Engineering topics
Eldred, Christopher
Publications and source records attributed to Eldred, Christopher.
Multiscale geometric mechanics formulations for GFD parameterization.
Abstract not provided.
Meshless Remap of Native Fields for Earth System Models via Generalized Moving Least Squares.
Abstract not provided.
Geometric Structures Underlying Parameterizations in Geophysical Fluid Dynamics.
Abstract not provided.
Structure-preserving, high-order and oscillation-limited transport operators.
Abstract not provided.
Structure-preserving numerical discretizations for domains with boundaries
This SAND report documents Exploratory Express LDRD Project 223790, "Structure-preserving numerical discretizations for domains with boundaries", which developed a method to incorporate consistent treatment of domain boundaries and arbitrary boundary conditions in discrete exterior calculus (DEC) for arbitrary polygonal (2D) and tensor-product structure prism (3D) grids. The new DEC required the development of novel discrete exterior derivatives, boundary operators, wedge products and Hodge stars. This was accomplished through the use of boundary extension and the blending of known 2D operators on the interior with 1D operators on the boundary. The Hodge star was based on the Voronoi Hodge star, and retained the limitation of a triangular circumcentric primal or dual grid along with low-order accuracy. In addition to the new DEC, two related software packages were written: one for the study of DEC operators on arbitrary polygonal and polyhedral grids using both symbolic and numerical approaches and one for a (thermal) shallow water testbed using TRiSK-type numerics. Immediately relevant (already funded, through CANGA) followup work is the development of a high-order, geometrically flexible Hodge star and structure-preserving, high-order, oscillation-limiting transport operators (using WENO) for n-forms on arbitrary 2D and 3D grids. This will provide all of the machinery required for a high-order version of TRiSK with boundaries on arbitrary 2D and tensor-product 3D grids, which is applicable to both the atmospheric (CRM in E3SM-MMF) and oceanic (MPAS-O) components of E3SM.
Thermodynamically consistent semi-compressible fluids: a variational perspective
This paper presents (Lagrangian) variational formulations for single and multicomponent semi-compressible fluids with both reversible (entropy-conserving) and irreversible (entropy-generating) processes. Semi-compressible fluids are useful in describing low-Mach dynamics, since they are soundproof. These models find wide use in many areas of fluid dynamics, including both geophysical and astrophysical fluid dynamics. Specifically, the Boussinesq, anelastic and pseudoincompressible equations are developed through a unified treatment valid for arbitrary Riemannian manifolds, thermodynamic potentials and geopotentials. By design, these formulations obey the 1st and 2nd laws of thermodynamics, ensuring their thermodynamic consistency. This general approach extends and unifies existing work, and helps clarify the thermodynamics of semi-compressible fluids. To further this goal, evolution equations are presented for a wide range of thermodynamic variables: entropy density s, specific entropy η, buoyancy b, temperature T, potential temperature θ and a generic entropic variable χ; along with a general definition of buoyancy valid for all three semicompressible models and arbitrary geopotentials. Finally, the elliptic equation for the pressure perturbation (the Lagrange multiplier that enforces semi-compressibility) is developed for all three equation sets in the case of reversible dynamics, and for the Boussinesq/anelastic equations in the case of irreversible dynamics; and some discussion is given of the difficulty in formulating it for the pseudoincompressible equations with irreversible dynamics.
Unprecedented cloud resolution in a GPU-enabled full-physics atmospheric climate simulation on OLCF’s summit supercomputer
Clouds represent a key uncertainty in future climate projection. While explicit cloud resolution remains beyond our computational grasp for global climate, we can incorporate important cloud effects through a computational middle ground called the Multi-scale Modeling Framework (MMF), also known as Super Parameterization. This algorithmic approach embeds high-resolution Cloud Resolving Models (CRMs) to represent moist convective processes within each grid column in a Global Climate Model (GCM). The MMF code requires no parallel data transfers and provides a self-contained target for acceleration. This study investigates the performance of the Energy Exascale Earth System Model-MMF (E3SM-MMF) code on the OLCF Summit supercomputer at an unprecedented scale of simulation. Hundreds of kernels in the roughly 10K lines of code in the E3SM-MMF CRM were ported to GPUs with OpenACC directives. A high-resolution benchmark using 4600 nodes on Summit demonstrates the computational capability of the GPU-enabled E3SM-MMF code in a full physics climate simulation.
Extending TRiSK with Higher-Order Hodge Stars and WENO/FCT Advection.
Abstract not provided.
Fourier Analyses of High-Order Continuous and Discontinuous Galerkin Methods
In this paper, we present a Fourier analysis of wave propagation problems subject to a class of continuous and discontinuous discretizations using high-degree Lagrange polynomials. This allows us to obtain explicit analytical formulas for the dispersion relation and group velocity and, for the first time to our knowledge, characterize analytically the emergence of gaps in the dispersion relation at specific wavenumbers, when they exist, and compute their specific locations. Wave packets with energy at these wavenumbers will fail to propagate correctly, leading to significant numerical dispersion. We also show that the Fourier analysis generates mathematical artifacts, and we explain how to remove them through a branch selection procedure conducted by analysis of eigenvectors and associated reconstructed solutions. The higher frequency eigenmodes, named erratic in this study, are also investigated analytically and numerically.
SCREAM: a performance-portable global cloud-resolving model based on the Energy Exascale Earth System Model.
Abstract not provided.
Total energy and potential enstrophy conserving schemes for the shallow water equations using Hamiltonian methods – Part 1: Derivation and properties
Abstract. The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar characteristics: conservation laws, inertia-gravity and Rossby waves, and a (quasi-) balanced state. In order to obtain realistic simulation results, it is desirable that numerical models have discrete analogues of these properties. Two prototypical examples of such schemes are the 1981 Arakawa and Lamb (AL81) C-grid total energy and potential enstrophy conserving scheme, and the 2007 Salmon (S07) Z-grid total energy and potential enstrophy conserving scheme. Unfortunately, the AL81 scheme is restricted to logically square, orthogonal grids, and the S07 scheme is restricted to uniform square grids. The current work extends the AL81 scheme to arbitrary non-orthogonal polygonal grids and the S07 scheme to arbitrary orthogonal spherical polygonal grids in a manner that allows for both total energy and potential enstrophy conservation, by combining Hamiltonian methods (work done by Salmon, Gassmann, Dubos, and others) and discrete exterior calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp, and others). Detailed results of the schemes applied to standard test cases are deferred to part 2 of this series of papers.