论文标题
减少固化问题的模型顺序
Model order reduction of solidification problems
论文作者
论文摘要
众所周知，由于kolmogorov $ n $宽度的缓慢衰减，因此很难以减少的基础建模。本文调查了这一挑战如何转移到凝固问题的背景下，并试图回答何时何地扩展减少订单模型（ROM）来解决凝固问题。在固化问题中，挑战本身不是对流，而是一个移动的固化前线。本文研究降低了及时移动的一维步骤功能的空间，这可以看作是数量的对流或移动的固化前线。此外，将2D固化测试案例的缩小空间与具有糊状区域的合金固化空间进行了比较。结果表明，不仅PDE本身，而且解决方案的平滑度对于奇异值的衰减至关重要，从而降低了空间表示的质量。
Advection driven problems are known to be difficult to model with a reduced basis because of a slow decay of the Kolmogorov $N$-width. This paper investigates how this challenge transfers to the context of solidification problems and tries to answer when and to what extend reduced order models (ROMs) work for solidification problems. In solidification problems, the challenge is not the advection per se, but rather a moving solidification front. This paper studies reduced spaces for 1D step functions that move in time, which can either be seen as advection of a quantity or as a moving solidification front. Furthermore, the reduced space of a 2D solidification test case is compared with the reduced space of an alloy solidification featuring a mushy zone. The results show that not only the PDE itself, but the smoothness of the solution is crucial for the decay of the singular values and thus the quality of a reduced space representation.
