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At least 145 records · Page 8

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NASA NTRS1984

Nonlinear computation of wing-body-vertical tail-wake flows at low supersonic speeds

A numerical method based on the conservation form of the full potential equation has been applied to the problem of three-dimensional supersonic flows with embedded subsonic regions. The governing equation is cast in a nonorthogonal coordinate system, and the theory of characteristics is used to accurately monitor the type-dependent flow field. A conservative switching scheme is employed to transition from the supersonic marching procedure to a subsonic relaxation algorithm and vice versa. The newly developed computer program can handle arbitrary geometries with fuselage, wing, vertical tail and wake components at combined angle of attack and sideslip. Results are presented for a low supersonic Mach numbers flow over the Shuttle orbiter (including the OMS pods and vertical tail), and for flows over a realistic fighter type configuration. Comparisons with experimental data are shown to be in good agreement for various cases.

Szema, K.-Y.↗

NASA NTRS1982

Relaxation solution of the full Euler equations

A numerical procedure for the relaxation solution of the full steady Euler equations is described. By embedding the Euler system in a second order surrogate system, central differencing may be used in subsonic regions while retaining matrix forms well suited to iterative solution procedures and convergence acceleration techniques. Hence, this method allows the development of stable, fully conservative differencing schemes for the solution of quite general inviscid flow problems. Results are presented for both subcritical and shocked supercritical internal flows. Comparisons are made with a standard time dependent solution algorithm. Previously announced in STAR as N82-24859

Johnson, G. M.↗

NASA NTRS1985

Computation of supersonic flows over three-dimensional configurations

An aerodynamic prediction technique based on the steady form of the full-potential equation has been applied to a variety of three-dimensional supersonic flow problems exhibiting embedded subsonic regions. A conservative switching scheme is employed to transition from the supersonic relaxation algorithm, and vice versa. Numerical solutions are obtained for a number of complex configurations, including advanced tactical fighter, Langley canard-wing fighter configuration, isolated shuttle orbiter, and mated shuttle orbiter configuration with external tank. The computed results are in good agreement with available experimental data.

Szema, K.-Y.↗

NASA NTRS1986

Comparison of Euler and full potential marching techniques for flows over complex configurations

Two recently developed aerodynamic prediction techniques based on the steady full potential equation and the unsteady Euler equations have been applied to a variety of three-dimensional supersonic flow problems exhibiting embedded subsonic regions. Both techniques utilize planar Gauss-Seidel relaxation in the marching direction and approximate factorization in the cross-flow plane. A conservative switching scheme and flux bias technique are employed in the full potential method to transition from the supersonic marching procedure to a subsonic relaxation algorithm and vice versa. A new unified approach with finite volume, high accuracy (up to third order) Total Variation Diminishing formulation (based on Roe's scheme) is used in the Euler solver. In the supersonic regions of the flow an 'infinitely large' time step is employed, and a finite time step is applied in the subsonic regions of the flow to reach the steady-state as a time-asymptote. Numerical solutions are obtained for a number of complex configurations, including: (1) an elliptic waverider, (2) a realistic fighter configuration, (3) the Space Shuttle, and (4) a Shuttle-like configuration. Both the Full Potential and Euler numerical results are in good agreement with available experimental data.

Szema, K. Y.↗

NASA NTRS1986

Three-dimensional, conservative, Euler computations using patched grid systems and explicit methods

The method of 'zonal approach' (in which the flow field is partitioned into regions with independent grids) for computation of flow over complex geometries, such as aircraft configuration, requires application of a grid-interfacing procedure. A three-dimensional conservative, boundary scheme for patched grids, applicable in generalized coordinates for arbitrary point distributions on a planar zonal surface is presented. The computation technique is derived within the framework of the Osher (1983) upwind scheme, using Euler equations. The three-dimensional interfacing method is applied to the computation of flow about a wing-canard combination using a two-zone, patched grid.

Hessenius, K. A.↗

NASA NTRS1985

Nonlinear potential analysis techniques for supersonic aerodynamic design

A numerical method based on the conservation form of the full potential equation has been applied to the problem of three-dimensional supersonic flows with embedded subsonic regions. The governing equation is cast in a nonorthogonal coordinate system, and the theory of characteristics is used to accurately monitor the type-dependent flow field. A conservative switching scheme is employed to transition from the supersonic marching procedure to a subsonic relaxation algorithm and vice versa. The newly developed computer program can handle arbitrary geometries with fuselage, canard, wing, flow through nacelle, vertical tail and wake components at combined angles of attack and sideslip. Results are obtained for a variety of configurations that include a Langley advanced fighter concept with fuselage centerline nacelle, Rockwell's Advanced Tactical Fighter (ATF) with wing mounted nacelles, and the Shuttle Orbiter configuration. Comparisons with available experiments were good.

Shankar, V.↗

NASA NTRS1985

Finite difference methods for the solution of unsteady potential flows

A brief review is presented of various problems which are confronted in the development of an unsteady finite difference potential code. This review is conducted mainly in the context of what is done for a typical small disturbance and full potential methods. The issues discussed include choice of equation, linearization and conservation, differencing schemes, and algorithm development. A number of applications including unsteady three-dimensional rotor calculation, are demonstrated.

Caradonna, F. X.↗

NASA NTRS1989

Recent progress on essentially non-oscillatory shock capturing schemes

An account is given of the construction of efficient implementations of 'essentially nonoscillatory' (ENO) schemes that approximate systems of hyperbolic conservation laws. ENO schemes use a local adaptive stencil to automatically obtain information from regions of smoothness when the solution develops discontinuities. Approximations employing ENOs can thereby obtain uniformly high accuracy to the very onset of discontinuities, while retaining a sharp and essentially nonoscillatory shock transition. For ease of implementation, ENO schemes applying the adaptive stencil concept to the numerical fluxes and employing a TVD Runge-Kutta-type time discretization are constructed.

Osher, Stanley↗

NASA NTRS1990

Energy conserving and potential-enstrophy dissipating schemes for the shallow water equations

To incorporate potential enstrophy dissipation into discrete shallow water equations with no or arbitrarily small energy dissipation, a family of finite-difference schemes have been derived with which potential enstrophy is guaranteed to decrease while energy is conserved (when the mass flux is nondivergent and time is continuous). Among this family of schemes, there is a member that minimizes the spurious impact of infinite potential vorticities associated with infinitesimal fluid depth. The scheme is, therefore, useful for problems in which the free surface may intersect with the lower boundary.

Arakawa, Akio↗

NASA NTRS1991

Micro- and meso-scale simulations of magnetospheric processes related to the aurora and substorm morphology

The primary methodology during the grant period has been the use of micro or meso-scale simulations to address specific questions concerning magnetospheric processes related to the aurora and substorm morphology. This approach, while useful in providing some answers, has its limitations. Many of the problems relating to the magnetosphere are inherently global and kinetic. Effort during the last year of the grant period has increasingly focused on development of a global-scale hybrid code to model the entire, coupled magnetosheath - magnetosphere - ionosphere system. In particular, numerical procedures for curvilinear coordinate generation and exactly conservative differencing schemes for hybrid codes in curvilinear coordinates have been developed. The new computer algorithms and the massively parallel computer architectures now make this global code a feasible proposition. Support provided by this project has played an important role in laying the groundwork for the eventual development or a global-scale code to model and forecast magnetospheric weather.

Swift, Daniel W.↗

NASA NTRS1995

Two-dimensional mesh embedding for Galerkin B-spline methods

A number of advantages result from using B-splines as basis functions in a Galerkin method for solving partial differential equations. Among them are arbitrary order of accuracy and high resolution similar to that of compact schemes but without the aliasing error. This work develops another property, namely, the ability to treat semi-structured embedded or zonal meshes for two-dimensional geometries. This can drastically reduce the number of grid points in many applications. Both integer and non-integer refinement ratios are allowed. The report begins by developing an algorithm for choosing basis functions that yield the desired mesh resolution. These functions are suitable products of one-dimensional B-splines. Finally, test cases for linear scalar equations such as the Poisson and advection equation are presented. The scheme is conservative and has uniformly high order of accuracy throughout the domain.

Shariff, Karim↗

NASA NTRS1998

Electromagnetics and Fluid Dynamics

Previous efforts focused on developing tools for design of low observables were sustained. The final product was the maturation of a high-order accurate finite-volume based code to solve Maxwell's equations. One of the primary achievements was the development and implementation of efficient filtering techniques which enhance the robustness of high-order and optimized schemes without significant adverse impact on accuracy. This has eliminated the stability barrier which restrains the common use of high-order schemes for conservative wave propagation phenomena on curvilinear meshes. A study was performed of crossing shock interactions under conditions of increasing interaction strength and asymmetry. In the first category, the observed computed topological bifurcations were correlated with the formation of various lines of coalescence and divergence evident in experimental and computed surf-ace oil maps. ne flow structure arising from asymmetric interactions was investigated with particular emphasis on: 1) vorticity dynamics, 2) shock-structure and 3) sidewall vortex loading. Several efforts of the prior year were successfully published in archival journals. The high-order algorithms developed for CEM have been implemented into the FDL3DI CFD code are presently undergoing extensive testing. Preliminary results are highly encouraging.

Gaitonde, Datta↗

NASA NTRSDate not supplied

Assessment of UMUSCL Scheme for DNS of Turbulent Flows

Direct Numerical Simulations (DNS) are performed using the FUN3D code ( https://fun3d.larc.nasa.gov) for three validation cases: (1) flow through a plane channel, (2) flow through a channel with a constriction, and (3) flow over a flat plate. FUN3D is a node-centered finite-volume code developed at the NASA Langley Research Center that solves the three-dimensional compressible Navier-Stokes equations on unstructured computational grids. The simulations are performed employing the 2nd-order unstructured monotonic upstream scheme for conservation laws (UMUSCL). The results are compared with available experimental and numerical data. The effect of the UMUSCL reconstruction parameter (κ) is assessed, and the results indicate that κ = 0.9 yields satisfactory results in terms of accuracy and robustness compared to available data. Further analyses of the results, along with additional test cases and grids will be presented in the final manuscript.

Direct Numerical Simulation↗

NASA NTRS1975

Upwind second-order difference schemes and applications in unsteady aerodynamic flows

Explicit second-order upwind difference schemes in combination with spatially symmetric schemes can produce larger stability bounds and better numerical resolution than symmetric schemes alone. However, if conservation form is essential, a special operator is required for transition between schemes. An operational approach has been devised for deriving transition operators so that strict conservation and local consistency are maintained. Various aspects of hybrid schemes are studied numerically for model linear and nonlinear equations. To demonstrate the utility of combining two different algorithms, MacCormack's explicit, noncentered, second-order method is combined with a completely upwind version, and numerical solutions of the Euler equations are obtained for two-dimensional, transonic flows with embedded supersonic regions and shock waves. The general utility of the operational approach for combining schemes is emphasized by deriving a second-order conservative scheme for the steady transonic small-disturbance potential equation.

Warming, R. F.↗

NASA NTRS1998

The Space-Time Conservation Element and Solution Element Method: A New High-Resolution and Genuinely Multidimensional Paradigm for Solving Conservation Laws: The Two Dimensional Time Marching Schemes - 1

A new high resolution and genuinely multidimensional numerical method for solving conservation laws is being, developed. It was designed to avoid the limitations of the traditional methods. and was built from round zero with extensive physics considerations. Nevertheless, its foundation is mathmatically simple enough that one can build from it a coherent, robust. efficient and accurate numerical framework. Two basic beliefs that set the new method apart from the established methods are at the core of its development. The first belief is that, in order to capture physics more efficiently and realistically, the modeling, focus should be placed on the original integral form of the physical conservation laws, rather than the differential form. The latter form follows from the integral form under the additional assumption that the physical solution is smooth, an assumption that is difficult to realize numerically in a region of rapid chance. such as a boundary layer or a shock. The second belief is that, with proper modeling of the integral and differential forms themselves, the resulting, numerical solution should automatically be consistent with the properties derived front the integral and differential forms, e.g., the jump conditions across a shock and the properties of characteristics. Therefore a much simpler and more robust method can be developed by not using the above derived properties explicitly.

Chang, Sin-Chung↗

NASA NTRS1979

An implicit algorithm for the conservative, transonic full-potential equation with effective rotated differencing

A new differencing scheme for the conservative full potential equation which effectively simulates rotated differencing is presented. The scheme was implemented by an appropriate upwind bias of the density coefficient along coordinate directions. A fast, fully implicit, approximate factorization iteration scheme was then used to solve the resulting difference equations. Solutions for a number of traditionally difficult transonic airfoil test cases are presented.

Holst, T. L.↗

DOE OSTI2022

A consistent and conservative Phase-Field method for multiphase incompressible flows

In the present study, a consistent and conservative Phase-Field method, including both the model and scheme, is developed for multiphase flows with an arbitrary number of immiscible and incompressible fluid phases. The consistency of mass conservation and the consistency of mass and momentum transport are implemented to address the issue of physically coupling the Phase-Field equation, which locates different phases, to the hydrodynamics. These two consistency conditions, as illustrated, provide the “optimal” coupling because (i) the new momentum equation resulting from them is Galilean invariant and implies the kinetic energy conservation, regardless of the details of the Phase-Field equation, and (ii) failures of satisfying the second law of thermodynamics or the consistency of reduction of the multiphase flow model only result from the same failures of the Phase-Field equation but are not due to the new momentum equation. Physical interpretation of the consistency conditions and their formulations are first provided, and general formulations that are obtained from the consistency conditions and independent of the interpretation of the velocity are summarized. Then, the present consistent and conservative multiphase flow model is completed by selecting a reduction consistent Phase-Field equation. Several novel techniques are developed to inherit the physical properties of the multiphase flows after discretization, including the gradient-based phase selection procedure, the momentum conservative method for the surface force, and the general theorems to preserve the consistency conditions on the discrete level. Equipped with those novel techniques, a consistent and conservative scheme for the present multiphase flow model is developed and analyzed. The scheme satisfies the consistency conditions, conserves the mass and momentum, and assures the summation of the volume fractions to be unity, on the fully discrete level and for an arbitrary number of phases. All those properties are numerically validated. Finally, numerical applications demonstrate that the present model and scheme are robust and effective in studying complicated multiphase dynamics, especially for those with large-density ratios.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2020

Entropy Stable Nonconforming Discretizations with the Summation-By-Parts Property for Curvilinear Coordinates

The entropy conservative/stable algorithm of Friedrichet al.(2018) for hyperbolic conservation laws on nonconforming p-refined/coarsened Cartesian grids, is extended to curvilinear grids for the compressible Euler equations. The primary focus is on constructing appropriate coupling procedures across the curvilinear nonconforming interfaces. A simple and flexible approach is proposed that uses interpolation operators from one element to the other. On the element faces,the analytic metrics are used to construct coupling terms, while metric terms in the volume are approximated to satisfy a discretization of the geometric conservation laws. The resulting scheme is entropy conservative/stable, elementwise conservative, and freestream preserving. The accuracy and stability properties of the resulting numerical algorithm are shown to be comparable to those ofthe original conforming scheme (∼p+ 1 convergence) in the context of the isentropic Euler vortex and the inviscid Taylor–Green vortex problems on manufactured high order grids.

David Del Rey Fernandez↗