Publications

 
 

2015


  1. 1.E. Hendricks, M.A. Kopera and F.X. Giraldo, Evaluation of the utility of static and adaptive mesh refinement for idealized tropical cyclone problems in a spectral element shallow water model, Monthly Weather Review (in review, 2015) (PDF).


  1. 2.G. Theurich, C. DeLuca, T. Campbell, F. Liu, K. Saint, M. Vertenstein, J. Chen, R. Oehmke, J. Doyle, T. Whitcomb, A. Wallcraft, M. Iredell, T. Black, A. DaSilva, T. Clune, R. Ferraro, P. Li, M. Kelley, I. Aleinov, V. Balaji, N. Zadeh, R. Jacob, B. Kirtman, F.X. Giraldo, D. McCarren, S. Sandgathe, S. Peckham, R. Dunlap, The Earth System Prediction Suite: towards a coordinated U.S. modeling capability, Bulletin of the American Meteorological Society, (in review, 2015) (PDF).


  1. 3.M. Yu, F.X. Giraldo, M. Peng, Z.J. Wang, Localized artificial viscosity stabilization of discontinuous Galerkin methods for nonhydrostatic mesoscale atmospheric modeling, Monthly Weather Review (in review, 2015) (PDF).


  1. 4.S. Marras, M. Nazarov, and F.X. Giraldo, A conservative, consistent, and grid adaptive stabilized spectral element method based on a dynamic LES model for the compressible Euler Equations: the case of low Mach stratified flow, Journal of Computational Physics, (in review, 2015) (PDF).


  1. 5.L.E., Carr, C.F. Borges, and F.X. Giraldo, A Matrix-free Polynomial-based Nonlinear Least-Squares Optimized Preconditioner and its application to Discontinuous Galerkin discretization of the Euler Equations, Journal of Scientific Computing (accepted, in press 2015) (PDF).


  1. 6.M.A. Kopera and F.X. Giraldo, Mass Conservation of Unified Continuous and Discontinuous Element-based Galerkin Methods on Dynamically Adaptive Grids with Application to Atmospheric Simulations, Journal of Computational Physics (accepted, in press 2015) (PDF).


  1. 7.S. Marras, J.F. Kelly, M. Moragues, A. Mueller, M.A. Kopera, M. Vazquez, F.X. Giraldo, G. Houzeaux, O. Jorba, A review of element-based Galerkin methods for numerical weather prediction. Finite Elements, Spectral Elements, and Discontinuous Galerkin, Archives of Computational Methods in Engineering, (accepted, in press 2015) (PDF).


  1. 8.S. Marras, and F.X. Giraldo, A Parameter-free Dynamic Alternative to Hyper-Viscosity for Coupled Transport Equations: Applications to the Simulation of 3D Squall Lines using Spectral Elements, Journal of Computational Physics, February 15 (2015) (PDF).


2014


  1. 9.S.J. Choi, F.X. Giraldo, J. Kim, and S. Shin, Verification of a Non-hydrostatic dynamical core using Horizontally Spectral Element and Vertically Finite Difference Methods: 2D aspects, Geoscientific Model Development, Vol. 7, 2717-2731 (2014) (PDF).


  1. 10.S. Marras, M.A. Kopera and F.X. Giraldo, Simulation of Shallow Water Jets with a Unified Element-based Continuous/Discontinuous Galerkin Model with Grid Flexibility on the Sphere, Quarterly Journal of the Royal Meteorological Society, (Dec. 19, 2014) (PDF).


  1. 11.M.A. Kopera and F.X. Giraldo, Analysis of Adaptive Mesh Refinement for IMEX Discontinuous Galerkin Solutions of the Compressible Euler Equations with Application in to  Atmospheric Simulations, Journal of Computational Physics Vol. 275, 92-117 (2014) (PDF).


  1. 12.L. Yelash, A. Mueller, M. Lukacova-Medvidova, F.X. Giraldo, V. Wirth, Adaptive Discontinuous Evolution Galerkin Method for Dry Atmospheric Flow, Journal of Computational Physics Vol. 268 106-133 (2014) (PDF).


2013


  1. 13.F.X. Giraldo, J.F. Kelly and E.M. Constantinescu, Implicit-Explicit Formulations for a 3D Nonhydrostatic Unified Model of the Atmosphere (NUMA), SIAM J. Sci. Comp., Vol. 35 (5), B1162-B1194 (2013) (PDF).


  1. 14.A. Mueller, J. Behrens, F.X. Giraldo, and V. Wirth, Comparison between Adaptive and Uniform Discontinuous Galerkin simulations in 2D Dry Bubble Experiments, J. Comp. Phys., Vol. 235, 371-393  (2013) (PDF).


2012


  1. 15.S. Marras, J.F. Kelly, F.X. Giraldo, and M. Vazquez, Variational Multiscale Stabilization and p-adaptivity of High-Order Spectral Elements for the Convection-Diffusion Equation, J. Comp. Phys.,  Vol. 231, 7187-7213 (2012) (PDF).


  1. 16.J.F. Kelly and F.X. Giraldo, Continuous and Discontinuous Galerkin Methods for a Scalable 3D Nonhydrostatic Atmospheric Model:  limited-area mode, J. Comp. Phys., Vol. 231, 7988-8008 (2012) (PDF).


  1. 17.S. Gabersek, F.X. Giraldo, and J. Doyle, Dry and moist idealized experiments with a two-dimensional spectral element model, Mon. Wea. Rev., Vol. 140, 3163-3182 (2012)  (PDF).


  1. 18.L.E. Carr, C.F. Borges, and F.X. Giraldo, An element-based spectrally-optimized approximate inverse preconditioner for the Euler equations, SIAM J. Sci. Comp., Vol. 34, B392-B420 (2012) (PDF).


  1. 19.J. Lindquist, B. Neta, and F.X. Giraldo, High-Order Non-Reflecting Boundary Conditions for Dispersive Waves in Polar Coordinates using Spectral Elements, Appl. Maths. Comp., Vol. 218, 6666-6676 (2012) (PDF).


  1. 20.J.A. Escobar-Vargas, P.J. Diamessis, F.X. Giraldo, High-order Discontinuous Element-based Schemes for the Inviscid Shallow Water Equations: Spectral Multidomain Penalty and Discontinuous Galerkin Methods, Appl. Maths. Comp., Vol. 218, 4825-4848  (2012) (PDF).


2010


  1. 21.F.X. Giraldo, M. Restelli, and M. Laeuter, Semi-Implicit Formulations of the Euler Equations: Applications to Nonhydrostatic Atmospheric Modeling, SIAM J. Sci. Comp., Vol. 32, 3394-3425 (2010) (PDF).


  1. 22.J. Lindquist, F.X. Giraldo, and B. Neta, Klein-Gordon Equation with Advection on Unbounded Domains using Spectral Elements and High-Order Non-Reflecting Boundary Conditions, Appl. Maths. Comp., Vol. 217, 2710-2723 (2010) (PDF).


  1. 23.J. Lindquist, B. Neta, and F.X. Giraldo, A Spectral Element Solution of the Klein-Gordon Equation with High-Order Non-Reflecting Boundary Conditions, Wave Motion, Vol. 47, 289-298 (2010) (PDF).


2009


  1. 24.F.X. Giraldo and M. Restelli, High-Order Semi-Implicit Time-Integration of a Triangular Discontinuous Galerkin Oceanic Shallow Water Model, Int. J. Num. Meths. Fluids, Vol. 63, 1077-1102 (2009) (PDF).


  1. 25.J.R. Dea, F.X. Giraldo, and B. Neta, High-Order Non-Reflecting Boundary Conditions for the Linearized 2D Euler Equations: No Mean Flow,  Wave Motion, Vol. 46, 210-220 (2009) (PDF).


  1. 26.M. Restelli and F.X. Giraldo, A Conservative Semi-Implicit Discontinuous Galerkin Method for the Navier-Stokes Equations in Nonhydrostatic Mesoscale Atmospheric Modeling, SIAM J. Sci. Comp., Vol. 31, 2231-2257 (2009) (PDF).


2008


  1. 27.M. Laueter, F.X. Giraldo, D. Hansdorf, and K. Dethloff, A Discontinuous Galerkin Method for the Shallow Water Equations with Spherical Triangular Coordinates, J. Comp. Phys., Vol. 227, 10226-10242 (2008) (PDF).


  1. 28.Y.J. Kim, F.X. Giraldo, M. Flatau, C.S. Liou, and M.S. Peng, A Sensitivity Study of the Kelvin Wave and the Madden-Julian Oscillation in Aqua-planet Simulations by the Naval Research Laboratory Spectral Element Atmospheric Model (NSEAM), J. Geophys. Res., Vol. 113 (2008) (PDF).


  1. 29.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) (PDF).


  1. 30.F.X. Giraldo and T. Warburton, A High-Order Triangular Discontinuous Oceanic Shallow Water Model, Int. J. Num. Meths. Fluids, Vol. 56, 899-925 (2008) (PDF).


2006


  1. 31.F.X. Giraldo, Hybrid Eulerian-Lagrangian Semi-Implicit Time-Integrators, Comp. Maths. Appls.,  Vol. 52, 1325-1342 (2006) (PDF).


  1. 32.F.X. Giraldo and M.A. Taylor, A Diagonal Mass Matrix Triangular Spectral Element Method based on Cubature Points, J. of Eng. Maths., Vol. 56, 307-322 (2006) (PDF).


  1. 33.F.X. Giraldo, High-order Triangle-based Discontinuous Galerkin Methods for Hyperbolic Equations on a Rotating Sphere, J. Comp. Phys., Vol. 214, 447-465 (2006) (PDF).


2005


  1. 34.F.X. Giraldo and T. Warburton, A Nodal Triangle-based Spectral Element Method for the Shallow Water Equations on the Sphere, J. Comp. Phys., Vol. 207, 129-150 (2005) (PDF).


  1. 35.F.X. Giraldo, Semi-implicit Time-Integrators for a Scalable Spectral Element Atmospheric Model, Quart. J. Roy. Meteor. Soc., Vol. 131, 2431-2454 (2005) (PDF).


2004


  1. 36.F.X. Giraldo and T. Rosmond, A Scalable Spectral Element Eulerian Atmospheric Model (SEE-AM) for NWP: Dynamical Core Tests, Mon. Wea. Rev., Vol.132, 133-153 (2004) (PDF).


2003


  1. 37.F.X. Giraldo, J.B. Perot, and P.F. Fischer, A Spectral Element Semi-Lagrangian (SESL) Method for the Spherical Shallow Water Equations, J. Comp. Phys., Vol.190, 623-650 (2003) (PDF).


  1. 38.F.X. Giraldo, Strong and Weak Lagrange-Galerkin Spectral Element Methods for the Shallow Water Equations, Comp. Maths. Appls. Vol. 45, 97-121 (2003) (PDF).


2002


  1. 39.F.X. Giraldo, J.S. Hesthaven, and T. Warburton, Nodal High-Order Discontinuous Galerkin Methods for the Spherical Shallow Water Equations, J. Comp. Phys., Vol. 181, 499-525 (2002) (PDF).


  1. 40.W. Chang, F.X. Giraldo, and J.B. Perot, Analysis of an Exact Fractional-Step Method, J. Comp. Phys., Vol. 180, 183-1995 (2002) (PDF).


2001


  1. 41.F.X. Giraldo, A Spectral Element Shallow Water Model on Spherical Geodesic Grids, Int. J. Num. Meths. Fluids, Vol. 35, 869-901 (2001) (PDF).


2000


  1. 42.F.X. Giraldo, The Lagrange-Galerkin Method for the 2D Shallow Water Equations on Adaptive Grids, Int. J. Num. Meths. Fluids, Vol. 33, 789-832 (2000) (PDF).


  1. 43.F.X. Giraldo, Lagrange-Galerkin Methods on Spherical Geodesic Grids: The Shallow Water Equations, J. Comp. Phys., Vol. 160, 336-368 (2000) (PDF).


1999


  1. 44.F.X. Giraldo, Trajectory Calculations for Spherical Geodesic Grids in Cartesian Space, Mon. Wea. Rev., Vol. 127, 1651-1662 (1999) (PDF).


  1. 45.F.X. Giraldo and B. Neta, Stability Analysis for Eulerian and Semi-Lagrangian Finite Element Formulation of the Advection-Diffusion Equation, Comp. Maths. Appls., Vol. 38, 97-112 (1999)


1998


  1. 46.F.X. Giraldo, The Lagrange-Galerkin Spectral Element Method on Unstructured Quadrilateral Grids, J. Comp. Phys., Vol. 147, 114-146 (1998) (PDF).


1997


  1. 47.F.X. Giraldo, Lagrange-Galerkin Methods on Spherical Geodesic Grids, J. Comp. Phys., Vol. 136, 197-213 (1997) (PDF).


  1. 48.B. Neta, F.X. Giraldo, and I.M. Navon, Analysis of the Turkel-Zwas scheme for the Two-Dimensional Shallow Water Equations in Spherical Coordinates, J. Comp. Phys., Vol. 133, 102-122 (1997) (PDF).