Modeling of ocean overflows using statically and dynamically adaptive vertical discretization techniques

• Applicant: Professor Dr. Vadym Aizinger
• Subject Area: Oceanography
• Term: from 2012 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 213809913

• Final Report Year: 2020

Final Report Abstract

One of the most pressing challenges facing the current generation of the multiresolution models of regional and global ocean circulation is the preservation of water masses in long-term simulations. In this context, any significant improvement in the accuracy of numerical advection schemes and any reduction in the rate of spurious mixing for temperature and salinity can substantially enhance physical significance of models’ results and ultimately advance the predictive power of climate projections. The particular target group of our project are unstructured threedimensional ocean models which are quickly catching up with their structured counterparts in terms of model skill and computational performance. Our aim is to exploit a greater flexibility of unstructured meshes in order to reduce spurious vertical mixing. To achieve this goal we developed computationally efficient techniques that allow to adapt the vertical layer structure either statically or dynamically. The newly developed numerical methodologies were implemented in the regional ocean model UTBEST3D, they further augment model’s geometric flexibility and adaptivity features. The statically adapted meshes improve the representation of the topographically complex sea beds and could particularly benefit simulations of processes taking place near the sea floor such as sedimentation. Our technique of dynamically adapting vertical layers is fully conservative and can be used to adjust the vertical mesh structure to better fit the simulated system. An interesting application of the techniques introduced in this project could be the thermohaline circulation in the deep ocean that plays a key role in the climate system and its dynamics.

Publications

• A multi-platform scaling study for an OpenMP parallelization of a discontinuous Galerkin ocean model, Computers and Fluids, Vol. 117, 325-335 2015
  B. Reuter, V. Aizinger, H. Köstler
  
• FESTUNG: A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method. Part I: Diffusion operator, Computers and Mathematics with Applications, Vol. 70, 11-46, 2015
  F. Frank, B. Reuter, V. Aizinger, P. Knabner
  
• Energy efficiency of the simulation of three-dimensional coastal ocean circulation on modern commodity and mobile processors, Computer Science – Research and Development, Vol. 31, 225-234, 2016
  M. Geveler, B. Reuter, V. Aizinger, D. Göddeke, S. Turek
  
• FESTUNG: A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method. Part II: Advection operator and slope limiting, Computers and Mathematics with Applications, Vol. 72, 1896-1925, 2016
  B. Reuter, V. Aizinger, M. Wieland, F. Frank, P. Knabner
  
• ESTUNG: A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method, Part III: Hybridized discontinuous Galerkin (HDG) formulation, Comput. Math. Appl., 75 (12), 4505-4533, 2018
  A. Jaust, B. Reuter, V. Aizinger, J. Schütz, P. Knabner
  
• Locally Filtered Transport for computational efficiency in multi-component advection-reaction models, Environmental Modelling & Software, Vol. 102, 185-198, 2018
  H. Hajduk, B.R. Hodges, V. Aizinger, B. Reuter
  
• Discontinuous Galerkin method for coupling hydrostatic free surface flows to saturated subsurface systems, Comput. Math. Appl., 77 (9), 2291-2309, 2019
  B. Reuter, A. Rupp, V. Aizinger, P. Knabner
  
• Bathymetry Reconstruction Using Inverse Shallow Water Models: Finite Element Discretization and Regularization. In H. van Brummelen, A. Corsini, S. Perotto, G. Rozza, (eds.): Numerical Methods for Flows: FEF 2017 Selected Contributions - Cham: Springer, 223-230, 2020
  H. Hajduk, D. Kuzmin, V. Aizinger
  
• FESTUNG 1.0: Overview, usage, and example applications of the MATLAB/GNU Octave toolbox for discontinuous Galerkin methods. Computers and Mathematics with Applications, in Press, 2020
  B. Reuter, H. Hajduk, A. Rupp, F. Frank, V Aizinger, P. Knabner
  
• FESTUNG: A MATLAB / GNU Octave toolbox for the discontinuous Galerkin method. Part IV: Generic problem framework and model-coupling interface. Commununications in Computational Physics, Vol. 28, 827-876, 2020
  B. Reuter, A. Rupp, V. Aizinger, F. Frank, P. Knabner