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NASA NTRS1991

An efficient massively parallel Euler solver for unstructured grids

A data parallel mesh-vertex upwind finite-volume scheme for solving the Euler equations on triangular unstructured meshes is described. A novel vertex-based partitioning of the problem is introduced which minimizes the computation and communication costs associated with distributing the computation to the processors of a massively parallel computer. Finally, the performance of this unstructured computation on 8K processors of the Connection Machine CM-2 is compared with one processor of a Cray-YMP. The experiments show that 8K processors of the CM-2 achieve approximately 70 percent of the performance of one processor of the Cray-YMP on the unstructured mesh computations described here.

Hammond, Steven W.↗

NASA NTRS1991

Thin-layer and full Navier-Stokes, locally-conical and three-dimensional asymmetric solutions

The unsteady, compressible thin-layer and full Navier-Stokes equations are used to numerically simulate steady and unsteady asymmetric, supersonic, locally-conical flows around a 5-deg-semiapex angle circular cone. The main computational scheme used for the present computations is the implicit, upwind, flux-difference splitting, finite-volume scheme. Comparisons of the solutions using the two sets of equations are presented for the flow asymmetry and its control. Computational studies are also presented to investigate the effects of the freestream Reynolds number and the locally-scaled Reynolds number on the flow asymmetry. These studies are carried out using the full Navier-Stokes equations. Three-dimensional, asymmetric flow solutions are also presented for a 5-deg-semiapex angle cone of unit length and a cone-cylinder configuration. The three-dimensional solutions are obtained by using the thin-layer equations and short-duration transient side-slip disturbances along with a very fine grid.

Kandil, O. A.↗

NASA NTRS1991

Use of finite volume schemes for transition simulation

The use of finite-volume methods in the study of spatially and temporally evolving transitional flows over a flat plate is investigated. Schemes are developed with both central and upwind differencing. The compressible Navier-Stokes equations are solved with a Runge-Kutta time stepping scheme. Disturbances are determined using linear theory and superimposed at the inflow boundary. Time accurate integration is then used to allow temporal and spatial disturbance evolution. Characteristic-based boundary conditions are employed. The requirements of using finite-volume algorithms are studied in detail. Special emphasis is placed on difference schemes, grid resolution, and disturbance amplitudes. Moreover, comparisons are made with linear theory for small amplitude disturbances. Both subsonic and supersonic flows are considered, and it is shown that the locations of branch 1 and branch 2 of the neutral stability curve are well predicted, given sufficient resolution.

Fenno, Charles C., Jr.↗

NASA NTRS1989

Review of a code development and calibration program in support of the aeroassist flight experiment

The code development and calibration program for the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) is reviewed, with emphasis directed toward support of the Aeroassist Flight Experiment (AFE). The flight project is designed to obtain data which will be used in the validation of computational fluid dynamic approximation methods. Comparisons between experimental data and numerical simulation focus on perfect-gas tests over a scale model of the AFE and on flight and ground tests which challenge some aspect of the thermochemical nonequilibrium model. In the first case, the gas model is simple, but the grid-related problems of defining the real vehicle are present. In the second case, the vehicle geometries are simple, but thermochemical processes must be modeled correctly in order to compare with the experimental data. These comparisons are described as calibration runs because they test elements of the numerical simulation, but no single data set adequately simulates the full-scale AFE flight conditions. Comparisons between computation and experiment over a broad range of data sets show generally good agreement, though some aspects of the numerical model require further development.

Gnoffo, Peter A.↗

NASA NTRS1991

Examination of a vortex-ring interaction phenomenon in an axisymmetric flow

Unsteady separated flow in an axisymmetric configuration is investigated, with the objective of analyzing vortex-ring formation and break-up and the ensuing interactions believed to be leading to breakdown of laminar flow. The model problem considered is an idealized representation of a combustor with a centerbody. Direct solution of the time-dependent incompressible Navier-Stokes equations is employed, with central-differencing for all spatial derivatives, to determine the response of this flow for Re = 2000, 5000 and 10,000. The last case revealed a rather novel unsteady vortex-ring interaction phenomenon. This case has been further investigated using third-order accurate upwind differencing for the convective terms. The flow is interrogated carefully by examining the corresponding instantaneous vorticity, stream-function and velocity fields, as well as by tracking mass-less marker particles in some of the critical regions. Such detailed examination is deemed essential, prior to assigning fundamental physical relevance to the observed vortex-interaction phenomenon.

Ghia, U.↗

NASA NTRS1991

Computation of steady and unsteady compressible quasi-axisymmetric vortex flow and breakdown

The unsteady, compressible Navier-Stokes equations are used to compute and analyze compressible quasi-axisymmetric isolated vortices. The Navier-Stokes equations are solved using an implicit, upwind, flux-difference splitting finite-volume scheme. The developed three-dimensional solver has been verified by comparing its solution profiles with those of a slender, quasi-axisymmetric vortex solver for a subsonic, isolated quasi-axisymmetric vortex in an unbounded domain. The Navier-Stokes solver is then used to solve for a supersonic quasi-axisymmetric vortex flow in a configured circular duct. Steady and unsteady vortex-shock interactions and breakdown have been captured. The problem has also been calculated using the Euler solver of the same code and the results are compared with those of the Navier-Stokes solver. The effect of the initial swirl has been tentatively studied.

Kandil, Osama A.↗

NASA NTRS1991

Numerical investigation of the flow over a double delta wing at high incidence

The vortical flowfield over a double-delta wing configuration, consisting of a sharp leading edge 76 deg sweep strake and a 40 deg sweep wing section is investigated. The governing equations are solved numerically with a partially upwind, finite-difference, factorized algorithm. The leeward side vortex system resulting from the strake and wing vortices is investigated for subsonic, high-Reynolds-number flow at various angles of incidence. At low angles of attack the strake and wing vortices remain separate over the wing section, while for flows at higher angles of attack the two vortices merge and vortex breakdown develops. Vortex breakdown appears initially at the trailing edge region of the wing section. As the angle of attack increases bursting occurs further upstream closer to the strake section. The effect of numerical grid density is investigated, and the solutions are compared with available experimental data.

Ekaterinaris, John A.↗

NASA NTRS1989

Ozone trends in Atlanta, Georgia - Have emission controls been effective?

Nine years of summertime ozone data from the Atlanta metropolitan area are analyzed and compared to local emissions of volatile organic carbon and nitrogen oxides. Trends from 1979 to 1987 were studied for the number of days per year ozone exceeded the NAAQS standard, the second-highest ozone level observed per year, and the first quartile summertime average ozone observed, as well as the mean difference between the ozone level observed downwind and upwind of the city. Because this last parameter is sensitive to chemical factors but relatively insensitive to the number of days each year with meteorological conditions conducive to ozone formation, its trend may be best suited for determining how effective emission controls have been in reducing O3 in the Atlanta area. In spite of the fact that sizeable reductions have been claimed for volatile organic carbon emissions over the past several years, the data give no indication that ozone levels have decreased and in fact, imply that summertime ozone production may have increased. The results imply that either emissions have not decreased as much as has been claimed or that ozone is not sensitive to anthropogenic volatile organic carbon emissions.

Lindsay, Ronald W.↗

NASA NTRS1990

Prediction of vortical flows on wings using incompressible Navier-Stokes equations

Grid-density and Reynolds-number effects on integral values and static pressure distributions are presently studied in the steady-state Navier-Stokes solutions obtained for the flow around a round-edged double delta wing using an upwind-relaxation finite-difference algorithm. It is found that while the computed longitudinal aerodynamic coefficients are in good agreement with extant experimental data, the magnitudes of suction-pressure peaks are underpredicted in the vicinity of the trailing edge. It is judged that additional computations employing finer-grid solutions in the vortical flow region are required.

Hsu, C.-H.↗

NASA NTRS1990

ENSAERO - A multidisciplinary program for fluid/structural interaction studies of aerospace vehicles

A computational procedure is developed that uses a moving zonal grid concept to model complex flexible aerospace vehicles. The Euler/Navier-Stokes equations are used to model the flow, and computations are made using efficient methods based on both central and upwind schemes. The structure is represented by a finite element method which can model general aerospace vehicles. Provisions are made to accommodate other disciplines such as controls and thermal loads. The code is capable of computing unsteady flows on flexible wings with vortical flows. Adaptation of this procedure for parallel processing and validation for complete aerospace configurations is in progress.

Guruswamy, G. P.↗

NASA NTRS1991

Spatial adaption procedures on unstructured meshes for accurate unsteady aerodynamic flow computation

Spatial adaption procedures for the accurate and efficient solution of steady and unsteady inviscid flow problems are described. The adaption procedures were developed and implemented within a two-dimensional unstructured-grid upwind-type Euler code. These procedures involve mesh enrichment and mesh coarsening to either add points in high gradient regions of the flow or remove points where they are not needed, respectively, to produce solutions of high spatial accuracy at minimal computational cost. The paper gives a detailed description of the enrichment and coarsening procedures and presents comparisons with alternative results and experimental data to provide an assessment of the accuracy and efficiency of the capability. Steady and unsteady transonic results, obtained using spatial adaption for the NACA 0012 airfoil, are shown to be of high spatial accuracy, primarily in that the shock waves are very sharply captured. The results were obtained with a computational savings of a factor of approximately fifty-three for a steady case and as much as twenty-five for the unsteady cases.

Rausch, Russ D.↗

NASA NTRS1991

Unsteady shock-vortex interaction on a flexible delta wing

Unsteady Navier-Stokes computations have been carried out for simulating transonic flows over a clipped delta wing undergoing oscillatory and ramp motions, including flexibility. The implicit upwind algorithm has been validated by comparing the solutions with experimental data for the oscillatory pitching motion cases. The numerical and experimental results agree well at moderate angles of attack, where a leading-edge vortex develops. The ramp motion cases have demonstrated the effects of unsteadiness of the flow field and structural flexibility on the wing responses. For the 10 deg ramp motion, a vortex breakdown is observed. The interaction with the shock wave plays an essential role in the process of the breakdown observed in the present calculation.

Obayashi, Shigeru↗

NASA NTRS1990

A numerical study of hypersonic stagnation heat transfer predictions at a coordinate singularity

The problem of grid induced errors associated with a coordinate singularity on heating predictions in the stagnation region of a three-dimensional body in hypersonic flow is examined. The test problem is for Mach 10 flow over an Aeroassist Flight Experiment configuration. This configuration is composed of an elliptic nose, a raked elliptic cone, and a circular shoulder. Irregularities in the heating predictions in the vicinity of the coordinate singularity, located at the axis of the elliptic nose near the stagnation point, are examined with respect to grid refinement and grid restructuring. The algorithm is derived using a finite-volume formulation. An upwind-biased total-variation diminishing scheme is employed for the inviscid flux contribution, and central differences are used for the viscous terms.

Grasso, Francesco↗

NASA NTRS1990

Numerical simulation of steady and unsteady asymmetric vortical flow

The unsteady, compressible, thin-layer, Navier-Stokes equations are solved to simulate steady and unsteady, asymmetric, vortical laminar flow around cones at high incidences and supersonic Mach numbers. The equations are solved by using an implicit, upwind, flux-difference splitting, finite-volume scheme. Locally conical flows are assumed and the solutions are obtained by forcing the conserved components of the flowfield vector to be equal at two axial stations located at 0.95 and 1.0. Computational examples cover steady and unsteady asymmetric flows around a circular cone and its control using side strakes. Unsteady asymmetric flows are also presented for elliptic- and diamond-section cones, which model asymmetric vortex shedding around round and sharp-edged delta wing flows.

Kandil, O. A.↗

NASA NTRS1991

CFD in the 1980's from one point of view

The present interpretive treatment of the development history of CFD in the 1980s gives attention to advancements in such algorithmic techniques as flux Jacobian-based upwind differencing, total variation-diminishing and essentially nonoscillatory schemes, multigrid methods, unstructured grids, and nonrectangular structured grids. At the same time, computational turbulence research gave attention to turbulence modeling on the bases of increasingly powerful supercomputers and meticulously constructed databases. The major future developments in CFD will encompass such capabilities as structured and unstructured three-dimensional grids.

Lomax, Harvard↗

NASA NTRS1991

Characteristic time-stepping or local preconditioning of the Euler equations

A derivation is presented of a local preconditioning matrix for multidimensional Euler equations, that reduces the spread of the characteristic speeds to the lowest attainable value. Numerical experiments with this preconditioning matrix are applied to an explicit upwind discretization of the two-dimensional Euler equations, showing that this matrix significantly increases the rate of convergence to a steady solution. It is predicted that local preconditioning will also simplify convergence-acceleration boundary procedures such as the Karni (1991) procedure for the far field and the Mazaheri and Roe (1991) procedure for a solid wall.

Van Leer, Bram↗

NASA NTRS1991

Generalized conjugate-gradient methods for the Navier-Stokes equations

A generalized conjugate-gradient method is used to solve the two-dimensional, compressible Navier-Stokes equations of fluid flow. The equations are discretized with an implicit, upwind finite-volume formulation. Preconditioning techniques are incorporated into the new solver to accelerate convergence of the overall iterative method. The superiority of the new solver is demonstrated by comparisons with a conventional line Gauss-Siedel Relaxation solver. Computational test results for transonic flow (trailing edge flow in a transonic turbine cascade) and hypersonic flow (M = 6.0 shock-on-shock phenoena on a cylindrical leading edge) are presented. When applied to the transonic cascade case, the new solver is 4.4 times faster in terms of number of iterations and 3.1 times faster in terms of CPU time than the Relaxation solver. For the hypersonic shock case, the new solver is 3.0 times faster in terms of number of iterations and 2.2 times faster in terms of CPU time than the Relaxation solver.

Ajmani, Kumud↗

NASA NTRS1991

Numerical flux formulas for the Euler and Navier-Stokes equations. II - Progress in flux-vector splitting

The accuracy of various numerical flux functions for the inviscid fluxes when used for Navier-Stokes computations is studied. The flux functions are benchmarked for solutions of the viscous, hypersonic flow past a 10 degree cone at zero angle of attack using first order, upwind spatial differencing. The Harten-Lax/Roe flux is found to give a good boundary layer representation, although its robustness is an issue. Some hybrid flux formulas, where the concepts of flux-vector and flux-difference splitting are combined, are shown to give unsatisfactory pressure distributions; there is still room for improvement. Investigations of low diffusion, pure flux-vector splittings indicate that a pure flux-vector splitting can be developed that eliminates spurious diffusion across the boundary layer. The resulting first-order scheme is marginally stable and not monotone.

Coirier, William J.↗