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At least 235 records · Page 13

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NASA NTRS1982

Finite area method for nonlinear conical flows

A fully conservative finite area method for the computation of steady inviscid flow about general conical bodies at incidence is described. The procedure utilizes the potential approximation and implements a body conforming mesh generator. The conical potential is assumed to have its best linear variation inside each mesh cell and a secondary interlocking cell system is used to establish the flux balance required to conserve mass. In the supersonic regions the scheme is desymmetrized by adding appropriate artificial viscosity in conservation form. The algorithm is nearly an order of a magnitude faster than present Euler methods and predicts known results accurately and qualitative features such as nodal point lift off correctly. Results are compared with those of other investigations.

Sritharan, S. S.↗

DOE OSTI2026

A sweeping positivity-preserving high-order finite difference WENO scheme for Euler equations

We develop a simple, high-order, conservative and robust positivity-preserving sweeping procedure for the density and the nonlinear pressure function in the compressible Euler equations. Using the scaling limiter in Zhang and Shu (J Comput Phys 229:3091–3120, 2010), we obtain a non-trivial extension of the scalar sweeping technique in Liu et al. (J Sci Comput 73:1028–1071, 2017) for the positivity of pressure. The sweeping procedure developed in this paper is a post-processing technique, which can be applied to any concave functions of the conserved variables in hyperbolic conservation law systems. Thus, it has applications beyond the Euler equations. This procedure preserves positivity and conservation of physical quantities without destroying the accuracy of the underlying scheme. The algorithm works for general schemes including finite difference, finite volume and discontinuous Galerkin methods; however, in this paper we focus on finite difference weighted essentially non-oscillatory (WENO) methods. As a result, we provide numerical tests of the fifth-order finite difference WENO scheme to demonstrate the accuracy and robustness of the technique.

Compressible Euler equations↗

DOE OSTI2021

iharm3D: Vectorized General Relativistic Magnetohydrodynamics

iharm3D is an open-source C code for simulating black hole accretion systems in arbitrary stationary spacetimes using ideal general-relativistic magnetohydrodynamics (GRMHD). It is an implementation of the HARM (“High Accuracy Relativistic Magnetohydrodynamics”) algorithm outlined in Gammie et al. (2003) with updates as outlined in McKinney & Gammie (2004) and Noble et al. (2006). The code is most directly derived from Ryan et al. (2015) but with radiative transfer portions removed. HARM is a conservative finite-volume scheme for solving the equations of ideal GRMHD, a hyperbolic system of partial differential equations, on a logically Cartesian mesh in arbitrary coordinates.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Toward Higher-order Accuracy in Self-gravitating Hydrodynamics

High-order algorithms have emerged in numerical astrophysics as a promising avenue to reduce truncation error (proportional to a power of the linear resolution Δ x ) with only a moderate increase to computational expense. Significant effort has been placed in the development of finite-volume algorithms for (magneto)hydrodynamics; however, state-of-the-art astrophysical simulations tightly couple a plenitude of physics, additionally including gravity, photon transport, cosmic-ray transport, chemistry, and/or diffusion, to name a few. Algorithms frequently operator-split this additional physics (often a first-order error in time) and/or adopt a model wherein their evaluation is limited to second-order accuracy in space. In this work, we present a fourth-order-accurate finite-volume scheme for self-gravitating hydrodynamics on a uniform Cartesian grid. The method supplies source terms for the gravitational acceleration ( ρ g ) and gravitational energy release ( ρ v · g ) associated with fourth-order-accurate solutions to the Poisson equation. Our scheme (1) guarantees the conservation of total linear momentum while (2) decreasing (in proportion to Δ x 4 ) the effects of spurious heating and/or cooling associated with truncation error in the gravity. We demonstrate expected convergence rates for the algorithm by measuring errors in test problems evolving self-gravity modified linear waves and 3D polytropic equilibria. We test robustness of the algorithm by integrating an induced “inside-out” adiabatic collapse. We also discuss a method to smoothly downgrade the solution to second-order spatial accuracy to avoid spurious overshoots near steep density and/or pressure gradients.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1976

Influence of nonconservative differencing on transonic streamline shapes

A computer program recently developed by South and Brandt (1976) which contained the Murman (1973) conservative finite-difference scheme is easily modified to use the Garabedian and Korn (1971) nonconservative finite difference scheme. This program solves the transonic small disturbance equation for only symmetric flow, but incorporates several iterative solution techniques. Results are presented for the case where the equally spaced computational grid extended to infinity in both the streamwise and normal directions. Streamline shapes are obtained along several grid lines by a streamwise integration of the normal component of the perturbation velocity. Comparison cases are run for a 10% thick parabolic arc airfoil at zero incidence for freestream Mach numbers of 0, 0.70, 0.84, and 0.95. It is shown that the use of a nonconservative finite-difference scheme in transonic flow calculations destroys the global mass balance when shocks are present. This lack of mass balance may prove to be more crucial in the case of an unconfined external flow.

Newman, P. A.↗

NASA NTRS1976

Electric load management and energy conservation

Electric load management and energy conservation relate heavily to the major problems facing power industry at present. The three basic modes of energy conservation are identified as demand reduction, increased efficiency and substitution for scarce fuels. Direct and indirect load management objectives are to reduce peak loads and have future growth in electricity requirements in such a manner to cause more of it to fall off the system's peak. In this paper, an overview of proposed and implemented load management options is presented. Research opportunities exist for the evaluation of socio-economic impacts of energy conservation and load management schemes specially on the electric power industry itself.

Kheir, N. A.↗

NASA NTRS1977

Improved methods for large-eddy simulations of turbulence

By using Fourier transforms for evaluating spatial derivatives, the accuracy of the large-eddy simulation of homogeneous isotropic turbulence is improved. Especially, the treatment of certain terms that arise in filtering the equations is considerably improved in both speed and accuracy. Use of vorticity as the principal variable is shown to be a viable and potentially useful alternative to the primitive variables. A method of deriving conservation properties of numerical schemes is given which is much simpler than previous methods and is widely applicable. The methods are applied to the computation of homogeneous isotropic turbulence, and it is found that the subgrid scale model is improved by using finite differences in place of 'exact' derivatives.

Mansour, N. N.↗

NASA NTRS1981

Transonic wing design using potential-flow codes - Successes and failures

The state-of-the-art of transonic wing design by use of computer codes based on the potential flow-theory is presented. The capabilities and limitations of these codes are exemplified by several experiment-theory correlations, including an assessment of pressure distribution from isolated wing and wing-body codes. Computer codes using both conservative and nonconservative differencing schemes were used, and the effects of boundary-layer corrections were considered. Results showed that calculations from a full potential, isolated code correlate well with data from an isolated wing test, but may give poor predictions of the aerodynamic characteristics of some wing-body configurations. Boundary-layer correlations were found to have only moderate effects on experiment-theory correlation. Aeroelastic effects were considered important for high aspect ratio wings of low to moderate thickness, and viscous effects were minimal for typical cruise conditions, even for Reynold's numbers as low as two million. The effect of wind-tunnel walls on experiment-theory correlations remained inconclusive. A wing-body code was used to calculate the flow field about a wing-body configuration with body-mounted engines, typical of the transonic Biz-Jet aircraft.

Hicks, R. M.↗

NASA NTRS1981

Solution of the transonic full potential equation in conservative form using an implicit algorithm

The paper presents numerical solutions of the full potential equation in conservative form. The iteration scheme used is a fully implicit approximate factorization technique and provides a significant improvement in convergence speed relative to standard successive line overrelaxation algorithms. The spatial differencing algorithm is centrally differenced in both subsonic and supersonic regions to maintain stability. This effectively approximates rotated differencing, thereby greatly improving the reliability of the algorithm.

Holst, T.↗

NASA NTRS1982

Transonic potential flow and coordinate generation for bodies in a wind tunnel

An accurate method has been developed for computation of transonic potential flow about a 2-D lifting airfoil or an axisymmetric body in a wind tunnel. The computational mesh is nearly orthogonal everywhere and is generated by a sequence of Schwarz-Christoffel transformations and shearings to obtain an '0' grid near the body. A conservative finite-volume scheme for the full-potential equation and exact boundary conditions is used together with 'retarded' density to solve efficiently transonic flow with embedded shocks and large regions of supersonic flow. Supersonic free-stream flows are also solved with captured bow shocks and embedded subsonic regions.

Doria, M. L.↗

NASA NTRS1989

A 17 degree of freedom anthropomorphic manipulator

A 17 axis anthropomorphic manipulator, providing coordinated control of two seven degree of freedom arms mounted on a three degree of freedom torso-waist assembly, is presented. This massively redundant telerobot, designated the Robotics Research K/B-2017 Dexterous Manipulator, employs a modular mechanism design with joint-mounted actuators based on brushless motors and harmonic drive gear reducers. Direct joint torque control at the servo level causes these high-output joint drives to behave like direct-drive actuators, facilitating the implementation of an effective impedance control scheme. The redundant, but conservative motion control system models the manipulator as a spring-loaded linkage with viscous damping and rotary inertia at each joint. This approach allows for real time, sensor-driven control of manipulator pose using a hierarchy of competing rules, or objective functions, to avoid unplanned collisions with objects in the workplace, to produce energy-efficient, graceful motion, to increase leverage, to control effective impedance at the tool or to favor overloaded joints.

Vold, Havard I.↗

NASA NTRS1992

Numerical simulation of turbomachinery flows with advanced turbulence models

A three dimensional full Navier-Stokes (FNS) code is used to simulate complex turbomachinery flows. The code incorporates an explicit multistep scheme and solves a conservative form of the density averaged continuity, momentum, and energy equations. A compressible low Reynolds number form of the k-epsilon turbulence model, and a q-omega model and an algebraic Reynolds stress model have been incorporated in a fully coupled manner to approximate Reynolds stresses. The code is used to predict the viscous flow field in a backswept transonic centrifugal compressor for which laser two focus data is available. The code is also used to simulate the tip clearance flow in a cascade. The code has been extended to include unsteady Euler solutions for predicting the unsteady flow through a cascade due to incoming wakes, simulating rotor-stator interactions.

Lakshminarayana, B.↗

NASA NTRS1992

Bypass transition in compressible boundary layers

Transition to turbulence in aerospace applications usually occurs in a strongly disturbed environment. For instance, the effects of free-stream turbulence, roughness and obstacles in the boundary layer strongly influence transition. Proper understanding of the mechanisms leading to transition is crucial in the design of aircraft wings and gas turbine blades, because lift, drag and heat transfer strongly depend on the state of the boundary layer, laminar or turbulent. Unfortunately, most of the transition research, both theoretical and experimental, has focused on natural transition. Many practical flows, however, defy any theoretical analysis and are extremely difficult to measure. Morkovin introduced in his review paper the concept of bypass transition as those forms of transition which bypass the known mechanisms of linear and non-linear transition theories and are currently not understood by experiments. In an effort to better understand the mechanisms leading to transition in a disturbed environment, experiments are conducted studying simpler cases, viz. the effects of free stream turbulence on transition on a flat plate. It turns out that these experiments are very difficult to conduct, because generation of free stream turbulence with sufficiently high fluctuation levels and reasonable homogeneity is non trivial. For a discussion see Morkovin. Serious problems also appear due to the fact that at high Reynolds numbers the boundary layers are very thin, especially in the nose region of the plate where the transition occurs, which makes the use of very small probes necessary. The effects of free-stream turbulence on transition are the subject of this research and are especially important in a gas turbine environment, where turbulence intensities are measured between 5 and 20 percent, Wang et al. Due to the fact that the Reynolds number for turbine blades is considerably lower than for aircraft wings, generally a larger portion of the blade will be in a laminar transitional state. The effects of large free stream turbulence in compressible boundary layers at Mach numbers are examined both in the subsonic and transonic regime using direct numerical simulations. The flow is computed over a flat plate and curved surface. while many applications operate in the transonic regime. Due the nature of their numerical scheme, a non-conservation formulation of the Navier-Stokes equations, it is a non-trivial extension to compute flow fields in the transonic regime. This project aims at better understanding the effects of large free-stream turbulence in compressible boundary layers at mach number both in the subsonic and transonic regime using direct numerical simulations. The present project aims at computing the flow over a flat plate and curved surface. This research will provide data which can be used to clarify mechanisms leading to transition in an environment with high free stream turbulence. This information is useful for the development of turbulence models, which are of great importance for CFD applications, and are currently unreliable for more complex flows, such as transitional flows.

Vandervegt, J. J.↗

NASA NTRS1993

The combustion program at CTR

Understanding and modeling of turbulent combustion are key problems in the computation of numerous practical systems. Because of the lack of analytical theories in this field and of the difficulty of performing precise experiments, direct numerical simulation (DNS) appears to be one of the most attractive tools to use in addressing this problem. The general objective of DNS of reacting flows is to improve our knowledge of turbulent combustion but also to use this information for turbulent combustion models. For the foreseeable future, numerical simulation of the full three-dimensional governing partial differential equations with variable density and transport properties as well as complex chemistry will remain intractable; thus, various levels of simplification will remain necessary. On one hand, the requirement to simplify is not necessarily a handicap: numerical simulations allow the researcher a degree of control in isolating specific physical phenomena that is inaccessible in experiments. CTR has pursued an intensive research program in the field of DNS for turbulent reacting flows since 1987. DNS of reacting flows is quite different from DNS of non-reacting flows: without reaction, the equations to solve are clearly the five conservation equations of the Navier Stokes system for compressible situations (four for incompressible cases), and the limitation of the approach is the Reynolds number (or in other words the number of points in the computation). For reacting flows, the choice of the equations, the species (each species will require one additional conservation equation), the chemical scheme, and the configuration itself is more complex.

Poinsot, Thierry J.↗

NASA NTRS1999

Factorizable Schemes for the Equations of Fluid Flow

We present an upwind high-resolution factorizable (UHF) discrete scheme for the compressible Euler equations that allows to distinguish between full-potential and advection factors at the discrete level. The scheme approximates equations in their general conservative form and is related to the family of genuinely multidimensional upwind schemes developed previously and demonstrated to have good shock-capturing capabilities. A unique property of this scheme is that in addition to the aforementioned features it is also factorizable, i.e., it allows to distinguish between full-potential and advection factors at the discrete level. The latter property facilitates the construction of optimally efficient multigrid solvers. This is done through a relaxation procedure that utilizes the factorizability property.

Sidilkover, David↗

NASA NTRS2008

Adjoint-Based Methodology for Time-Dependent Optimization

This paper presents a discrete adjoint method for a broad class of time-dependent optimization problems. The time-dependent adjoint equations are derived in terms of the discrete residual of an arbitrary finite volume scheme which approximates unsteady conservation law equations. Although only the 2-D unsteady Euler equations are considered in the present analysis, this time-dependent adjoint method is applicable to the 3-D unsteady Reynolds-averaged Navier-Stokes equations with minor modifications. The discrete adjoint operators involving the derivatives of the discrete residual and the cost functional with respect to the flow variables are computed using a complex-variable approach, which provides discrete consistency and drastically reduces the implementation and debugging cycle. The implementation of the time-dependent adjoint method is validated by comparing the sensitivity derivative with that obtained by forward mode differentiation. Our numerical results show that O(10) optimization iterations of the steepest descent method are needed to reduce the objective functional by 3-6 orders of magnitude for test problems considered.

Yamaleev, N. K.↗

NASA NTRS2016

Convection in Condensible-Rich Atmospheres

Condensible substances are nearly ubiquitous in planetary atmospheres. For the most familiar case—water vapor in Earth’s present climate—the condensible gas is dilute, in the sense that its concentration is everywhere small relative to the noncondensible background gases. A wide variety of important planetary climate problems involve nondilute condensible substances. These include planets near or undergoing a water vapor runaway and planets near the outer edge of the conventional habitable zone, for which CO2 is the condensible. Standard representations of convection in climate models rely on several approximations appropriate only to the dilute limit, while nondilute convection differs in fundamental ways from dilute convection. In this paper, a simple parameterization of convection valid in the nondilute as well as dilute limits is derived and used to discuss the basic character of nondilute convection. The energy conservation properties of the scheme are discussed in detail and are verified in radiative-convective simulations. As a further illustration of the behavior of the scheme, results for a runaway greenhouse atmosphere for both steady instellation and seasonally varying instellation corresponding to a highly eccentric orbit are presented. The latter case illustrates that the high thermal inertia associated with latent heat in nondilute atmospheres can damp out the effects of even extreme seasonal forcing.

Convection↗

NASA NTRS2009

The a(4) Scheme-A High Order Neutrally Stable CESE Solver

The CESE development is driven by a belief that a solver should (i) enforce conservation laws in both space and time, and (ii) be built from a nondissipative (i.e., neutrally stable) core scheme so that the numerical dissipation can be controlled effectively. To provide a solid foundation for a systematic CESE development of high order schemes, in this paper we describe a new high order (4-5th order) and neutrally stable CESE solver of a 1D advection equation with a constant advection speed a. The space-time stencil of this two-level explicit scheme is formed by one point at the upper time level and two points at the lower time level. Because it is associated with four independent mesh variables (the numerical analogues of the dependent variable and its first, second, and third-order spatial derivatives) and four equations per mesh point, the new scheme is referred to as the a(4) scheme. As in the case of other similar CESE neutrally stable solvers, the a(4) scheme enforces conservation laws in space-time locally and globally, and it has the basic, forward marching, and backward marching forms. Except for a singular case, these forms are equivalent and satisfy a space-time inversion (STI) invariant property which is shared by the advection equation. Based on the concept of STI invariance, a set of algebraic relations is developed and used to prove the a(4) scheme must be neutrally stable when it is stable. Numerically, it has been established that the scheme is stable if the value of the Courant number is less than 1/3

Chang, Sin-Chung↗