Multiscale Modeling &Simulation, Volume 18, Issue 2, Page 543-571, January 2020.
Long simulation times in climate science typically require coarse grids due to computational constraints. Nonetheless, unresolved subscale information significantly influences the prognostic variables and cannot be neglected for reliable long-term simulations. This is typically done via parametrizations, but their coupling to the coarse grid variables often involves simple heuristics. We explore a novel upscaling approach inspired by multiscale finite element methods. These methods are well established in porous media applications, where mostly stationary or quasi stationary situations prevail. In advection-dominated problems arising in climate simulations, the approach needs to be adjusted. We do so by performing coordinate transforms that make the effect of transport milder in the vicinity of coarse element boundaries. The idea of our method is quite general, and we demonstrate it as a proof-of-concept on a one-dimensional passive advection-diffusion equation with oscillatory background velocity and diffusion.

中文翻译：

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对流诱导坐标的瞬态对流扩散方程的多尺度有限元

2020年1月，《多尺度建模与仿真》，第18卷，第2期，第543-571页。
由于计算限制，气候科学中较长的模拟时间通常需要粗网格。但是，未解决的分量表信息会严重影响预后变量，因此对于可靠的长期模拟不能忽略。这通常是通过参数设置完成的，但是它们与粗糙网格变量的耦合通常涉及简单的启发式方法。我们探索了一种受多尺度有限元方法启发的新颖的放大方法。这些方法在多孔介质应用中已得到很好的确立，在这些应用中，大多数情况是固定的或准固定的情况。在气候模拟中出现的以对流为主的问题中，需要对方法进行调整。我们通过执行坐标变换来做到这一点，该变换使在粗糙元素边界附近的传输效果更缓和。