Search NASA⌕ Search

SEARCH · Search NASA

Results for “splitting methods”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Evaluation of a velocity-split solution of the Navier-Stokes equations for fighter forebodies

A velocity-splitting method of solving the three-dimensional Navier-Stokes equations, originally designed for afterbody flows, is examined for its applicability for predicting fighter forebody flows. Results from the AFTEND Code are compared with wind tunnel data for two fighter configurations at a Mach number of 0.9 and angles-of-attack from 0 deg to 20 deg. Results compare well with data, and in areas where data do not exist, the viscous AFTEND results show realistic effects of viscosity compared to inviscid predictions. The inviscid results themselves are in general superior to results obtained from a small-disturbance transonic potential code.

Yaros, S. F.↗
NASA NTRS1987

Research in computational fluid dynamics

The numerical integration of quasi-one-dimensional unsteady flow problems which involve finite rate chemistry are discussed, and are expressed in terms of conservative form Euler and species conservation equations. Hypersonic viscous calculations for delta wing geometries is also examined. The conical Navier-Stokes equations model was selected in order to investigate the effects of viscous-inviscid interations. The more complete three-dimensional model is beyond the available computing resources. The flux vector splitting method with van Leer's MUSCL differencing is being used. Preliminary results were computed for several conditions.

Murman, Earll M.↗
NASA NTRS1987

Numerical solutions of Navier-Stokes equations for a Butler wing

The flow field is simulated on the surface of a Butler wing in a uniform stream. Results are presented for the Mach number 3.5 and Reynolds number of 2,000,000. The simulation is done by integrating the viscous Navier-Stokes equations. These equations govern the unsteady, viscous, compressible and heat conducting flow of an ideal gas. The equations are written in curvilinear coordinates so that the wing surface is represented accurately. O-type and H-type grids have been used for this study, and results are compared. The governing equations are solved by the McCormack time-split method, and the results are compared with other theoretical and experimental results. The codes are written in FORTRAN, vectorized and currently run on the CDC Vector Processing System (VPS-32) computer.

Abolhassani, Jamshid S.↗
NASA NTRS1987

A computational analysis of flow separation over five different airfoil geometries at high angles-of-attack

The flux splitting method of Van Leer (1982) and an implicit, upwind-biased, finite-volume scheme of Rumsey (1985) for solving the two-dimensional Reynolds-averaged Navier-Stokes equations were applied to analyze five airfoil geometries (the NACA 0012, 12-percent Joukowski, NACA 4412, NACA 65-015, and LS1-0417 sections), at high angles of attack. The effect of grid density and grid extent on the Strouhal number of the unsteady flow was computed, as well as the effect of variations in Mach number, Reynolds number, and angle of attack. It was found, that past an angle of attack of 20 deg, Strouhal numbers were independent of angle of attack (at a constant value of 0.115), agreeing well with the experimental findings of Tyler (1931).

Rumsey, Christopher L.↗
NASA NTRS1987

Numerical solutions of Navier-Stokes equations for a Butler wing

The flow field is simulated on the surface of a Butler wing in a uniform stream. Results are presented for Mach number 3.5 and Reynolds number of 2,000,000. The simulation is done by integrating the viscous Navier-Stokes equations. These equations govern the unsteady, viscous, compressible and heat conducting flow of an ideal gas. The equations are written in curvilinear coordinates so that the wing surface is represented accurately. The O-type and H-type grids have been used for this study, and results are compared. The governing equations are solved by the MacCormack time-split method, and the results are compared with other theoretical and experimental results. The codes are written in FORTRAN, vectorized and currently run on the CDC Vector Processing System (VPS-32) computer.

Abolhassani, Jamshid S.↗
NASA NTRS1988

A Study of Flow Separation in Transonic Flow Using Inviscid and Viscous Computational Fluid Dynamics (CFD) Schemes

A comparison of flow separation in transonic flows is made using various computational schemes which solve the Euler and the Navier-Stokes equations of fluid mechanics. The flows examined are computed using several simple two-dimensional configurations including a backward facing step and a bump in a channel. Comparison of the results obtained using shock fitting and flux vector splitting methods are presented and the results obtained using the Euler codes are compared to results on the same configurations using a code which solves the Navier-Stokes equations.

Rhodes, J. A.↗
NASA NTRS1987

Numerical simulation of homogeneous, isotropic, compressible turbulence

A new numerical algorithm is developed and applied to the direct simulation of compressible, homogeneous turbulent flows at low Mach numbers. A split method in time first solves a subset of the equations explicitly, followed by an implicit treatment of the pressure terms. The definition of an average sound speed over the entire field allows the implicit equations to be solved analytically, while relaxing the severe time limit imposed by the large sound speeds. Results from direct simulations on 96(3) grids provide a data base against which a new subgrid-scale model for compressible homogeneous turbulence is tested. This model reduces to the linear combination model in the absence of compressibility.

Erlebacher, G.↗
NASA NTRS1988

A numerical study of ENO and TVD schemes for shock capturing

The numerical performance of a second-order upwind-based total variation diminishing (TVD) scheme and that of a uniform second-order essentially non-oscillatory (ENO) scheme for shock capturing are compared. The TVD scheme used is a modified version of Liou, using the flux-difference splitting (FDS) of Roe and his superbee function as the limiter. The construction of the basic ENO scheme is based on Harten, Engquist, Osher, and Chakravarthy, and the 2-D extensions are obtained by using a Strang-type of fractional-step time-splitting method. Numerical results presented include both steady and unsteady, 1-D and 2-D calculations. All the chosen test problems have exact solutions so that numerical performance can be measured by comparing the computer results to them. For 1-D calculations, the standard shock-tube problems of Sod and Lax are chosen. A very strong shock-tube problem, with the initial density ratio of 400 to 1 and pressure ratio of 500 to 1, is also used to study the behavior of the two schemes. For 2-D calculations, the shock wave reflection problems are adopted for testing. The cases presented in this report include flows with Mach numbers of 2.9, 5.0, and 10.0.

Chang, Shih-Hung↗
NASA NTRS1989

Flux-split algorithms for the multi-dimensional Euler equations with real gases

Upwind algorithms are developed for the numerical solution of the multidimensional Euler equations for real gases. Flux-splitting methods are derived which account for a general equation of state. Approximations to the state equation based on physical arguments result in simplified algorithms which may be implemented into existing perfect-gas codes. Applications of the method to several high-Mach-number high-temperature flows are presented for two and three space dimensions.

Grossman, B.↗
NASA NTRS1989

Flux splitting algorithms for two-dimensional viscous flows with finite-rate chemistry

The Roe flux-difference splitting method has been extended to treat two-dimensional viscous flows with nonequilibrium chemistry. The derivations have avoided unnecessary assumptions or approximations. For spatial discretization, the second-order Roe upwind differencing is used for the convective terms and central differencing for the viscous terms. An upwind-based TVD scheme is applied to eliminate oscillations and obtain a sharp representation of discontinuities. A two-stage Runge-Kutta method is used to time integrate the discretized Navier-Stokes and species transport equations for the asymptotic steady solutions. The present method is then applied to two types of flows: the shock wave/boundary layer interaction problems and the jet in cross flows.

Shuen, Jian-Shun↗
NASA NTRS1989

Oscillatory flow with heat transfer in a square cavity

A computational study is presented for the flow inside an oscillatory cavity. The numerical scheme employs a semi-implicit, time-splitting method to integrate the two-dimensional full Navier-Stokes equations satisfying continuity to machine accuracy. The efficient use of direct solvers for the uncoupled momentum and pressure equations is demonstrated. The oscillatory cavity flow is studied considering the effects of heat transfer, Reynolds number, and oscillatory Stokes number.

Biringen, S.↗
NASA NTRS1990

Oscillatory flow with heat transfer in a square cavity

A computational study is presented for the flow inside an oscillatory cavity. The numerical scheme employs a semiimplicit, time-splitting method to integrate the two-dimensional full Navier-Stokes equations satisfying continuity to machine accuracy. The efficient use of direct solvers for the uncoupled momentum and pressure equations is demonstrated. The oscillatory cavity flow is studied considering the effects of heat transfer, Reynolds number and oscillatory Stokes number.

Danabasoglu, G.↗
NASA NTRS1990

Computation of convective flow with gravity modulation in rectangular cavities

In this work, a computational study is presented for the investigation of gravity modulation (g-jitter) effects in thermally driven cavity flows at terrestrial and microgravity environments. The two-dimensional, time-dependent Navier-Stokes equations are numerically integrated by a time-split method using direct matrix solvers. Computations at terrestrial gravity are utilized to assess the effects of adiabatic side-wall boundary conditions as well as the full nonlinearity of the governing equations on the sinusoidally forced Benard problem studied by Gresho and Sani. The low-g calculations focus on the establishment of critical frequency ranges and consider the effects of modulation direction and randomness. The applicability of linear analysis in the excitable frequency range at low g is also discussed.

Biringen, S.↗
NASA NTRS1989

Flux splitting algorithms for two-dimensional viscous flows with finite-rate chemistry

The Roe flux difference splitting method was extended to treat 2-D viscous flows with nonequilibrium chemistry. The derivations have avoided unnecessary assumptions or approximations. For spatial discretization, the second-order Roe upwind differencing is used for the convective terms and central differencing for the viscous terms. An upwind-based TVD scheme is applied to eliminate oscillations and obtain a sharp representation of discontinuities. A two-state Runge-Kutta method is used to time integrate the discretized Navier-Stokes and species transport equations for the asymptotic steady solutions. The present method is then applied to two types of flows: the shock wave/boundary layer interaction problems and the jet in cross flows.

Shuen, Jian-Shun↗
NASA NTRS1991

On the application of ENO scheme with subcell resolution to conservation laws with stiff source terms

Two approaches are used to extend the essentially non-oscillatory (ENO) schemes to treat conservation laws with stiff source terms. One approach is the application of the Strang time-splitting method. Here the basic ENO scheme and the Harten modification using subcell resolution (SR), ENO/SR scheme, are extended this way. The other approach is a direct method and a modification of the ENO/SR. Here the technique of ENO reconstruction with subcell resolution is used to locate the discontinuity within a cell and the time evolution is then accomplished by solving the differential equation along characteristics locally and advancing in the characteristic direction. This scheme is denoted ENO/SRCD (subcell resolution - characteristic direction). All the schemes are tested on the equation of LeVeque and Yee (NASA-TM-100075, 1988) modeling reacting flow problems. Numerical results show that these schemes handle this intriguing model problem very well, especially with ENO/SRCD which produces perfect resolution at the discontinuity.

Chang, Shih-Hung↗
NASA NTRS1990

Numerical simulation of spatially-evolving instability

A computational study of the spatial stability of plane Poiseuille flow is presented. The numerical scheme employs a time-splitting method to integrate the full Navier-Stokes equations using spectral collocation/finite-difference discretization on a non-staggered mesh. The eigenvalue decomposition procedure is applied for the solution of the Poisson equations using the capacitance matrix technique. The buffer domain method is incorporated for the outflow boundary conditions. The input perturbation velocities are obtained by solving the Orr-Sommerfeld equation for the nonlinear eigenvalue problem employing the companion matrix method. Computational results are compared with the linear theory for two-dimensional disturbances.

Danabasoglu, G.↗
NASA NTRS1992

Calculation of two-dimensional shear-driven cavity flows at high Reynolds numbers

The time-dependent Navier-Stokes equations are numerically integrated for two-dimensional incompressible viscous flow in a shear-driven square cavity. Using a time-splitting method and finite differences on a staggered mesh, the momentum and pressure equations are directly solved by a tensor product method where one finite difference direction is diagonalized by eigenvalue decomposition. The effects of increasing Reynolds number are studied and the developing boundary layer is captured by using a finely clustered mesh. At Re = 30,000 the flow is in a continuously developing unsteady regime. Power spectrum plots indicate that the unsteady flow oscillates with one fundamental frequency and exhibits some characteristics of transition between laminar and turbulent states.

Huser, A.↗
NASA NTRS1992

Numerical simulations using a dynamic solution-adaptive grid algorithm, with applications to unsteady internal flows

An investigation into the numerical simulation of unsteady flows is undertaken using a two-stage Runge-Kutta scheme coupled with the dynamic solution-adaptive grid algorithm developed by the authors. The inviscid fluxes are described by a modified Advective Upwind Split Method to eliminate the need for artificial dissipation. A well-documented numerical example containing moving discontinuities is presented that demonstrates the ability of the coupled grid/solver scheme to accurately capture unsteady flowfield phenomena. Applications are to a typical inlet diffuser configuration at Mach 3.0 with excessive back pressure inducing inlet unstart.

Benson, Rusty A.↗