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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 145 records · Page 8
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NASA NTRS1987

Composite grid and finite-volume LU implicit scheme for turbine flow analysis

A composite grid was generated in an attempt to improve grid quality for a typical turbine blade with large camber in terms of mesh control, smoothness, and orthogonality. This composite grid consists of the C grid (or O grid) in the immediate vicinity of the blade and the H grid in the upstream region and in the middle of the blade passage between the C grids. It provides a good boundary layer resolution around the leading edge region for viscous calculation, has orthogonality at the blade surface and slope continuity at the C-H (or O-H) interface, and has flexibility in controlling the mesh distribution in the upstream region without using excessive grid points. This composite grid eliminates the undesirable qualities of a single grid when generated for a typical turbine geometry. A finite-volume lower-upper (LU) implicit schemes can be used in solving for the turbine flows on the composite grid. This grid has a special grid node that is connected to more than four neighboring nodes in two dimensions and to more than six nodes in three dimensions. But the finite-volume approach poses no problem at the special point because each interior cell has only four neighboring cells in two dimensions and only six cells in three dimensions. The finite-volume LU implicit scheme was demonstrated to be robust and efficient for both external and internal flows in a broad flow regime.

Choo, Yung K.↗
NASA NTRS1987

Vectorizable implicit algorithms for the flux-difference split, three-dimensional Navier-Stokes equations

The computational efficiency of four vectorizable implicit algorithms is assessed when applied to calculate steady-state solutions to the three-dimensional, incompressible Navier-Stokes equations in general coordinates. Two of these algorithms are characterized as hybrid schemes; that is, they combine some approximate factorization in two coordinate directions with relaxation in the remaining spatial direction. The other two algorithms utilize an approximate factorization approach which yields two-factor algorithms for three-dimensional systems. All four algorithms are implemented in identical high-resolution upwind schemes for the flux-difference split Navier-Stokes equations. These highly nonlinear schemes are obtained by extending an implicit Total Variation Diminishing (TVD) scheme recently developed for linear one-dimensional systems of hyperbolic conservation laws to the three-dimensional Navier-Stokes equations. The computation of vortical flow over a sharp-edged, thin delta wing has been chosen as a common numerical test case. The convergence of the algorithms is discussed and the accuracy of the computed flow-field results is assessed. The validity of the present results are demonstrated by a comparison with experimental data.

Hartwich, P. M.↗
NASA NTRS1988

A stiffly-stable implicit Runge-Kutta algorithm for CFD applications

A stiffly-stable implicit Runge-Kutta integration algorithm is derived for CFD applications spanning the range of semidiscrete theories. The algorithm family contains the one-step 'theta' algorithms, including backwards Euler and the trapezoidal rule, and provides a versatile framework to identify expressions governing algorithm stability characteristics. Parameters of a Runge-Kutta optimal implicit algorithm, second-order accurate in time and stiffly-stable, are established. This algorithm is implemented within a weak statement finite element semidiscrete formulation for one- and two-dimensional conservation law systems. Numerical results are compared to theta-algorithm solutions, for unsteady quasi-one-dimensional Euler predictions with shocks, and for a specially derived two-dimensional conservation law system modeling the Euler equations.

Baker, A. J.↗
NASA NTRS1988

Calculations of three-dimensional flows using the isenthalpic Euler equations with implicit flux-vector splitting

A numerical method for solving the isenthalpic form of the Euler equations is developed. The method is based on the concept of flux vector splitting in its implicit form applied to a cell centered finite volume scheme. Approximate factorization is implemented in solving the implicit part of the governing equations. Time marching to a steady state solution requires short computational times due to the relative efficiency of the basic method. Computational times are further reduced by the implementation of multigrid. Results for several basic cases are shown.

Cannizzaro, Frank E.↗
NASA NTRS1988

Unsteady delta-wing flow computation using an implicit factored Euler scheme

The conservative unsteady Euler equations for the flow relative motion in the moving frame of reference are used to solve for the steady and unsteady flows around sharp-edged delta wings. The resulting equations are solved by using an implicit approximately-factored finite-volume scheme. Implicit second-order and explicit second- and fourth-order dissipations are added to the scheme. The boundary conditions are explicitly satisfied. The grid is generated by locally using a modified Joukowski transformation in cross-flow planes at the grid chord stations. The computational applications cover a steady flow around a delta wing whose results serve as the initial conditions for the unsteady flow around a pitching delta wing about a large angle of attack. The steady results are compared with the experimental data and the periodic solution is achieved within the third cycle of oscillation.

Kandil, Osama A.↗
NASA NTRS1988

Unsteady transonic airfoil computation using implicit Euler scheme on body-fixed grid

The unsteady Euler equations have been derived for the flow relative motion with respect to a frame of reference that is rigidly attached to the moving airfoil. The grid is generated once by an elliptic solver without a need for dynamic grid computation. An implicit factored finite-volume scheme has been developed and implemented through a fully vectorized computer program. Implicit second-order and explicit second and fourth-order dissipations are added to the scheme. The boundary conditions are explicitly satisfied. The scheme is applied to steady and unsteady transonic airfoil flows and the results are in good agreement with the experimental data. For forced harmonic airfoil motions, periodic solutions are achieved within the third cycle of oscillation.

Kandil, Osama A.↗
NASA NTRS1989

Upwind-biased, point-implicit relaxation strategies for viscous, hypersonic flows

An upwind-biased point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for three-dimensional viscous hypersonic flows in chemical and thermal nonequilibrium is described. Details of the algorithm development, in the context of an 11-species two-temperature reacting gas model, are emphasized. Because of the point-implicit relaxation strategy, the algorithm remains stable at large Courant numbers without the necessity of solving large block-tridiagonal systems. Predictions for the hypersonic flow of air in chemical and thermal nonequilibrium (velocity = 8917 m/s, altitude = 78 km) over the Aeroassist Flight Experiment configuration, obtained on a multidomain grid, are discussed.

Gnoffo, Peter A.↗
NASA NTRS1990

An upwind-biased, point-implicit relaxation algorithm for viscous, compressible perfect-gas flows

An upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for three-dimensional, viscous, compressible, perfect-gas flows is described. The algorithm is derived using a finite-volume formulation in which the inviscid components of flux across cell walls are described with Roe's averaging and Harten's entropy fix with second-order corrections based on Yee's Symmetric Total Variation Diminishing scheme. Viscous terms are discretized using central differences. The relaxation strategy is well suited for computers employing either vector or parallel architectures. It is also well suited to the numerical solution of the governing equations on unstructured grids. Because of the point-implicit relaxation strategy, the algorithm remains stable at large Courant numbers without the necessity of solving large, block tri-diagonal systems. Convergence rates and grid refinement studies are conducted for Mach 5 flow through an inlet with a 10 deg compression ramp and Mach 14 flow over a 15 deg ramp. Predictions for pressure distributions, surface heating, and aerodynamics coefficients compare well with experiment data for Mach 10 flow over a blunt body.

Gnoffo, Peter A.↗
NASA NTRS1990

Numerical solution of 3D Navier-Stokes equations with upwind implicit schemes

An upwind MUSCL type implicit scheme for the three-dimensional Navier-Stokes equations is presented. Comparison between different approximate Riemann solvers (Roe and Osher) are performed and the influence of the reconstructions schemes on the accuracy of the solution as well as on the convergence of the method is studied. A new limiter is introduced in order to remove the problems usually associated with non-linear upwind schemes. The implementation of a diagonal upwind implicit operator for the three-dimensional Navier-Stokes equations is also discussed. Finally the turbulence modeling is assessed. Good prediction of separated flows are demonstrated if a non-equilibrium turbulence model is used.

Marx, Yves P.↗
NASA NTRS1990

Implicit solution of three-dimensional internal turbulent flows

The scalar form of the approximate factorization method was used to develop a new code for the solution of three-dimensional internal laminar and turbulent compressible flows. The Navier-Stokes equations in their Reynolds-averaged form are iterated in time until a steady solution is reached. Evidence is given to the implicit and explicit artificial damping schemes that proved to be particularly efficient in speeding up convergence and enhancing the algorithm robustness. A conservative treatment of these terms at domain boundaries is proposed in order to avoid undesired mass and/or momentum artificial fluxes. Turbulence effects are accounted for by the zero-equation Baldwin-Lomax turbulence model and the q-omega two-equation model. For the first, an investigation on the model behavior in case of multiple boundaries is performed. The flow in a developing S-duct is then solved in the laminar regime at Reynolds number (Re) 790 and in the turbulent regime at Re=40,000 using the Baldwin-Lomax model . The Stanitz elbow is then solved using an inviscid version of the same code at M(sub inlet)=0.4. Grid dependence and convergence rate are investigated showing that for this solver the implicit damping scheme may play a critical role for convergence characteristics. The same flow at Re=2.5x10(exp 6) is solved with the Baldwin-Lomax and the q-omega models. Both approaches showed satisfactory agreement with experiments, although the q-omega model is slightly more accurate.

Michelassi, V.↗
NASA NTRS1989

Adaptive implicit-explicit methods for flow problems

Studies on the adaptive implicit-explicit (AIE) method for large-scale problems are presented. The AIE method is based on dynamic grouping of the elements into the implicit and explicit subsets as dictated by the element level stability and accuracy considerations. The method has been applied to various flow problems including the incompressible flow and convection-diffusion problems, and it has been demonstrated that substantial savings in CPU time and memory can be achieved.

Liou, J.↗
NASA NTRS1990

Implicit and explicit computations of flows past cavities with and without yaw

Implicit and explicit computations are presented to study the supersonic, turbulent flows past three-dimensional, rectangular cavities at 0 and 45 deg yaw angle. The Reynolds-averaged, unsteady, compressible, complete Navier-Stokes equations are solved time-accurately, including the Reynolds stresses. The number of major vortices inside and the separation characteristics on the cavity floor are different for cavities with length-to-depth ratios of 3.0 and 6.7. Due to the oscillations of the shear layer, which randomly exposes the cavity flow to the external flow, vortices are shed into the mainstream. When the upstream flow approaches a cavity at yaw, the width-to-depth ratio also becomes an important parameter. The dominant rotational planes of the major vortices incline at an angle to the vertical plane due to yaw. The execution of the implicit scheme is about three times faster, but it requires about four times more computer memory.

Baysal, Oktay↗
NASA NTRS1991

Implicit solution of three-dimensional internal turbulent flows

The scalar form of the approximate factorization method was used to develop a new code for the solution of three dimensional internal laminar and turbulent compressible flows. The Navier-Stokes equations in their Reynolds-averaged form were iterated in time until a steady solution was reached. Evidence was given to the implicit and explicit artificial damping schemes that proved to be particularly efficient in speeding up convergence and enhancing the algorithm robustness. A conservative treatment of these terms at the domain boundaries was proposed in order to avoid undesired mass and/or momentum artificial fluxes. Turbulence effects were accounted for by the zero-equation Baldwin-Lomax turbulence model and the q-omega two-equation model. The flow in a developing S-duct was then solved in the laminar regime in a Reynolds number (Re) of 790 and in the turbulent regime at Re equals 40,000 by using the Baldwin-Lomax model. The Stanitz elbow was then solved by using an invicid version of the same code at M sub inlet equals 0.4. Grid dependence and convergence rate were investigated, showing that for this solver the implicit damping scheme may play a critical role for convergence characteristics. The same flow at Re equals 2.5 times 10(exp 6) was solved with the Baldwin-Lomax and the q-omega models. Both approaches show satisfactory agreement with experiments, although the q-omega model was slightly more accurate.

Michelassi, V.↗
NASA NTRS1990

Application of implicit numerical techniques to the solution of the three-dimensional diffusion equation

Implicit techniques for calculating three-dimensional, time-dependent heat diffusion in a cube are tested with emphasis on storage efficiency, accuracy, and speed of calculation. For this purpose, a tensor product technique with both Chebyshev collocation and finite differences and a generalized conjugate gradient technique with finite differences are used in conjunction with Crank-Nicolson discretization. An Euler explicit finite difference calculation is performed for use as a benchmark. The implicit techniques are found to be competitive with the Euler explicit method in terms of storage efficiency and speed of calculation and offer advantages both in accuracy and stability. Mesh stretching in the finite difference calculations is shown to markedly improve the accuracy of the solution.

Peltier, Leonard Joel↗
NASA NTRS1991

An intrinsically n-dimensional generalized flux vector splitting implicit finite element Euler algorithm

A generalized flux-vector splitting implicit Galerkin finite-element algorithm for the Euler equations in curvilinear coordinates for ideal and reacting gases is derived. For an arbitrary equation of state, the curvilinear-coordinate flux vector is split in kinematic and kinetic components, and the associated jacobian matrix eigenvalues explicitly depend on the metric data. After directional semidiscretization, the terminal ordinary differential-equation system is solved via a nonlinearly stable implicit Runge-Kutta scheme in concert with an accurate tensor matrix product factorization. The results for selected two-dimensional supersonic and axisymmetric hypersonic flows validate the algorithm and verify its robustness for curvilinear-coordinate computations. The evolution towards a steady state is achieved for large Courant numbers without indication of numerical instabilities.

Iannelli, G. S.↗
NASA NTRS1991

Transient modeling/analysis of hyperbolic heat conduction problems employing mixed implicit-explicit alpha method

This paper describes the evaluation of mixed implicit-explicit finite element formulations for hyperbolic heat conduction problems involving non-Fourier effects. In particular, mixed implicit-explicit formulations employing the alpha method proposed by Hughes et al. (1987, 1990) are described for the numerical simulation of hyperbolic heat conduction models, which involves time-dependent relaxation effects. Existing analytical approaches for modeling/analysis of such models involve complex mathematical formulations for obtaining closed-form solutions, while in certain numerical formulations the difficulties include severe oscillatory solution behavior (which often disguises the true response) in the vicinity of the thermal disturbances, which propagate with finite velocities. In view of these factors, the alpha method is evaluated to assess the control of the amount of numerical dissipation for predicting the transient propagating thermal disturbances. Numerical test models are presented, and pertinent conclusions are drawn for the mixed-time integration simulation of hyperbolic heat conduction models involving non-Fourier effects.

Tamma, Kumar K.↗
NASA NTRS1991

Acceleration of convergence by shifting the spectrum of implicit finite difference operators associated with the equations of gas dynamics

Eigensystem analysis techniques are applied to finite difference formulations of the Navier-Stokes equations in one dimension. Spectra of the resulting implicit difference operators are computed. The largest eigenvalues are calculated by using a combination of the Frechet derivative of the operators and Arnoldi's method. The accuracy of Arnoldi's method is tested by comparing the rate of convergence of the iterative method with the dominant eigenvalue of the original iteration matrix. On the basis of the pattern of eigenvalue distributions for various flow configurations, a shifting of the implicit operators in question is devised. This procedure has improved the rates of convergence of CFD codes by 20 - 50 percent.

Cheer, A.↗
NASA NTRS1990

Efficient parallel solution of parabolic equations - Implicit methods on the Cedar multicluster

A class of implicit methods for the parallel solution of linear parabolic differential equations based on Pade and Chebyshev rational approximations to the matrix exponential are presented. It is pointed out that this approach incorporates both natural hierarchical parallelism, improved intrinsic efficiency, and fewer timesteps. These advantages lead to an extremely fast family of methods for the solution of certain time-dependent problems. These techniques are illustrated with numerical experiments on the University of Illinois Cedar multicluster architecture. The experiments indicate that implicit methods of very high degree offer great promise for the solution of certain parabolic problems when in computational environment with parallel resources. Hierarchically organized parallel computers, such as the Cedar multicluster, are found to be especially attractive for these schemes.

Gallopoulos, E.↗