Multiscale finite elements through advection-induced coordinates for transient advection-diffusion equations.

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Konrad Simon, Jörn Behrens

Long simulation times in climate sciences typically require coarse grids dueto computational constraints. Nonetheless, unresolved subscale informationsignificantly influences the prognostic variables and can not be neglected forreliable long term simulations. This is typically done via parametrizations buttheir coupling to the coarse grid variables often involves simple heuristics.We explore a novel up-scaling approach inspired by multi-scale finite elementmethods. These methods are well established in porous media applications, wheremostly stationary or quasi stationary situations prevail. Inadvection-dominated problems arising in climate simulations the approach needsto be adjusted. We do so by performing coordinate transforms that make theeffect of transport milder in the vicinity of coarse element boundaries. Theidea of our method is quite general and we demonstrate it as a proof-of-concepton a one-dimensional passive advection-diffusion equation with oscillatorybackground velocity and diffusion.

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