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At least 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Coherent structures in a turbulent mixing layer - A comparison between direct numerical simulations and experiments

An eduction scheme has been developed in an attempt to determine the characteristics of large-scale vortical structures in a turbulent mixing layer. This analysis scheme has been applied to a set of experimental data taken in a new, larger mixing layer facility designed to minimize boundary and resonance effects. A similar scheme has been developed to apply to the results of a direct numerical simulation of a temporally growing mixing layer. A comparison of the two approaches shows important similarities in the coherent structures. The numerical simulations indicate that low levels of coherent forcing can dramatically change the evolution of the mixing layer. In the absence of such forcing, the numerical simulations and experiments show a lack of regularity in the transverse position, spacing, amplitude, shape and spanwise coherence of the large-scale vortical structures.

Metcalfe, R. W.↗
NASA NTRS1991

An iterative implicit diagonally-dominant factorization algorithm for solving the Navier-Stokes equations

Presented here is an algorithm for solving the multidimensional unsteady Navier-Stokes equations for compressible flows. It is based on a diagonally-dominant approximate factorization procedure. The factorization error and the timewise linearization error associated with this procedure are reduced by performing Newton-type inner iterations at each time step. The inviscid fluxes are evaluated by the fourth-order central differencing scheme amended with a numerical dissipation directly proportional to the entire dissipative part of the truncation error intrinsic to the third order biased upwind scheme. The important features of the proposed solution are elucidated by the numerical results of the convection of a vortex and the backward-facing step flows.

Chen, Shu-Cheng↗
NASA NTRS1996

High Resolution Euler Solvers Based on the Space-Time Conservation Element and Solution Element Method

The I-D, quasi I-D and 2-D Euler solvers based on the method of space-time conservation element and solution element are used to simulate various flow phenomena including shock waves, Mach stem, contact surface, expansion waves, and their intersections and reflections. Seven test problems are solved to demonstrate the capability of this method for handling unsteady compressible flows in various configurations. Numerical results so obtained are compared with exact solutions and/or numerical solutions obtained by schemes based on other established computational techniques. Comparisons show that the present Euler solvers can generate highly accurate numerical solutions to complex flow problems in a straightforward manner without using any ad hoc techniques in the scheme.

Wang, Xiao-Yen↗
DOE OSTI2022

Evaluation of a quasi-steady-state approximation of the cloud droplet growth equation (QDGE) scheme for aerosol activation in global models using multiple aircraft data over both continental and marine environments

This research introduces a numerically efficient aerosol activation scheme and evaluates it by using stratus and stratocumulus cloud data sampled during multiple aircraft campaigns in Canada, Chile, Brazil, and China. The scheme employs a quasi-steady-state approximation of the cloud droplet growth equation (QDGE) to efficiently simulate aerosol activation, the vertical profile of supersaturation, and the activated cloud droplet number concentration (CDNC) near the cloud base. The calculated maximum supersaturation values using the QDGE scheme were compared with multiple parcel model simulations under various aerosol and environmental conditions. The differences are all below 0.18 %, indicating good performance and accuracy of the QDGE scheme. We evaluated the QDGE scheme by specifying observed environmental thermodynamic variables and aerosol information from 31 cloud cases as input and comparing the simulated CDNC with cloud observations. The average of mean relative error ($\overline{MRE}$) of the simulated CDNC for cloud cases in each campaign ranges from 17.30 % in Brazil to 25.90 % in China, indicating that the QDGE scheme successfully reproduces observed variations in CDNC over a wide range of different meteorological conditions and aerosol regimes. Additionally, we carried out an error analysis by calculating the maximum information coefficient (MIC) between the MRE and input variables for the individual campaigns and all cloud cases. MIC values were then sorted by aerosol properties, pollution level, environmental humidity, and dynamic condition according to their relative importance to MRE. Based on the error analysis, we found that the magnitude of MRE is more relevant to the specification of input aerosol pollution level in marine regions and aerosol hygroscopicity in continental regions than to other variables in the simulation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

An implicit, sharp numerical treatment of viscous terms at arbitrarily shaped liquid-gas interfaces in evaporative flows

We report a novel methodology for accurate treatment of viscous terms in evaporation problems. The proposed scheme is an extension of the sharp viscous treatment of Kang et al. (2000) [7] to 3D phase change problems. To ensure accuracy and grid converging solutions, a new implicit approach to computing viscous fluxes across the phase interfaces is proposed, which was previously unavailable in fixed grid numerical schemes. Analytical relations were derived for the jump in velocity gradients across the 2D and 3D phase interfaces, an important constituent of the proposed scheme. The relations show a non-vanishing jump in the tangential gradients across the phase interface that are associated with evaporative flux and interfacial curvature. The proposed methodology demonstrated first order accuracy in canonical test cases. It is general and applicable to arbitrarily oriented interfaces, and can be readily implemented in existing evaporation flow solvers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2003

Finite Volume Methods: Foundation and Analysis

Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems. They are extensively used in fluid mechanics, porous media flow, meteorology, electromagnetics, models of biological processes, semi-conductor device simulation and many other engineering areas governed by conservative systems that can be written in integral control volume form. This article reviews elements of the foundation and analysis of modern finite volume methods. The primary advantages of these methods are numerical robustness through the obtention of discrete maximum (minimum) principles, applicability on very general unstructured meshes, and the intrinsic local conservation properties of the resulting schemes. Throughout this article, specific attention is given to scalar nonlinear hyperbolic conservation laws and the development of high order accurate schemes for discretizing them. A key tool in the design and analysis of finite volume schemes suitable for non-oscillatory discontinuity capturing is discrete maximum principle analysis. A number of building blocks used in the development of numerical schemes possessing local discrete maximum principles are reviewed in one and several space dimensions, e.g. monotone fluxes, E-fluxes, TVD discretization, non-oscillatory reconstruction, slope limiters, positive coefficient schemes, etc. When available, theoretical results concerning a priori and a posteriori error estimates are given. Further advanced topics are then considered such as high order time integration, discretization of diffusion terms and the extension to systems of nonlinear conservation laws.

Barth, Timothy↗
NASA NTRS1986

Entropy conservative finite element schemes

The question of entropy stability for discrete approximations to hyperbolic systems of conservation laws is studied. The amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison. To this end, two main ingredients are used: entropy variables and the construction of certain entropy conservative schemes in terms of piecewise-linear finite element approximations. It is then shown that conservative schemes are entropy stable, if and (for three-point schemes) only if, they contain more numerical viscosity than the abovementioned entropy conservation ones.

Tadmor, E.↗
NASA NTRS1988

High-resolution shock-capturing schemes for inviscid and viscous hypersonic flows

The development of robust, accurate, and efficient implicit shock-capturing schemes for multidimensional compressible Navier-Stokes equations in the hypersonic and real gas flow regimes is presently undertaken by extending a class of implicit total variation-diminishing (TVD) schemes suitable for transonic and supersonic, multidimensional Euler and Navier-Stokes equations to hypersonic computations. Numerical aspects of TVD schemes are identified which affect the convergence rate for hypersonic Mach numbers and real gas flows, but which have a negligible effect on low Mach number or perfect gas flows.

Yee, H. C.↗
NASA NTRS1996

Multigrid Acceleration of Time-Accurate DNS of Compressible Turbulent Flow

An efficient scheme for the direct numerical simulation of 3D transitional and developed turbulent flow is presented. Explicit and implicit time integration schemes for the compressible Navier-Stokes equations are compared. The nonlinear system resulting from the implicit time discretization is solved with an iterative method and accelerated by the application of a multigrid technique. Since we use central spatial discretizations and no artificial dissipation is added to the equations, the smoothing method is less effective than in the more traditional use of multigrid in steady-state calculations. Therefore, a special prolongation method is needed in order to obtain an effective multigrid method. This simulation scheme was studied in detail for compressible flow over a flat plate. In the laminar regime and in the first stages of turbulent flow the implicit method provides a speed-up of a factor 2 relative to the explicit method on a relatively coarse grid. At increased resolution this speed-up is enhanced correspondingly.

Broeze, Jan↗
NASA NTRS1976

A three-dimensional, time-dependent model of Mobile Bay

A three-dimensional, time-variant mathematical model for momentum and mass transport in estuaries was developed and its solution implemented on a digital computer. The mathematical model is based on state and conservation equations applied to turbulent flow of a two-component, incompressible fluid having a free surface. Thus, bouyancy effects caused by density differences between the fresh and salt water, inertia from thare river and tidal currents, and differences in hydrostatic head are taken into account. The conservation equations, which are partial differential equations, are solved numerically by an explicit, one-step finite difference scheme and the solutions displayed numerically and graphically. To test the validity of the model, a specific estuary for which scaled model and experimental field data are available, Mobile Bay, was simulated. Comparisons of velocity, salinity and water level data show that the model is valid and a viable means of simulating the hydrodynamics and mass transport in non-idealized estuaries.

Pitts, F. H.↗
NASA NTRS1986

Numerical experiments with a symmetric high-resolution shock-capturing scheme

Characteristic-based explicit and implicit total variation diminishing (TVD) schemes for the two-dimensional compressible Euler equations have recently been developed. This is a generalization of recent work of Roe and Davis to a wider class of symmetric (non-upwind) TVD schemes other than Lax-Wendroff. The Roe and Davis schemes can be viewed as a subset of the class of explicit methods. The main properties of the present class of schemes are that they can be implicit, and, when steady-state calculations are sought, the numerical solution is independent of the time step. In a recent paper, a comparison of a linearized form of the present implicit symmetric TVD scheme with an implicit upwind TVD scheme originally developed by Harten and modified by Yee was given. Results favored the symmetric method. It was found that the latter is just as accurate as the upwind method while requiring less computational effort. Currently, more numerical experiments are being conducted on time-accurate calculations and on the effect of grid topology, numerical boundary condition procedures, and different flow conditions on the behavior of the method for steady-state applications. The purpose here is to report experiences with this type of scheme and give guidelines for its use.

Yee, H. C.↗
NASA NTRS1990

Numerical study of unsteady shockwave reflections using an upwind TVD scheme

An unsteady TVD Navier-Stokes solver was developed and applied to the problem of shock reflection on a circular cylinder. The obtained numerical results were compared with the Schlieren photos from an experimental study. These results show that the present computer code has the ability of capturing moving shocks.

Hsu, Andrew T.↗
NASA NTRS1994

Low-dissipation and -dispersion Runge-Kutta schemes for computational acoustics

In this paper, we investigate accurate and efficient time advancing methods for computational acoustics, where non-dissipative and non-dispersive properties are of critical importance. Our analysis pertains to the application of Runge-Kutta methods to high-order finite difference discretization. In many CFD applications multi-stage Runge-Kutta schemes have often been favored for their low storage requirements and relatively large stability limits. For computing acoustic waves, however, the stability consideration alone is not sufficient, since the Runge-Kutta schemes entail both dissipation and dispersion errors. The time step is now limited by the tolerable dissipation and dispersion errors in the computation. In the present paper, it is shown that if the traditional Runge-Kutta schemes are used for time advancing in acoustic problems, time steps greatly smaller than that allowed by the stability limit are necessary. Low-Dissipation and -Dispersion Runge-Kutta (LDDRE) schemes are proposed, based on an optimization that minimizes the dissipation and dispersion errors for wave propagation. Order optimizations of both single-step and two-step alternating schemes are considered. The proposed LDDRK schemes are remarkably more efficient than the classical Runge-Kutta schemes for acoustic computations. Moreover, low storage implementations of the optimized schemes are discussed. Special issues of implementing numerical boundary conditions in the LDDRK schemes are also addressed.

Hu, F. Q.↗
NASA NTRS2006

Convergence Acceleration for Multistage Time-Stepping Schemes

The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 could be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. Numerical dissipation operators (based on the Roe scheme, a matrix formulation, and the CUSP scheme) as well as the number of RK stages are considered in evaluating the RK/implicit scheme. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. In two dimensions, turbulent flows over an airfoil at subsonic and transonic conditions are computed. The effects of mesh cell aspect ratio on convergence are investigated for Reynolds numbers between 5.7 x 10(exp 6) and 100.0 x 10(exp 6). Results are also obtained for a transonic wing flow. For both 2-D and 3-D problems, the computational time of a well-tuned standard RK scheme is reduced at least a factor of four.

Swanson, R. C.↗
NASA NTRS1989

A class of high resolution explicit and implicit shock-capturing methods

An attempt is made to give a unified and generalized formulation of a class of high resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock wave computations. Included is a systematic review of the basic design principle of the various related numerical methods. Special emphasis is on the construction of the basis nonlinear, spatially second and third order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and the flux vector splitting approaches. Generalization of these methods to efficiently include equilibrium real gases and large systems of nonequilibrium flows are discussed. Some issues concerning the applicability of these methods that were designed for homogeneous hyperbolic conservation laws to problems containing stiff source terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for 1-, 2- and 3-dimensional gas dynamics problems.

Yee, H. C.↗
NASA NTRS1993

General-Purpose Time-Accurate Adaptive-Grid Method

Adaptive-grid method provides for generation of time-accurate grids used to solve wide variety of problems numerically. Intended use in computation of compressible flows. Part of solution method including algebraic grid-movement scheme; algorithm solving, by use of explicit numerical-integration scheme, Euler equations of unsteady flow; and temporal coupling routine utilizing grid-prediction/correction method to link dynamic grid with Euler-equation-solving algorithm. Improves ability to adapt grid to multiple features of solution and involves use of coarse grid in prediction stage of temporal coupling reducing central-processing-unit cost of obtaining new grid.

Bockelie, Michael J.↗
NASA NTRS1995

A compact solution to computational acoustics

This paper demonstrates that the linearized, dimensional Euler equations for acoustic computation can be accurately solved as a set of decoupled first-order wave equations, and that if ordered properly, this system of simple waves has unambiguous, easily implemented boundary conditions, allowing waves of same group speeds to pass through numerical boundaries or comply with wall conditions. Thus, the task of designing a complex multi-dimensional scheme with approximate far-field boundary conditions reduces to the design of higher order schemes for the one-dimensional simple wave equation. A compact finite-difference scheme and a characteristically exact but numerically n(th) order accurate boundary condition are introduced for solving the first order wave equation. Spanning a three-point two-level stencil, this low-dispersion implicit scheme has a third order spatial accuracy when used on nonuniform meshes, fourth order accurate on uniform meshes, and a temporal accuracy of second order due to the choice of trapezoidal integration for algorithmic simplicity. The robustness and accuracy of the scheme are demonstrated through a series of numerical experiments and comparisons with published results. When tested on the one-dimensional wave equation on a uniform grid, this scheme allows a Gaussian wave packet to pass through any finite domain with low numerical dispersion characteristic of a spatially fourth-order scheme and reflections at numerical boundaries maintained below truncation error. On highly stretched and irregular grids, only mild dispersions are found in the solution while solutions by other methods fail or are severely distorted. Yet, this scheme is no more sophisticated to solve or implement than the Crank-Nicolson scheme. This scheme has been tested on four categories of the ICASE/LaRC benchmark problems, which include propagation of acoustic and convective waves in Cartesian and cylindrical domains, reflection of acoustic wave at stationary/moving boundaries, and sound generation by gust-blade interaction.

Fung, K.-Y.↗