Search NASASearch

SEARCH · Search NASA

Results for “Implicit 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 181 records · Page 10

Accuracy of a class of concurrent algorithms for transient finite element analysis

The accuracy of a new class of concurrent procedures for transient finite element analysis is examined. A phase error analysis is carried out which shows that wave retardation leading to unacceptable loss of accuracy may occur if a Courant condition based on the dimensions of the subdomains is violated. Numerical tests suggest that this Courant condition is conservative for typical structural applications and may lead to a marked increase in accuracy as the number of subdomains is increased. Theoretical speed-up ratios are derived which suggest that the algorithms under consideration can be expected to exhibit a performance superior to that of globally implicit methods when implemented on parallel machines.

Ortiz, Michael

Computation of aircraft component flow fields at transonic Mach numbers using a three-dimensional Navier-Stokes algorithm

A computer analysis was developed for calculating steady (or unsteady) three-dimensional aircraft component flow fields. This algorithm, called ENS3D, can compute the flow field for the following configurations: diffuser duct/thrust nozzle, isolated wing, isolated fuselage, wing/fuselage with or without integrated inlet and exhaust, nacelle/inlet, nacelle (fuselage) afterbody/exhaust jet, complete transport engine installation, and multicomponent configurations using zonal grid generation technique. Solutions can be obtained for subsonic, transonic, or hypersonic freestream speeds. The algorithm can solve either the Euler equations for inviscid flow, the thin shear layer Navier-Stokes equations for viscous flow, or the full Navier-Stokes equations for viscous flow. The flow field solution is determined on a body-fitted computational grid. A fully-implicit alternating direction implicit method is employed for the solution of the finite difference equations. For viscous computations, either a two layer eddy-viscosity turbulence model or the k-epsilon two equation transport model can be used to achieve mathematical closure.

Shrewsbury, George D.

Element-by-element and implicit-explicit finite element formulations for computational fluid dynamics

Preconditioner algorithms to reduce the computational effort in FEM analyses of large-scale fluid-dynamics problems are presented. A general model problem is constructed on the basis of the convection-diffusion equation and the two-dimensional vorticity/stream-function formulation of the Navier-Stokes equations; this problem is then analyzed using element-by-element, implicit-explicit, and adaptive implicit-explicit approximation schemes. Numerical results for the two-dimensional advection and rigid-body rotation of a cosine hill, flow past a circular cylinder, and driven cavity flow are presented in extensive graphs and shown to be in good agreement with those obtained using implicit methods.

Tezduyar, T. E.

Numerical simulation of flow through a two-strut scramjet inlet

A three-dimensional, Reynolds-averaged Navier-Stokes code has been used to numerically analyze flow through a two-strut, supersonic combustion ramjet (scramjet) inlet configuration. It solves the governing equations in full conservation form using either a fully explicit or explicit-implicit method. An algebraic, two-layer eddy-viscosity model is used for turbulent flow calculations. The analysis allows inclusion of end effects that are caused by the aft placement of the cowl on the underside of the inlet. A special grid has been developed to accommodate the struts embedded in the inlet flowfield. Detailed numerical results are presented here for the two-strut configuration, and a comparison is made with the available experimental results.

Kumar, Ajay

Evolution of midplate hotspot swells: Numerical solutions

The evolution of midplate hotspot swells on an oceanic plate moving over a hot, upwelling mantle plume is numerically simulated. The plume supplies a Gaussian-shaped thermal perturbation and thermally-induced dynamic support. The lithosphere is treated as a thermal boundary layer with a strongly temperature-dependent viscosity. The two fundamental mechanisms of transferring heat, conduction and convection, during the interaction of the lithosphere with the mantle plume are considered. The transient heat transfer equations, with boundary conditions varying in both time and space, are solved in cylindrical coordinates using the finite difference ADI (alternating direction implicit) method on a 100 x 100 grid. The topography, geoid anomaly, and heat flow anomaly of the Hawaiian swell and the Bermuda rise are used to constrain the models. Results confirm the conclusion of previous works that the Hawaiian swell can not be explained by conductive heating alone, even if extremely high thermal perturbation is allowed. On the other hand, the model of convective thinning predicts successfully the topography, geoid anomaly, and the heat flow anomaly around the Hawaiian islands, as well as the changes in the topography and anomalous heat flow along the Hawaiian volcanic chain.

Liu, Mian

Extension of a three-dimensional viscous wing flow analysis user's manual: VISTA 3-D code

Three-dimensional unsteady viscous effects can significantly influence the performance of fixed and rotary wing aircraft. These effects are important in both flows about helicopter rotors in forward flight and flows about three-dimensional (swept and tapered) supercritical wings. A computational procedure for calculating such flow field was developed. The procedure is based upon an alternating direction technique employing the Linearized Block Implicit method for solving three-dimensional viscous flow problems. In order to demonstrate the viability of this method, two- and three-dimensional problems are computed. These include the flow over a two-dimensional NACA 0012 airfoil under steady and oscillating conditions, and the steady, skewed, three-dimensional flow on a flat plate. Although actual three-dimensional flows over wings were not obtained, the ground work was laid for considering such flows. In this report a description of the computer code is given.

Weinberg, Bernard C.

Extension of a three-dimensional viscous wing flow analysis

Three-dimensional unsteady viscous effects can significantly influence the performance of fixed and rotary wing aircraft. These effects are important in both flows about helicopter rotors in forward flight and flows about 3-D (swept and tapered) supercritical wings. A computational procedure for calculating such flow field is developed, and therefore would be of great value in the design process as well as in understanding the corresponding flow phenomena. The procedure is based upon an alternating direction technique employing the Linearized Block Implicit method for solving 3-D viscous flow problems. In order to demonstrate the viability of this method, 2-D and 3-D problems are computed. These include the flow over a 2-D NACA 0012 airfoil under steady and oscillating conditions, and the steady, skewed, 3-D flow on a flat plate. Although actual 3-D flows over wings were not obtained, the ground work was laid for considering such flows. The description of the computational procedure and results are given.

Weinberg, Bernard C.

An expert system for setting time steps in dynamic finite element programs

An expert system, ETUDES - Expert Time integration control Using Deep and Surface Knowledge System, which addresses the determination of the timestep for time integration of linear structural dynamic equations is described. This timestep may also be applicable for a moderately nonlinear simulation of the same structure. The program also determines whether an explicit or implicit method is most efficient for the particular simulation. A production rule programming system written in OPS5 is used for the implementation of this prototype expert system. Issues relating to the expert system architecture for this application, such as knowledge representation and structure, as well as domain knowledge are discussed. The prototype is evaluated by measuring its performance in various benchmark model problems.

Ramirez, Martin R.

Implicit solvers for unstructured meshes

Implicit methods were developed and tested for unstructured mesh computations. The approximate system which arises from the Newton linearization of the nonlinear evolution operator is solved by using the preconditioned GMRES (Generalized Minimum Residual) technique. Three different preconditioners were studied, namely, the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over relaxation (SSOR). The preconditioners were optimized to have good vectorization properties. SSOR and ILU were also studied as iterative schemes. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also studied. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Venkatakrishnan, V.

Prediction of the Thrust Performance and the Flowfield of Liquid Rocket Engines

In an effort to improve the current solutions in the design and analysis of liquid propulsive engines, a computational fluid dynamics (CFD) model capable of calculating the reacting flows from the combustion chamber, through the nozzle to the external plume, was developed. The Space Shuttle Main Engine (SSME) fired at sea level, was investigated as a sample case. The CFD model, FDNS, is a pressure based, non-staggered grid, viscous/inviscid, ideal gas/real gas, reactive code. An adaptive upwinding differencing scheme is employed for the spatial discretization. The upwind scheme is based on fourth order central differencing with fourth order damping for smooth regions, and second order central differencing with second order damping for shock capturing. It is equipped with a CHMQGM equilibrium chemistry algorithm and a PARASOL finite rate chemistry algorithm using the point implicit method. The computed flow results and performance compared well with those of other standard codes and engine hot fire test data. In addition, the transient nozzle flowfield calculation was also performed to demonstrate the ability of FDNS in capturing the flow separation during the startup process.

Wang, T.-S.

Numerical simulation of icing, deicing, and shedding

An algorithm has been developed to numerically model the concurrent phenomena of two-dimensional transient heat transfer, ice accretion, ice shedding and ice trajectory which arise from the use of electrothermal pad. The Alternating Direction Implicit method is used to simultaneously solve the heat transfer and accretion equations occurring in the multilayered body covered with ice. In order to model the phase change between ice and water, a technique was used which assumes a phase for each node. This allows the equations to be linearized such that a direct solution is possible. This technique requires an iterative procedure to find the correct phase at each node. The computer program developed to find this solution has been integrated with the NASA-Lewis flow/trajectory code LEWICE.

Wright, W. B.

Implicit solvers for unstructured meshes

Implicit methods for unstructured mesh computations are developed and tested. The approximate system which arises from the Newton-linearization of the nonlinear evolution operator is solved by using the preconditioned generalized minimum residual technique. These different preconditioners are investigated: the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over-relaxation (SSOR). The preconditioners have been optimized to have good vectorization properties. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also investigated. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Venkatakrishnan, V.

Numerical analysis of a thermal deicer

An algorithm has been developed to numerically model the concurrent phenomena of two-dimensional transient heat transfer, ice accretion and ice shedding which arise from the use of an electrothermal pad. The Alternating Direction Implicit method is used to simultaneously solve the heat transfer and accretion equations occurring in a multilayered body covered with ice. In order to model the phase change between ice and water, a technique was used which assumes a phase for each node. This allows the equations to be linearized such that a direct solution is possible. This technique requires an iterative procedure to find the correct phase at each node. The computer program developed to find this solution has been integrated with the NASA/Lewis flow/trajectory code LEWICE.

Wright, W. B.

Simulation of 3-D shear flows around a nozzle-afterbody at high speeds

3D, compressible, unsteady, Reynolds-averaged Navier-Stokes equations are presently solved by a finite-volume and alternating-direction-implicit method in order to simulate supersonic and hypersonic turbulent shear flows. The effect of turbulence is incorporated via a modified Baldwin-Lomax eddy viscosity model which reflects the influence of high-speed compressibility, multiple walls, near-wall vortices, and turbulent memory effects, as well as local equilibrium effects. Attention is given to the simulation of the flow around the nozzle-afterbody of a generic, scramjet-propelled hypersonic vehicle; computed pressure distributions are consonant with experimental surface and off-surface flow surveys.

Baysal, Oktay

A nonlinear relaxation/quasi-Newton algorithm for the compressible Navier-Stokes equations

A highly efficient implicit method for the computation of steady, two-dimensional compressible Navier-Stokes flowfields is presented. The discretization of the governing equations is hybrid in nature, with flux-vector splitting utilized in the streamwise direction and central differences with flux-limited artificial dissipation used for the transverse fluxes. Line Jacobi relaxation is used to provide a suitable initial guess for a new nonlinear iteration strategy based on line Gauss-Seidel sweeps. The applicability of quasi-Newton methods as convergence accelerators for this and other line relaxation algorithms is discussed, and efficient implementations of such techniques are presented. Convergence histories and comparisons with experimental data are presented for supersonic flow over a flat plate and for several high-speed compression corner interactions. Results indicate a marked improvement in computational efficiency over more conventional upwind relaxation strategies, particularly for flowfields containing large pockets of streamwise subsonic flow.

Edwards, Jack R.

Natural convection between concentric spheres

A finite-difference solution for steady natural convective flow in a concentric spherical annulus with isothermal walls has been obtained. The stream function-vorticity formulation of the equations of motion for the unsteady axisymmetric flow is used; interest lying in the final steady solution. Forward differences are used for the time derivatives and second-order central differences for the space derivatives. The alternating direction implicit method is used for solution of the discretization equations. Local one-dimensional grid adaptation is used to resolve the steep gradients in some regions of the flow at large Rayleigh numbers. The break-up into multi-cellular flow is found at high Rayleigh numbers for air and water, and at significantly low Rayleigh numbers for liquid metals. Excellent agreement with previous experimental and numerical data is obtained.

Garg, Vijay K.

Navier-Stokes computation of compressible turbulent flows with a second order closure, part 1

A second order closure turbulence model for compressible flows is developed and implemented in a 2D Reynolds-averaged Navier-Stokes solver. From the beginning where a kappa-epsilon turbulence model was implemented in the bidiagonal implicit method of MACCORMACK (referred to as the MAC3 code) to the final stage of implementing a full second order closure in the efficient line Gauss-Seidel algorithm, numerous work was done, individually and collectively. Besides the collaboration itself, the final product of this work is a second order closure derived from the Launder, Reece, and Rodi model to account for near wall effects, which has been called FRAME model, which stands for FRench-AMerican-Effort. During the reporting period, two different problems were worked out. The first was to provide Ames researchers with a reliable compressible boundary layer code including a wide collection of turbulence models for quick testing of new terms, both in two equations and in second order closure (LRR and FRAME). The second topic was to complete the implementation of the FRAME model in the MAC5 code. The work related to these two different contributions is reported. dilatation in presence of stron shocks. This work, which has been conducted during a work at the Center for Turbulence Research with Zeman aimed also to cros-check earlier assumptions by Rubesin and Vandromme.

Haminh, Hieu

An efficient nonlinear relaxation technique for the three-dimensional, Reynolds-averaged Navier-Stokes equations

An efficient implicit method for the computation of steady, three-dimensional, compressible Navier-Stokes flowfields is presented. A nonlinear iteration strategy based on planar Gauss-Seidel sweeps is used to drive the solution toward a steady state, with approximate factorization errors within a crossflow plane reduced by the application of a quasi-Newton technique. A hybrid discretization approach is employed, with flux-vector splitting utilized in the streamwise direction and central differences with artificial dissipation used for the transverse fluxes. Convergence histories and comparisons with experimental data are presented for several 3-D shock-boundary layer interactions. Both laminar and turbulent cases are considered, with turbulent closure provided by a modification of the Baldwin-Barth one-equation model. For the problems considered (175,000-325,000 mesh points), the algorithm provides steady-state convergence in 900-2000 CPU seconds on a single processor of a Cray Y-MP.

Edwards, Jack R.