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Sierra/Solid Mechanics 5.16 User's Guide

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra/SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra/SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutions of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes. This document describes the functionality and input syntax for Sierra/SM.

36 MATERIALS SCIENCE↗

Model of Mixing Layer With Multicomponent Evaporating Drops

A mathematical model of a three-dimensional mixing layer laden with evaporating fuel drops composed of many chemical species has been derived. The study is motivated by the fact that typical real petroleum fuels contain hundreds of chemical species. Previously, for the sake of computational efficiency, spray studies were performed using either models based on a single representative species or models based on surrogate fuels of at most 15 species. The present multicomponent model makes it possible to perform more realistic simulations by accounting for hundreds of chemical species in a computationally efficient manner. The model is used to perform Direct Numerical Simulations in continuing studies directed toward understanding the behavior of liquid petroleum fuel sprays. The model includes governing equations formulated in an Eulerian and a Lagrangian reference frame for the gas and the drops, respectively. This representation is consistent with the expected volumetrically small loading of the drops in gas (of the order of 10 3), although the mass loading can be substantial because of the high ratio (of the order of 103) between the densities of liquid and gas. The drops are treated as point sources of mass, momentum, and energy; this representation is consistent with the drop size being smaller than the Kolmogorov scale. Unsteady drag, added-mass effects, Basset history forces, and collisions between the drops are neglected, and the gas is assumed calorically perfect. The model incorporates the concept of continuous thermodynamics, according to which the chemical composition of a fuel is described probabilistically, by use of a distribution function. Distribution functions generally depend on many parameters. However, for mixtures of homologous species, the distribution can be approximated with acceptable accuracy as a sole function of the molecular weight. The mixing layer is initially laden with drops in its lower stream, and the drops are colder than the gas. Drop evaporation leads to a change in the gas-phase composition, which, like the composition of the drops, is described in a probabilistic manner

Bellan, Josette↗

Sierra/SolidMechanics 4.56 User's Guide

Siera/SolidMechanics (Sierra / SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra / SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra / SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutions of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes . This document describes the functionality and input syntax for Sierra/SM.

97 MATHEMATICS AND COMPUTING↗

Discrete ion stochastic continuum overdamped solvent algorithm for modeling electrolytes

In this paper we develop a methodology for the mesoscale simulation of strong electrolytes. The methodology is an extension of the fluctuating immersed-boundary approach that treats a solute as discrete Lagrangian particles that interact with Eulerian hydrodynamic and electrostatic fields. In both algorithms the immersed-boundary method of Peskin is used for particle-field coupling. Hydrodynamic interactions are taken to be overdamped, with thermal noise incorporated using the fluctuating Stokes equation, including a "dry diffusion" Brownian motion to account for scales not resolved by the coarse-grained model of the solvent. Long-range electrostatic interactions are computed by solving the Poisson equation, with short-range corrections included using an immersed-boundary variant of the classical particle-particle particle-mesh technique. Also included is a short-range repulsive force based on the Weeks-Chandler-Andersen potential. This methodology is validated by comparison to Debye-Hückel theory for ion-ion pair correlation functions, and Debye-Hückel-Onsager theory for conductivity, including the Wien effect for strong electric fields. In each case, good agreement is observed, provided that hydrodynamic interactions at the typical ion-ion separation are resolved by the fluid grid.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Sierra/SolidMechanics 4.58 User's Guide

Sierra / SolidMechanics (Sierra / SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra / SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra / SM has a versatile library of continuum and structural elements, an d a large library of material models. The code is written for parallel computing environments enabling scalable solutions of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes . This document describes the functionality and input syntax for Sierra / SM.

36 MATERIALS SCIENCE↗

Off-shell vertices in heavy particle effective theories and B → Dπℓν

We study the modifications to decay amplitudes in heavy to heavy semileptonic decays with multiple hadrons in the final state due to intermediate heavy hadrons being off-shell or having a finite width. Combining Heavy Hadron Chiral Perturbation Theory (HHχPT) with a BCFW on-shell factorization formula, we show that these effects induce O (1/M) corrections to the standard results computed in the narrow-width approximation and therefore are important in extracting form factors from data. A combination of perturbative unitarity, analyticity, and reparameterization invariance fully determine these corrections in terms of known Isgur-Wise functions without the need to introduce new form factors. In doing so, we develop a novel technique to compute the boundary term at complex infinity in the BCFW formula for theories with derivatively coupled scalars. While we have used the $\overline{B}$ → Dπℓν decay as an example, these techniques can generally be applied to effective field theories with (multiple) distinct reference vectors. Article PDF

Chiral Lagrangian↗

Detailed Studies on the Structure and Dynamics of Reacting Dusty Flows at Normal and Microgravity

Dusty reacting flows are of particular interest for a wide range of applications. Inert particles can alter the flammability and extinction limits of a combustible mixture. Reacting particles can release substantial amount of heat and can be used either for power generation or propulsion. Accumulation of combustible particles in air can result in explosions which, for example, can occur in grain elevators, during lumber milling and in mine galleries. Furthermore, inert particles are used as flow velocity markers in reacting flows, and their velocity is measured by non-intrusive laser diagnostic techniques. Despite their importance, dusty reacting flows have been less studied and understood compared to gas phase as well as sprays. The addition of solid particles in a flowing gas stream can lead to strong couplings between the two phases, which can be of dynamic, thermal, and chemical nature. The dynamic coupling between the two phases is caused by the inertia that causes the phases to move with different velocities. Furthermore, gravitational, thermophoretic, photophoretic, electrophoretic, diffusiophoretic, centrifugal, and magnetic forces can be exerted on the particles. In general, magnetic, electrophoretic, centrifugal, photophoretic, and diffusiophoretic can be neglected. On the other hand, thermophoretic forces, caused by steep temperature gradients, can be important. The gravitational forces are almost always present and can affect the dynamic response of large particles. Understanding and quantifying the chemical coupling between two phases is a challenging task. However, all reacting particles begin this process as inert particles, and they must be heated before they participate in the combustion process. Thus, one must first understand the interactions of inert particles in a combustion environment. The in-detail understanding of the dynamics and structure of dusty flows can be only advanced by considering simple flow geometries such as the opposed-jet, stagnation-type. In such configurations the imposed strain rate is well characterized, and the in-depth understanding of the details of the physico-chemical processes can be systematically obtained. A number of computational and experimental studies on spray and particle flows have been conducted in stagnation-type configurations. Numerically, the need for a hybrid Eulerian-Lagrangian approach has been identified by Continillo and Sirignano, and the use of such approach has allowed for the prediction of the phenomenon of droplet flow reversal. Gomez and Rosner have conducted a detailed study on the particle response in the opposed-jet configuration, and the particle thermophoretic diffusivities were determined experimentally. Sung, Law and co-workers have conducted numerical studies on the effect of strain rate and temperature gradients on the dynamics of inert particles, as a way of understanding potential errors in experimental LDV data that may arise from thermophoretic forces. This investigation is a combined experimental and numerical study on the details of reacting dusty flows. The specific tasks are: (1) Experimental determination of laminar flame speeds, and extinction strain rates of dusty flows at normal- and micro-gravity as functions of the particle type, particle initial diameter, particle initial number density, and gas phase chemical composition; (2) Detailed numerical simulation of the experiments. Results are compared with experiments and the adequacy of theoretical models is assessed; and (3) Provision of enhanced insight into the thermo-chemical coupling between the two phases.

Andac, M. Gurhan↗

Structure and Growth of the Marine Boundary Layer

LANDSAT visible imagery and a one-dimensional Lagrangian boundary layer model were used to hypothesize the nature and the development of the marine boundary layer during a winter episode of strong seaward cold air advection. Over-water heating and moistening of the cold, dry continental air is estimable from linear relations involving horizontal gradients of the near-surface air temperature and humidity. A line of enhanced convection paralleling the Atlantic U.S. coast from south of New York Bay to the vicinity of Virginia Beach, VA was attributed to stronger convergence at low levels. This feature was characterized as a mesoscale front. With the assistance of a three-dimensional mesoscale boundary layer model, initialized with data obtained from the MASEX, the marine boundary layer can be mapped over the entire Atlantic coastal domain and the evolution of the boundary layer can be studied as a function of different characteristics of important surface level forcings. The effects on boundary layer growth due to the magnitude and pattern of sea surface temperature, to the shape of the coastline, and to atmospheric conditions, such as the orientation of the prevailing wind are examined.

Mccumber, M.↗

Center of mass estimation in closed vortices - A verification in principle and practice

The problem of tracking closed mesoscale vortices using center of mass estimation techniques is studied. Three estimators are evaluated using data from a warm core Gulf Stream ring. The comparisons show that a method based on the intersection of perpendicular bisectors and one using a least-squares fit of a conic section perform comparably. The perpendicular bisector algorithm is used in conjunction with a Gaussian ring model and a star-shaped survey pattern to produce an expected error curve as a function of vortex translation, survey speed and vortex size. For typical ring parameters, center estimation is usually possible to within + or - 5 km. The feasibility of using differing data sets to construct a history of ring motion based on a coordinate system moving with the ring is also investigated. In this way, the validity of using satellite-derived data and drifter trajectories to estimate the center of mass of a mesoscale feature is assessed. The results of the analysis demonstrate that the location of the deeper structure of the ring and the surface expression are sufficiently well correlated to permit dynamically relevant calculations based on surface measurements. It is shown that satellite-derived data can be used to approximate the center of mass trajectory to within the error in the individual center estimates for the period analyzed. The Lagrangian-drifter-derived centers are offset from the center of mass trajectory in a manner consistent with kinematic arguments.

Hooker, S. B.↗

LSPRAY: Lagrangian Spray Solver for Applications With Parallel Computing and Unstructured Gas-Phase Flow Solvers

Sprays occur in a wide variety of industrial and power applications and in the processing of materials. A liquid spray is a phase flow with a gas as the continuous phase and a liquid as the dispersed phase (in the form of droplets or ligaments). Interactions between the two phases, which are coupled through exchanges of mass, momentum, and energy, can occur in different ways at different times and locations involving various thermal, mass, and fluid dynamic factors. An understanding of the flow, combustion, and thermal properties of a rapidly vaporizing spray requires careful modeling of the rate-controlling processes associated with the spray's turbulent transport, mixing, chemical kinetics, evaporation, and spreading rates, as well as other phenomena. In an attempt to advance the state-of-the-art in multidimensional numerical methods, we at the NASA Lewis Research Center extended our previous work on sprays to unstructured grids and parallel computing. LSPRAY, which was developed by M.S. Raju of Nyma, Inc., is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and/or Monte Carlo probability density function (PDF) solver. The LSPRAY solver accommodates the use of an unstructured mesh with mixed triangular, quadrilateral, and/or tetrahedral elements in the gas-phase solvers. It is used specifically for fuel sprays within gas turbine combustors, but it has many other uses. The spray model used in LSPRAY provided favorable results when applied to stratified-charge rotary combustion (Wankel) engines and several other confined and unconfined spray flames. The source code will be available with the National Combustion Code (NCC) as a complete package.

Raju, Manthena S.↗

Graph-based quantum response theory and shadow Born–Oppenheimer molecular dynamics

Graph-based linear scaling electronic structure theory for quantum-mechanical molecular dynamics simulations [A. M. N. Niklasson et al., J. Chem. Phys. 144, 234101 (2016)] is adapted to the most recent shadow potential formulations of extended Lagrangian Born–Oppenheimer molecular dynamics, including fractional molecular-orbital occupation numbers [A. M. N. Niklasson, J. Chem. Phys. 152, 104103 (2020) and A. M. N. Niklasson, Eur. Phys. J. B 94, 164 (2021)], which enables stable simulations of sensitive complex chemical systems with unsteady charge solutions. The proposed formulation includes a preconditioned Krylov subspace approximation for the integration of the extended electronic degrees of freedom, which requires quantum response calculations for electronic states with fractional occupation numbers. For the response calculations, we introduce a graph-based canonical quantum perturbation theory that can be performed with the same natural parallelism and linear scaling complexity as the graph-based electronic structure calculations for the unperturbed ground state. Further, the proposed techniques are particularly well-suited for semi-empirical electronic structure theory, and the methods are demonstrated using self-consistent charge density-functional tight-binding theory both for the acceleration of self-consistent field calculations and for quantum-mechanical molecular dynamics simulations. Graph-based techniques combined with the semi-empirical theory enable stable simulations of large, complex chemical systems, including tens-of-thousands of atoms.

74 ATOMIC AND MOLECULAR PHYSICS↗

Pressure Fluctuations Induced by a Hypersonic Turbulent Boundary Layer

Direct numerical simulations (DNS) are used to examine the pressure fluctuations generated by a spatially-developed Mach 5.86 turbulent boundary layer. The unsteady pressure field is analyzed at multiple wall-normal locations, including those at the wall, within the boundary layer (including inner layer, the log layer, and the outer layer), and in the free stream. The statistical and structural variations of pressure fluctuations as a function of wall-normal distance are highlighted. Computational predictions for mean velocity pro les and surface pressure spectrum are in good agreement with experimental measurements, providing a first ever comparison of this type at hypersonic Mach numbers. The simulation shows that the dominant frequency of boundary-layer-induced pressure fluctuations shifts to lower frequencies as the location of interest moves away from the wall. The pressure wave propagates with a speed nearly equal to the local mean velocity within the boundary layer (except in the immediate vicinity of the wall) while the propagation speed deviates from the Taylor's hypothesis in the free stream. Compared with the surface pressure fluctuations, which are primarily vortical, the acoustic pressure fluctuations in the free stream exhibit a significantly lower dominant frequency, a greater spatial extent, and a smaller bulk propagation speed. The freestream pressure structures are found to have similar Lagrangian time and spatial scales as the acoustic sources near the wall. As the Mach number increases, the freestream acoustic fluctuations exhibit increased radiation intensity, enhanced energy content at high frequencies, shallower orientation of wave fronts with respect to the flow direction, and larger propagation velocity.

Lian Duan↗

High-Order Mesh hr-adaptivity for Surface Fitting to Implicit Geometries

We present an ℎ𝑟-adaptivity framework for morphing a given mesh to fit a target surface prescribed as the zero isocontour of a discrete function. In this framework, high-order meshing is posed as a variational minimization problem that depends on the mesh quality prescribed via the target matrix optimization paradigm (TMOP) and position of a subset of mesh nodes with respect to the target surface. The proposed formulation ensures that the variational problem is converged and mesh quality degradation near the surface is limited, even when the mesh topology is incompatible with the target surface. Additionally, a mesh subset-based approach and ℎ-refinement is introduced to efficiently increase fitting accuracy while reducing the computational cost of the mesh morphing problem. The ℎ𝑟-adaptivity technique extends to different element types in two- and three-dimensions, and can be used in existing finite element and spectral element frameworks to obtain high-order body-fitted meshes. Various numerical experiments demonstrate the robustness and accuracy of the fitting approach for problems of practical interest such as Lagrangian hydrodynamics and topology optimization.

97 MATHEMATICS AND COMPUTING↗

Automatic Differentiation in MetaPhysicL and Its Applications in MOOSE

Efficient solution via Newton’s method of nonlinear systems of equations requires an accurate representation of the Jacobian, corresponding to the derivatives of the component residual equations with respect to the degrees of freedom. In practice these systems of equations often arise from spatial discretization of partial differential equations used to model physical phenomena. These equations may involve domain motion or material equations that are complex functions of the systems’ degrees of freedom. Computing the Jacobian by hand in these situations is arduous and prone to error. Finite difference approximations of the Jacobian or its action are prone to truncation error, especially in multiphysics settings. Symbolic differentiation packages may be used, but often result in an excessive number of terms in realistic model scenarios. An alternative to symbolic and numerical differentiation is automatic differentiation (AD), which propagates derivatives with every elementary operation of a computer program, corresponding to continual application of the chain rule. Automatic differentiation offers the guarantee of an exact Jacobian at a relatively small overhead cost. In this work, we outline the adoption of AD in the Multiphysics Object Oriented Simulation Environment (MOOSE) via the MetaPhysicL package. We describe the application of MOOSE’s AD capability to several sets of physics that were previously infeasible to model via hand-coded or Jacobian-free simulation techniques, including arbitrary Lagrangian-Eulerian and level-set simulations of laser melt pools, phase-field simulations with free energies provided through neural networks, and metallic nuclear fuel simulations that require inner Newton loop calculation of nonlinear material properties.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Extension of the Time-Spectral Approach to Overset Solvers for Arbitrary Motion

Forced periodic flows arise in a broad range of aerodynamic applications such as rotorcraft, turbomachinery, and flapping wing configurations. Standard practice involves solving the unsteady flow equations forward in time until the initial transient exits the domain and a statistically stationary flow is achieved. It is often required to simulate through several periods to remove the initial transient making unsteady design optimization prohibitively expensive for most realistic problems. An effort to reduce the computational cost of these calculations led to the development of the Harmonic Balance method [1, 2] which capitalizes on the periodic nature of the solution. The approach exploits the fact that forced temporally periodic flow, while varying in the time domain, is invariant in the frequency domain. Expanding the temporal variation at each spatial node into a Fourier series transforms the unsteady governing equations into a steady set of equations in integer harmonics that can be tackled with the acceleration techniques afforded to steady-state flow solvers. Other similar approaches, such as the Nonlinear Frequency Domain [3,4,5], Reduced Frequency [6] and Time-Spectral [7, 8, 9] methods, were developed shortly thereafter. Additionally, adjoint-based optimization techniques can be applied [10, 11] as well as frequency-adaptive methods [12, 13, 14] to provide even more flexibility to the method. The Fourier temporal basis functions imply spectral convergence as the number of harmonic modes, and correspondingly number of time samples, N, is increased. Some elect to solve the equations in the frequency domain directly, while others choose to transform the equations back into the time domain to simplify the process of adding this capability to existing solvers, but each harnesses the underlying steady solution in the frequency domain. These temporal projection methods will herein be collectively referred to as Time-Spectral methods. Time-Spectral methods have demonstrated marked success in reducing the computational costs associated with simulating periodic forced flows, but have yet to be fully applied to overset or Cartesian solvers for arbitrary motion with dynamic hole-cutting. Overset and Cartesian grid methodologies are versatile techniques capable of handling complex geometry configurations in practical engineering applications, and the combination of the Time-Spectral approach with this general capability potentially provides an enabling new design and analysis tool. In an arbitrary moving-body scenario for these approaches, a Lagrangian body moves through a fixed Eulerian mesh and mesh points in the Eulerian mesh interior to the solid body are removed (cut or blanked), leaving a hole in the Eulerian mesh. During the dynamic motion some gridpoints in the domain are blanked and do not have a complete set of time-samples preventing a direct implementation of the Time-Spectral method. Murman[6] demonstrated the Time-Spectral approach for a Cartesian solver with a rigid domain motion, wherein the hole cutting remains constant. Similarly, Custer et al. [15, 16] used the NASA overset OVERFLOW solver and limited the amount of relative motion to ensure static hole-cutting and interpolation. Recently, Mavriplis and Mundis[17] demonstrated a qualitative method for applying the Time-Spectral approach to an unstructured overset solver for arbitrary motion. The goal of the current work is to develop a robust and general method for handling arbitrary motion with the Time-Spectral approach within an overset or Cartesian mesh method, while still approaching the spectral convergence rate of the original Time-Spectral approach. The viscous OVERFLOW solver will be augmented with the new Time-Spectral algorithm and the capability of the method for benchmark problems in rotorcraft and turbomachinery will be demonstrated. This abstract begins with a brief synopsis of the Time-Spectral approach for overset grids and provides details of e current approach to allow for arbitrary motion. Model problem results in one and two dimensions are included to demonstrate the viability of the method and the convergence properties. Section IV briefly outlines the implementation into the OVERFLOW solver, and the abstract closes with a description of the benchmark test cases which will be included in the final paper.

Leffell, Joshua Isaac↗

Drop Breakup in Fixed Bed Flows as Model Stochastic Flow Fields

We examine drop breakup in a class of stochastic flow fields as a model for the flow through fixed fiber beds and to elucidate the general mechanisms whereby drops breakup in disordered, Lagrangian unsteady flows. Our study consists of two parallel streams of investigation. First, large scale numerical simulations of drop breakup in a class of anisotropic Gaussian fields will be presented. These fields are generated spectrally and have been shown in a previous publication to be exact representations of the flow in a dilute disordered bed of fibers if close interactions between the fibers and the drops are dynamically unimportant. In these simulations the drop shape is represented by second and third order small deformation theories which have been shown to be excellent for the prediction of drop breakup in steady strong flows. We show via these simulations that the mechanisms of drop breakup in these flows are quite different than in steady flows. The predominant mechanism of breakup appears to be very short lived twist breakups. Moreover, the occurrence of breakup events is poorly predicted by either the strength of the local flow in which the drop finds itself at breakup, or the degree of deformation that the drop achieves prior to breakup. It is suggested that a correlation function of both is necessary to be predictive of breakup events. In the second part of our research experiments are presented where the drop deformation and breakup in PDMS/polyisobutylene emulsions is considered. We consider very dilute emulsions such that coalescence is unimportant. The flows considered are simple shear and the flow through fixed fiber beds. Turbidity, small angle light scattering, dichroism and microscopy are used to interrogate the drop deformation process in both flows. It is demonstrated that breakup at very low capillary numbers occurs in both flows but larger drop deformation occurs in the fixed bed flow. Moreover, it is witnessed that breakup in the bed occurs continuously during flow and apparently with uniform probability through the bed length. The drop deformations witnessed in our experiments are larger than those predicted by the numerical simulations, and future plans to investigate these differences are discussed.

Shaqfeh, Eric S. G.↗

Implementation of the NCAR Community Land Model (CLM) in the NASA/NCAR finite-volume Global Climate Model (fvGCM)

In this study, the NCAR CLM version 2.0 land-surface model was integrated into the NASA/NCAR fvGCM. The CLM was developed collaboratively by an open interagency/university group of scientists and based on well-proven physical parameterizations and numerical schemes that combine the best features of BATS, NCAR-LSM, and IAP94. The CLM design is a one-dimensional point model with 1 vegetation layer, along with sub-grid scale tiles. The features of the CLM include 10-uneven soil layers with water, ice, and temperature states in each soil layer, and five snow layers, with water flow, refreezing, compaction, and aging allowed. In addition, the CLM utilizes two-stream canopy radiative transfer, the Bonan lake model and topographic enhanced streamflow based on TOPMODEL. The DAO fvGCM uses a genuinely conservative Flux-Form Semi-Lagrangian transport algorithm along with terrain- following Lagrangian control-volume vertical coordinates. The physical parameterizations are based on the NCAR Community Atmosphere Model (CAM-2). For our purposes, the fvGCM was run at 2 deg x 2.5 deg horizontal resolution with 55 vertical levels. The 10-year climate from the fvGCM with CLM2 was intercompared with the climate from fvGCM with LSM, ECMWF and NCEP. We concluded that the incorporation of CLM2 did not significantly impact the fvGCM climate from that of LSM. The most striking difference was the warm bias in the CLM2 surface skin temperature over desert regions. We determined that the warm bias can be partially attributed to the value of the drag coefficient for the soil under the canopy, which was too small resulting in a decoupling between the ground surface and the canopy. We also discovered that the canopy interception was high compared to observations in the Amazon region. A number of experiments were then performed focused on implementing model improvements. In order to correct the warm bias, the drag coefficient for the soil under the canopy was considered a function of LAI (Leaf Area Index). Analysis of the results revealed that there was a substantial impact, and the warm and dry bias in the CLM2 was significantly reduced. For the interception scheme, the canopy throughfall was increased to allow for more infiltration of precipitation into the soil, resulting in increased low-level moisture and a decrease in the interception loss ratio (canopy evaporation to precipitation).

Radakovich, Jon D.↗

A survey of the core-congruential formulation for geometrically nonlinear TL finite elements

This article presents a survey of the core-congruential formulation (CCF) for geometrically nonlinear mechanical finite elements based on the total Lagrangian (TL) kinematic description. Although the key ideas behind the CCF can be traced back to Rajasekaran and Murray in 1973, it has not subsequently received serious attention. The CCF is distinguished by a two-phase development of the finite element stiffness equations. The initial phase developed equations for individual particles. These equations are expressed in terms of displacement gradients as degrees of freedom. The second phase involves congruential-type transformations that eventually binds the element particles of an individual element in terms of its node-displacement degrees of freedom. Two versions of the CCF, labeled direct and generalized, are distinguished. The direct CCF (DCCF) is first described in general form and then applied to the derivation of geometrically nonlinear bar, and plane stress elements using the Green-Lagrange strain measure. The more complex generalized CCF (GCCF) is described and applied to the derivation of 2D and 3D Timoshenko beam elements. Several advantages of the CCF, notably the physically clean separation of material and geometric stiffnesses, and its independence with respect to the ultimate choice of shape functions and element degrees of freedom, are noted. Application examples involving very large motions solved with the 3D beam element display the range of applicability of this formulation, which transcends the kinematic limitations commonly attributed to the TL description.

Felippa, Carlos A.↗