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At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Computational Study of Axisymmetric Off-Design Nozzle Flows

Computational Fluid Dynamics (CFD) analyses of axisymmetric circular-arc boattail nozzles operating off-design at transonic Mach numbers have been completed. These computations span the very difficult transonic flight regime with shock-induced separations and strong adverse pressure gradients. External afterbody and internal nozzle pressure distributions computed with the Wind code are compared with experimental data. A range of turbulence models were examined, including the Explicit Algebraic Stress model. Computations have been completed at freestream Mach numbers of 0.9 and 1.2, and nozzle pressure ratios (NPR) of 4 and 6. Calculations completed with variable time-stepping (steady-state) did not converge to a true steady-state solution. Calculations obtained using constant timestepping (timeaccurate) indicate less variations in flow properties compared with steady-state solutions. This failure to converge to a steady-state solution was the result of using variable time-stepping with large-scale separations present in the flow. Nevertheless, time-averaged boattail surface pressure coefficient and internal nozzle pressures show reasonable agreement with experimental data. The SST turbulence model demonstrates the best overall agreement with experimental data.

DalBello, Teryn↗
NASA NTRS2011

Multiple-Beam Detection of Fast Transient Radio Sources

A method has been designed for using multiple independent stations to discriminate fast transient radio sources from local anomalies, such as antenna noise or radio frequency interference (RFI). This can improve the sensitivity of incoherent detection for geographically separated stations such as the very long baseline array (VLBA), the future square kilometer array (SKA), or any other coincident observations by multiple separated receivers. The transients are short, broadband pulses of radio energy, often just a few milliseconds long, emitted by a variety of exotic astronomical phenomena. They generally represent rare, high-energy events making them of great scientific value. For RFI-robust adaptive detection of transients, using multiple stations, a family of algorithms has been developed. The technique exploits the fact that the separated stations constitute statistically independent samples of the target. This can be used to adaptively ignore RFI events for superior sensitivity. If the antenna signals are independent and identically distributed (IID), then RFI events are simply outlier data points that can be removed through robust estimation such as a trimmed or Winsorized estimator. The alternative "trimmed" estimator is considered, which excises the strongest n signals from the list of short-beamed intensities. Because local RFI is independent at each antenna, this interference is unlikely to occur at many antennas on the same step. Trimming the strongest signals provides robustness to RFI that can theoretically outperform even the detection performance of the same number of antennas at a single site. This algorithm requires sorting the signals at each time step and dispersion measure, an operation that is computationally tractable for existing array sizes. An alternative uses the various stations to form an ensemble estimate of the conditional density function (CDF) evaluated at each time step. Both methods outperform standard detection strategies on a test sequence of VLBA data, and both are efficient enough for deployment in real-time, online transient detection applications.

Thompson, David R.↗
NASA NTRS1988

An algorithm for unsteady flows with strong convection

An implicit ADI numerical method for the calculation of 2-D unsteady flows with strong convection effects is described. The method is based on the conventional Crank-Nicholson approach for parabolic equations but an upwind-downwind differencing is used for the first order spatial derivatives associated with convection. The differencing is carried out in the current and previous time plane in such a way that the algorithm is second order accurate in both space and time. The difference equations are factored into sequential operators, one in each independent spatial variable; the solution at each time step may then be computed as a sequence of tridiagonal matrix problems. The method may be used in a noniterative manner although iteration at each time step is recommended in situations where the effects of convection are strong.

Peridier, Vallorie↗
NASA NTRS1989

Algorithms and software for nonlinear structural dynamics

The objective of this research is to develop efficient methods for explicit time integration in nonlinear structural dynamics for computers which utilize both concurrency and vectorization. As a framework for these studies, the program WHAMS, which is described in Explicit Algorithms for the Nonlinear Dynamics of Shells (T. Belytschko, J. I. Lin, and C.-S. Tsay, Computer Methods in Applied Mechanics and Engineering, Vol. 42, 1984, pp 225 to 251), is used. There are two factors which make the development of efficient concurrent explicit time integration programs a challenge in a structural dynamics program: (1) the need for a variety of element types, which complicates the scheduling-allocation problem; and (2) the need for different time steps in different parts of the mesh, which is here called mixed delta t integration, so that a few stiff elements do not reduce the time steps throughout the mesh.

Belytschko, Ted↗
NASA NTRS1996

Multigrid Methods for Fully Implicit Oil Reservoir Simulation

In this paper we consider the simultaneous flow of oil and water in reservoir rock. This displacement process is modeled by two basic equations: the material balance or continuity equations and the equation of motion (Darcy's law). For the numerical solution of this system of nonlinear partial differential equations there are two approaches: the fully implicit or simultaneous solution method and the sequential solution method. In the sequential solution method the system of partial differential equations is manipulated to give an elliptic pressure equation and a hyperbolic (or parabolic) saturation equation. In the IMPES approach the pressure equation is first solved, using values for the saturation from the previous time level. Next the saturations are updated by some explicit time stepping method; this implies that the method is only conditionally stable. For the numerical solution of the linear, elliptic pressure equation multigrid methods have become an accepted technique. On the other hand, the fully implicit method is unconditionally stable, but it has the disadvantage that in every time step a large system of nonlinear algebraic equations has to be solved. The most time-consuming part of any fully implicit reservoir simulator is the solution of this large system of equations. Usually this is done by Newton's method. The resulting systems of linear equations are then either solved by a direct method or by some conjugate gradient type method. In this paper we consider the possibility of applying multigrid methods for the iterative solution of the systems of nonlinear equations. There are two ways of using multigrid for this job: either we use a nonlinear multigrid method or we use a linear multigrid method to deal with the linear systems that arise in Newton's method. So far only a few authors have reported on the use of multigrid methods for fully implicit simulations. Two-level FAS algorithm is presented for the black-oil equations, and linear multigrid for two-phase flow problems with strong heterogeneities and anisotropies is studied. Here we consider both possibilities. Moreover we present a novel way for constructing the coarse grid correction operator in linear multigrid algorithms. This approach has the advantage in that it preserves the sparsity pattern of the fine grid matrix and it can be extended to systems of equations in a straightforward manner. We compare the linear and nonlinear multigrid algorithms by means of a numerical experiment.

Molenaar, J.↗
NASA NTRS2001

Time-Accurate Solutions of Incompressible Navier-Stokes Equations for Potential Turbopump Applications

Two numerical procedures, one based on artificial compressibility method and the other pressure projection method, are outlined for obtaining time-accurate solutions of the incompressible Navier-Stokes equations. The performance of the two method are compared by obtaining unsteady solutions for the evolution of twin vortices behind a at plate. Calculated results are compared with experimental and other numerical results. For an un- steady ow which requires small physical time step, pressure projection method was found to be computationally efficient since it does not require any subiterations procedure. It was observed that the artificial compressibility method requires a fast convergence scheme at each physical time step in order to satisfy incompressibility condition. This was obtained by using a GMRES-ILU(0) solver in our computations. When a line-relaxation scheme was used, the time accuracy was degraded and time-accurate computations became very expensive.

Kiris, Cetin↗
NASA NTRS1973

Nonlinear vibrations of rectangular plates.

A finite-difference method is developed to determine the large amplitude dynamic responses of thin elastic plates subjected to uniform pressure pulse-type loads. Four different sets of boundary conditions are considered. Some specific problems are solved. The results are compared with approximate solutions obtained by Yamaki (1961). The numerical method presented provides an accurate and efficient approximate solution to the problem, and should be useful as a check on other approximate methods. The grid-size and the time-step necessary for obtaining numerical stability depend on the particular problem. For many cases the method converges rapidly and a rather large grid-size and time-step is adequate.

Bayles, D. J.↗
NASA NTRS1989

Personal computer study of finite-difference methods for the transonic small disturbance equation

Calculation of unsteady flow phenomena requires careful attention to the numerical treatment of the governing partial differential equations. The personal computer provides a convenient and useful tool for the development of meshes, algorithms, and boundary conditions needed to provide time accurate solution of these equations. The one-dimensional equation considered provides a suitable model for the study of wave propagation in the equations of transonic small disturbance potential flow. Numerical results for effects of mesh size, extent, and stretching, time step size, and choice of far-field boundary conditions are presented. Analysis of the discretized model problem supports these numerical results. Guidelines for suitable mesh and time step choices are given.

Bland, Samuel R.↗
NASA NTRS1990

Personal computer study of finite-difference methods for the transonic small disturbance equation

Calculation of unsteady flow phenomena requires careful attention to the numerical treatment to the governing partial differential equations. The personal computer provides a convenient and useful tool for the development of meshes, algorithms, and boundary conditions needed to provide time accurate solution of these equations. The one-dimensional equation considered provides a suitable model for the study of wave propagation in the equations of transonic small disturbance potential flow. Numerical results for effects of mesh size, extent, and stretching, time step size, and choice of far-field boundary conditions are presented. Analysis of the discretized model problem supports these numerical results. Guidelines for suitable mesh and time step choices are given.

Bland, Samuel R.↗
NASA NTRS1992

Spatial and temporal adaptive procedures for the unsteady aerodynamic analysis of airfoils using unstructured meshes

An algorithm which combines spatial and temporal adaption for the time integration of the two dimensional Euler equations on unstructured meshes of triangles is presented. Spatial adaption involves mesh enrichment to add elements in high gradient regions of the flow and mesh coarsening to remove elements where they are no longer needed. Temporal adaption is a time accurate, local time stepping procedure which integrates the flow equations in each cell according to the local numerical stability constraint. The flow solver utilizes a four stage Runge-Kutta time integration scheme with an upwind flux-split spatial discretization. Results obtained using spatial and temporal adaption indicate that highly accurate solutions can be obtained with a significant savings of computing time over global time stepping.

Hooker, John R.↗
NASA NTRS2013

High-Order Space-Time Methods for Conservation Laws

Current high-order methods such as discontinuous Galerkin and/or flux reconstruction can provide effective discretization for the spatial derivatives. Together with a time discretization, such methods result in either too small a time step size in the case of an explicit scheme or a very large system in the case of an implicit one. To tackle these problems, two new high-order space-time schemes for conservation laws are introduced: the first is explicit and the second, implicit. The explicit method here, also called the moment scheme, achieves a Courant-Friedrichs-Lewy (CFL) condition of 1 for the case of one-spatial dimension regardless of the degree of the polynomial approximation. (For standard explicit methods, if the spatial approximation is of degree p, then the time step sizes are typically proportional to 1/p(exp 2)). Fourier analyses for the one and two-dimensional cases are carried out. The property of super accuracy (or super convergence) is discussed. The implicit method is a simplified but optimal version of the discontinuous Galerkin scheme applied to time. It reduces to a collocation implicit Runge-Kutta (RK) method for ordinary differential equations (ODE) called Radau IIA. The explicit and implicit schemes are closely related since they employ the same intermediate time levels, and the former can serve as a key building block in an iterative procedure for the latter. A limiting technique for the piecewise linear scheme is also discussed. The technique can suppress oscillations near a discontinuity while preserving accuracy near extrema. Preliminary numerical results are shown

Huynh, H. T.↗
NASA NTRS2014

A Radiation Chemistry Code Based on the Greens Functions of the Diffusion Equation

Ionizing radiation produces several radiolytic species such as.OH, e-aq, and H. when interacting with biological matter. Following their creation, radiolytic species diffuse and chemically react with biological molecules such as DNA. Despite years of research, many questions on the DNA damage by ionizing radiation remains, notably on the indirect effect, i.e. the damage resulting from the reactions of the radiolytic species with DNA. To simulate DNA damage by ionizing radiation, we are developing a step-by-step radiation chemistry code that is based on the Green's functions of the diffusion equation (GFDE), which is able to follow the trajectories of all particles and their reactions with time. In the recent years, simulations based on the GFDE have been used extensively in biochemistry, notably to simulate biochemical networks in time and space and are often used as the "gold standard" to validate diffusion-reaction theories. The exact GFDE for partially diffusion-controlled reactions is difficult to use because of its complex form. Therefore, the radial Green's function, which is much simpler, is often used. Hence, much effort has been devoted to the sampling of the radial Green's functions, for which we have developed a sampling algorithm This algorithm only yields the inter-particle distance vector length after a time step; the sampling of the deviation angle of the inter-particle vector is not taken into consideration. In this work, we show that the radial distribution is predicted by the exact radial Green's function. We also use a technique developed by Clifford et al. to generate the inter-particle vector deviation angles, knowing the inter-particle vector length before and after a time step. The results are compared with those predicted by the exact GFDE and by the analytical angular functions for free diffusion. This first step in the creation of the radiation chemistry code should help the understanding of the contribution of the indirect effect in the formation of DNA damage and double-strand breaks.

Plante, Ianik↗
NASA NTRS1987

Concurrent and vectorized mixed time, explicit nonlinear structural dynamics algorithms

A nonlinear structural dynamics program with an element library that exploits parallel processing is described. The aim is to exploit scheduling-allocation so that parallel processing and vectorization can effectively be treated in a general purpose program with explicit time integration and different time steps in different parts of the mesh. The program uses an element group scheme, which, as a by-product, also provides an automatic scheme for assigning different time steps to different parts of the mesh. The program has been tested on the Alliant FX/8; it shows a fivefold improvement in speed over compiler optimization.

Belytschko, Ted↗
NASA NTRS1992

Spatial and temporal adaptive procedures for the unsteady aerodynamic analysis of airfoils using unstructured meshes

An algorithm which combines spatial and temporal adaption for the time integration of the two-dimensional Euler equations on unstructured meshes of triangles is presented. Spatial adaption involves mesh enrichment to add elements in high gradient regions of the flow and mesh coarsening to remove elements where they are no longer needed. Temporal adaption is a time accurate, local time stepping procedure which integrates the flow equations in each cell according to the local numerical stability constraint. The flow solver utilizes a four-stage Runge-Kutta time integration scheme with an upwind flux-split spatial discretization. Results obtained using spatial and temporal adaption indicate that highly accurate solutions can be obtained with a significant savings of computing time over global time stepping.

Hooker, John R.↗
NASA NTRS2000

Sensitivity of Age-of-Air Calculations to the Choice of Advection Scheme

The age of air has recently emerged as a diagnostic of atmospheric transport unaffected by chemical parameterizations, and the features in the age distributions computed in models have been interpreted in terms of the models' large-scale circulation field. This study shows, however, that in addition to the simulated large-scale circulation, three-dimensional age calculations can also be affected by the choice of advection scheme employed in solving the tracer continuity equation, Specifically, using the 3.0deg latitude X 3.6deg longitude and 40 vertical level version of the Geophysical Fluid Dynamics Laboratory SKYHI GCM and six online transport schemes ranging from Eulerian through semi-Lagrangian to fully Lagrangian, it will be demonstrated that the oldest ages are obtained using the nondiffusive centered-difference schemes while the youngest ages are computed with a semi-Lagrangian transport (SLT) scheme. The centered- difference schemes are capable of producing ages older than 10 years in the mesosphere, thus eliminating the "young bias" found in previous age-of-air calculations. At this stage, only limited intuitive explanations can be advanced for this sensitivity of age-of-air calculations to the choice of advection scheme, In particular, age distributions computed online with the National Center for Atmospheric Research Community Climate Model (MACCM3) using different varieties of the SLT scheme are substantially older than the SKYHI SLT distribution. The different varieties, including a noninterpolating-in-the-vertical version (which is essentially centered-difference in the vertical), also produce a narrower range of age distributions than the suite of advection schemes employed in the SKYHI model. While additional MACCM3 experiments with a wider range of schemes would be necessary to provide more definitive insights, the older and less variable MACCM3 age distributions can plausibly be interpreted as being due to the semi-implicit semi-Lagrangian dynamics employed in the MACCM3. This type of dynamical core (employed with a 60-min time step) is likely to reduce SLT's interpolation errors that are compounded by the short-term variability characteristic of the explicit centered-difference dynamics employed in the SKYHI model (time step of 3 min). In the extreme case of a very slowly varying circulation, the choice of advection scheme has no effect on two-dimensional (latitude-height) age-of-air calculations, owing to the smooth nature of the transport circulation in 2D models. These results suggest that nondiffusive schemes may be the preferred choice for multiyear simulations of tracers not overly sensitive to the requirement of monotonicity (this category includes many greenhouse gases). At the same time, age-of-air calculations offer a simple quantitative diagnostic of a scheme's long-term diffusive properties and may help in the evaluation of dynamical cores in multiyear integrations. On the other hand, the sensitivity of the computed ages to the model numerics calls for caution in using age of air as a diagnostic of a GCM's large-scale circulation field.

Eluszkiewicz, Janusz↗
NASA NTRS1974

Numerical calculations of velocity and pressure distribution around oscillating airfoils

An analytical procedure based on the Navier-Stokes equations was developed for analyzing and representing properties of unsteady viscous flow around oscillating obstacles. A variational formulation of the vorticity transport equation was discretized in finite element form and integrated numerically. At each time step of the numerical integration, the velocity field around the obstacle was determined for the instantaneous vorticity distribution from the finite element solution of Poisson's equation. The time-dependent boundary conditions around the oscillating obstacle were introduced as external constraints, using the Lagrangian Multiplier Technique, at each time step of the numerical integration. The procedure was then applied for determining pressures around obstacles oscillating in unsteady flow. The obtained results for a cylinder and an airfoil were illustrated in the form of streamlines and vorticity and pressure distributions.

Bratanow, T.↗
NASA NTRS2017

The Root Cause of the Overheating Problem

Previously we identified the receding flow, where two fluid streams recede from each other, as an open numerical problem, because all well-known numerical fluxes give an anomalous temperature rise, thus called the overheating problem. This phenomenon, although presented in several textbooks, and many previous publications, has scarcely been satisfactorily addressed and the root cause of the overheating problem not well understood. We found that this temperature rise was solely connected to entropy rise and proposed to use the method of characteristics to eradicate the problem. However, the root cause of the entropy production was still unclear. In the present study, we identify the cause of this problem: the entropy rise is rooted in the pressure flux in a finite volume formulation and is implanted at the first time step. It is found theoretically inevitable for all existing numerical flux schemes used in the finite volume setting, as confirmed by numerical tests. This difficulty cannot be eliminated by manipulating time step, grid size, spatial accuracy, etc, although the rate of overheating depends on the flux scheme used. Finally, we incorporate the entropy transport equation, in place of the energy equation, to ensure preservation of entropy, thus correcting this temperature anomaly. Its applicability is demonstrated for some relevant 1D and 2D problems. Thus, the present study validates that the entropy generated ab initio is the genesis of the overheating problem.

Liou, Meng-Sing↗
NASA NTRS2014

First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems

A time-dependent extension of the first-order hyperbolic system method for advection-diffusion problems is introduced. Diffusive/viscous terms are written and discretized as a hyperbolic system, which recovers the original equation in the steady state. The resulting scheme offers advantages over traditional schemes: a dramatic simplification in the discretization, high-order accuracy in the solution gradients, and orders-of-magnitude convergence acceleration. The hyperbolic advection-diffusion system is discretized by the second-order upwind residual-distribution scheme in a unified manner, and the system of implicit-residual-equations is solved by Newton's method over every physical time step. The numerical results are presented for linear and nonlinear advection-diffusion problems, demonstrating solutions and gradients produced to the same order of accuracy, with rapid convergence over each physical time step, typically less than five Newton iterations.

Mazaheri, Alireza↗