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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

A finite difference informed random walker (FDiRW) solver for strongly inhomogeneous diffusion problems

In nature, many complex multi-physics coupling problems exhibit strong diffusivity inhomogeneity. For instance, in the context of radionuclide absorption by porous wasteform materials within a flowing waste stream, the difference of species’ diffusivity in solid and liquid phases spans by 3~8 orders of magnitude. To solve the diffusion equations with strongly inhomogeneous diffusivity, traditional discretization-based methods, such as the Finite Difference Method (FDM), require infinitesimally small time steps (<10 -10 ) as high spatial resolutions are employed in most microstructure evolution processes, leading to prohibitively high computational costs. Here, this work developed an integrated numerical approach (FDiRW: Finite Difference informed Random Walk) to tackle this challenge. The idea is that utilizing the Random Walk concept, the fast diffusion is modeled as a superposition of point source’s solution for a concentration distribution while FDM is used to obtain the point source’s solution at each node. A mesh-coarsening algorithm is developed to generate an exclusive coarse mesh for FDiRW approach to maximize its efficiency. The effectiveness of the coarse mesh-based FDiRW approach is validated by benchmarking Finite Difference solutions. Numerical results demonstrated that FDiRW achieves a remarkable 1000x computational efficiency improvement over FDM while preserving desired accuracy for a medium-sized model of 192 × 192 × 192 grids. Finally, as models scale up, a floating-point operations (PLOPs) analysis of the FDiRW algorithm reveals that its computational complexity grows quadratically in terms of the number of nodes employed in computation.

36 MATERIALS SCIENCE↗
NASA NTRS1985

The propagation of solar flare particles in a turbulent coronal loop

Energetic solar flare particles, both electrons and protons, must survive the turbulent environment of a flaring loop and propogate to the lower corona or chromosphere in order to produce hard X-ray and gamma ray bursts. This plasma turbulence, often observed in soft X-ray line widths to be in excess of 100 km/s, is presumably capable of efficiently scattering the fast flare particles. This prevents to some degree the free streaming of accelerated particles and depending on the amplitude of the turbulence, restricts the particles to diffusive propagation along the length of the loop to the target chromosphere. In addition this turbulence is capable of performing additional acceleration of the fast particles by the second order Fermi mechanism. For compact flares with rise times 10s, the acceleration effect is small and the propagation of the particles is governed by spatial diffusion and energy loss in the ambient medium. The solution of the time dependent diffusion equation with velocity dependent diffusion and energy loss coefficients yields for the case of nonrelativistic protons particle precipitation rates which are necessary for calculating thick target gamma ray emission and also yields the total thin target emissivity.

Ryan, J. M.↗
NASA NTRS1990

The generalized diffusion-convection equation

Starting from the Boltzmann equation, a transport equation is derived for energetic particles in a moving magnetized plasma in which the scattering centers that keep the particles quasi-isotropic are moving with a velocity that is not necessarily the same as that of the plasma. The scattering is characterized by three very loose constraints: (1) there is a rest frame for each scatterer in which the particles scatter elastically; (2) in this frame the scattering will not disturb an isotropic distribution; and (3) the momentum transfer in an average collision may be described by a tensor operating on the particles original momentum. Since the strength of the scattering is not specified, the derivation should be as valid for plasma microturbulence as for hard-sphere scattering. The results show clearly which phenomena are responsible for tying the particles to the plasma in the transport equation.

Jones, Frank C.↗
NASA NTRS1990

An adaptive grid algorithm for one-dimensional nonlinear equations

Richards' equation, which models the flow of liquid through unsaturated porous media, is highly nonlinear and difficult to solve. Step gradients in the field variables require the use of fine grids and small time step sizes. The numerical instabilities caused by the nonlinearities often require the use of iterative methods such as Picard or Newton interation. These difficulties result in large CPU requirements in solving Richards equation. With this in mind, adaptive and multigrid methods are investigated for use with nonlinear equations such as Richards' equation. Attention is focused on one-dimensional transient problems. To investigate the use of multigrid and adaptive grid methods, a series of problems are studied. First, a multigrid program is developed and used to solve an ordinary differential equation, demonstrating the efficiency with which low and high frequency errors are smoothed out. The multigrid algorithm and an adaptive grid algorithm is used to solve one-dimensional transient partial differential equations, such as the diffusive and convective-diffusion equations. The performance of these programs are compared to that of the Gauss-Seidel and tridiagonal methods. The adaptive and multigrid schemes outperformed the Gauss-Seidel algorithm, but were not as fast as the tridiagonal method. The adaptive grid scheme solved the problems slightly faster than the multigrid method. To solve nonlinear problems, Picard iterations are introduced into the adaptive grid and tridiagonal methods. Burgers' equation is used as a test problem for the two algorithms. Both methods obtain solutions of comparable accuracy for similar time increments. For the Burgers' equation, the adaptive grid method finds the solution approximately three times faster than the tridiagonal method. Finally, both schemes are used to solve the water content formulation of the Richards' equation. For this problem, the adaptive grid method obtains a more accurate solution in fewer work units and less computation time than required by the tridiagonal method. The performance of the adaptive grid method tends to degrade as the solution process proceeds in time, but still remains faster than the tridiagonal scheme.

Gutierrez, William E.↗
NASA NTRS1993

CFD analyses of combustor and nozzle flowfields

The objectives of the research are to improve design capabilities for low thrust rocket engines through understanding of the detailed mixing and combustion processes. A Computational Fluid Dynamic (CFD) technique is employed to model the flowfields within the combustor, nozzle, and near plume field. The computational modeling of the rocket engine flowfields requires the application of the complete Navier-Stokes equations, coupled with species diffusion equations. Of particular interest is a small gaseous hydrogen-oxygen thruster which is considered as a coordinated part of an ongoing experimental program at NASA LeRC. The numerical procedure is performed on both time-marching and time-accurate algorithms, using an LU approximate factorization in time, flux split upwinding differencing in space. The integrity of fuel film cooling along the wall, its effectiveness in the mixing with the core flow including unsteady large scale effects, the resultant impact on performance and the assessment of the near plume flow expansion to finite pressure altitude chamber are addressed.

Tsuei, Hsin-Hua↗
NASA NTRS1994

Multi-dimensional combustor flowfield analyses in gas-gas rocket engine

The objectives of the present research are to improve design capabilities for low thrust rocket engines through understanding of the detailed mixing and combustions processes. Of particular interest is a small gaseous hydrogen-oxygen thruster which is considered as a coordinated part of an on-going experimental program at NASA LeRC. Detailed computational modeling requires the application of the full three-dimensional Navier Stokes equations, coupled with species diffusion equations. The numerical procedure is performed on both time-marching and time-accurate algorithms and using an LU approximate factorization in time, flux split upwinding differencing in space. The emphasis in this paper is focused on using numerical analysis to understand detailed combustor flowfields, including the shear layer dynamics created between fuel film cooling and the core gas in the vicinity on the nearby combustor wall; the integrity and effectiveness of the coolant film; three-dimensional fuel jets injection/mixing/combustion characteristics; and their impacts on global engine performance.

Tsuei, Hsin-Hua↗
NASA NTRS1994

The Flux-integral Method for Multidimensional Convection and Diffusion

The flux-integral method is a procedure for constructing an explicit, single-step, forward-in-time, conservative, control volume update of the unsteady, multidimensional convection-diffusion equation. The convective plus diffusive flux at each face of a control-volume cell is estimated by integrating the transported variable and its face-normal derivative over the volume swept out by the convecting velocity field. This yields a unique description of the fluxes, whereas other conservative methods rely on nonunique, arbitrary pseudoflux-difference splitting procedures. The accuracy of the resulting scheme depends on the form of the subcell interpolation assumed, given cell-average data. Cellwise constant behavior results in a (very artificially diffusive) first-order convection scheme. Second-order convection-diffusion schemes correspond to cellwise linear (or bilinear) subcell interpolation. Cellwise quadratic subcell interpolants generate a highly accurate convection-diffusion scheme with excellent phase accuracy. Under constant-coefficient conditions, this is a uniformly third-order polynomial interpolation algorithm (UTOPIA).

Leonard, B. P.↗
DOE OSTI2023

Required toroidal confinement for fusion and omnigeneity

Deuterium–tritium (DT) burning requires a long energy confinement times compared to collision times, so the particle distribution functions must approximate local Maxwellians. Non-equilibrium thermodynamics is applicable, which gives relations among transport, entropy production, the collision frequency, and the deviation from a Maxwellian. The distribution functions are given by the Fokker–Planck equation, which is an advection–diffusion equation. A large hyperbolic operator, the Vlasov operator with the particle trajectories as its characteristics, equals a small diffusive operator, the collision operator. The collisionless particle trajectories would be chaotic in stellarators without careful optimization. This would lead to rapid entropy production and transport—far beyond what is consistent with a self-sustaining DT burn. Omnigeneity is the weakest general condition that is consistent with a sufficiently small entropy production associated with the thermal particle trajectories. Omnigeneity requires that the contours of constant magnetic field strength be unbounded in at least one of the two angular coordinates in magnetic surfaces and that there be a symmetry in the field-strength wells along the field lines. Even in omnigenous plasmas, fluctuations due to microturbulence can produce chaotic particle trajectories and the gyro-Bohm transport is seen in many stellarator and tokamak experiments. The higher the plasma temperature above 10 keV, the smaller the transport must be compared to gyro-Bohm for a self-sustaining DT burn. The hot alphas of DT fusion heat the electrons. When the ion–electron equilibration time is long compared to the ion energy confinement time, a self-sustaining DT burn is not possible, which sets a limit on the electron temperature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1994

Stochastic acceleration of energetic ions in Jupiter's magnetosphere

An equation governing the combined radial diffusion and stochastic acceleration of super-Alfvenic ions by magnetohydrodynamic waves in Jupiter's outer magnetosphere is derived. The formulation is based upon a total energy invariant of the adiabatic transport which applies to an isotropic distribution undergoing rapid pitch angle scattering by waves. An analytic solution to the double diffusion equation is obtained and numerical results are presented for two models of ion injection. The first model assumes S(+) and O(+) are injected throughout a broad region of space through photoionization of Jupiter's magnetospheric neutral wind and obtain an initial energy corresponding to the local corotation energy after pickup by the planetary magnetic field. The second model assumes a monoenergetic distribution of energetic protons is implanted in the middle magnetosphere by the action of field-aligned potential drops in Jupiter's auroral ionosphere. For both light and heavy ions the injection process creates a seed population of particles which are further accelerated nonadiabatically by the MHD waves and adiabatically through radial diffusion. A comparison of the theoretical results with a recent data analysis of Voyager low-energy charged particle measurements is made with very good agreement, thus providing a rigorous quantitative account of and definitive explanation for the high-energy ion component of Jupiter's magnetosphere.

Barbosa, D. D.↗
DOE OSTI2024

Resistive drift wave turbulence and anomalous transport of multi-species plasma

Anomalous transport of multi-species plasma is considered with the generalized Hasegawa–Wakatani model. It is shown that the transport of all plasma species is described by fractional diffusion equations with the same effective diffusion coefficient. Strongly enhanced perturbations of heavy impurity density are found in long-living plasma flow vortices.

Physics↗
NASA NTRS1981

Mixing of a passive scalar in isotropic and sheared homogeneous turbulence

In order to calculate the velocity and scalar fields, the three dimensional, time-dependent equations of motion and the diffusion equation were solved numerically. The following cases were treated: isotropic, homogeneous turbulence with decay of a passive scalar; and homogeneous turbulent shear flow with a passive scalar whose mean varies linearly in the spanwise direction. The solutions were obtained at relatively low Reynolds numbers so that all of the turbulent scales could be resolved without modeling. Turbulent statistics such as integral length scales, Taylor microscales, Kolmogorov length scale, one- and two-point correlations of velocity-velocity and velocity-scalar, turbulent Prandtl/Schmidt number, r.m.s. values of velocities, the scalar quantity and pressure, skewness, decay rates, and decay exponents were calculated. The results are compared with the available expermental results, and good agreement is obtained.

Shirani, E.↗
NASA NTRS1981

Centrifugally driven diffusion of Iogenic plasma

The plasma distribution around Io as measured by Voyager 1 displays an asymmetric discontinuity at Io's orbit that has been suggested to be the signature of centrifugally driven interchange diffusion fed by plasma derived from Io. This hypothesis is explored further and found to be valid. The particular form for the diffusion coefficient appropriate to centrifugally driven turbulence is derived. The nonlinear character of this kind of diffusion is thereby made explicit. Solutions to the nonlinear, time-independent and linearized, time-dependent diffusion equations are given. These display a markedly conservative behavior. The nonlinear, steady state solutions are identical in form to the solutions of the previously studied equation of linear, atmospherically driven diffusion. The linearized, time-dependent solutions exhibit a negative feed-back quality that buffers the response of the density to changes in the source strength. Estimates of the source strength, the diffusion coefficient, and the signal propagation speed are also given.

Siscoe, G. L.↗
NASA NTRS1986

The propagation of solar flare particles in a coronal loop

A time-dependent diffusion equation with velocity-dependent diffusion and energy-loss coefficients was solved for the case where energetic solar particles are injected into a coronal loop and then diffuse out the ends of the loop into the lower corona/chromosphere. The solution yields for the case of relativistic electrons, precipitation rates and populations which are necessary for calculating thick and thin target X-ray emission. It follows that the thick target emission is necessarily delayed with respect to the particle acceleration on injection by more than the mere travel time of the particle over the loop length. In addition the time-dependent electron population at the top of the loop is calculated. This is useful in estimating the resulting micron-wave emission. The results show relative timing differences in the different emission processes which are functions of particle species, energy and the point of injection of the particles into the loop. Equivalent quantities are calculated for non-relativistic protons.

Ryan, J. M.↗
NASA NTRS1987

The thermal stability of coronal loops by nonlinear diffusion asymptotics

A nonlinear reaction-diffusion equation and some additional constraints are derived which describe the time-dependent behavior of the temperature structure of the plasma in coronal loops. The equation is analyzed using nonlinear diffusion asymptotics, in particular singular perturbation techniques, and the results are interpreted in the context of the physical problem of the thermal stability and temporal behavior of the plasma. The results are consistent with the possibility of cyclic thermal behavior of the plasma, as suggested by Kuin and Martens (1982).

Pakkert, J. W.↗