概念,通过简化的Carreau流模型优化非牛顿流体流动。 我们通过完全时空有限元方法近似KKT系统的解决方案来解决优化问题,而不是更传统的时间步法技术与空间有限元离散化相结合。 其中,有限元方法在空间中以3D,在时间1D中配制,在优化循环中以1D为单位,产生了一个5D整体框架。
This work presents a 5D concept to optimizing non-Newtonian fluid flows through a simplified Carreau flow model. We solve the optimization problem by approximating the solution of the KKT System with fully space-time finite element methods instead of the more traditional time-stepping technique combined with spatial finite element discretization. Therein, the finite element method is formulated in 3D in space, 1D in time, and 1D in the optimization loop, yielding a 5D overall framework.