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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Grid generation in three dimensions by Poisson equations with control of cell size and skewness at boundary surfaces

An algorithm for generating computational grids about arbitrary three-dimensional bodies is developed. The elliptic partial differential equation (PDE) approach developed by Steger and Sorenson and used in the NASA computer program GRAPE is extended from two to three dimensions. Forcing functions which are found automatically by the algorithm give the user the ability to control mesh cell size and skewness at boundary surfaces. This algorithm, as is typical of PDE grid generators, gives smooth grid lines and spacing in the interior of the grid. The method is applied to a rectilinear wind-tunnel case and to two body shapes in spherical coordinates.

Sorenson, R. L.↗
DOE OSTI2016

WHITE DWARF MERGERS ON ADAPTIVE MESHES. I. METHODOLOGY AND CODE VERIFICATION

The Type Ia supernova (SN Ia) progenitor problem is one of the most perplexing and exciting problems in astrophysics, requiring detailed numerical modeling to complement observations of these explosions. One possible progenitor that has merited recent theoretical attention is the white dwarf (WD) merger scenario, which has the potential to naturally explain many of the observed characteristics of SNe Ia. To date there have been relatively few self-consistent simulations of merging WD systems using mesh-based hydrodynamics. This is the first paper in a series describing simulations of these systems using a hydrodynamics code with adaptive mesh refinement. In this paper we describe our numerical methodology and discuss our implementation in the compressible hydrodynamics code CASTRO, which solves the Euler equations, and the Poisson equation for self-gravity, and couples the gravitational and rotation forces to the hydrodynamics. Standard techniques for coupling gravitation and rotation forces to the hydrodynamics do not adequately conserve the total energy of the system for our problem, but recent advances in the literature allow progress and we discuss our implementation here. We present a set of test problems demonstrating the extent to which our software sufficiently models a system where large amounts of mass are advected on the computational domain over long timescales. Future papers in this series will describe our treatment of the initial conditions of these systems and will examine the early phases of the merger to determine its viability for triggering a thermonuclear detonation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Simulation of the effective concentration profiles in InGaAs/GaAs heterostructures containing δ-doped layers

InGaAs/GaAs heterostructures containing quantum wells and δ-doped layers are studied theoretically and experimentally. On the basis of the procedure of self-consistently solving the Schrödinger equation and Poisson equation, the differential capacitance and the apparent electron concentration profiles are numerically calculated for structures with different mutual arrangements of the quantum well and the δ layer. The results of the calculations are compared with the result of analyzing the experimental capacitance-voltage characteristics of the structures. The systematic features of the behavior of the apparent concentration profiles and capacitance-voltage characteristics in relation to the geometric properties of the structure, the temperature, and the doping level are established.

36 MATERIALS SCIENCE↗
DOE OSTI2017

An adaptive fast multipole accelerated Poisson solver for complex geometries

Here, we present a fast, direct and adaptive Poisson solver for complex two-dimensional geometries based on potential theory and fast multipole acceleration. More precisely, the solver relies on the standard decomposition of the solution as the sum of a volume integral to account for the source distribution and a layer potential to enforce the desired boundary condition. The volume integral is computed by applying the FMM on a square box that encloses the domain of interest. For the sake of efficiency and convergence acceleration, we first extend the source distribution (the right-hand side in the Poisson equation) to the enclosing box as a $C$ 0 function using a fast, boundary integral-based method. We demonstrate on multiply connected domains with irregular boundaries that this continuous extension leads to high accuracy without excessive adaptive refinement near the boundary and, as a result, to an extremely efficient “black box” fast solver.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1988

Three-dimensional zonal grids about arbitrary shapes by Poisson's equation

A method for generating 3-D finite difference grids about or within arbitrary shapes is presented. The 3-D Poisson equations are solved numerically, with values for the inhomogeneous terms found automatically by the algorithm. Those inhomogeneous terms have the effect near boundaries of reducing cell skewness and imposing arbitrary cell height. The method allows the region of interest to be divided into zones (blocks), allowing the method to be applicable to almost any physical domain. A FORTRAN program called 3DGRAPE has been written to implement the algorithm. Lastly, a method for redistributing grid points along lines normal to boundaries will be described.

Sorenson, Reese L.↗
NASA NTRS1988

Three-dimensional zonal grids about arbitrary shapes by Poisson's equation

A method for generating 3-D finite difference grids about or within arbitrary shapes is presented. The 3-D Poisson equations are solved numerically, with values for the inhomogeneous terms found automatically by the algorithm. Those inhomogeneous terms have the effect near boundaries of reducing cell skewness and imposing arbitrary cell height. The method allows the region of interest to be divided into zones (blocks), allowing the method to be applicable to almost any physical domain. A FORTRAN program called 3DGRAPE has been written to implement the algorithm. Lastly, a method for redistributing grid points along lines normal to boundaries will be described.

Sorenson, Reese L.↗
DOE OSTI2014

The charge conserving Poisson-Boltzmann equations: Existence, uniqueness, and maximum principle

The present article is concerned with the charge conserving Poisson-Boltzmann (CCPB) equation in high-dimensional bounded smooth domains. The CCPB equation is a Poisson-Boltzmann type of equation with nonlocal coefficients. First, under the Robin boundary condition, we get the existence of weak solutions to this equation. The main approach is variational, based on minimization of a logarithm-type energy functional. To deal with the regularity of weak solutions, we establish a maximum modulus estimate for the standard Poisson-Boltzmann (PB) equation to show that weak solutions of the CCPB equation are essentially bounded. Then the classical solutions follow from the elliptic regularity theorem. Second, a maximum principle for the CCPB equation is established. In particular, we show that in the case of global electroneutrality, the solution achieves both its maximum and minimum values at the boundary. However, in the case of global non-electroneutrality, the solution may attain its maximum value at an interior point. In addition, under certain conditions on the boundary, we show that the global non-electroneutrality implies pointwise non-electroneutrality.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

A fourth-order Cartesian grid embeddedboundary method for Poisson’s equation

In this paper, we present a fourth-order algorithm to solve Poisson's equation in two and three dimensions. We use a Cartesian grid, embedded boundary method to resolve complex boundaries. We use a weighted least squares algorithm to solve for our stencils. We use convergence tests to demonstrate accuracy and we show the eigenvalues of the operator to demonstrate stability. We compare accuracy and performance with an established second-order algorithm. We also discuss in depth strategies for retaining higher-order accuracy in the presence of nonsmooth geometries.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

PVRD-FASP: A Unified Solver for Modeling Carrier and Defect Transport in Photovoltaic Devices

In our paper, we present a simulator for modeling transport of charge carriers and electrically active defect centers in solar cells by treating them on an equal footing, which allows us to address metastability and reliability issues. The exact nonlinear differential equations set solved by our solver is presented. The formulation of such differential equations, namely the continuity equations, drift-diffusion equation, and Poisson equation, for studying charge and defect transport is explained. The parameters needed for forming the differential equations are taken from first principle calculations. The solver is verified with test cases built on PN heterojunctions, Cu diffusion in single crystal CdTe and comparing Silvaco simulations with our numerical results.

14 SOLAR ENERGY↗
NASA NTRS1984

Two-dimensional computer simulation of EMVJ and grating solar cells under AMO illumination

A computer program, SCAP2D (Solar Cell Analysis Program in 2-Dimensions), is used to evaluate the Etched Multiple Vertical Junction (EMVJ) and grating solar cells. The aim is to demonstrate how SCAP2D can be used to evaluate cell designs. The cell designs studied are by no means optimal designs. The SCAP2D program solves the three coupled, nonlinear partial differential equations, Poisson's Equation and the hole and electron continuity equations, simultaneously in two-dimensions using finite differences to discretize the equations and Newton's Method to linearize them. The variables solved for are the electrostatic potential and the hole and electron concentrations. Each linear system of equations is solved directly by Gaussian Elimination. Convergence of the Newton Iteration is assumed when the largest correction to the electrostatic potential or hole or electron quasi-potential is less than some predetermined error. A typical problem involves 2000 nodes with a Jacobi matrix of order 6000 and a bandwidth of 243.

Gray, J. L.↗
NASA NTRS1999

Piezoelectric Field Enhanced Second-Order Nonlinear Optical Susceptibilities in Wurtzite GaN/AlGaN Quantum Wells

Second-order nonlinear optical processes including second-harmonic generation, optical rectification, and difference-frequency generation associated with intersubband transitions in wurtzite GaN/AlGaN quantum well (QW) are investigated theoretically. Taking into account the strain-induced piezoelectric (PZ) effects, we solve the electronic structure of the QW from coupled effective-mass Schrodinger equation and Poisson equation including the exchange-correlation effect under the local-density approximation. We show that the large PZ field in the QW breaks the symmetry of the confinement potential profile and leads to large second-order susceptibilities. We also show that the interband optical pump-induced electron-hole plasma results in an enhancement in the maximum value of the nonlinear coefficients and a redshift of the peak position in the nonlinear optical spectrum. By use of the difference-frequency generation, THz radiation can be generated from a GaN/Al(0.75)Ga(0.25)N with a pump laser of 1.55 micron.

Liu, Ansheng↗
DOE OSTI2017

A stochastic asymptotic-preserving scheme for a kinetic-fluid model for disperse two-phase flows with uncertainty

In this paper we consider a kinetic-fluid model for disperse two-phase flows with uncertainty. We propose a stochastic asymptotic-preserving (s-AP) scheme in the generalized polynomial chaos stochastic Galerkin (gPC-sG) framework, which allows the efficient computation of the problem in both kinetic and hydrodynamic regimes. The s-AP property is proved by deriving the equilibrium of the gPC version of the Fokker–Planck operator. The coefficient matrices that arise in a Helmholtz equation and a Poisson equation, essential ingredients of the algorithms, are proved to be positive definite under reasonable and mild assumptions. The computation of the gPC version of a translation operator that arises in the inversion of the Fokker–Planck operator is accelerated by a spectrally accurate splitting method. Numerical examples illustrate the s-AP property and the efficiency of the gPC-sG method in various asymptotic regimes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1979

The accurate solution of Poisson's equation by expansion in Chebyshev polynomials

A Chebyshev expansion technique is applied to Poisson's equation on a square with homogeneous Dirichlet boundary conditions. The spectral equations are solved in two ways - by alternating direction and by matrix diagonalization methods. Solutions are sought to both oscillatory and mildly singular problems. The accuracy and efficiency of the Chebyshev approach compare favorably with those of standard second- and fourth-order finite-difference methods.

Haidvogel, D. B.↗