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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

An interactive adaptive remeshing algorithm for the two-dimensional Euler equations

An interactive adaptive remeshing algorithm utilizing a frontal grid generator and a variety of time integration schemes for the two-dimensional Euler equations on unstructured meshes is presented. Several device dependent interactive graphics interfaces have been developed along with a device independent DI-3000 interface which can be employed on any computer that has the supporting software including the Cray-2 supercomputers Voyager and Navier. The time integration methods available include: an explicit four stage Runge-Kutta and a fully implicit LU decomposition. A cell-centered finite volume upwind scheme utilizing Roe's approximate Riemann solver is developed. To obtain higher order accurate results a monotone linear reconstruction procedure proposed by Barth is utilized. Results for flow over a transonic circular arc and flow through a supersonic nozzle are examined.

Slack, David C.↗
NASA NTRS2018

Design of a Modular Monolithic Implicit Solver for Multi-Physics Applications

The design of a modular multi-physics high-order space-time finite-element framework is presented together with its extension to allow monolithic coupling of different physics. One of the main objectives of the framework is to perform efficient high- fidelity simulations of capsule/parachute systems. This problem requires simulating multiple physics including, but not limited to, the compressible Navier-Stokes equations, the dynamics of a moving body with mesh deformations and adaptation, the linear shell equations, non-re effective boundary conditions and wall modeling. The solver is based on high-order space-time - finite element methods. Continuous, discontinuous and C1-discontinuous Galerkin methods are implemented, allowing one to discretize various physical models. Tangent and adjoint sensitivity analysis are also targeted in order to conduct gradient-based optimization, error estimation, mesh adaptation, and flow control, adding another layer of complexity to the framework. The decisions made to tackle these challenges are presented. The discussion focuses first on the "single-physics" solver and later on its extension to the monolithic coupling of different physics. The implementation of different physics modules, relevant to the capsule/parachute system, are also presented. Finally, examples of coupled computations are presented, paving the way to the simulation of the full capsule/parachute system.

Carton De Wiart, Corentin↗
NASA NTRS1984

Numerical simulation of the tip vortex off a low-aspect-ratio wing at transonic speed

The viscous transonic flow around a low-aspect-ratio wing has been computed using an implicit, three-dimensional, 'thin-layer' Navier-Stokes solver. The grid around the geometry of interest is obtained numerically as a solution to a Dirichlet problem for the cube. The geometry chosen for this study is a low-aspect-ratio wing with large sweep, twist, taper, and camber. The topology chosen to wrap the mesh around the wing with good tip resolution is a C-O type mesh. Using this grid, the flow around the wing was computed for a free-stream Mach number of 0.82 at an angle of attack of 5 deg. At this Mach number, an oblique shock forms on the upper surface of the wing, and a tip vortex and three-dimensional flow separation off the wing surface are observed. Particle path lines indicate that the three-dimensional flow separation on the wing surface is part of the roots of the tip-vortex formation. The lifting of the tip vortex before the wing trailing edge is clearly observed by following the trajectory of particles released around the wing tip.

Mansour, N. N.↗
NASA NTRS1986

Transonic airfoil calculations including wind tunnel wall-interference effects

The results of Reynolds-averaged time-dependent inviscid and turbulent compressible Navier-Stokes computations using the implicit finite-difference approach of Steger (1978), modified by incorporating a pressure boundary condition, (PBC) to account for wall interference are compared with experimental data on a NACA 64A010 airfoil (Johnson and Bachalo, 1980) in graphs and briefly characterized. The computational approach is the same as that used by King and Johnson (1980), but a 137 x 50 mesh is used instead of a 97 x 35 mesh, and special care is taken in resolving the nose, shock, and trailing-edge regions. Imposition of PBC is shown to improve significantly the accuracy of the computations for the flowfield on the upper surface of the airfoil, shifting the shock forward to its experimentally measured position in the case of turbulent flow. The failure of the method, even with PBC, to match the experimental shock location in the case of a flow with a separation bubble is attributed to inadequacies in the algebraic turbulence model employed (Baldwin and Lomax, 1978).

King, L. S.↗
NASA NTRS1992

Unstructured grid methods for compressible flows

The implementation of the finite element method on unstructured triangular grids is described and the development of centered finite element schemes for the solution of the compressible Euler equation on general triangular and tetrahedral grids is discussed. Explicit and implicit Lax-Wendroff type methods and a method based upon the use of explicit multistep timestepping are considered. In the latter case, the convergence behavior of the method is accelerated by the incorporation of a fully unstructured multigrid procedure. The advancing front method for generating unstructured grids of triangles and tetrahedra is described and the application of adaptive mesh techniques to both steady and transient flow analysis is illustrated.

Morgan, K.↗
NASA NTRS1988

Parametric study of grid size, time step and turbulence modeling on Navier-Stokes computations over airfoils

An upwind-biased implicit approximate factorization algorithm is applied to several steady and unsteady turbulent flows. The thin layer form of the compressible Navier-Stokes equation is used. Both the flux vector splitting and flux difference splitting methods are used to determine fluxes, and the results are compared. Flux difference splitting predicts results more accurately than flux vector splitting on a given mesh size, but, in its present implementation, is more severely limited by the maximum CFL number for unsteady time accurate flows. Physical aspects of the computations are also examined. An equilibrium turbulent boundary layer model computes generally better steady and unsteady results than a nonequilibrium model when there is little to no boundary layer separation. Conversely, when a significant region of separation exists, the nonequilibrium model performs in better agreement with experiment.

Rumsey, Christopher L.↗
NASA NTRS1992

Investigation of forced unsteady separated flows using velocity-vorticity form of Navier-Stokes equations

The phenomenon of forced unsteady separation and eruption of boundary-layer vorticity is a highly-complex, high-Reynolds number flow phenomenon, which abruptly leads to the formation of a dynamic stall vortex as demonstrated earlier by the authors for a NACA 0015 airfoil undergoing constant rate pitch-up motion. This, as well as the results of other researchers, have convincingly demonstrated a complex vortical structure within the state of unsteady separation prior to the evolution of dynamic stall. This phenomenon of vortex eruption, although observed in studying dynamic stall phenomena, is also associated with transition from laminar to turbulence flow and its generic nature has been stressed by many researchers including the present investigators. An unsteady Navier-Stokes (NS) analysis is developed for arbitrarily maneuvering bodies using velocity-vorticity variables; this formulation is nearly form-invariant under a generalized non-inertial coordinate transformation. A fully-implicit uniformly second-order accurate method is used, with the nonlinear convective terms approximated using a biased third-order upwind differencing scheme to be able to simulate higher-Re flows. No explicit artificial dissipation is added. The numerical method is fully vectorized and currently achieves a computational index of 7 micro-seconds per time step per mesh point, using a single processor on a CRAY Y-MP. The simulation results show that the energetic free shear from the leading edge is responsible for the wall viscous layer to abruptly erupt near the center of the counterclockwise rotating eddy in the unsteady boundary layer. Primary, secondary, tertiary and quaternary vortices have been observed before the dynamic stall vortex evolves and gathers its maximum strength. This study will discuss the simulation results of Reynolds number up to Re = 45,000 and will also discuss the efforts of initial acceleration in a specific maneuver, on the evolution of the stall vortex.

Ghia, K. N.↗
NASA NTRS1993

Navier-Stokes flowfield computation of wing/rotor interaction for a tilt rotor aircraft in hover

The download on the wing produced by the rotor-induced downwash of a tilt rotor aircraft in hover is of major concern because of its severe impact on payload-carrying capability. A method has been developed to help gain a better understanding of the fundamental fluid dynamics that causes this download, and to help find ways to reduce it. In particular, the method is employed in this work to analyze the effect of a tangential leading edge circulation-control jet on download reduction. Because of the complexities associated with modeling the complete configuration, this work focuses specifically on the wing/rotor interaction of a tilt rotor aircraft in hover. The three-dimensional, unsteady, thin-layer compressible Navier-Stokes equations are solved using a time-accurate, implicit, finite difference scheme that employs LU-ADI factorization. The rotor is modeled as an actuator disk which imparts both a radical and an azimuthal distribution of pressure rise and swirl to the flowfield. A momentum theory blade element analysis of the rotor is incorporated into the Navier-Stokes solution method. Solution blanking at interior points of the mesh has been shown here to be an effective technique in introducing the effects of the rotor and tangential leading edge jet. Results are presented both for a rotor alone and for wing/rotor interaction. The overall mean characteristics of the rotor flowfield are computed including the flow acceleration through the rotor disk, the axial and swirl velocities in the rotor downwash, and the slipstream contraction. Many of the complex tilt rotor flow features are captured including the highly three-dimensional flow over the wing, the recirculation fountain at the plane of symmetry, wing leading and trailing edge separation, and the large region of separated flow beneath the wing. Mean wing surface pressures compare fairly well with available experimental data, but the time-averaged download/thrust ratio is 20-30 percent higher than the measured value. The discrepancy is due to a combination of factors that are discussed. Leading edge tangential blowing, of constant strength along the wing span, is shown to be effective in reducing download. The jet serves primarily to reduce the pressure on the wing upper surface. The computation clearly shows that, because of the three-dimensionality of the flowfield, optimum blowing would involve a spanwise variation in blowing strength.

Fejtek, Ian G.↗
NASA NTRS1985

Accuracy of schemes for the Euler equations with non-uniform meshes

The effect of non-uniform grids on the solution of the Euler equations is analyzed. A Runge-Kutta type scheme based on a finite volume formulation is considered. It is shown that for arbitrary grids the scheme can be inconsistent even though it is second-order accurate for uniform grids. An improvement is suggested which leads to at least first-order accuracy for general grids. Test cases are presented in both two- and three-space dimensions. Applications to finite difference and implicit algorithms are also given.

Turkel, E.↗
NASA NTRS1990

Viscous computations using a direct solver

Laminar viscous flows over airfoils are investigated analytically, applying the flux-difference splitting scheme of Roe (1986) to solve the thin-layer Navier-Stokes equations. Central-difference discretization is used for the viscous terms, and a fully implicit implementation is employed to minimize the Reynolds-number effect on convergence. Results for flows at freestream Mach number 0.5 and Reynolds number 5000 over NACA0012 airfoils at angles of attack 0 and 3 deg are presented graphically and discussed in detail. Good agreement with previous calculations is obtained, with accurate reproduction of essential features despite the use of coarser meshes.

Venkatakrishnan, V.↗
NASA NTRS1990

Three-dimensional flux-split Euler schemes involving unstructured dynamic meshes

Improved algorithms for the solution of the 3-D time dependent Euler equations are presented for aerodynamic analysis involving unstructured dynamic meshes. The improvements were developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves either an explicit time integration scheme using a multistage Runge-Kutta procedure or an implicit time integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. With the implicit Gauss-Seidel procedure, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady flow results are presented for both the NACA 0012 airfoil and the ONERA M6 wing to demonstrate applications of the new Euler solvers. A description of the Euler solvers is presented along with results and comparisons which assess the capability.

Batina, John T.↗
NASA NTRS1976

An efficient numerical method for solving the time-dependent compressible Navier-Stokes equations at high Reynolds number

A fine-mesh method incorporating two new operators, which drastically reduces the computation time, has been developed for solving the time-dependent Navier-Stokes equations at flight Reynolds numbers. The approach time-splits the equations into a hyperbolic part and a parabolic part, solves the hyperbolic part by a new explicit numerical method based on characteristics theory, and solves the parabolic part by a new efficient implicit parabolic method. The method has reduced the computation time by one and two orders of magnitude from that required previously to solve for the interaction of a shock wave with a boundary layer on a flat plate.

Maccormack, R. W.↗
NASA NTRS1991

Accuracy of an unstructured-grid upwind-Euler algorithm for the ONERA M6 wing

Improved algorithms for the solution of the three-dimensional, time-dependent Euler equations are presented for aerodynamic analysis involving unstructured dynamic meshes. The improvements have been developed recently to the spatial and temporal discretizations used by unstructured-grid flow solvers. The spatial discretization involves a flux-split approach that is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves either an explicit time-integration scheme using a multistage Runge-Kutta procedure or an implicit time-integration scheme using a Gauss-Seidel relaxation procedure, which is computationally efficient for either steady or unsteady flow problems. With the implicit Gauss-Seidel procedure, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady flow results are presented for both the NACA 0012 airfoil and the Office National d'Etudes et de Recherches Aerospatiales M6 wing to demonstrate applications of the new Euler solvers. The paper presents a description of the Euler solvers along with results and comparisons that assess the capability.

Batina, John T.↗
NASA NTRS1990

Three-dimensional flux-split Euler schemes involving unstructured dynamic meshes

Improved algorithms for the solution of the three-dimensional time-dependent Euler equations are presented for aerodynamic analysis involving unstructured dynamic meshes. The improvements have been developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves either an explicit time-integration scheme using a multi-stage Runge-Kutta procedure or an implicit time-integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. With the implicit Gauss-Seidel procedure, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady flow results are presented for both the NACA 0012 airfoil and the ONERA M6 wing to demonstrate applications of the new Euler solvers. The paper presents a description of the Euler solvers along with results and comparisons which assess the capability.

Batina, John T.↗
NASA NTRS1998

3D Navier-Stokes Time Accurate Solutions Using Multipartitioning Parallel Computation Methodology

A parallel CFD code solving 3D time accurate Navier-Stokes equations with multipartitioning parallel Methodology is being developed in collaboration with Ohio State University within the Air Vehicle Directorate, at Wright Patterson Air Force Base. The advantage of the multipartitioning parallel method is that the domain decomposition will not introduce domain boundaries for the implicit operators. A ring structure data communication is employed so that the implicit time accurate method can be implemented for multi-processors with the same accuracy as for the single processor. No sub-iteration is needed at the domain boundaries. The code has been validated for some typical unsteady flows, which include Coutte Flow, flow passing a cylinder. The code now is being employed for a large scale time accurate wall jet transient flow computation. 'ne preliminary results are promising. The mesh has been refined to capture more details of the flow field. The mesh refinement computation is in progress and would be difficult to successfully implement without the parallel computation techniques used. A modified version of the code with more efficient inversion of the diagonalized block matrix is currently being tested.

Zha, Ge-Cheng↗
NASA NTRS1980

Forebody and base region real-gas flow in severe planetary entry by a factored implicit numerical method. I - Computational fluid dynamics

A new code for the simulation of full (forebody and base region) flowfields about bluff bodies in the hypersonic regime of severe planetary entry is described. The present 'maximally conservative, maximally differenced' formulation of the unsteady compressible Navier-Stokes equations for 2-D axisymmetric 3-D flow is contrasted for stability with previous formulations of Viviand, Kutler, et al, and Thomas and Lombard. Discrete metric relations peculiar to the axisymmetric finite volume formulation are presented along with a general discussion of their relations to and consequences of failure to close computational cells. A computational mesh of curvilinear coordinate topology singular in the flow regime is presented that permits aligned capturing of the major physical features of the complex flowfield.

Lombard, C. K.↗
NASA NTRS1997

Visualization of Unsteady Computational Fluid Dynamics

The current compute environment that most researchers are using for the calculation of 3D unsteady Computational Fluid Dynamic (CFD) results is a super-computer class machine. The Massively Parallel Processors (MPP's) such as the 160 node IBM SP2 at NAS and clusters of workstations acting as a single MPP (like NAS's SGI Power-Challenge array and the J90 cluster) provide the required computation bandwidth for CFD calculations of transient problems. If we follow the traditional computational analysis steps for CFD (and we wish to construct an interactive visualizer) we need to be aware of the following: (1) Disk space requirements. A single snap-shot must contain at least the values (primitive variables) stored at the appropriate locations within the mesh. For most simple 3D Euler solvers that means 5 floating point words. Navier-Stokes solutions with turbulence models may contain 7 state-variables. (2) Disk speed vs. Computational speeds. The time required to read the complete solution of a saved time frame from disk is now longer than the compute time for a set number of iterations from an explicit solver. Depending, on the hardware and solver an iteration of an implicit code may also take less time than reading the solution from disk. If one examines the performance improvements in the last decade or two, it is easy to see that depending on disk performance (vs. CPU improvement) may not be the best method for enhancing interactivity. (3) Cluster and Parallel Machine I/O problems. Disk access time is much worse within current parallel machines and cluster of workstations that are acting in concert to solve a single problem. In this case we are not trying to read the volume of data, but are running the solver and the solver outputs the solution. These traditional network interfaces must be used for the file system. (4) Numerics of particle traces. Most visualization tools can work upon a single snap shot of the data but some visualization tools for transient problems require dealing with time.

Haimes, Robert↗
NASA NTRS2003

Implicit Approaches for Moving Boundaries in a 3-D Cartesian Method

This work considers numerical simulation of three-dimensional flows with time-evolving boundaries. Such problems pose a variety of challenges for numerical schemes, and have received a substantial amount of attention in the recent literature. Since such simulations are unsteady, time-accurate solution of the governing equations is required. In special cases, the body motion can be treated by a uniform rigid motion of the computational domain. For the more general situation of relative-body motion, however, this simplification is unavailable and the simulations require a mechanism for ensuring that the mesh evolves with the moving boundaries. This involves a "remeshing" of the computational domain (either localized or global) at each physical timestep, and places a premium on both the speed and robustness of the remeshing algorithms. This work presents a method which includes unsteady flow simulation, rigid domain motion, and relative body motion using a time-evolving Cartesian grid system in three dimensions.

Murman, Scott M.↗