Work in this project involves the construction of cutting-edge numerical methods for solving partial differential equations such as those used in aerodynamics, atmospheric, and ocean modeling. We focus on element-based Galerkin methods (spectral element, discontinuous Galerkin, entropy-stable and kinetic-energy-preserving methods) to approximate the spatial derivatives with advanced time-integration methods (such as Jacobian-free Newton-Krylov, implicit-explicit, parallel-in-time, multirate). The purpose of using these methods is to be able to construct highly accurate solutions to large-scale problems on parallel computers taking into account both multi-core and many-core computers. Knowledge in iterative solvers, preconditioners, Message-Passage Interface (MPI), and GPU computing is of significant interest since we are solving these problems on state-of-the-art supercomputers. These types of applications require the use of unstructured and adaptive grids so knowledge or interest in such techniques is valuable. The project also involves the construction of better non-reflecting boundary conditions for the Navier-Stokes equations.
The Associate should be well-versed in fluid dynamics and/or geophysical fluid dynamics and have a strong mathematical background, especially in the areas of numerical analysis, scientific computing, and partial differential equations. Knowledge in super-parameterization, reduced-order modeling, and scientific machine learning is a plus. Strong programming skills (object-oriented Fortran, C/C++, and Julia) are also essential.
References
Maciej Waruszewski, Jeremy E. Kozdon, Lucas C. Wilcox, Thomas H. Gibson, Francis X. Giraldo. Entropy stable discontinuous Galerkin methods for balance laws in non-conservative form: applications to Euler with gravity, Journal of Computational Physics (in press, 2022).
Md Badrul Hasan, Stephen R. Guimond, Meilin Yu, Sohail Reddy, Francis X. Giraldo, The effects of numerical dissipation on hurricane rapid intensification with observational heating, Journal of Advances in Modeling Earth Systems (in press, 2022)
Francis X. Giraldo. An Introduction to Element-Based Galerkin Methods on Tensor-Product Bases: Analysis, Algorithms, and Applications, Springer Texts in Computational Science and Engineering, Series Volume 24, ISBN: 978-3-030-55068-4 (2020)
D.S. Abdi, L. Wilcox, T. Warburton, F.X. Giraldo, A GPU-accelerated continuous and discontinuous Galerkin non-hydrostatic atmospheric model, International Journal for High-Performance Computing Applications
D.S. Abdi and F.X. Giraldo, Efficient construction of unified continuous and discontinuous Galerkin formulations for the 3D Euler equations, Journal of Computational Physics, Vol. 320, 46-68 (2016)
F.X. Giraldo and M. Restelli, A Study of Spectral Element and Discontinuous Galerkin Methods for the Navier-Stokes Equations in Nonhydrostatic Mesoscale Atmospheric Modeling: Equation Sets and Test Cases, J. Comp. Phys., Vol. 227, 3849-3877 (2008)
Computational; Atmospheric; Discontinuous; Numerical; Element; Galerkin; Geophysical; Modeling; Spectral; Storm surge; Ocean; Implicit; Time; Integration;