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At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

A Gauss-Radau-Laguerre Discrete Variable Representation for Use in Continuum Electron Dynamics

In this work, we detail an implementation, suitable for calculations on highly correlated ionizing systems, of a modified finite element discrete variable representation (FE-DVR) appended with a Gauss-Radau-Laguerre element. The appended element includes exterior complex scaling (ECS) to impose outgoing wave boundary conditions on treatments of processes involving continuum electrons. In this “infinite range” ECS (irECS), the complications that introduce reflections from the end of the grid when the last ECS finite element has finite range are avoided by the use of the Laguerre-weighted exponentially decaying tails, while outgoing wave boundary conditions are still imposed via the ECS transformation. For highly correlated systems in the absence of strong external fields we find that accurate two-electron integrals are essential in this modified FE-DVR. To accurately compute the two-electron integrals over the entire ECS contour, we present a detailed examination of the implications from the boundary terms that arise in a solution of Poisson’s equation with the Radau-Laguerre basis. A boundary term correction is necessary, and when included, the Radau-Laguerre DVR can accurately describe highly correlated states such as the doubly excited states of helium over the entire ECS contour.

elements↗
DOE OSTI2026

Non-conformal interface-cohesive modeling with the shifted boundary method

The accurate simulation of boundary- and interface-dominated problems on complex geometries remains challenging when boundary- or interface-fitted meshes are difficult to generate, particularly for curved boundaries, polycrystalline microstructures, and dense interface networks. The Shifted Boundary Method (SBM) alleviates this meshing burden by shifting the enforcement of boundary conditions from the true boundary to a nearby surrogate boundary and recovering the effect of the true boundary through geometric correction terms, thereby enabling standard finite element spaces on non-boundary-fitted meshes. In this report, we develop a general shiftedboundary and shifted-interface framework within the open-source MOOSE framework. We first present a general SBM implementation for complex geometries on non-boundary-fitted meshes. We then adopt the Shifted Interface Method (SIM) for internal interfaces and develop a unified shifted-interface treatment in which the interface law is enforced on a surrogate interface and the effect of the true interface is recovered through shifted jumps, fluxes, and tractions. This perspective brings scalar thermal-contact and vector-valued cohesive-zone mechanics into a single framework, the latter realized as the Shifted Cohesive Zone Method (SCZM) and coupled with history-dependent constitutive models from NEML2. We further extend the MOOSE mesh infrastructure to support cohesive-zone calculations on distributed meshes. The framework is verified and demonstrated through three progressive studies: Poisson’s equation on a smoothed starshaped domain, a manufactured thermal-contact problem on a non-interface-fitted mesh, and a two-dimensional polycrystalline representative volume element combining crystal plasticity with cohesive grain-boundary interfaces. Across these studies, the shifted formulations reproduce boundary- and interface-fitted reference solutions with high fidelity, indicating that the proposed framework provides an accurate and efficient route to boundary- and interface-dominated simulations on arbitrary geometries without requiring fitted meshes.

Yang, Cheng-Hau↗
NASA NTRS1974

Unsteady lift forces on highly cambered airfoils moving through a gust

An unsteady airfoil theory in which the flow is linearized about the steady potential flow of the airfoil is presented. The theory is applied to an airfoil entering a gust. After transformation to the W-plane, the problem is formulated in terms of a Poisson's equation. The solutions are expanded in a Fourier-Bessel series. The theory is applied to a circular arc with arbitrary camber. Closed form expressions for the velocity and pressure on the surface of the airfoil are obtained. The unsteady aerodynamic forces are then calculated and shown to contain two terms. One in an explicit closed analytical form represents the contribution of the oncoming vortical disturbance, the other depends on a single quadrature and accounts for the effect of the wake.

Atassi, H.↗
NASA NTRS1975

Efficiency of silicon solar cells as a function of base layer resistivity

This paper reports on a theoretical study of the limitations on silicon solar-cell efficiency for both n(+)-p and n(+)-p-p(+) type cells. Detailed calculations have been made of solar-cell operation using a general computer analysis program for semiconductor devices. The computer program, which simultaneously solves Poisson's equation and the electron and hole quasi-Fermi level equations, provides an accurate numerical solution of solar-cell operation without limiting assumptions or approximations. It is found that minority-carrier lifetime and heavy doping effects in the n(+) surface region present serious limitations to efficiency in low-resistivity silicon solar cells.

Dunbar, P. M.↗
NASA NTRS1977

Numerical simulation of spacecraft charging phenomena

A numerical simulation program is being constructed having the following features: (1) infinite circular cylindrical geometry with angle-dependence, (2) inclusion of incident particles, photoelectrons, secondary electrons, backscattered electrons, any gun emissions, and any internal current pathways including surface conductive layers, (3) quasistatic time-dependent iteration, in which sheath potential changes during particle transit times are ignored, (4) use of approximate, locally-dependent space charge density expressions in solving Poisson's equation for sheath potentials, with use of numerical orbit-following to determine surface currents, and (5) incident particle velocity distributions isotropic or beam-like, or some superposition of these. Rationales for each of these features are discussed.

Laframboise, J. G.↗
NASA NTRS1977

NASCAP user's manual

The NASCAP (NASA Charging Analyzer Program) code simulates the charging process for a complex object in either tenuous plasma or ground test environment. Detailed specifications needed to run the code are presented. The object definition section, OBJDEF, allows the test object to be easily defined in the cubic mesh. The test object is composed of conducting sections which may be wholly or partially covered with thin dielectric coatings. The potential section, POTENT, obtains the electrostatic potential in the space surrounding the object. It uses the conjugate gradient method to solve the finite element formulation of Poisson's equation. The CHARGE section of NASCAP treats charge redistribution among the surface cells of the object as well as charging through radiation bombardment. NASCAP has facilities for extensive graphical output, including several types of object display plots, potential contour plots, space charge density contour plots, current density plots, and particle trajectory plots.

Mandell, M. J.↗
NASA NTRS1977

NASCAP, a three-dimensional Charging Analyzer Program for complex spacecraft

A computer code, NASCAP (NASA Charging Analyzer Program), has been developed by Systems, Science and Software under contract to NASA-LeRC to simulate the charging of a complex spacecraft in geosynchronous orbit. The capabilities of the NASCAP code include a fully three-dimensional solution of Poisson's equation about an object having considerable geometrical and material complexity, particle tracking, shadowing in sunlight, calculation of secondary emission, backscatter and photoemission, and graphical output. A model calculation shows how the NASCAP code may be used to improve our understanding of the spacecraft-plasma interaction.

Katz, I.↗
NASA NTRS1977

Modeling of pressure spectra in a turbulent shear flow

The development of the pressure spectrum has been followed from its separation into turbulent-turbulent and turbulent-mean square contributions to a unified spectral model. The model is obtained by Fourier transforming the integral solution to Poisson's equation for an isotropic, homogeneous, constant mean shear flow. The variations in the asymptotic form for the mean-shear spectrum is discussed. It is noted that the spectra are associated with the particular velocity field selected, and that by an appropriate choice of spectral forms, the mean-square pressure of the flow may be calculated.

Beuther, P.↗
NASA NTRS1979

Design of high-perveance confined-flow guns for periodic-permanent-magnet-focused tubes

An approach to the design of high perveance, low compression guns is described in which confinement is used to stabilize the beam for subsequent periodic-permanent-magnet focusing. The computed results for two cases are presented. A magnetic boundary value problem was solved for the scalar potential from which the axial magnetic field was computed. A solution was found by iterating between Poisson's equation and the electron trajectory calculations. Magnetic field values were varied in magnitude until a laminar beam with minimum scalloping was produced.

Stankiewicz, N.↗
NASA NTRS1981

Rigorous numerical treatment of the no-slip condition in a vorticity formulation

It is shown that a rigorous mathematical treatment of the boundary conditions for rigid no-slip surfaces requires, in general, that two passes be made in solving Poisson's equation. A Fourier solution procedure was the key to this realization. It is also shown that a corresponding method exists for finite and, for the same local approximation, the usual one step method gives the same result for the geometry considered here. The more fundamental two step method gives a new insight into the physical significance of boundary vorticity.

Gazdag, J.↗
NASA NTRS1981

Simulation of three-dimensional incompressible flows with a vortex-in-cell method

A new method for the numerical simulation of three-dimensional incompressible flows is described. The vortex-in-cell (VIC) method presented traces the motion of the vortex filaments in the velocity field which these filaments create. The velocity field is not calculated directly by the Biot-Savart law of interaction but by creating a mesh-record of the vorticity field, then integrating a Poisson's equation via the fast Fourier transform to generate a mesh-record of the velocity field. The computed scales of motion are assumed to be essentially inviscid. Viscous of subgrid-scale effects are incorporated into a filtering procedure in wave vector space. Results of tracing a periodic array of single vortex rings are compared with a Green's function calculation. The agreement is very good.

Couet, B.↗
NASA NTRS1982

Two-Dimensional Grids About Airfoils and Other Shapes

GRAPE computer program generates two-dimensional finite-difference grids about airfoils and other shapes by use of Poisson differential equation. GRAPE can be used with any boundary shape, even one specified by tabulated points and including limited number of sharp corners. Numerically stable and computationally fast, GRAPE provides aerodynamic analyst with efficient and consistant means of grid generation.

Sorenson, R.↗
NASA NTRS1981

Electrostatic shocks in the auroral magnetosphere

A 1d unmagnetized double layer simulation is presented along with analytic considerations of the Langmuir-Bohm criterion for double layer formation. It is found that this requirement of large electron drift is not reduced by trapped thermal electron and ion populations; the assumption of a nonthermal population which requires the preexistence of the double layer cannot reduce the required electron drift. It is noted that negative charge density spikes and holes in ion phase space accompany the double layer. A magnetized BGK mode solution to Poisson's equation for the potential profile perpendicular to B for cold counter-streaming electrons and ions shows how the spatial structure changes in a magnetized plasma.

Hudson, M. K.↗
NASA NTRS1982

Differential charging of high-voltage spacecraft - The equilibrium potential of insulated surfaces

A theory is presented for the steady-state potential of insulated surfaces near exposed high voltages. The term 'insulated surfaces' is used to mean either dielectric surfaces or electrically isolated metallic surfaces. The potential is bounded below by the zero of the material's I-V curve assuming total suppression of secondary electrons, and above by assuming total extraction of secondaries. Within these bounds, the material's surface potential is determined consistently with the solution to Poisson's equation external to the vehicle. The theory is compared with rocket experiments and with SCATHA satellite data. Also, an explanation is suggested for the observed 'snapover' of solar cell coverslips from near plasma ground potential to near the potential of positively biased interconnects with increasing bias voltage.

Katz, I.↗
NASA NTRS1983

An implicit, transonic, full-potential code for cascade flow on H-grid topology

A transonic, full-potential code is developed for computing the flow through two-dimensional cascades using an H-type grid topology that employs an implicit approximate-factorization scheme. The body-conforming H-grid is generated numerically by solving Poisson's equation. The flow-solution algorithm at the coordinate mapping singularity associated with this grid is investigated using two different types of finite-difference schemes. The grid-geometry effect on these schemes is also studied by noting free-stream capturing properties. It is found that by implementing a consistent spatial differencing scheme, the mapping singularities can be resolved numerically, and the grid-geometry-induced error minimized. The code is verified by computing model cascade flow problems.

Kwak, D.↗
NASA NTRS1984

On the connection between multigrid and cyclic reduction

A technique is shown whereby it is possible to relate a particular multigrid process to cyclic reduction using purely mathematical arguments. This technique suggest methods for solving Poisson's equation in 1-, 2-, or 3-dimensions with Dirichlet or Neumann boundary conditions. In one dimension the method is exact and, in fact, reduces to cyclic reduction. This provides a valuable reference point for understanding multigrid techniques. The particular multigrid process analyzed is referred to here as Approximate Cyclic Reduction (ACR) and is one of a class known as Multigrid Reduction methods in the literature. It involves one approximation with a known error term. It is possible to relate the error term in this approximation with certain eigenvector components of the error. These are sharply reduced in amplitude by classical relaxation techniques. The approximation can thus be made a very good one.

Merriam, M. L.↗