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At least 343 records · Page 19

(U) A Theoretical Study of Asay Foil Trajectories (V.02)

We consider the trajectory of a generic Asay foil ejecta momentum diagnostic sensor, for scenarios where ejecta are produced at a planar surface and fly ballistically through a perfect vacuum to the sensor. To do so, we build upon a previously established mathematical formalism derived for the analytic study of stationary sensors (i.e., piezopins). First, we derive the momentum conservation equation for the problem, in a form amenable to accelerating sensors, in terms of a generic ejecta source areal mass function (“source model”). This defines an integro-differential equation (IDE) for the foil trajectory. When ejecta production is instantaneous - as is generally assumed in momentum diagnostic data analyses - the IDE leads to an implicit and easily calculable closed-form solution for the foil trajectory in a perfect system, as long as the ejecta particle velocity distribution is twice-integrable. General properties of the instant-production trajectory solution indicate the existence of a boundary condition the particle velocity distribution must satisfy in order for the analytically predicted foil trajectories to be compatible with certain features commonly observed in foil data. This boundary condition is identical to one derived previously from a consideration of piezopin data. Armed with the analytic solution for instant production, we also consider various techniques used to extract time-dependent cumulative ejecta masses from foil trajectories, and derive an expression for the error imposed by using an approximated equation of motion. This analytic trajectory solution furthermore makes it possible to examine the common practice of presenting inferred cumulative ejecta masses as a function of a normalized implied velocity; we derive conditions under which this methodology is and is not meaningful. We also propose a strategy for extending the instant-production trajectory solution to time-dependent source functions.

42 ENGINEERING↗

Data-Driven Recommendation of Optimal Tuning Scheme for Range-Separated Hybrid Functionals in Solution-Phase UV/Vis Absorption Energy Prediction

Time-dependent density functional theory (TDDFT) combined with range-separated hybrid (RSH) functionals and a tuned range-separation parameter γ offers a computationally economical approach for high-throughput excited- state property predictions. The γ-tuning procedure in the gas phase is well established. However, no agreement on the best γ- tuning procedure has been made when considering the solvent effect with implicit solvent models like the polarizable continuum model (PCM). To answer that question, this study created a diverse dataset with 937 molecules with experimental solutionphase UV/vis absorption spectra. Three γ-tuning methods, the gasphase γ-tuning (GPγT), the partial vertical γ-tuning (PVγT), and the strict vertical γ-tuning (SVγT), were evaluated for the ωPBEh functional over the entire dataset. Additional benchmarks are done for the optimally tuned screened range-separated hybrid combined with the PCM approach (SRSH-PCM) and the solvation-mediated tuning procedure (sol-med-OT). Our findings revealed that the optimal γ-values obtained by the PVγT and the SVγT are significantly smaller than the GPγT. This trend holds consistently across all molecules in our dataset, and we explained the origin of this phenomenon. TDDFT calculations with PVγTand SVγT-tuned γ-values and default global Fock exchange fraction achieve superior performance compared to those using GPγTtuned or default γ and slightly outperform SRSH-PCM and sol-med-OT with similar or lesser computational cost. Furthermore, we found that the smaller γ-values from SVγT captured the expected 1/(εR) asymptotic behavior in the solution phase, resulting in accurate prediction of solution-phase CT excitations, consistent with the screened asymptote behavior encoded in SRSH-PCM. These results show that SVγT is the best scheme for high-throughput UV/vis absorption spectrum calculations using the ωPBEh functional from a data-driven perspective.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Multiscale model predictive control of battery systems for frequency regulation markets using physics-based models

In this work, we propose a multiscale model predictive control (MPC) framework for stationary battery systems that exploits high-fidelity models to trade-off short-term economic incentives provided by energy and frequency regulation (FR) markets and long-term degradation effects. We find that the MPC framework can drastically reduce long-term degradation while properly responding to FR and energy market signals (compared to MPC formulations that use low-fidelity models). Our results also provide evidence that sophisticated battery models can be embedded within closed-loop MPC simulations by using modern nonlinear programming solvers (we provide an efficient and easy-to-use implementation in Julia). We use insights obtained with our simulations to design a low-complexity MPC formulation that matches the behavior obtained with high-fidelity models. This is done by designing a suitable terminal penalty term that implicitly captures long-term degradation. The results suggest that complex degradation behavior can be accounted for in low-complexity MPC formulations by properly designing the cost function. We believe that our proof-of-concept results can be of industrial relevance, as battery vendors are seeking to participate in fast-changing electricity markets while maintaining asset integrity.

42 ENGINEERING↗

Semantic embedding for quantum algorithms

The study of classical algorithms is supported by an immense understructure, founded in logic, type, and category theory, that allows an algorithmist to reason about the sequential manipulation of data irrespective of a computation’s realizing dynamics. As quantum computing matures, a similar need has developed for an assurance of the correctness of high-level quantum algorithmic reasoning. Parallel to this need, many quantum algorithms have been unified and improved using quantum signal processing (QSP) and quantum singular value transformation (QSVT), which characterize the ability, by alternating circuit ansätze, to transform the singular values of sub-blocks of unitary matrices by polynomial functions. However, while the algebraic manipulation of polynomials is simple (e.g., compositions and products), the QSP/QSVT circuits realizing analogous manipulations of their embedded polynomials are non-obvious. This work constructs and characterizes the runtime and expressivity of QSP/QSVT protocols where circuit manipulation maps naturally to the algebraic manipulation of functional transforms (termed semantic embedding). In this way, QSP/QSVT can be treated and combined modularly, purely in terms of the functional transforms they embed, with key guarantees on the computability and modularity of the realizing circuits. We also identify existing quantum algorithms whose use of semantic embedding is implicit, spanning from distributed search to proofs of soundness in quantum cryptography. The methods used, based in category theory, establish a theory of semantically embeddable quantum algorithms, and provide a new role for QSP/QSVT in reducing sophisticated algorithmic problems to simpler algebraic ones.

Physics↗

Field-Dependent Ionic Conductivities from Generalized Fluctuation-Dissipation Relations

We derive a relationship for the electric field dependent ionic conductivity in terms of fluctuations of time integrated microscopic variables. We demonstrate this formalism with molecular dynamics simulations of solutions of differing ionic strength with implicit solvent conditions and molten salts. These calculations are aided by a novel nonequilibrium statistical reweighting scheme that allows for the conductivity to be computed as a continuous function of the applied field. In strong electrolytes, we find the fluctuations of the ionic current are Gaussian, and subsequently, the conductivity is constant with applied field. In weaker electrolytes and molten salts, we find the fluctuations of the ionic current are strongly non-Gaussian, and the conductivity increases with applied field. Furthermore, this nonlinear behavior, known phenomenologically for dilute electrolytes as the Onsager-Wien effect, is general and results from the suppression of ionic correlations at large applied fields, as we elucidate through both dynamic and static correlations within nonequilibrium steady states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

(U) An Analytic Examination of Piezoelectric Ejecta Mass Measurements

Ongoing efforts to validate a Richtmyer-Meshkov instability (RMI) based ejecta source model [1, 2, 3] in LANL ASC codes use ejecta areal masses derived from piezoelectric sensor data [4, 5, 6]. However, the standard technique for inferring masses from sensor voltages implicitly assumes instantaneous ejecta creation [7], which is not a feature of the RMI source model. To investigate the impact of this discrepancy, we define separate “areal mass functions” (AMFs) at the source and sensor in terms of typically unknown distribution functions for the ejecta particles, and derive an analytic relationship between them. Then, for the case of single-shock ejection into vacuum, we use the AMFs to compare the analytic (or “true”) accumulated mass at the sensor with the value that would be inferred from piezoelectric voltage measurements. We confirm the inferred mass is correct when creation is instantaneous, and furthermore prove that when creation is not instantaneous, the inferred values will always overestimate the true mass. Finally, we derive an upper bound for the error imposed on a perfect system by the assumption of instantaneous ejecta creation. When applied to shots in the published literature, this bound is frequently less than several percent. Errors exceeding 15% may require velocities or timescales at odds with experimental observations.

47 OTHER INSTRUMENTATION↗

Assessment of an Unstructured-Grid Method for Predicting 3-D Turbulent Viscous Flows

A method is presented for solving turbulent flow problems on three-dimensional unstructured grids. Spatial discretization is accomplished by a cell-centered finite-volume formulation using an accurate linear reconstruction scheme and upwind flux differencing. Time is advanced by an implicit backward-Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the sublayer region of the boundary layer. A systematic assessment of the method is presented to devise guidelines for more strategic application of the technology to complex problems. The assessment includes the accuracy in predictions of skin-friction coefficient, law-of-the-wall behavior, and surface pressure for a flat-plate turbulent boundary layer, and for the ONERA M6 wing under a high Reynolds number, transonic, separated flow condition.

Frink, Neal T.↗

Tetrahedral Finite-Volume Solutions to the Navier-Stokes Equations on Complex Configurations

A review of the algorithmic features and capabilities of the unstructured-grid flow solver USM3Dns is presented. This code, along with the tetrahedral grid generator, VGRIDns, is being extensively used throughout the U.S. for solving the Euler and Navier-Stokes equations on complex aerodynamic problems. Spatial discretization is accomplished by a tetrahedral cell-centered finite-volume formulation using Roe's upwind flux difference splitting. The fluxes are limited by either a Superbee or MinMod limiter. Solution reconstruction within the tetrahedral cells is accomplished with a simple, but novel, multidimensional analytical formula. Time is advanced by an implicit backward-Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the near-wall region of the boundary layer. The issues of accuracy and robustness of USM3Dns Navier-Stokes capabilities are addressed for a flat-plate boundary layer, and a full F-16 aircraft with external stores at transonic speed.

Frink, Neal T.↗

Tetrahedral Finite-Volume Solutions to the Navier-Stokes Equations on Complex Configurations

A review of the algorithmic features and capabilities of the unstructured-grid flow solver USM3Dns is presented. This code, along with the tetrahedral grid generator, VGRIDns, is being extensively used throughout the U.S. for solving the Euler and Navier-Stokes equations on complex aerodynamic problems. Spatial discretization is accomplished by a tetrahedral cell-centered finite-volume formulation using Roe's upwind flux difference splitting. The fluxes are limited by either a Superbee or MinMod limiter. Solution reconstruction within the tetrahedral cells is accomplished with a simple, but novel, multidimensional analytical formula. Time is advanced by an implicit backward-Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the near-wall region of the boundary layer. The issues of accuracy and robustness of USM3Dns Navier-Stokes capabilities are addressed for a flat-plate boundary layer, and a full F-16 aircraft with external stores at transonic speed.

Frink, N. T.↗

An implicit solution for Asay foil trajectories generated by separable, sustained-production ejecta source models

We present a simple implicit solution for the time-dependent trajectory of a thin Asay foil ejecta diagnostic for the general case where the impinging ejecta cloud is generated by a source function characterized by an arbitrary (sustained) time dependence and a time-independent (stationary) particle velocity distribution. In the limit that the source function time dependence becomes a delta function, this solution—which is amenable to rapid numerical calculations of arbitrary accuracy—exactly recovers a previously published solution for the special case of instantaneous ejecta production. We also derive simple expressions for the free-surface arrival (catch-up) time as well as the true ejecta areal mass accumulation on the accelerating foil and place bounds on the level of error incurred when applying instant-production mass solutions to a sustained-production trajectory. We demonstrate these solutions with example calculations for hypothetical source functions spanning a wide range of ejecta production durations, velocity distributions, and temporal behaviors. These calculations demonstrate how the foil trajectory is often insensitive to the temporal dependence of the source function, instead being dominated by the velocity distribution. We quantify this insensitivity using a “compatibility score” metric. Under certain conditions, one may capitalize upon this insensitivity to obtain a good approximation of the second integral of the velocity distribution from the observed foil trajectory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Improving the convergence rate of parabolic ADI methods

The rate of convergence to steady state of parabolic Alternating Direction Implicit (ADI) solvers is analyzed in terms of the L(2)-norms of the residuals. The analysis allows one to predict the number of iterations necessary for convergence as function of the Courant number, Lambda. A simple modification of existing ADI codes is devised. It improves the convergence rate substantially and is insensitive to the Courant number in a large range of Lambda.

Abarbanel, S. S.↗

On the Circulation Manifold for Two Adjacent Lifting Sections

The circulation functional relative to two adjacent lifting sections is studied for two cases. In the first case we consider two adjacent circles. The circulation is computed as a function of the displacement of the secondary circle along the axis joining the two centers and of the angle of attack of the secondary circle, The gradient of such functional is computed by deriving a set of elliptic functions with respect both to their argument and to their Period. In the second case studied, we considered a wing-flap configuration. The circulation is computed by some implicit mappings, whose differentials with respect to the variation of the geometrical configuration in the physical space are found by divided differences. Configurations giving rise to local maxima and minima in the circulation manifold are presented.

Zannetti, Luca↗

Tensor-Product Preconditioners for Higher-Order Space-Time Discontinuous Galerkin Methods

space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equat ions. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

Diosady, Laslo T.↗

Realizability-preserving DG-IMEX method for the two-moment model of fermion transport

Building on the framework of Zhang & Shu [1], [2], we develop a realizability-preserving method to simulate the transport of particles (fermions) through a background material using a two-moment model that evolves the angular moments of a phase space distribution function f . The two-moment model is closed using algebraic moment closures; e.g., as proposed by Cernohorsky & Bludman [3] and Banach & Larecki [4]. Variations of this model have recently been used to simulate neutrino transport in nuclear astrophysics applications, including core-collapse supernovae and compact binary mergers. We employ the discontinuous Galerkin (DG) method for spatial discretization (in part to capture the asymptotic diffusion limit of the model) combined with implicit-explicit (IMEX) time integration to stably bypass short timescales induced by frequent interactions between particles and the background. Appropriate care is taken to ensure the method preserves strict algebraic bounds on the evolved moments (particle density and flux) as dictated by Pauli's exclusion principle, which demands a bounded distribution function (i.e., f ϵ [0,1]). This realizability-preserving scheme combines a suitable CFL condition, a realizability-enforcing limiter, a closure procedure based on Fermi-Dirac statistics, and an IMEX scheme whose stages can be written as a convex combination of forward Euler steps combined with a backward Euler step. The IMEX scheme is formally only first-order accurate, but works well in the diffusion limit, and — without interactions with the background — reduces to the optimal second-order strong stability-preserving explicit Runge-Kutta scheme of Shu & Osher [5]. Numerical results demonstrate the realizability-preserving properties of the scheme. As a result, we also demonstrate that the use of algebraic moment closures not based on Fermi-Dirac statistics can lead to unphysical moments in the context of fermion transport.

97 MATHEMATICS AND COMPUTING↗

ORNL_AISD-Ex: Quantum chemical prediction of UV/Vis absorption spectra for over 10 million organic molecules

We performed calculations of electronic excitation energies and associated oscillator strengths based on the time-dependent density-functional tight-binding (TD-DFTB) method [1]. The SMILES (Simplified molecular-input line-entry system) strings of the molecules from the AISD HOMO-LUMO database [2] were converted to a 3D atomistic structure and stored in a PDB file after preliminary geometry optimization using the Merck Molecular Force Field (MMFF94) in RDKit [3,4]. The primary information stored in the PDB file archive consists of Cartesian coordinates for each atom of the molecule in their 3D location in space, along with summary information about the structure, sequence, and experiment. We then performed molecular geometry optimization using the density-functional tight-binding (DFTB) method [5] in the electronic ground state, followed by single-point excited states calculations, as described below. We note that, since RDKit employs a random choice for the generation of molecular conformers, the molecular geometries obtained in this dataset could be different from the ones that were generated when the AISD HOMO-LUMO dataset was generated. The computed excitation energies and associated oscillator strengths can be converted to predict UV/Vis absorption spectra, where excitation energies correspond to absorption peak positions, and oscillator strengths are a good measure of the probability of absorption of visible or UV light in transitions between electronic ground and excited states. The conversion of SMILES strings to 3D Cartesian coordinates of fully DFTB-optimized molecules was successful for 10,502,904 out of 10,502,917 molecules. For these molecules, both geometry optimizations and excited states calculations were successful. The DFTB calculations did not complete for 13 molecules of the original AISD HOMO-LUMO dataset. We still provide information about the geometry of these molecules. The molecules are diverse for chemical compositions (which span 5 non-hydrogen elements: oxygen, carbon, nitrogen, fluorine, sulfur) and molecular size (the smallest molecule contains 5 non-hydrogen atoms, and the largest molecule contains 71 non-hydrogen atoms). The DFTB method [5] is an approximation to density functional theory (DFT), utilizing a minimal basis set in conjunction with a two-center approximation to the electronic Hamiltonian and overlap matrix elements. The DFTB total energy is the sum of an electronic and a repulsive energy contribution, and their calculation requires optimized electronic parameters and diatomic repulsive potential energy functions. All DFTB calculations were performed using the DFTB+ code [6] (version 21.2) and the wrapper for DFTB+ in the Atomic Simulation Environment (ASE) (version 3.22.1) [7], which performed an internal conversion of Cartesian coordinates from PDB to the .gen file format. For the geometry optimizations on the electronic ground state potential energy surface of the molecules, we have chosen the third-order DFTB (DFTB3) method [5c] and employed the matching 3ob set of electronic parameters and repulsive potentials [8]. The empirical γ-damping for hydrogen bond correction, and Grimme's D3 empirical dispersion correction with Becke-Johnson damping (D3(BJ)) [9] dispersion correction was included to improve the description of non-covalent interactions. For excited states single-point energy calculations, we employed the TD-DFTB method in conjunction with the DFTB2 method [5b] and the matching mio [5b,10] and halorg [11] parameter sets. We opted to request the simultaneous calculation of 50 excited states for singlet transition to investigate sufficient number of excited states, based on linear response theory using the Casida equation [Ref: T. A. Niehaus, S. Suhai, F. Della Sala, P Lugli, M. Elstner, G. Seifert, and Th. Frauenheim. Tight-binding approach to time-dependent density-functional response theory. Phys. Rev. B, 63:085108, 2001] and the ARPACK diagonalizer [R. B. Lehoucq, D. C. Sorensen, and C. Yang. Arpack users guide: Solution of large-scale eigenvalue problems by implicitly restarted arnoldi methods, 1997. 46, 51]. The dataset contains 1001 tar.gz files. Tar files are named as “ornl_aisd_ex_1.tar.gz†through “ornl_aisd_ex_1000.tar.gzâ€. Additionally, the 13 failed molecules are in “ornl_aisd_ex_unprocessed.tar.gzâ€. Except for the tar files listed below, each tar file contains 10,500 molecules. Tar files numbered 34, 121, 128, 352, 360, 429, 495, 509, 518, 627, 676, 668, and 862 contain 10,499 molecules each. The last tar file numbered 1000 contains 13,417 molecules. The total size of the uncompressed dataset is over 283 Gigabytes. The code for calculating the electronic excitation energies and statistical analysis of the dataset is provided at the following GitLab repository: https://github.com/ORNL/Analysis-of-Large-Scale-Molecular-Datasets-with-Python Calculating the UV spectrum of a molecule requires performing 3 main operations: 1. Converting the smiles string representation of a molecule into a geometric structure where each atom is assigned XYZ coordinates. The geometric structure is written to the file smiles.pdb. 2. Using smiles.pdb to compute the relaxed geometry of the molecule, which corresponds with the position of the atoms at the position of equilibrium at the ground state. This generates the files band.out, detailed.out, and geo_end.gen. 3. Using geo_end.gen to calculate the UV spectrum of the molecule which is written into the file EXC.DAT. Every molecule in the dataset has its own directory. The files contained in each molecule directory are as follows: 1. geo_end.gen 2. detailed.out 3. band.out 4. EXC.DAT 5. smiles.pdb REFERENCES [1] Niehaus, T. A.; Suhai, S.; Della Salla, F.; Lugli, P.; Elstner, M.; Seifert, G.; Frauenheim, Th. Tight-binding approach to time-dependent density-functional response theory. Phys. Rev. B, 2001, 63, 085108/1-9. [2] Blanchard, A.; Gounley, J.; Metha, K.; Yoo, P.; Irle, S. AISD HOMO-LUMO. DOI: 10.13139/ORNLNCCS/1869409 [3] RDKit: Cheminformatics and Machine Learning Software. 2013, [http://www.rdkit.org] [4] Tosco, P.; Stiefl, N. and Landrum, G. Bringing the MMFF force field to the RDKit: implementation and validation. J Cheminform. 2014, 6, 1–4. [5] a) Porezag, D.; Frauenheim, T.; Kohler, T.; Seifert, G.; Kaschner, Construction of tight-binding-like potentials on the basis of density-functional theory: Application to carbon, R. Phys. Rev. B 1995, 51, 12947-12957; b) Elstner, M.; Porezag, D.; Jungnickel, G.; Elsner, J.; Haugk, M.; Frauenheim, Th.; Suhai, S.; Seifert, G.; Phys. Rev. B 1998, 58, 7260-7268; c) Gaus, M.; Cui, Q.; Elstner, M. DFTB3: Extension of the Self-Consistent-Charge Density-Functional Tight-Binding Method (SCC-DFTB), J. Chem. Theory Comput. 2011, 7, 931-948; d) Cui, Q.; Elstner, M. Density functional tight binding: values of semi-empirical methods in an ab initio era, Phys. Chem. Chem. Phys. 2014, 16, 14368-14377. [6] Hourahine, B. et al. DFTB+, a software package for efficient approximate density functional theory based atomistic simulations, J. Chem. Phys. 2020, 152, 124101/1-19. [7] Larsen, A. H. et al. The atomic simulation environment—a Python library for working with atoms. J. Phys.: Cond. Matter 2017, 29, 273002. [8] Kubillus, M.; Kubar, T.; Gaus, M.; Rezac, J.; Elstner, M. Parameterization of the DFTB3 Method for Br, Ca, Cl, F, I, K, and Na in Organic and Biological Systems, J. Chem. Theory Comput. 2015, 11, 332-342. [9] Brandenburg, J. G.; Grimme, S. Accurate Modeling of Organic Molecular Crystals by Dispersion-Corrected Density Functional Tight Binding (DFTB), J. Phys. Chem. Lett. 2014, 5, 1785−1789. [10] a) Niehaus, T. A.; Elstner, M.; Frauenheim, Th.; Suhai, S. Application of an approximate density-functional method to sulfur containing compounds. J. Mol. Struct.: THEOCHEM 2001, 541, 185-94; b) Elstner, M.; Hobza, P.; Frauenheim, Th.; Suhai, S.; Kaxiras, E. Hydrogen bonding and stacking interactions of nucleic acid base pairs: A density-functional-theory based treatment. J. Chem. Phys. 2001, 114, 5149-55. [11] Kubar, T.; Bodrog, Z.; Gaus, M.; Köhler, C.; Aradi, B.; Frauenheim, Th.; Elstner, M. Parametrization of the SCC-DFTB Method for Halogens. J. Chem. Theory Comput. 2013, 9, 2939-49.

36 MATERIALS SCIENCE↗

iAPBS: a programming interface to Adaptive Poisson-Boltzmann Solver

The Adaptive Poisson-Boltzmann Solver (APBS) is a state-of-the-art suite for performing Poisson-Boltzmann electrostatic calculations on biomolecules. The iAPBS package provides a modular programmatic interface to the APBS library of electrostatic calculation routines. The iAPBS interface library can be linked with a Fortran or C/C++ program thus making all of the APBS functionality available from within the application. Several application modules for popular molecular dynamics simulation packages -- Amber, NAMD and CHARMM are distributed with iAPBS allowing users of these packages to perform implicit solvent electrostatic calculations with APBS.

electrostatics↗

THOR: A NEW AND FLEXIBLE GLOBAL CIRCULATION MODEL TO EXPLORE PLANETARY ATMOSPHERES

We have designed and developed, from scratch, a global circulation model (GCM) named THOR that solves the three-dimensional nonhydrostatic Euler equations. Our general approach lifts the commonly used assumptions of a shallow atmosphere and hydrostatic equilibrium. We solve the “pole problem” (where converging meridians on a sphere lead to increasingly smaller time steps near the poles) by implementing an icosahedral grid. Irregularities in the grid, which lead to grid imprinting, are smoothed using the “spring dynamics” technique. We validate our implementation of spring dynamics by examining calculations of the divergence and gradient of test functions. To prevent the computational time step from being bottlenecked by having to resolve sound waves, we implement a split-explicit method together with a horizontally explicit and vertically implicit integration. We validate our GCM by reproducing the Earth and hot-Jupiter-like benchmark tests. THOR was designed to run on graphics processing units (GPUs), which allows for physics modules (radiative transfer, clouds, chemistry) to be added in the future, and is part of the open-source Exoclimes Simulation Platform (www.exoclime.org).

79 ASTRONOMY AND ASTROPHYSICS↗

Finite difference solution to the three-dimensional, incompressible thermal energy boundary-layer equation

An implicit numerical method has been adopted for the solution to the three-dimensional, energy boundary-layer equation. The energy equation is written in terms of a dimensionless temperature function, the relative stagnation-enthalpy difference, and transformed by the introduction of a Blasius-type transformation of coordinates as well as dimensionless stream functions. The method is applied to the problem consisting of an infinite cylinder joined with its axis perpendicular to a thin, flat, heated plate. A Prandtl number equal to one is simply considered.

Fillo, J. A.↗