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Results for “Generalized relaxation equation”

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At least 109 records · Page 6

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NASA NTRS1982

A conservative finite difference algorithm for the unsteady transonic potential equation in generalized coordinates

An implicit, approximate-factorization, finite-difference algorithm has been developed for the computation of unsteady, inviscid transonic flows in two and three dimensions. The computer program solves the full-potential equation in generalized coordinates in conservation-law form in order to properly capture shock-wave position and speed. A body-fitted coordinate system is employed for the simple and accurate treatment of boundary conditions on the body surface. The time-accurate algorithm is modified to a conventional ADI relaxation scheme for steady-state computations. Results from two- and three-dimensional steady and two-dimensional unsteady calculations are compared with existing methods.

Bridgeman, J. O.↗

NASA NTRS1986

A shock capturing technique for hypersonic, chemically relaxing flows

A fully coupled, shock capturing technique is presented for chemically reacting flows at high Mach numbers. The technique makes use of a total variation diminishing (TVD) dissipation operator which results in sharp, crisp shocks. The eigenvalues and eigenvectors of the fully coupled system, which includes species conversion equations in addition to the gas dynamics equations, are analytically derived for a general reacting gas. Species production terms for a model dissociating gas are introduced and are included in the algorithm. The convective terms are solved using a first-order TVD scheme while the source terms are solved using a fourth-order Runge-Kutta scheme to enhance stability. Results from one-dimensional numerical experiments are shown for a two species and a three species gas.

Eberhardt, S.↗

DOE OSTI2024

Uniformly decaying subspaces for error-mitigated quantum computation

Here, we present a general condition to obtain subspaces that decay uniformly in a system governed by the Lindblad master equation and use them to perform error-mitigated quantum computation. The expectation values of dynamics encoded in such subspaces are unbiased estimators of noise-free expectation values. In analogy to the decoherence free subspaces which are left invariant by the action of Lindblad operators, we show that the uniformly decaying subspaces are left invariant (up to orthogonal terms) by the action of the dissipative part of the Lindblad equation. We apply our theory to a system of qubits and qudits undergoing relaxation with varying decay rates and show that such subspaces can be used to eliminate bias up to first-order variations in the decay rates without requiring full knowledge of noise. Since such a bias cannot be corrected through standard symmetry verification, our method can improve error mitigation in dual-rail qubits and, given partial knowledge of noise, can perform better than probabilistic error cancellation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1987

A numerical method for the solution of three dimensional, incompressible, viscous flows over slender bodies

A marching iterative method for the solution of the three dimensional, incompressibhle, steady and parabolized Navier-Stokes equations is described. The equations are written in primitive variables and discretized in general axisymmetric orthogonal coordinate systems. The coupled set of finite-difference equations are solved without any splitting or factorization errors. Moreover, the continuity equation and the two crossflow momentum equations are exactly satisfied at every step of the iterative process. The solution scheme is equivalent to the solution of one Poisson equation by the Successive Plane Over Relaxation method and has good convergence properties. Other existing solution methods resemble a Jacobi-type iterative scheme and therefore are less efficient. Numerical experiments include the laminar, incompressible flow over prolate spheroids at incidence.

Rosenfeld, Moshe↗

NASA NTRS1985

Three dimensional CSCM method for the compressible Navier-Stokes equations with application to a multi-nozzle exhaust flowfield

The effective design of three-dimensional flow systems such as a clustered multinozzle shrouded exhaust system requires detailed analysis of the internal flowfield. It is pointed out that new numerical techniques on the most modern vector computers are making these analyses practicable. In this paper, the upwind differenced implicit conservative supracharacteristics method (CSCM) for three-dimensional viscous flow is presented. The new method is an implicit 'method of planes' symmetric Gauss-Seidel relaxation scheme. The data is conveniently stored on successive planes along the streamwise coordinate, and the system of equations is solved twice in each successive plane of the streamwise coordinate. The developed new three-dimensional compressible Navier-Stokes algorithm combines the best features of the storage and computationally efficient space marching procedures with the generality of time dependent techniques to solve flows with elliptic and streamwise separated flows.

Bardina, J.↗

DOE OSTI2023

Capturing membrane structure and function in lattice Boltzmann models

Here, we develop a mesoscopic approach to model the nonequilibrium behavior of membranes at the cellular scale. Relying on lattice Boltzmann methods, we develop a solution procedure to recover the Nernst-Planck equations and Gauss's law. A general closure rule is developed to describe mass transport across the membrane, which is able to account for protein-mediated diffusion based on a coarse-grained representation. We demonstrate that our model is able to recover the Goldman equation from first principles and show that hyperpolarization occurs when membrane charging dynamics are controlled by multiple relaxation timescales. The approach provides a promising way to characterize non-equilibrium behaviors that arise due to the role of membranes in mediating transport based on realistic three-dimensional cell geometries.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS1979

The structure and appearance of winds from supercritical accretion disks. I - Numerical models

Equations for the structure and appearance of supercritical accretion disks and the radiation-driven winds which emanate from them are derived and solved by a steady-state hydrodynamic computer code with a relaxation technique used in stellar structure problems. The present model takes into account the mass of the accreting star, the total accretion rate, a generalization of the disk alpha parameter which accounts for heating by processes in addition to viscosity, and the ratio of the total luminosity to the Eddington luminosity. Solutions indicate that for accretion onto a hard-surfaced star, steady, optically thick winds result for even slightly supercritical accretion, and the object will appear as a supergiant star with a high mass loss rate and a nonblackbody spectrum. Winds from black hole accretion disks are expected to depend on the form of the accretion interior to the critical radius, possibly consisting of no ejection at all, a wind similar to that of a hard-surfaced star, or a column of material ejected from a hole in the accretion disk.

Meier, D. L.↗

NASA NTRS1996

Multigrid Method for Modeling Multi-Dimensional Combustion with Detailed Chemistry

A highly accurate and efficient numerical method is developed for modeling 3-D reacting flows with detailed chemistry. A contravariant velocity-based governing system is developed for general curvilinear coordinates to maintain simplicity of the continuity equation and compactness of the discretization stencil. A fully-implicit backward Euler technique and a third-order monotone upwind-biased scheme on a staggered grid are used for the respective temporal and spatial terms. An efficient semi-coarsening multigrid method based on line-distributive relaxation is used as the flow solver. The species equations are solved in a fully coupled way and the chemical reaction source terms are treated implicitly. Example results are shown for a 3-D gas turbine combustor with strong swirling inflows.

Zheng, Xiaoqing↗

NASA NTRS1982

Relaxation solution of the full Euler equations

A numerical procedure for the relaxation solution of the full steady Euler equations is described. By embedding the Euler system in a second order surrogate system, central differencing may be used in subsonic regions while retaining matrix forms well suited to iterative solution procedures and convergence acceleration techniques. Hence, this method allows the development of stable, fully conservative differencing schemes for the solution of quite general inviscid flow problems. Results are presented for both subcritical and shocked supercritical internal flows. Comparisons are made with a standard time dependent solution algorithm.

Johnson, G. M.↗

NASA NTRS1982

Relaxation solution of the full Euler equations

Johnson, G. M.↗

NASA NTRS1984

Computer simulation of surface and film processes

All the investigations which were performed employed in one way or another a computer simulation technique based on atomistic level considerations. In general, three types of simulation methods were used for modeling systems with discrete particles that interact via well defined potential functions: molecular dynamics (a general method for solving the classical equations of motion of a model system); Monte Carlo (the use of Markov chain ensemble averaging technique to model equilibrium properties of a system); and molecular statics (provides properties of a system at T = 0 K). The effects of three-body forces on the vibrational frequencies of triatomic cluster were investigated. The multilayer relaxation phenomena for low index planes of an fcc crystal was analyzed also as a function of the three-body interactions. Various surface properties for Si and SiC system were calculated. Results obtained from static simulation calculations for slip formation were presented. The more elaborate molecular dynamics calculations on the propagation of cracks in two-dimensional systems were outlined.

Tiller, W. A.↗

NASA NTRS1993

Euler solutions for blunt bodies using triangular meshes - Artificial viscosity forms and numerical boundary conditions

A finite volume method is used to calculate compressible inviscid flows over blunt bodies using, in general, unstructured grids. Artificial viscosity forms are derived based on a simplified least squares procedure. The extra second order terms are consistent with the governing equations, hence a systematic treatment of the numerical boundary conditions can be easily implemented. A special treatment of blunt bodies may be required. The discrete equations are linearized and the resulting system is solved by a relaxation method. Preliminary results indicate that the effect of the numerical dissipation is minimal. For subsonic flows over smooth bodies, the solution is practically vorticity-free and the total pressure loss is of the same order as the truncation error. Finally, some extensions of the present method are briefly discussed.

Winterstein, R.↗

NASA NTRS1983

Some Recent Developments in the Endochronic Theory with Application to Cyclic Histories

Constitutive equations with only two easily determined material constants predict the stress (strain) response of normalized mild steel to a variety of general strain (stress) histories, without a need for special unloading-reloading rules. The equations are derived from the endochronic theory of plasticity of isotropic materials with an intrinsic time scale defined in the plastic strain space. Agreement between theoretical predictions and experiments are are excellent quantitatively in cases of various uniaxial constant amplitude histories, variable uniaxial strain amplitude histories and cyclic relaxation. The cyclic ratcheting phenomenon is predicted by the present theory.

Valanis, K. C.↗

NASA NTRS1983

A finite element solution of three-dimensional inviscid rotational flows through curved ducts

A previously developed two-dimensional finite element algorithm for the solution of steady Euler equations is extended to three-dimensional problems. Starting with the general three-dimensional problem, the formulation of steady, rotational flows is presented. The boundary conditions for steady flows where the rotationality is introduced through entropy or total enthalpy gradients are introduced. A three-dimensional flow through a curved duct is analyzed as a sample problem, demonstrating the efficiency of the relaxation scheme. The accuracy of the numerical results is investigated by calculating the velocity and vorticity distributions at different sections of the channel, including the exit.

Ecer, A.↗

NASA NTRS1993

A coarse-grid correction/nonlinear relaxation algorithm for the three-dimensional, compressible Navier-Stokes equations

A combined coarse-grid correction/upwind relaxation strategy to provide rapid convergence for 3D high-speed viscous flowfields is discussed an evaluated. The construction and analysis of a simple two-grid acceleration procedure based on 'hyperbolic' multigrid concepts is presented. Numerical simulations of a 2D compression-corner flowfield, a 3D crossing shock/turbulent boundary layer interaction, and a 3D scramjet inlet flowfield are presented to illustrate the benefits of the approach. Results indicate that the procedure generally converges two or more times faster than the baseline algorithm.

Edwards, Jack R.↗

DOE OSTI2022

Langevin dynamics of generalized spins as SU( N ) coherent states

Classical models of spin systems traditionally retain only the dipole moments, but a quantum spin state will frequently have additional structure. Spins of magnitude S have N = 2⁢S + 1 levels. Alternatively, the spin state is fully characterized by a set of N 2 - 1 local physical observables, which we interpret as generalized spin components. For example, a spin with S = 1 has three dipole components and five quadrupole components. Further, these components evolve under a generalization of the classical Landau-Lifshitz dynamics, which can be extended with noise and damping terms. In this paper, we reformulate the dynamical equations of motion as a Langevin dynamics of SU(N) coherent states in the Schrödinger picture. This viewpoint is especially useful as the basis for an efficient numerical method to sample spin configurations in thermal equilibrium and to simulate the relaxation and driven motion of topological solitons. To illustrate the approach, we simulate a nonequilibrium relaxation process that creates CP 2 skyrmions, which are topological defects with both dipole and quadrupole character.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1988

Lightning-related fields in the ionosphere

Lightning-related transient electric fields and conduction current densities due to the redistribution of charge by the return stroke, but not directly associated with the high-intensity current channel, are investigated via a simulation of Maxwell's equations. The investigation presents evidence to suggest that the lightning-related charge redistribution and subsequent relaxation, rather than the high intensity current, is the source of the major component of the transient field and energy coupled to the ionosphere. A time domain finite element analysis is employed in the simulation, using a conductivity profile obtained simultaneously with electric field measurements which agree, in general terms, with the simulations. It is concluded that prior depictions of these phenomena underestimate the fraction of the total energy that couples to and dissipates within the ionosphere and magnetosphere.

Baginski, M. E.↗

NASA NTRS1993

Ratchetting behavior in viscoplasticity - A technical note

Viscoplastic models that use the Armstrong and Frederick (1966) kinematic hardening relationship are known to generally overpredict the observed accumulation of ratchet strains. The reason for this behavior is a consequence of the mathematics used to describe Hooke's law and the evolution equations for plastic strain and back stress. Conditions for ratchetting exist whenever there is a cycle-averaged mean stress present over a cyclic loading path. Two types of controlled loading paths are often studied: cyclic relaxation is the ratchet mechanism associated with displacement (strain) control, while cyclic creep is the ratchet mechanism associated with load (stress) control. Overcoming the possible adverse trends in predicted ratchetting behavior is a difficult task, and how one ought to go about doing this is not yet completely clear. We therefore choose to discuss the mathematical cause of ratchetting and how it has been dealt with to date, but make no attempt to correct this flaw.

Freed, Alan D.↗