Abstract:The application of partitioned schemes to fluid-structure interaction (FSI) allows the use of already developed solvers specifically designed for the efficient solution of the corresponding subproblems. In this work, we propose and describe a loosely coupled partitioned scheme based on the recently introduced generalized-structure additively partitioned Runge-Kutta (GARK) framework. The resulting scheme combines implicit-explicit (IMEX) and multirate approaches while coupling of the subproblems is realized both on the level of the discrete time steps and at the level of interior Runge-Kutta stages. Specifically, we allow for varying micro step sizes for the fluid subproblem and therefore extend the multirate GARK framework based on constant micro steps. Furthermore, we derive the order conditions for this extension allowing for coupled time integration schemes of up to third order and discuss specific choices of the Runge-Kutta coefficients complying with the geometric conservation law. Finally, numerical experiments are carried out for uniform flow on a moving grid as well as the classical FSI test case of a moving piston.

Background: Wind power forecasts of the expected wind feed-in for the next hours or days are necessary to integrate the generated volatile wind energy into power systems. Most forecasting models predict in some sense the best value, but they ignore the other possible outcomes which may arise because of forecasting uncertainties. Probabilistic forecasts, on the other hand, also predict a distribution of possible outcomes with their respective probabilities that specific power values will occur and therefore have higher information content. In this work, we address two problems that hinder the introduction of probabilistic forecasts in practice: (1) no measurement data are available for some wind farms and (2) the flexible aggregation of probabilistic forecasts for changing wind farm portfolios. Methods: We present an approach based on copulas that can solve both problems by modeling the spatial correlation structure between reference wind farms. By sampling from the resulting joint probability distribution, probability forecasts can be upscaled from reference wind farms to wind farms without power measurements. Furthermore, the results can be aggregated to probability forecasts of portfolios of arbitrary and changing size. Results: We perform experiments by applying our procedure to three use cases. The results are quantitatively evaluated with different probabilistic scores. For single target wind farms, our approach is as good as a state-of-the-art reference even if no data are available for the wind farm under consideration. For portfolios, our approach also allows forecasts to be made if no data is available for some wind farms and also to aggregate flexible portfolios of changing sizes, which was not possible before. Conclusion: Our work solves two problems that hindered the introduction of quantile probabilistic forecasts in the application. This work opens a pathway for many different applications, e.g., predictive grid securities with stochastic optimization, better marketing of renewable energies, or allow to compensate for forecast errors in various applications.

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We extend the multirate GARK approach by Günther and Sandu [1, 2] to the case of non‐constant micro steps per macro step to be able to cover time adaptivity, arriving at our so‐called TAMGARK scheme and derive order conditions for arbitrary non‐constant micro step sizes. The TAMGARK scheme is applied to the classical piston problem [3] to study the interaction between the piston and inviscid fluid flow in one spatial dimension. We demonstrate the functionality of the chosen time‐adaptation strategy and the ability of the overall scheme to preserve the order of the basic schemes. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)