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  • 1
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    Society for Industrial and Applied Mathematics
    In:  Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 18 (2). pp. 543-571.
    Publication Date: 2021-01-08
    Description: 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.
    Type: Article , PeerReviewed
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  • 2
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    Springer
    In:  In: Computational Science – ICCS 2019. Lecture Notes in Computer Science, 11539 . Springer, Berlin, Germany, pp. 393-409.
    Publication Date: 2020-05-13
    Description: We introduce a new parallelizable numerical multiscale method for advection-dominated problems as they often occur in engineering and geosciences. State of the art multiscale simulation methods work well in situations in which stationary and elliptic scenarios prevail but are prone to fail when the model involves dominant lower order terms which is common in applications. We suggest to overcome the associated difficulties through a reconstruction of subgrid variations into a modified basis by solving many independent (local) inverse problems that are constructed in a semi-Lagrangian step. Globally the method looks like a Eulerian method with multiscale stabilized basis. The method is extensible to other types of Galerkin methods, higher dimensions, nonlinear problems and can potentially work with real data. We provide examples inspired by tracer transport in climate systems in one and two dimensions and numerically compare our method to standard methods.
    Type: Book chapter , NonPeerReviewed
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  • 3
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    Springer
    In:  In: Computational Science – ICCS 2018. , ed. by Shi, Y. Lecture Notes in Computer Science, 10861 . Springer, Cham, Switzerland, pp. 56-68. ISBN 978-3-319-93701-4
    Publication Date: 2018-09-03
    Description: Adaptive mesh refinement (AMR) can be used to improve climate simulations since these exhibit features on multiple scales which would be too expensive to resolve using non-adaptive meshes. In particular, long-term climate simulations only allow for low resolution simulations using current computational resources. We apply AMR to single components of the existing earth system model (ESM) instead of constructing a complex ESM based on AMR. In order to compatibly incorporate AMR into an existing model, we explore the applicability of a tree-based data structure. Using a numerical scheme for tracer transport in ECHAM6, we test the performance of AMR with our data structure utilizing an idealized test case. The numerical results show that the augmented data structure is compatible with the data structure of the original model and also demonstrate improvements of the efficiency compared to non-adaptive meshes.
    Type: Book chapter , NonPeerReviewed
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