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NASA NTRS1988

Inhomogeneous conditions at open boundaries for wave propagation problems

Absorbing boundary conditions contain differential operators even for first-order systems. There is a fundamental difficulty with this, since the conditions are applied on the ingoing variables, and the approximations necessarily become weakly unstable. This difficulty is more pronounced for inhomogeneous boundary conditions which occur if there is a source outside the computational domain D, or if the initial data are nonzero outside D. In this paper this is further investigated and it is shown that reasonable estimates can still be obtained if the solution is smooth. However, it is demonstrated that the approximations are less robust. A cure for this is proposed and an implementation of high-order conditions for first-order systems is described.

Gustafsson, Bertil↗

NASA NTRS1988

A panel method procedure for interference assessment in slotted-wall wind tunnels

This paper describes a method for three-dimensional wind tunnel interference assessment developed specifically for slotted-wall tunnels. The method is an adaptation to the assessment problem of a previously published high-order panel method procedure for simulating the flow in slotted-wall tunnel test sections. The method uses a mixed outer boundary condition, primarily a Neumann condition, with measured pressure constraints used to control only those boundary phenomena which can not be specified accurately a priori. Assessment results are illustrated from a calibration test with variations in wall geometry, and from tests of a generic subsonic transport aircraft configuration.

Kemp, William B., Jr.↗

NASA NTRS1989

Integrated flight/propulsion control system design based on a centralized approach

An integrated flight/propulsion control system design is presented for the piloted longitudinal landing task with a modern, statically unstable, fighter aircraft. A centralized compensator based on the Linear Quadratic Gaussian/Loop Transfer Recovery methodology is first obtained to satisfy the feedback loop performance and robustness specificiations. This high-order centralized compensator is then partitioned into airframe and engine sub-controllers based on modal controllability/observability for the compensator modes. The order of the sub-controllers is then reduced using internally-balanced realization techniques and the sub-controllers are simplified by neglecting the insignificant feedbacks. These sub-controllers have the advantage that they can be implemented as separate controllers on the airframe and the engine while still retaining the important performance and stability characteristics of the full-order centralized compensator. Command prefilters are then designed for the closed-loop system with the simplified sub-controllers to obtain the desired system response to airframe and engine command inputs, and the overall system performance evaluation results are presented.

Garg, Sanjay↗

NASA NTRS1989

Discussion of the potential and limitations of direct and large-eddy simulations

The full text of the discussion paper presented at the Whither Turbulence Workshop on the potential and limitations of direct and large-eddy simulations is provided. Particular emphasis is placed on discussing the role of numerics and mathematical theory in direct simulations of both compressible and incompressible flows. A variety of unresolved issues with large-eddy simulations such as their implementation in high-order finite difference codes, problems with defiltering, and modifications to accommodate integrations to solid boundaries are elaborated on. These as well as other points are discussed in detail along with the authors' views concerning the prospects for future research.

Hussaini, M. Y.↗

NASA NTRS1988

A spectral multi-domain technique for viscous compressible reacting flows

The first application of a spectral multidomain method for viscous compressible flow is presented. The method imposes a global flux balance condition at the interface so that high-order continuity of the solution is preserved. The solution scheme can be adapted to the particular requirement in each subdomain. To illustrate these advantages, a Mach 11 shock calculation is presented to study the chemical kinetics initiated as air passes through a fully resolved shock wave.

Macaraeg, M. G.↗

NASA NTRS1989

Corotation torques in the solar nebula - The cutoff function

The behavior of high-order corotation resonances in a disk of finite thickness is examined. The torque exerted at an mth-order resonance is determined by employing a vertically averaged disturbing function, and the ratio of this torque to that exerted on a cold, two-dimensional disk is identified as the so-called torque cutoff function. This function is then used to calculate contributions from the corotation torques to eccentricity variations of a perturber's orbit assumed orbiting in the disk.

Ward, William R.↗

NASA NTRS1989

Direct simulations of turbulent flow using finite-difference schemes

A high-order accurate finite-difference approach is presented for calculating incompressible turbulent flow. The methods used include a kinetic energy conserving central difference scheme and an upwind difference scheme. The methods are evaluated in test cases for the evolution of small-amplitude disturbances and fully developed turbulent channel flow. It is suggested that the finite-difference approach can be applied to complex geometries more easilty than highly accurate spectral methods. It is concluded that the upwind scheme is a good candidate for direct simulations of turbulent flows over complex geometries.

Rai, Man Mohan↗

NASA NTRS1989

Numerical investigation of chemically reacting flows in ramjet dump combustors

The time-dependent Navier-Stokes equations, including second-order turbulence model, are numerically integrated by using four-stage Runge-Kutta scheme to predict the steady-state supersonic flow structures in ramjet dump combustors. The formulation is derived for reacting flows with finite-rate chemistry. In the present study, it is firstly attempted to assess the accuracy of existing high-order turbulence model in supersonic flows. The comparison shows reasonable agreement between calculated and measured data in terms of velocity distributions. It is indicated that a modified constant C-mu for calculating turbulent eddy viscosity is needed in the supersonic flow regime and the adaptive meshing is preferred to capture the recirculation zone. In the reacting flow calculation, the results from a test case of hydrogen and air combustion at premixed conditon show that the rearward facing step is able to increase flow residence time and stabilize the flame in supersonic flows.

Hsieh, Kwang-Chung↗

NASA NTRS1988

An approximation technique for computing optimal fixed-order controllers for infinite-dimensional systems

The finite-dimensional approximation of the infinite-dimensional Bernstein/Hyland optimal projection theory is investigated analytically. The approach yields fixed-finite-order controllers which are optimal with respect to high-order approximating finite-dimensional plant models. The technique is illustrated by computing a sequence of first-order controllers for a one-dimensional SISO parabolic (heat/diffusion) system using a spline-based Ritz-Galerkin finite-element approximation. The numerical studies indicate convergence of the feedback gains with less than 2-percent performance degradation over full-order LQG controllers.

Bernstein, Dennis S.↗

NASA NTRS1989

A time accurate finite volume high resolution scheme for three dimensional Navier-Stokes equations

A time accurate, three-dimensional, finite volume, high resolution scheme for solving the compressible full Navier-Stokes equations is presented. The present derivation is based on the upwind split formulas, specifically with the application of Roe's (1981) flux difference splitting. A high-order accurate (up to the third order) upwind interpolation formula for the inviscid terms is derived to account for nonuniform meshes. For the viscous terms, discretizations consistent with the finite volume concept are described. A variant of second-order time accurate method is proposed that utilizes identical procedures in both the predictor and corrector steps. Avoiding the definition of midpoint gives a consistent and easy procedure, in the framework of finite volume discretization, for treating viscous transport terms in the curvilinear coordinates. For the boundary cells, a new treatment is introduced that not only avoids the use of 'ghost cells' and the associated problems, but also satisfies the tangency conditions exactly and allows easy definition of viscous transport terms at the first interface next to the boundary cells. Numerical tests of steady and unsteady high speed flows show that the present scheme gives accurate solutions.

Liou, Meng-Sing↗

NASA NTRS1989

Numerical solutions of forward-flight rotor flow using an upwind method

A finite-volume upwind algorithm for solving the 3-D Euler equations with a moving grid has been developed for computing helicopter forward-flight rotor flows. The computed pressure distributions and shock positions of high-speed rotor flow are compared with various experimental data as well as with other numerical results, and the agreement is encouraging. A comparison of quasi-steady solutions with unsteady solutions reveals that when a shock occurs in the flowfield, the assumption of quasi-steady flow may fail due to the time-lag of the shock motion. Similarly, three-dimensional effects cannot be neglected. Sufficient subiterations for each time step are required to avoid numerical lag effects in using the present method. The redistribution of the residual due to the coordinate transformation is discussed. For high-order MUSCL-type schemes, a coordinate-independent solution can be obtained by interpolating primitive variables.

Chen, C. L.↗

NASA NTRS1989

Integrated flight/propulsion control system design based on a centralized approach

Garg, Sanjay↗

NASA NTRS1989

Geopotential models in the Australian region

The ability of three high-order geopotential models (OSU81, GPM2 and OSU86E) to recover the gravity anomaly field (delta g) in the Australian region was tested. The region was divided into 2 x 2 deg blocks, and the mean and rms of the residual gravity (delta g measured - delta g modeled) was found to estimate the fit of the model to the point gravity data. The results showed that OSU81 and GPM2 performed similarly, recovering the delta g with a mean value of less than plus or minus 5 mGal in 63 and 70 percent of the blocks, respectively. However, both these models achieved a fit of worse that was plus or minus 13 mGal in 6 to 7 percent of cases. These were in areas either on or near the coast, or in the Central Australian region, inferring that for a precise geoid slope determination in these regions, a detailed analysis of delta g in region is needed. On the other hand, OSU86E produced a very good result, having a mean fit of less than plus or minus 5 mGal in 80 percent of the blocks, and worse than plus or minus 13 mGal in only 1 percent of cases. The rms values for this model were also improved over the other two models, indicating that for applications requiring highest precision, the preferred model is OSU86E.

Kearsley, A. H. W.↗

NASA NTRS1989

A spectral multi-domain technique applied to high-speed chemically reacting flows

The first applications of a spectral multidomain method for viscous compressible flow is presented. The method imposes a global flux balance condition at the interface so that high-order continuity of the solution is preserved. The global flux balance is imposed in terms of a spectral integral of the discrete equations across adjoining domains. Since the discretized equations interior to each domain solved are uncoupled from each other, and since the interface relation has a block structure, the solution scheme can be adapted to the particular requirements of each subdomain. The spectral multidomain technique presented is well-suited for the multiple scales associated with the chemically reacting and transition flows in hypersonic research. A nonstaggered multidomain discretization is used for the chemically reacting flow calculation, and the first implementation of a staggered multidomain mesh is presented for accurately solving the stability equation for a viscous compressible fluid.

Macaraeg, Michele G.↗

NASA NTRS1989

Dynamics of Pluto

The present study of the Pluto orbit yielded by the LONGSTOP 1B, 100-Myr numerical integration of the outer planets has given attention to the 3:2 resonance in mean motion with Neptune up to degree 2 in eccentricities and inclinations. Confirmations are obtained for both the 19,900-year period longitudinal libration and the 3.78-Myr period libration of the Pluto pericenter argument. Because chaos originates with small divisors, possible resonances have been searched for among the frequencies associated with the critical arguments. The macroscopic stability of the orbit of Pluto is explainable in terms of the association of high-order resonances with small chaotic regions.

Milani, A.↗

NASA NTRS1989

A multi-domain spectral computation of three-dimensional laminar horseshoe vortex flow using incompressible Navier-Stokes equations

Multidomain spectral methods are presently used to numerically simulate a strut-wall intersection's laminar horseshoe vortex flow through direct solution of the three-dimensional, incompressible, time-dependent Navier-Stokes equations. Direct expansion in Chebyshev polynomials and spectral element method spatial discretization of flow dependence are used to achieve high-order accuracy, and minimal dispersion errors. Low and moderate Reynolds number results are presented to illustrate the method application.

Tan, C. S.↗

NASA NTRS1989

Spectral element simulations of laminar and turbulent flows in complex geometries

Spectral element methods are high-order weighted residual techniques based on spectral expansions of variables and geometry for the Navier-Stokes (NS) and transport equations. Here, practical aspects of these methods and their efficient implementation are examined, and several examples of flows in truly complex geometries are presented. The spectral element discretization for NS equations is introduced, and the convergence of the method is addressed. An efficient data management scheme is discussed in the context of parallel processing computations. The method is validated by comparing the spectral element solutions with the exact eigensolutions for the Orr-Sommerfeld equations in two and three dimensions. Computer-aided flow visualizations are presented for an impulsive flow past a sharp edge wedge. Three-dimensional states of channel flow disrupted by an array of cylindrical eddy promoters are studied, and the results of a direct simulation of the turbulent flow in a plane channel are presented.

Karniadakis, George EM↗

NASA NTRS1989

Spectral element methods for the incompressible Navier-Stokes equations

Spectral element methods are high-order weighted-residual techniques for partial differential equations that combine the geometric flexibility of finite element techniques with the rapid convergence rate of spectral schemes. The theoretical foundations and numerical implementation of spectral element methods for the incompressible Navier-Stokes equations are presented, considering the construction and analysis of optimal-order spectral element discretizations for elliptic and saddle (Stokes) problems, as well as the efficient solution of the resulting discrete equations by rapidly convergent tensor-product-based iterative procedures. Several examples of spectral element simulation of moderate Reynolds number unsteady flow in complex geometry are presented.

Maday, Yvon↗