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Non-oscillatory forward-in-time integrators for viscous incompressible flows past a sphere

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journal contribution
posted on 25.02.2019, 14:23 by Joanna Szmelter, Piotr K. Smolarkiewicz, Zhao Zhang, Zhixin Cao
A non-oscillatory forward-in-time (NFT) integrator is developed to provide solutions of the Navier-Stokes equations for incompressible flows. Simulations of flows past a sphere are chosen as a benchmark representative of a class of engineering flows past obstacles. The methodology is further extended to moderate Reynolds number, stably stratified flows under gravity, for Froude numbers that typify the characteristic regimes of natural flows past distinct isolated features of topography in weather and climate models. The key elements of the proposed method consist of the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA) and a robust non-symmetric Krylov-subspace elliptic solver. The solutions employ a finite volume spatial discretisation on unstructured and hybrid meshes and benefit from a collocated arrangement of all flow variables while being inherently stable. The development includes the implementation of viscous terms with the detachededdy simulation (DES) approach employed for turbulent flows. Results demonstrate that the proposed methodology enables direct comparisons of the numerical solutions with corresponding laboratory studies of viscous and stratified flows while illustrating accuracy, robustness and flexibility of the NFT schemes. The presented simulations also offer a better insight into stably stratified flows past a sphere.


This work was supported in part by the funding received from the European Research Council under the European Unions Seventh Framework Programme (FP7/2012/ERC Grant agreement no. 320375) and the Horizon 2020 Research and Innovation Programme (ESIWACE Grant agreement no. 675191 and ESCAPE Grant agreement no. 671627).



  • Mechanical, Electrical and Manufacturing Engineering

Published in

Journal of Computational Physics


SZMELTER, J. ... et al, 2019. Non-oscillatory forward-in-time integrators for viscous incompressible flows past a sphere. Journal of Computational Physics, 386, pp.365-383.


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