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Large eddy simulation of non-Boussinesq gravity currents with a DG method

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Abstract

We present results of three-dimensional direct numerical simulations (DNS) and large eddy simulations (LES) of turbulent gravity currents with a discontinuous Galerkin finite elements method. In particular, we consider the lock-exchange test case as a benchmark for gravity currents. Since, to the best of our knowledge, non-Boussinesq three-dimensional reference DNS are not available in the literature for this test case, we first perform a DNS experiment. The DNS provides an accurate description of the turbulent phenomena and highlights some differences with respect to the Boussinesq regime, like the non-symmetric pattern in the evolution of instabilities at the interfacial region and the fact that less turbulent structures are present due to greater stratification. A periodic pattern is also evident in the time evolution of turbulent mixing. The DNS is then employed to assess the performance of different LES models. In particular, we have considered the isotropic dynamic model and an anisotropic dynamic model. The LES results provide a first indication about the superiority of dynamic models with respect to no-model LES. However, the considered Reynolds numbers in the non-Boussinesq context are still too low to draw firm conclusions about the superiority of the present explicit LES approach with respect to an implicit LES approach.

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Acknowledgements

This paper contains some revised and extended results from the first author’s PhD thesis work. We would like to acknowledge the careful and constructive remarks by the Editor and by two anonymous reviewers, which have helped in improving the clarity of the paper. We are happy to acknowledge the continuous help of M. Restelli and M. Tugnoli with the application of the FEMILARO code. The results of this research have been achieved using the computational resources made available at CINECA (Italy) by the LISA high performance computing Project DECLES: Large Eddy Simulation of Density Currents and Variable Density Flows, HPL13PJ6YS.

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Correspondence to Caterina Bassi.

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Communicated by Tim Colonius.

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Bassi, C., Abbà, A., Bonaventura, L. et al. Large eddy simulation of non-Boussinesq gravity currents with a DG method. Theor. Comput. Fluid Dyn. 34, 231–247 (2020). https://doi.org/10.1007/s00162-020-00525-z

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