2018
Discontinuous Galerkin scheme for the spherical shallow water equations with applications to tsunami modeling and prediction
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A wetting and drying algorithm for discontinuous Galerkin method on adaptive grids
Bonev, B., Hesthaven, J.S., Giraldo, F.X., Kopera, M.A., J. Comput. Phys. (2018, accepted) pdf
Simulation of turbulent flow over a backward-facing step at Re=9000
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Report on a DNS* simulation with statistical results useful for numerical code benchmarking, as well as some insights into structures in a reattaching flow.
Kopera, M.A., Kerr, R.M., Barkley, D., Blackburn, H., Phys. Fluids (2017, in review). pdf
A Residual-based Shock Capturing Scheme for the Continuous/Discontinuous Spectral Element Solution of the 2D Shallow Water Equations
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A mass-conservative stabilisation technique for CG/DG methods based on adaptive artificial viscosity calculated locally from the solution residual.
Marras, S., Kopera, M.A., Constantinescu, E.M., Suckale, J., Giraldo, F.X., Adv. Water Res. (2018, accepted) arXiv preprint, arXiv:1607.04547. pdf
Strong scaling for numerical weather prediction at petascale with the atmospheric model NUMA.
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Scaling of NUMA for up to over three million cores on MIRA supercomputer
Müller, A., Kopera, M.A, Marras, S., Wilcox, L.C., Isaac, T., and Giraldo, F.X., Int. J. High Perform. Comput. Appl. (2018, accepted) arXiv preprint arXiv:1511.01561 pdf
2016
Evaluation of the utility of static and adaptive mesh refinement for idealized tropical cyclone problems in a spectral element shallow water model
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NUMA2D AMR technique applied for some idealized tropical cyclones shows some promising results
Hendricks, E., Kopera, M.A. and Giraldo, F.X., Mon. Weather Rev. 144(10) 3697-3724 (2016) pdf
2015
A review of element-based Galerkin methods for numerical weather prediction. Finite elements, spectral elements, and discontinuous Galerkin
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A review paper with a particular focus on how stabilization and adaptive mesh refinement become more important as numerical weather prediction approaches smaller scales
Marras, S., Kelly, J.F., Moragues, M., Mueller, A., Kopera, M.A., Vazquez, M., Giraldo, F.X., Houseaux, G., Jorba, O. Archives of Computational Methods in Engineering, pp. 1-50 (2015) pdf
Mass conservation of the unified continuous and discontinuous element-based Galerkin methods on dynamically adaptive grids with application to atmospheric simulations
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Paper provides mathematical proof and in-depth numerical study of mass conservation of CG/DG methods on non-conforming adaptive meshes.
Kopera, M.A. and Giraldo, F.X., J. Comput. Phys. 297, pp. 90-103 (2015) pdf
2014
Simulation of shallow water jets with a unified element-based continuous/discontinuous Galerkin model with grid flexibility on the sphere
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A comparison of different grid configurations for CG/DG shallow water model with curved elements on a sphere.
Marras, S., Kopera, M.A. and Giraldo, F.X., Q. J. R. Meteorol. Soc. (2014) DOI:10.1002/qj.2474 pdf
Analysis of adaptive mesh refinement for IMEX discontinuous Galerkin solutions of the compressible Euler equations with application to atmospheric simulations
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In-depth study of the interaction of AMR and IMEX schemes in the context of atmospheric simulations with DG.
Kopera, M.A. and Giraldo, F.X., J. Comput. Phys. 275, pp. 92-117, (2014) pdf