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At least 55 records · Page 3

An efficient numerical method for solving the incompressible Navier-Stokes equations

This paper describes an efficient numerical method for solving the steady incompressible Navier-Stokes equations. The method is a fully implicit method based on the generalized Galerkin method, and the resulting system of equations is solved in a sweeping mode by iterative line relaxation. Results of the present method are compared with published results for separating and reattaching flows, and parametric studies showing the effects of step size, boundary locations, and Reynolds number are presented. The present method is substantially faster than previously published methods; typical run times range from 10 sec to 1 min of 7600 CPU time; and, based on results obtained to date, it is stable at any Reynolds number.

Murphy, J. D.↗

Vectorizable implicit algorithms for the flux-difference split, three-dimensional Navier-Stokes equations

The computational efficiency of four vectorizable implicit algorithms is assessed when applied to calculate steady-state solutions to the three-dimensional, incompressible Navier-Stokes equations in general coordinates. Two of these algorithms are characterized as hybrid schemes; that is, they combine some approximate factorization in two coordinate directions with relaxation in the remaining spatial direction. The other two algorithms utilize an approximate factorization approach which yields two-factor algorithms for three-dimensional systems. All four algorithms are implemented in identical high-resolution upwind schemes for the flux-difference split Navier-Stokes equations. These highly nonlinear schemes are obtained by extending an implicit Total Variation Diminishing (TVD) scheme recently developed for linear one-dimensional systems of hyperbolic conservation laws to the three-dimensional Navier-Stokes equations. The computation of vortical flow over a sharp-edged, thin delta wing has been chosen as a common numerical test case. The convergence of the algorithms is discussed and the accuracy of the computed flow-field results is assessed. The validity of the present results are demonstrated by a comparison with experimental data.

Hartwich, P. M.↗

Using High Frequency Passive Microwave, A-train, and TRMM Data to Evaluate Hydrometer Structure in the NASA GEOS-5 Data Assimilation System

Validating water vapor and prognostic condensate in global models remains a challenging research task. Model parameterizations are still subject to a large number of tunable parameters; furthermore, accurate and representative in situ observations are very sparse, and satellite observations historically have significant quantitative uncertainties. Progress on improving cloud / hydrometeor fields in models stands to benefit greatly from the growing inventory ofA-Train data sets. ill the present study we are using a variety of complementary satellite retrievals of hydrometeors to examine condensate produced by the emerging NASA Modem Era Retrospective Analysis for Research and Applications, MERRA, and its associated atmospheric general circulation model GEOS5. Cloud and precipitation are generated by both grid-scale prognostic equations and by the Relaxed Arakawa-Schubert (RAS) diagnostic convective parameterization. The high frequency channels (89 to 183.3 GHz) from AMSU-B and MRS on NOAA polar orbiting satellites are being used to evaluate the climatology and variability of precipitating ice from tropical convective anvils. Vertical hydrometeor structure from the Tropical Rainfall Measuring Mission (TRMM) and CloudSat radars are used to develop statistics on vertical hydrometeor structure in order to better interpret the extensive high frequency passive microwave climatology. Cloud liquid and ice water path data retrieved from the Moderate Resolution Imaging Spectroradiometer, MODIS, are used to investigate relationships between upper level cloudiness and tropical deep convective anvils. Together these data are used to evaluate cloud / ice water path, gross aspects of vertical hydrometeor structure, and the relationship between cloud extent and surface precipitation that the MERRA reanalysis must capture.

Robertson, Franklin↗

A semi-direct procedure using a local relaxation factor and its application to an internal flow problem

Generally, fast direct solvers are not directly applicable to a nonseparable elliptic partial differential equation. This limitation, however, is circumvented by a semi-direct procedure, i.e., an iterative procedure using fast direct solvers. An efficient semi-direct procedure which is easy to implement and applicable to a variety of boundary conditions is presented. The current procedure also possesses other highly desirable properties, i.e.: (1) the convergence rate does not decrease with an increase of grid cell aspect ratio, and (2) the convergence rate is estimated using the coefficients of the partial differential equation being solved.

Chang, S. C.↗

Novel Relaxation Time Approximation to the Relativistic Boltzmann Equation

In this work, we show that the widely used relaxation time approximation to the relativistic Boltzmann equation contains basic flaws, being incompatible with micro- and macroscopic conservation laws if the relaxation time depends on energy or general matching conditions are applied. We propose a new approximation that fixes such fundamental issues and maintains the basic properties of the linearized Boltzmann collision operator. We show how this correction affects transport coefficients, such as the bulk viscosity and particle diffusion.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Three-dimensional adaptive grid generation for body-fitted coordinate system

This report describes a numerical method for generating 3-D grids for general configurations. The basic method involves the solution of a set of quasi-linear elliptic partial differential equations via pointwise relaxation with a local relaxation factor. It allows specification of the grid spacing off the boundary surfaces and the grid orthogonality at the boundary surfaces. It includes adaptive mechanisms to improve smoothness, orthogonality, and flow resolution in the grid interior.

Chen, S. C.↗

Three-dimensional adaptive grid generation for body-fitted coordinate system

This report describes a numerical method for generating 3-D grids for general configurations. The basic method involves the solution of a set of quasi-linear elliptic partial differential equations via pointwise relaxation with a local relaxation factor. It allows specification of the grid spacing off the boundary surfaces and the grid orthogonality at the boundary surfaces. It includes adaptive mechanisms to improve smoothness, orthogonality, and flow resolution in the grid interior.

Chen, S. C.↗

Kinetic relaxation of a non-Maxwellian monatomic gas in a state of gross rest

The kinetic relaxation of a monatomic gas in a state of gross rest is studied by use of Maxwell's second-order moment equation. The molecular models considered range from the hard sphere to the Maxwell molecule. The development is exact for an ellipsoidal distribution and becomes a good approximation for more general distributions. The results show that the relaxation of second-order moments is nearly exponential for power-law molecules and that the characteristic time mu/p appears as the principal controlling parameter while the power-law constant plays a secondary role. Comparisons between results of numerical simulations using Bird's direct simulation Monte Carlo method and theory show excellent agreement for both hard-sphere and Maxwell molecules.

Baganoff, D.↗

Lifetime renormalization of weakly anharmonic superconducting qubits. I. Role of number nonconserving terms

The dynamics of a weakly anharmonic superconducting qubit in a complex electromagnetic environment is generally well described by an effective multimode Kerr Hamiltonian at sufficiently weak excitation. This Hamiltonian can be embedded in a master equation with losses determined by the details of the electromagnetic environment. Recent experiments indicate, however, that when a superconducting circuit is driven with microwave signals populating the system with sufficiently high excitations, the observed relaxation rates appear to be substantially different from expectations based on the electromagnetic environment of the qubit alone. This issue is a limiting factor in the optimization of superconducting qubit readout schemes. We claim here that an effective master equation with drive-power-dependent parameters is an efficient approach to model such quantum dynamics. In this sequence of papers, we derive effective master equations, whose parameters exhibit nonlinear dependence on the excitation level of the circuit as well as the electromagnetic environment of the qubit. Further, we show that the number nonconserving terms in the qubit nonlinearity generally lead to a renormalization of dissipative parameters of the effective master equation, while the number conserving terms give rise to a renormalization of the system frequencies. Here, in Paper I, we consider the excitation-relaxation dynamics of a transmon qubit that is prepared in a certain initial state, but is not driven otherwise. A unitary transformation technique is introduced to study the renormalization of (i) qubit relaxation due to coupling to a generic bath and (ii) Purcell decay. Analytic expressions are provided for the dependence of the nonlinear dissipative terms on the details of the electromagnetic environment of the qubit. The perturbation technique based on unitary transformations developed here is generalized to the continuously driven case in Paper II.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

The practical application of a finite difference method for analyzing transonic flow over oscillating airfoils and wings

Separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances was performed. The steady velocity potential was obtained first from the well known nonlinear equation for steady transonic flow. The unsteady velocity potential was then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. The results of an investigation into the relaxation-solution-instability problem was discussed. Concepts examined include variations in outer boundary conditions, a coordinate transformation so that the boundary condition at infinity may be applied to the outer boundaries of the finite difference region, and overlapping subregions. The general conclusion was that only a full direct solution in which all unknowns are obtained at the same time will avoid the solution instabilities of relaxation. An analysis of the one-dimensional form of the unsteady transonic equation was studied to evaluate errors between exact and finite difference solutions. Pressure distributions were presented for a low-aspect-ratio clipped delta wing at Mach number of 0.9 and for a moderate-aspect-ratio rectangular wing at a Mach number of 0.875.

Weatherill, W. H.↗

Flux-split algorithms for flows with non-equilibrium chemistry and vibrational relaxation

The present consideration of numerical computation methods for gas flows with nonequilibrium chemistry thermodynamics gives attention to an equilibrium model, a general nonequilibrium model, and a simplified model based on vibrational relaxation. Flux-splitting procedures are developed for the fully-coupled inviscid equations encompassing fluid dynamics and both chemical and internal energy-relaxation processes. A fully coupled and implicit large-block structure is presented which embodies novel forms of flux-vector split and flux-difference split algorithms valid for nonequilibrium flow; illustrative high-temperature shock tube and nozzle flow examples are given.

Grossman, B.↗

Comparison of solutions of the Navier-Stokes and interacting boundary layer equations for separated turbulent flow

Comparisons are presented between numerical solutions of the Navier-Stokes and interacting boundary-layer equations for the subsonic separated turbulent flow over an axisymmetric boattail configuration for which experimental data was available. Comparisons were made using a standard algebraic turbulence model and its modification using a streamwise relaxation model. Grid size studies were performed to provide an approximate assessment of the sensitivity of each method to mesh size. In general, good agreement was observed between the solutions of the Navier-Stokes and interacting boundary-layer equations; however, the interaction approach responded more strongly to the modified turbulence model thereby giving better agreement with experimental data.

Vatsa, V. N.↗

Numerical analysis of flow non-uniformity in the hot gas manifold of the Space Shuttle main engine

Three-dimensional viscous flow in a conceptual hot gas manifold (HGM) for the Space Shuttle Main Engine High Pressure Fuel Turbopump (SSME HPFTP) was numerically analyzed. A finite difference scheme was used to solve the Navier-Stokes equations. The exact geometry of the SSME HGM was modeled using boundary fitted curvilinear coordinates and the General Interpolants Method (GIM) code. Slight compressibility of the subsonic flow was modeled using a linearized equation of state with artificial compressibility. A time relaxation method was used to obtain a steady state solution. The feasibility and potential usefulness of computational methods in assisting the design of SSME components which involves the flow of fluids within complex geometrical shapes is demonstrated.

Thoenes, J.↗

General relaxation schemes in multigrid algorithms for higher order singularity methods

Relaxation schemes based on approximate and incomplete factorization technique (AF) are described. The AF schemes allow construction of a fast multigrid method for solving integral equations of the second and first kind. The smoothing factors for integral equations of the first kind, and comparison with similar results from the second kind of equations are a novel item. Application of the MD algorithm shows convergence to the level of truncation error of a second order accurate panel method.

Oskam, B.↗

Transonic perturbation analysis of wing-fuselage-nacelle-pylon configurations with powered jet exhausts

A transonic small perturbation method has been developed for the analysis of general wing-fuselage-nacelle-pylon configurations with powered jet exhausts. Finite difference successive line relaxation algorithm is used to solve the small disturbance potential equation in conservative form. The nacelle tangency condition and the jet exhaust plume contact conditions are fulfilled in a quasi-cylindrical fashion on a surface fitting the Cartesian grid. The pylon tangency condition is treated in a quasi-planar manner as for the wing. Viscous displacement effects on the wing are modeled by suitable shape changes including the placement of a viscous ramp at the base of the shock. Computed results of a transport configuration show satisfactory correlation with test data.

Wai, J. C.↗

Surfactant Facilitated Spreading of Aqueous Drops on Hydrophobic Surfaces

Microgravity technologies often require aqueous phases to spread over nonwetting hydrophobic solid surfaces. Surfactants facilitate the wetting of water on hydrophobic surfaces by adsorbing on the water/air and hydrophobic solid/water interfaces and lowering the surface tensions of these interfaces. The tension reductions decrease the contact angle, which increases the equilibrium wetted area. Hydrocarbon surfactants; (i.e., amphiphiles with a hydrophobic moiety consisting of an extended chain of (aliphatic) methylene -CH2- groups attached to a large polar group to give aqueous solubility) are capable of reducing the contact angles on surfaces which are not very hydrophobic, but do not reduce significantly the contact angles of the very hydrophobic surfaces such as parafilm, polyethylene or self assembled monolayers. Trisiloxane surfactants (amphiphiles with a hydrophobe consisting of methyl groups linked to a trisiloxane backbone in the form of a disk ((CH3)3-Si-O-Si-O-Si(CH3)3) and an extended ethoxylate (-(OCH2CH2)a-) polar group in the form of a chain with four or eight units) can significantly reduce the contact angle of water on a very hydrophobic surface and cause rapid and complete (or nearly complete) spreading (termed superspreading). The overall goal of the research described in this proposal is to establish and verify a theory for how trisiloxanes cause superspreading, and then use this knowledge as a guide to developing more general hydrocarbon based surfactant systems which superspread. We propose that the trisiloxane surfactants superspread because their structure allows them to strongly lower the high hydrophobic solid/aqueous tension when they adsorb to the solid surface. When the siloxane adsorbs, the hydrophobic disk parts of the molecule adsorb onto the surface removing the surface water. Since the cross-sectional area of the disk is larger than that of the extended ethoxylate chain, the disks can form a space-filling mat on the surface which removes a significant amount of the surface water. In this presentation, we report the results of measurements of the molecular packing and rates of kinetic exchange of the trisiloxane surfactants at the air/water interface in order to confirm our picture of trisiloxane packing, and provide additional insight into the superspreading process. We used the pendant bubble technique as a Langmuir trough to measure the trisiloxane equation of state which relates the tension to the surface concentration. From these measurements we obtain accurate values for the maximum packing density. We find that trisiloxanes with 4 and 8 ethoxylate groups have the same maximum packing concentration, indicating that the maximum packing is controlled by the cross section of the head group. For trisiloxanes with larger than eight ethoxylates, the maximum packing increases with ethoxylate number, indicating that the disposition of the ethoxylate chain (i.e., its effective size) is controlling. This supports our picture of superspreading: The superspreading ability of trisiloxanes decreases considerably for trisiloxanes with larger than eight ethoxylates; the packing measurements indicate that for the higher ethoxylate number trisiloxanes, the compact nonpolar head groups are pushed apart by the ethoxylate chain. They leave spaces of surface water on adsorption and do not lower the solid tension as much as their lower chain analogues. Finally the report measurements of the dynamic tension reduction accompanying the adsorption of trisiloxanes onto an initially clean interface using the pendant bubble technique, and we obtain from these relaxations, the equation of state and a mass transfer model, the rate constants for kinetic exchange. We find that the rate constants for desorption of trisiloxanes are generally much slower than for analogous aliphatic polyethoxylate surfactants with identical ethoxylate chain lengths. When an aqueous drop of a superspreader solution is placed on a hydrophobic surface and begins to spread, the lower desorption rates allows the tension at the drop center to remain reduced relative to the tension of the expanding periphery, thus strengthening Marangoni forces which can assist the spreading. Marangoni forces can be especially significant in the case of superspreaders because their maximum equilibrium reduction in tension is several dynes/cm lower than for aliphatic surfactants.

Kumar, Nitin↗

On the factorization and fitting of molecular scattering information

The reported analysis is based on the factored IOS T-matrix. It is shown that line shape measurements may be used over a range of temperatures to evaluate inelastic scattering cross sections. Basic factorization or parameterization relations are derived by considering the wavefunction equations. The parameterization of cross sections is considered, taking into account the differential scattering amplitude and cross section, integral cross sections, phenomenological cross sections for general relaxation processes, and viscosity and diffusion cross sections. Thermal averages and rates are discussed, giving attention to integral cross sections and rates, and general phenomenological cross sections. The results of computational studies are also presented.

Goldflam, R.↗

Advances in upwind relaxation methods

Numerical techniques for solving the compressible Euler and Navier-Stokes equations are discussed with an emphasis on characteristic-based schemes. Two popular approaches, flux difference splitting and flux vector splitting, are described in one-dimensional Cartesian coordinates and then extended to three-dimensional generalized coordinates. A technique for increasing the spatial accuracy is presented, followed by a discussion of numerical dissipation mechanisms. An introduction to the use of implicit time integration schemes for accelerating the convergence rate to steady-state solutions including Newton's method, relaxation strategies, and approximate factorization techniques and their implementation on a vector processor concludes the chapter.

Walters, R. W.↗