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At least 1,153 records · Page 64

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NASA NTRS1988

A conservative approach for flow field calculations on multiple grids

In the computation of flow fields about complex configurations, it is very difficult to construct body-fitted coordinate systems. An alternative approach is to use several grids at once, each of which is generated independently. This procedure is called the multiple grids or zonal grids approach and its applications are investigated in this study. The method follows the conservative approach and provides conservation of fluxes at grid interfaces. The Euler equations are solved numerically on such grids for various configurations. The numerical scheme used is the finite-volume technique with a three-state Runge-Kutta time integration. The code is vectorized and programmed to run on the CDC VPS-32 computer. Some steady state solutions of the Euler equations are presented and discussed.

Kathong, Monchai↗

NASA NTRS1991

Solution of steady-state, two-dimensional conservation laws by mathematical programming

A truly two-dimensional algorithm is created for solving the steady-state two-dimensional conservation-law problem. An overdetermined system of algebraic equations is obtained through discretization by finite-volume formulas. These equations are perturbed nonsingularly and are solved by an efficient geometrically oriented l(1) procedure. The basic algorithm and the theory for the linear case f(u) = u are presented, and computational results for the nonlinear case f(u) = sq u are also analyzed. It is noted that the l(1) procedure captures boundary shocks as well as oblige and zigzag interior shocks in bands that are one cell wide, and the solution values are accurate up to the edge of the shock.

Lavery, John E.↗

NASA NTRS1991

FLIP MHD - A particle-in-cell method for magnetohydrodynamics

The fluid-implicit-particle, or 'FLIP' method presently extended to 2D and 3D MHD flow incorporates a Lagrangian field representation and yields a grid magnetic Reynolds number of up to 16 while preserving contact continuities that retain the Galilean invariance of the MHD flow equations. Analytical arguments and numerical examples demonstrate the conservation of mass, momentum, magnetic flux, and energy; 2D calculation results for the illustrative cases of contact discontinuity convection, Rayleigh-Taylor unstable flow.

Brackbill, J. U.↗

NASA NTRS1993

Numerical vorticity capturing for vortex-solid body interaction problems

A new numerical method based on adding a term to the Euler/Navier-Stokes equations has been demonstrated it can effectively treat vortex-dominated flows using low-order numerical schemes and coarse grids. The numerical diffusion introduced by convection schemes can be eliminated by modifying the velocity field as a result of solving the modified flow governing equations. The modification of the velocity field, which conserves the total vorticity, essentially convects the vorticity toward its local extreme to offset the numerical diffusion. This method preserves the vortex structure even when vortices travel on coarse grid region. The method is implemented with two distinctive codes: a Navier-Stokes flow solver based on vorticity-velocity formulation and an Euler code based on velocity-pressure formulation. Problems presented in this paper include airfoil dynamic stall, vortex airfoil interaction, and vortex-fuselage interactions.

Wang, Clin M.↗

NASA NTRS1959

Water-Landing Characteristics of a Reentry Capsule

Experimental and theoretical investigations have been made to determine the water-landing characteristics of a conical-shaped reentry capsule having a segment of a sphere as the bottom. For the experimental portion of the investigation, a 1/12-scale model capsule and a full-scale capsule were tested for nominal flight paths of 65 deg and 90 deg (vertical), a range of contact attitudes from -30 deg to 30 deg, and a full-scale vertical velocity of 30 feet per second at contact. Accelerations were measured by accelerometers installed at the centers of gravity of the model and full-scale capsules. For the model test the accelerations were measured along the X-axis (roll) and Z-axis (yaw) and for the full-scale test they were measured along the X-axis (roll), Y-axis (pitch), and Z-axis (yaw). Motions and displacements of the capsules that occurred after contact were determined from high-speed motion pictures. The theoretical investigation was conducted to determine the accelerations that might occur along the X-axis when the capsule contacted the water from a 90 deg flight path at a 0 deg attitude. Assuming a rigid body, computations were made from equations obtained by utilizing the principle of the conservation of momentum. The agreement among data obtained from the model test, the full-scale test, and the theory was very good. The accelerations along the X-axis, for a vertical flight path and 0 deg attitude, were in the order of 40g. For a 65 deg flight path and 0 deg attitude, the accelerations along the X-axis were in the order of 50g. Changes in contact attitude, in either the positive or negative direction from 0 deg attitude, considerably reduced the magnitude of the accelerations measured along the X-axis. Accelerations measured along the Y- and Z-axes were relatively small at all test conditions.

John R McGehee↗

NASA NTRS1999

A Sectored-One-Dimensional Model for Simulating Combustion Instabilities in Premix Combustors

A one-dimensional, CFD based combustor simulation has been developed that exhibits self-excited, thermoacoustic oscillations in premixed combustor geometries that typically have large, abrupt changes in cross sectional area. The combustor geometry is approximated by dividing it into a finite number of one-dimensional sectors. Within each sector, the equations of motion are integrated numerically, along with a species transport and a reaction equation. Across the sectors, mass and energy are conserved, and momentum loss is prescribed using appropriately compatible boundary conditions that account for the area change. The resulting simulation and associated boundary conditions essentially represent a one-dimensional, multi-block technique. Details of the simulation code are presented herein. Results are then shown comparing experimentally observed and simulated operation of a particular combustor rig that exhibited different instabilities at different operating points. It will be shown that the simulation closely matched the rig data in oscillation amplitudes, frequencies, and operating points at which the instabilities occurred. Finally, advantages and limitations of the simulation technique are discussed.

Paxson, Daniel E.↗

NASA NTRS1958

Water Landing Characteristics of a Reentry Capsule

John R McGehee↗

NASA NTRS1983

Computational methods for ideal compressible flow

Conservative dissipative difference schemes for computing one dimensional flow are introduced, and the recognition and representation of flow discontinuities are discussed. Multidimensional methods are outlined. Second order finite volume schemes are introduced. Conversion of difference schemes for a single linear convection equation into schemes for the hyperbolic system of the nonlinear conservation laws of ideal compressible flow is explained. Approximate Riemann solvers are presented. Monotone initial value interpolation; and limiters, switches, and artificial dissipation are considered.

Vanleer, B.↗

DOE OSTI2020

A simple and effective five-equation two-phase numerical model for liquid-vapor phase transition in cavitating flows

Numerical difficulties, notably the non-monotonic behavior of the Wood speed of sound and the volume fraction positivity, associated with the reduced five-equation two-phase flow model of Kapila et al. (2001) [A.K. Kapila, R. Menikoff, J.B. Bdzil, S.F. Son, D.S. Stewart, 2001. Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations, Physics of Fluids 13(10), 3002–3024] have been resolved in the past through the introduction of a frozen speed of sound and an algebraic approach for mechanical relaxation afforded by a pressure non-equilibrium six-equation model proposed by [R. Saurel, F. Petitpas, R.A. Berry, 2009. Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixture, J. Comput. Phys. 228, 1678–1712]. By contrast, it is explored and demonstrated in this work that these difficulties can in fact still be resolved within the numerical scheme for solving the reduced five-equation model by numerically replacing the Wood speed of sound for the estimates of wave speeds in the approximate Riemann solver HLLC with the monotonic mixture speed of sound for a transport five-equation model. For shock interface (artificial mixture separating pure or nearly pure fluids) interaction problems, with the apparent advantage of monotonic behavior of the speed of sound in the interface, the effect of the numerical replacement is also confined to the interface. Differences other than the behavior of the speed of sound within the interface in the solutions due to the replacement diminish with increasing resolution when reasonable solution can be obtained with Wood speed of sound. For cavitating/expansion problems in physical fluid mixture, it is pointed out and explained why acoustics in the numerical solutions still propagate at the Wood speed of sound (therefore consistent with the reduced five-equation model) even though in some cases a much higher speed of sound like the numerical replacement above for solving the reduced five-equation model or the frozen speed of sound for solving a six-equation model is used for the estimates of wave speeds in the HLLC scheme. A variant of the five-equation two-phase flow model by Saurel et al. (2008) [R. Saurel, F. Petitpas, R. Abgrall, 2008. Modelling phase transition in metastable liquids: application to cavitating and flashing flows, J. Fluid Mech. 607, 313–350] is then constructed for liquid-vapor phase transition in cavitating flows. The relaxation toward thermo-chemical equilibrium during phase transition is achieved by solving a simple system of algebraic equations for the equilibrium state variables for better efficiency, following Pelanti and Shyue (2014) [M. Pelanti, K.-M. Shyue, 2014. A mixture-energy-consistent six-equation two-phase numerical model for fluid with interfaces, cavitation and evaporation waves. J. Comput. Phys. 259, 331–357]. Therefore, the current model retains both the simplicity afforded by the five-equation model and the efficiency of the algebraic relaxation solver. An alternative algebraic approach for handling the non-conservative term (the so-called K∇ · u term) in the reduced five-equation model for mechanical equilibrium of a liquid-vapor mixture is also explored by enforcing the thermal equilibrium at the same time. Finally, numerical results of sample tests in both one and two dimensions in the literature as well as that in three dimensions demonstrate the effectiveness and ability of the proposed model to simulate cavitating flows. An interesting mechanism of shock generation by acoustics in water due to phase transition is then found by the numerical simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1988

The use of multigrid techniques in the solution of the Elrod algorithm for a dynamically loaded journal bearing

A numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed, utilizing a multigrid iterative technique. The code is compared with a presently existing direct solution in terms of computational time and accuracy. The model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobssen-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via liquid striations. The mixed nature of the equations (elliptic in the full film zone and nonelliptic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time.

Woods, Claudia M.↗

DOE OSTI2022

Quasilinear theory for inhomogeneous plasma

Here, this paper presents quasilinear theory (QLT) for a classical plasma interacting with inhomogeneous turbulence. The particle Hamiltonian is kept general; for example, relativistic, electromagnetic and gravitational effects are subsumed. A Fokker–Planck equation for the dressed ‘oscillation-centre’ distribution is derived from the Klimontovich equation and captures quasilinear diffusion, interaction with the background fields and ponderomotive effects simultaneously. The local diffusion coefficient is manifestly positive-semidefinite. Waves are allowed to be off-shell (i.e. not constrained by a dispersion relation), and a collision integral of the Balescu–Lenard type emerges in a form that is not restricted to any particular Hamiltonian. This operator conserves particles, momentum and energy, and it also satisfies the H -theorem, as usual. As a spin-off, a general expression for the spectrum of microscopic fluctuations is derived. For on-shell waves, which satisfy a quasilinear wave-kinetic equation, the theory conserves the momentum and energy of the wave–plasma system. The action of non-resonant waves is also conserved, unlike in the standard version of QLT. Dewar's oscillation-centre QLT of electrostatic turbulence is proven formally as a particular case and given a concise formulation. Also discussed as examples are relativistic electromagnetic and gravitational interactions, and QLT for gravitational waves is proposed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

A meshless stochastic method for Poisson–Nernst–Planck equations

A plethora of biological, physical, and chemical phenomena involve transport of charged particles (ions). Its continuum-scale description relies on the Poisson–Nernst–Planck (PNP) system, which encapsulates the conservation of mass and charge. The numerical solution of these coupled partial differential equations is challenging and suffers from both the curse of dimensionality and difficulty in efficiently parallelizing. We present a novel particle-based framework to solve the full PNP system by simulating a drift–diffusion process with time- and space-varying drift. We leverage Green’s functions, kernel-independent fast multipole methods, and kernel density estimation to solve the PNP system in a meshless manner, capable of handling discontinuous initial states. The method is embarrassingly parallel, and the computational cost scales linearly with the number of particles and dimension. We use a series of numerical experiments to demonstrate both the method’s convergence with respect to the number of particles and computational cost vis-à-vis a traditional partial differential equation solver.

Chemistry↗

NASA NTRS1990

Some Aspects of Essentially Nonoscillatory (ENO) Formulations for the Euler Equations, Part 3

An essentially nonoscillatory (ENO) formulation is described for hyperbolic systems of conservation laws. ENO approaches are based on smart interpolation to avoid spurious numerical oscillations. ENO schemes are a superset of Total Variation Diminishing (TVD) schemes. In the recent past, TVD formulations were used to construct shock capturing finite difference methods. At extremum points of the solution, TVD schemes automatically reduce to being first-order accurate discretizations locally, while away from extrema they can be constructed to be of higher order accuracy. The new framework helps construct essentially non-oscillatory finite difference methods without recourse to local reductions of accuracy to first order. Thus arbitrarily high orders of accuracy can be obtained. The basic general ideas of the new approach can be specialized in several ways and one specific implementation is described based on: (1) the integral form of the conservation laws; (2) reconstruction based on the primitive functions; (3) extension to multiple dimensions in a tensor product fashion; and (4) Runge-Kutta time integration. The resulting method is fourth-order accurate in time and space and is applicable to uniform Cartesian grids. The construction of such schemes for scalar equations and systems in one and two space dimensions is described along with several examples which illustrate interesting aspects of the new approach.

Chakravarthy, Sukumar R.↗

NASA NTRS1992

Polarimetric signatures of a canopy of dielectric cylinders based on first and second order vector radiative transfer theory

Complete polarimetric signatures of a canopy of dielectric cylinders overlying a homogeneous half space are studied with the first and second order solutions of the vector radiative transfer theory. The vector radiative transfer equations contain a general nondiagonal extinction matrix and a phase matrix. The energy conservation issue is addressed by calculating the elements of the extinction matrix and the elements of the phase matrix in a manner that is consistent with energy conservation. Two methods are used. In the first method, the surface fields and the internal fields of the dielectric cylinder are calculated by using the fields of an infinite cylinder. The phase matrix is calculated and the extinction matrix is calculated by summing the absorption and scattering to ensure energy conservation. In the second method, the method of moments is used to calculate the elements of the extinction and phase matrices. The Mueller matrix based on the first order and second order multiple scattering solutions of the vector radiative transfer equation are calculated. Results from the two methods are compared. The vector radiative transfer equations, combined with the solution based on method of moments, obey both energy conservation and reciprocity. The polarimetric signatures, copolarized and depolarized return, degree of polarization, and phase differences are studied as a function of the orientation, sizes, and dielectric properties of the cylinders. It is shown that second order scattering is generally important for vegetation canopy at C band and can be important at L band for some cases.

Tsang, Leung↗

DOE OSTI2022

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. I. The O ( N ) model

The functional renormalization group (FRG) approach is a powerful tool for studies of a large variety of systems, ranging from statistical physics over the theory of the strong interaction to gravity. The practical application of this approach relies on the derivation of so-called flow equations, which describe the change of the quantum effective action under the variation of a coarse-graining parameter. In the present work, we discuss in detail a novel approach to solve such flow equations. This approach relies on the fact that RG equations can be rewritten such that they exhibit similarities with the conservation laws of fluid dynamics. This observation can be exploited in different ways. First of all, we show that this allows to employ powerful numerical techniques developed in the context of fluid dynamics to solve RG equations. In particular, it allows us to reliably treat the emergence of nonanalytic behavior in the RG flow of the effective action as it is expected to occur in studies of, e.g., spontaneous symmetry breaking. Second, the analogy between RG equations and fluid dynamics offers the opportunity to gain novel insights into RG flows and their interpretation in general, including the irreversibility of RG flows. Further, we work out this connection in practice by applying it to zero-dimensional quantum-field theoretical models. The generalization to higher-dimensional models is also discussed. Our findings are expected to help improving future FRG studies of quantum field theories in higher dimensions both on a qualitative and quantitative level.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Current-conserving relativistic linear response for collisional plasmas

Here we investigate the response of a relativistic plasma to electromagnetic fields in the framework of the Boltzmann equation incorporating a collision term in the relaxation rate approximation selected in a form assuring current conservation. We obtain an explicit solution for the linearized perturbation of the Fermi–Dirac equilibrium distribution in terms of the average relaxation rate k. We study the resulting covariant, gauge invariant, and current conserving form of the polarization tensor in the ultrarelativistic and non-relativistic limits. We evaluate the susceptibility in the ultrarelativistic limit and explore their dependence on k. Finally, we study the dispersion relations for the longitudinal and transverse poles of the propagator. We show that for k >2ω p , where ω p is the plasma frequency, the plasma wave modes are overdamped. In the opposite case, k$\ll$ ω p , the propagating plasma modes are weakly damped.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Local conservation of energy in fully implicit PIC algorithms

We consider the issue of strict, fully discrete local energy conservation for a whole class of fully implicit local-charge- and global-energy-conserving particle-in-cell (PIC) algorithms. Earlier studies demonstrated these algorithms feature strict global energy conservation. However, whether a local energy conservation theorem exists (in which the local energy update is governed by a flux balance equation at every mesh cell) for these schemes is unclear. In this study, we show that a local energy conservation theorem indeed exists. We begin our analysis with the 1D electrostatic PIC model without orbit-averaging, and then generalize our conclusions to account for orbit averaging, multiple dimensions, and electromagnetic models (Darwin). In all cases, a temporally, spatially, and particle-discrete local energy conservation theorem is shown to exist, proving that these formulations (as originally proposed in the literature), in addition to being locally charge conserving and globally energy conserving, are strictly locally energy conserving as well. In contrast to earlier proofs of local conservation in the literature, which only considered continuum time, our result is valid for the fully implicit time-discrete version of all models considered, including important features such as orbit averaging. We demonstrate the local-energy-conservation property numerically with a paradigmatic numerical example.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Revisiting shear stress tensor evolution: Nonresistive magnetohydrodynamics with momentum-dependent relaxation time

This study aims to develop second-order relativistic viscous magnetohydrodynamics (MHD) derived from kinetic theory within an extended relaxation time approximation (momentum/energy dependent) for the collision kernel. The investigation involves a detailed examination of shear stress tensor evolution equations and associated transport coefficients. The Boltzmann equation is solved using a Chapman-Enskog-like gradient expansion for a charge-conserved conformal system, incorporating a momentum-dependent relaxation time. The derived relativistic nonresistive, viscous second-order MHD equations for the shear stress tensor reveal significant modifications in the coupling with dissipative charge current and magnetic field due to the momentum dependence of the relaxation time. By utilizing a power law parametrization to quantify the momentum dependence of the relaxation time, the anisotropic magnetic field-dependent shear coefficients in the Navier-Stokes limit have been investigated. The resulting viscous coefficients are seen to be sensitive to the momentum dependence of the relaxation time.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗