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At least 1,225 records · Page 68

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NASA NTRS1988

An explicit Runge-Kutta method for 3D turbulent incompressible flows

A computer code has been developed to solve for the steady-state solution of the 3D incompressible Reynolds-averaged Navier-Stokes equations. The approach is based on the cell-center, central-difference, finite-volume formulation and an explicit one-step, multistage Runge-Kutta time-stepping scheme. The Baldwin-Lomax turbulence model is used. Techniques to accelerate the rate of convergence to a steady-state solution include the preconditioned method, the local time stepping, and the implicit residual smoothing. Improvements in computational efficiency have been demonstrated in several areas. This numerical procedure has been used to simulate the turbulent horseshoe vortex flow around an airfoil/flat-plate juncture.

Sung, Chao-Ho↗

NASA NTRS1990

Extension of a streamwise upwind algorithm to a moving grid system

A new streamwise upwind algorithm was derived to compute unsteady flow fields with the use of a moving-grid system. The temporally nonconservative LU-ADI (lower-upper-factored, alternating-direction-implicit) method was applied for time marching computations. A comparison of the temporally nonconservative method with a time-conservative implicit upwind method indicates that the solutions are insensitive to the conservative properties of the implicit solvers when practical time steps are used. Using this new method, computations were made for an oscillating wing at a transonic Mach number. The computed results confirm that the present upwind scheme captures the shock motion better than the central-difference scheme based on the beam-warming algorithm. The new upwind option of the code allows larger time-steps and thus is more efficient, even though it requires slightly more computational time per time step than the central-difference option.

Obayashi, Shigeru↗

NASA NTRS1992

Grid generation and flow solution method for Euler equations on unstructured grids

A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme, which uses Delaunay triangulation, generates the field points for the mesh based on cell aspect ratios and allows clustering of grid points near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss-Seidel procedure that is completely vectorizable. Also, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for an NACA 0012 airfoil as well as a two element configuration. Flow solution results are shown for a two dimensional flow over the NACA 0012 airfoil and for a two element configuration in which the solution was obtained through an adaptation procedure and compared with an exact solution. Preliminary three dimensional results also are shown in which the subsonic flow over a business jet is computed.

Anderson, W. Kyle↗

NASA NTRS1991

Numerical prediction of wakes in cascades and compressor rotors including the effects of mixing. II - Rotor passage flow and wakes including the effects of spanwise mixing

The results of a numerical investigation to predict the flow field including wakes and mixing in axial-flow compressor rotors are presented. The wake behavior in a moderately loaded compressor rotor is studied numerically using a 3D incompressible Navier-Stokes solver with a high Reynolds number form of a turbulence model. The equations are solved using a time dependent implicit technique. The agreement between the measured data and the predictions is good; including the blade boundary-layer profiles, wake mean-velocity profiles, and decay. The ability of the pseudocompressibility scheme to predict the entire flow field including the near and far wake profiles and its decay characteristics, effect of loading, and the viscous losses of a 3D rotor flow field are demonstrated. The mixing in the downstream regions away from the hub and annulus walls is dominated by wake diffusion. In regions away from the walls the radial mixing is predominantly caused by the transport of mass, momentum, and energy by the radial component of velocity in the wake.

Lakshminarayana, B.↗

NASA NTRS1993

Time-accurate Navier-Stokes calculations with multigrid acceleration

An efficient method for calculating unsteady flows is presented, with emphasis on a modified version of the thin-layer Navier-Stokes equations. Fourier stability analysis is used to illustrate the effect of treating the source term implicitly instead of explicity, as well as to illustrate other algorithmic choices. A 2D circular cylinder (with a Reynolds number of 1200 and a Mach number of 0.3) is calculated. The present scheme requires only about 10 percent of the computer time required by global minimum time stepping.

Melson, N. D.↗

NASA NTRS1993

A solution-adaptive hybrid-grid method for the unsteady analysis of turbomachinery

A solution-adaptive method for the time-accurate analysis of two-dimensional flows in turbomachinery is described. The method employs a hybrid structured-unstructured zonal grid topology in conjunction with appropriate modeling equations and solution techniques in each zone. The viscous flow region in the immediate vicinity of the airfoils is resolved on structured O-type grids while the rest of the domain is discretized using an unstructured mesh of triangular cells. Implicit, third-order accurate, upwind solutions of the Navier-Stokes equations are obtained in the inner regions. In the outer regions, the Euler equations are solved using an explicit upwind scheme that incorporates a second-order reconstruction procedure. An efficient and robust grid adaptation strategy, including both grid refinement and coarsening capabilities, is developed for the unstructured grid regions. Grid adaptation is also employed to facilitate information transfer at the interfaces between unstructured grids in relative motion. Results for grid adaptation to various features pertinent to turbomachinery flows are presented. Good comparisons between the present results and experimental measurements and earlier structured-grid results are obtained.

Mathur, Sanjay R.↗

NASA NTRS1994

A grid generation and flow solution method for the Euler equations on unstructured grids

A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme utilizes Delaunay triangulation and self-generates the field points for the mesh based on cell aspect ratios and allows for clustering near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss Seidel procedure which is completely vectorizable. In addition, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for a National Advisory Committee for Aeronautics (NACA) 0012 airfoil as well as a two-element configuration. Flow solution results are shown for two-dimensional flow over the NACA 0012 airfoil and for a two-element configuration in which the solution has been obtained through an adaptation procedure and compared to an exact solution. Preliminary three-dimensional results are also shown in which subsonic flow over a business jet is computed.

Anderson, W. Kyle↗

NASA NTRS1995

On the Dynamics of Implicit Linear Multistep Methods

Some new guidelines on the usage of implicit linear multistep methods (LMMs) as time-dependent approaches for obtaining steady-state numerical solutions in computational fluid dynamics (CFD) are explored. The commonly used implicit LMMs in CFD belong to the class of superstable time discretizations. It can be shown that the nonlinear asymptotic behavior in terms of bifurcation diagrams and basins of attractions of these schemes can provide an improved range of initial data and time step over the linearized stability limit.

Yee, H. C.↗

NASA NTRS1997

Implicit/Multigrid Algorithms for Incompressible Turbulent Flows on Unstructured Grids

An implicit code for computing inviscid and viscous incompressible flows on unstructured grids is described. The foundation of the code is a backward Euler time discretization for which the linear system is approximately solved at each time step with either a point implicit method or a preconditioned Generalized Minimal Residual (GMRES) technique. For the GMRES calculations, several techniques are investigated for forming the matrix-vector product. Convergence acceleration is achieved through a multigrid scheme that uses non-nested coarse grids that are generated using a technique described in the present paper. Convergence characteristics are investigated and results are compared with an exact solution for the inviscid flow over a four-element airfoil. Viscous results, which are compared with experimental data, include the turbulent flow over a NACA 4412 airfoil, a three-element airfoil for which Mach number effects are investigated, and three-dimensional flow over a wing with a partial-span flap.

Anderson, W. Kyle↗

NASA NTRS2001

Parameterizations of Depositional Growth of Cloud Ice in a Bulk Microphysical Scheme

The conversion of cloud ice to snow by depositional growth, designated P(sub SFI), in the Goddard Cumulus Ensemble Model cloud physics parameterization is examined. The original formulation of P(sub SFI) is shown to produce excessive conversion of cloud ice to snow because of an implicit assumption that the relative humidity is 100% with respect to water even though the air may actually be quite less humid. Two possible corrections to this problem are proposed, the first involving application of a relative humidity dependent correction factor to the original formulation of P(sub SFI), and the second involving a new formulation of P(sub SFI) based on the equation for depositional growth of cloud ice.

Braun, Scott A.↗

DOE OSTI2022

Quasi-Helmholtz decomposition, Gauss' laws and charge conservation for finite element particle-in-cell

Development of particle-in-cell (PIC) methods using finite element based methods (FEMs) have been a topic of renewed interest; this has largely been driven by (a) the ability of finite element methods to better model geometry, (b) better understanding of function spaces that are necessary to represent all Maxwell quantities, and (c) more recently, the fundamental rubrics that should be obeyed in space and time so as to satisfy Gauss' laws and the equation of continuity. In that vein, methods have been developed recently that satisfy these equations and are agnostic to time stepping methods. While this development is indeed a significant advance, it should be noted that implicit FEM transient solvers support an underlying null space that corresponds to a gradient of a scalar potential ∇Φ(r) (or t∇Φ(r) in the case of wave equation solvers). While explicit schemes do not suffer from this drawback, they are only conditionally stable with time step sizes that are mesh dependent and very small. Furthermore, the null space produces spurious charge that can corrupt the desired physics of a PIC simulation. The way to overcome this bottleneck, and indeed, satisfy all four Maxwell's equation is to use a quasi-Helmholtz formulation on a tessellation. In the re-formulation presented, we strictly satisfy the equation of continuity and Gauss' laws for both the electric and magnetic flux densities. Results illustrating the efficacy of this scheme will be demonstrated by analyzing non-neutral beams with space-charge and the adiabatic expansion of a neutral plasma with realistic parameters (Debye length and real mass ratios).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1987

Computational and experimental investigation of cavity flowfields

This paper presents a computational and experimental investigation of supersonic flow past a cavity in a flat plate. The source of the particular interest in this problem is the ongoing study of the aerodynamic interference effects between a separating store and its bay in the parent body. An upwind relaxation scheme, utilizing flux vector splitting and line-Gauss-Seidel iterations, is used to solve Reynolds-averaged Navier-Stokes equations. Spatial discretizations of this two-dimensional analysis are based on implicit and finite-volume methods. Turbulence is modeled and shocks are captured. The flowfield of the symmetry plane at the half-width is computationally visualized and all flow properties are computed. Experimental tests are conducted in the Langley Unitary Plan Wind Tunnel to measure wall pressures and to capture schlieren photographs. Qualitative as well as quantitative data of computations and experiments agree very well. These two vehicles of investigation are merged to show open, closed and transitional cavity flow behaviors.

Baysal, O.↗

NASA NTRS1983

On numerical simulation of viscous flows

Numerical simulation methods for viscous incompressible laminar flows are reviewed, with a focus on finite-difference schemes. The approaches to high/moderate-Reynolds-number flows (strong-viscous-interaction model or single sets of equations) and the factors affecting the versatility, reliability, and accuracy of the analysis algorithms are considered; approximate-factorization implicit solution techniques for low-Reynolds-number flows are discussed; and the procedures used in a number of specific problems are indicated.

Ghia, K. N.↗

DOE OSTI2019

On the implicit immersed boundary method in coupled discrete element and lattice Boltzmann method

The coupled discrete element method and lattice Boltzmann method (DEMLBM) has increasingly drawn attention of researchers in geomechanics due to its mesoscopic nature since 2000. Immersed boundary method (IBM) and immersed moving boundary (IMB) are two popular schemes for coupling fluid particle in DEMLBM. This work aims at coupling DEM and LBM using the latest IBM algorithm and investigating its accuracy, computational efficiency, and applicability. Two benchmark tests, interstitial fluid flow in an ideal packing and single particle sedimentation in viscous fluid, are carried out to demonstrate the accuracy of IBM through semi-empirical Ergun equation, finite element method (FEM), and IMB. Then, simulations of particle migration with relatively large velocity in Poiseuille flow are utilized to address limitations of IBM in DEMLBM modeling. In addition, advantages and deficiencies of IBM are discussed and compared with IMB. It is found that the accuracy of IBM can be only guaranteed when sufficient boundary points are used and it is not suitable for geomechanical problems involving large fluid or particle velocity.

58 GEOSCIENCES↗

DOE OSTI2019

Realizability-preserving DG-IMEX method for the two-moment model of fermion transport

Building on the framework of Zhang & Shu [1], [2], we develop a realizability-preserving method to simulate the transport of particles (fermions) through a background material using a two-moment model that evolves the angular moments of a phase space distribution function f . The two-moment model is closed using algebraic moment closures; e.g., as proposed by Cernohorsky & Bludman [3] and Banach & Larecki [4]. Variations of this model have recently been used to simulate neutrino transport in nuclear astrophysics applications, including core-collapse supernovae and compact binary mergers. We employ the discontinuous Galerkin (DG) method for spatial discretization (in part to capture the asymptotic diffusion limit of the model) combined with implicit-explicit (IMEX) time integration to stably bypass short timescales induced by frequent interactions between particles and the background. Appropriate care is taken to ensure the method preserves strict algebraic bounds on the evolved moments (particle density and flux) as dictated by Pauli's exclusion principle, which demands a bounded distribution function (i.e., f ϵ [0,1]). This realizability-preserving scheme combines a suitable CFL condition, a realizability-enforcing limiter, a closure procedure based on Fermi-Dirac statistics, and an IMEX scheme whose stages can be written as a convex combination of forward Euler steps combined with a backward Euler step. The IMEX scheme is formally only first-order accurate, but works well in the diffusion limit, and — without interactions with the background — reduces to the optimal second-order strong stability-preserving explicit Runge-Kutta scheme of Shu & Osher [5]. Numerical results demonstrate the realizability-preserving properties of the scheme. As a result, we also demonstrate that the use of algebraic moment closures not based on Fermi-Dirac statistics can lead to unphysical moments in the context of fermion transport.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

On differentiable local bounds preserving stabilization for Euler equations

This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A differentiable local bounds preserving method has been developed, which combines a Rusanov artificial diffusion operator and a differentiable shock detector. Nonlinear stabilization schemes are usually stiff and highly nonlinear. This issue is mitigated by the differentiability properties of the proposed method. Moreover, in order to further improve the nonlinear convergence, we also propose a continuation method for a subset of the stabilization parameters. The resulting method has been successfully applied to steady and transient problems with complex shock patterns. Numerical experiments show that it is able to provide sharp and well resolved shocks. Furthermore, the importance of the differentiability is assessed by comparing the new scheme with its non-differentiable counterpart. Numerical experiments suggest that, for up to moderate nonlinear tolerances, the method exhibits improved robustness and nonlinear convergence behavior for steady problems. Additionally, in the case of transient problem, we also observe a reduction in the computational cost.

42 ENGINEERING↗

DOE OSTI2023

Integration of a Frost Mortality Scheme Into the Demographic Vegetation Model FATES

Frost is damaging to plants when air temperature drops below their tolerance threshold. The set of mechanisms used by cold-tolerant plants to withstand freezing is called “hardening” and typically take place in autumn to protect against winter damage. The recent incorporation of a hardening scheme in the demographic vegetation model FATES opens up the possibility to investigate frost mortality to vegetation. Previously, the hardening scheme was used to improve hydraulic processes in cold-tolerant plants. In this study, we expand upon the existing hardening scheme by implementing hardiness-dependent frost mortality into CLM5.0-FATES to study the impacts of frost on vegetation in temperate and boreal sites from 1950 to 2015. Our results show that the original freezing mortality approach of FATES, where each plant type had a fixed freezing tolerance threshold—an approach common to many other dynamic vegetation models, was restricted to predicting plant type distribution. The main results emerging from the new scheme are a high autumn and spring frost mortality, especially at colder sites, and increasing mid-winter frost mortality due to global warming, especially at warmer sites. We demonstrate that the new frost scheme is a major step forward in dynamically representing vegetation in ESMs by for the first time including a level of frost tolerance that is responding to the environment and includes some level of cost (implicitly) and benefit. By linking hardening and frost mortality in a land surface model, we open new ways to explore the impact of frost events in the context of global warming.

54 ENVIRONMENTAL SCIENCES↗

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↗