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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
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Multiblock, Multigrid Solution Of Euler Equations

Method of numerical solution of Euler equations of three-dimensional flow of compressible fluid involves combination of multiblock and multigrid strategies. In multiblock strategy, flow field divided, into multiple smaller, more computationally-convenient zones and computational grid fitted to applicable flow boundaries generated in each block. In multigrid strategy used here, different quantities computed, variously, on finer or coarser grids. Minimizing cost of computation by using fewest grid points yielding acceptably accurate values of affected variable. Multigrid strategy found effective in accelerating convergence to steady state, while multiblock strategy provides geometric flexibility.

Melson, N. Duane↗
NASA NTRS1994

Numerical Simulation of the Instability of an Inviscid Liquid Jet in a Coflowing Compressible Airstream

The nonlinear interfacial instability of a liquid jet in a coflowing compressible airstream is studied numerically. A high-resolution scheme which has second-order accuracy in space and time is coupled with a Lagrangian marker particle algorithm to visualize the large-scale motion of the interfaces in compressible flow. A numerical algorithm based on an approximate equation of state of a compressible liquid is developed to allow this two-fluid system to be governed by the nonlinear unsteady Euler equations in conservative form. The initial growth of small disturbances given by the simulations agrees well with linear theory. The process of jet disruption in compressible flow is demonstrated to consist of the formation of liquid spikes, interweaving of the gas and liquid and stretching and detachment of the liquid main center core.

Li, H. -S.↗
NASA NTRS1988

Accurate multigrid solution of the Euler equations on unstructured and adaptive meshes

A method for accurately solving inviscid compressible flow in the subcritical and supercritical regimes about complex configurations is presented. The method is based on the use of unstructured triangular meshes in two dimensions, and special emphasis is placed on the accuracy and efficiency of the solutions. High accuracy is achieved by careful scaling of the artificial dissipation terms, and by reformulating the inner and outer boundary conditions for both the convective and dissipative operators. An adaptive grid refinement strategy is presented which enhances the solution accuracy for complex flows. When coupled with an unstructured multigrid algorithm, this method is shown to produce an efficient solver for flows about arbitrary configurations.

Mavriplis, Dimitri J.↗
NASA NTRS1988

Accurate multigrid solution of the Euler equations on unstructured and adaptive meshes

A method for accurately solving inviscid compressible flow in the subcritical and supercritical regimes about complex configurations is presented. The method is based on the use of unstructured triangular meshes in two dimensions, and special emphasis is placed on the accuracy and efficiency of the solutions. High accuracy is achieved by careful scaling of the artificial dissipation terms, and by reformulating the inner and outer boundary conditions for both the convective and dissipative operators. An adaptive grid refinement strategy is presented which enhances the solution accuracy for complex flows. When coupled with an unstructured multigrid algorithm, this method is shown to produce an efficient solver for flows about artibrary configurations.

Mavriplis, Dimitri J.↗
NASA NTRS1978

Lagrangian computation of inviscid compressible flows

A Lagrangian method is developed to solve the Euler equations of gas dynamics. The solution of the equations is obtained by a numerical computation with the well-known Flux-Corrected-Transport (FCT) numerical method. This procedure is modified so that the boundary treatment is accurate and relatively simple. Shock waves and other flow discontinuities are captured monotonically without any type of fitting procedures. The Lagrangian method is employed so that the problem of mesh generation is completely avoided. The method is applicable to all Mach numbers except the low subsonic range where compressibility effects are small. The method is applied to a one-dimensional Riemann problem (shock tube) and to a two-dimensional supersonic channel flow with reflecting shock waves.

Klopfer, G. H.↗
NASA NTRS1988

Three-dimensional unsteady transonic viscous-inviscid interaction using the Euler and boundary-layer equations

The objective of this study is the development of a numerical technique which can provide three-dimensional, time-accurate, compressible, turbulent flow solutions in a practical and relatively economical way. The approach taken is that of the method of viscous-inviscid interaction. The Euler equations are assumed to govern the outer inviscid portion of the flow, and the viscous layer close to the solid wall is described by a set of integral boundary-layer equations. The viscous solutions are obtained in a direct fashion with a weighted-average phase error scheme. The method of equivalent sources is used for viscous-inviscid coupling. Steady-state and unsteady computations for an AGARD airfoil and a wing show that satisfactory engineering solutions can be obtained for attached, high Reynolds number flows using this method. Quasi-unsteady interactions are shown to produce similar results to those provided by true-unsteady interactions. Considerable computer resources can be saved for some cases by using quasi-unsteady interactions.

Whitfield, David L.↗
NASA NTRS1984

Time dependent computation of the Euler equations for designing 2-D cascades, including the case of transonic shock free design

A numerical method to solve the inverse problem for airfoil cascades is described. The case of compressible, inviscid flow is considered. The proposed method is based on the finite difference approximation of the time-dependent Euler equations. Numerical examples show the capability of the method to design subsonic or transonic shockless blades.

Zannetti, L.↗
NASA NTRS1993

Directionally adaptive finite element method for multidimensional Euler and Navier-Stokes equations

A directionally adaptive finite element method for multidimensional compressible flows is presented. Quadrilateral and hexahedral elements are used because they have several advantages over triangular and tetrahedral elements. Unlike traditional methods that use quadrilateral/hexahedral elements, our method allows an element to be divided in each of the three directions in 3D and two directions in 2D. Some restrictions on mesh structure are found to be necessary, especially in 3D. The refining and coarsening procedures, and the treatment of constraints are given. A new implementation of upwind schemes in the constrained finite element system is presented. Some example problems, including a Mach 10 shock interaction with the walls of a 2D channel, a 2D viscous compression corner flow, and inviscid and viscous 3D flows in square channels, are also shown.

Tan, Zhiqiang↗
NASA NTRS1991

h-p adaptive finite element methods in computational fluid dynamics

The principal ideas of h-p adaptive finite element methods for fluid dynamics problems are discussed. Applications include acoustics, compressible Euler and both compressible and incompressible Navier-Stokes equations. Several numerical examples illustrate the presented concepts.

Oden, J. T.↗
NASA NTRS1997

Effective Control of Computationally Simulated Wing Rock in Subsonic Flow

The unsteady compressible, full Navier-Stokes (NS) equations and the Euler equations of rigid-body dynamics are sequentially solved to simulate the delta wing rock phenomenon. The NS equations are solved time accurately, using the implicit, upwind, Roe flux-difference splitting, finite-volume scheme. The rigid-body dynamics equations are solved using a four-stage Runge-Kutta scheme. Once the wing reaches the limit-cycle response, an active control model using a mass injection system is applied from the wing surface to suppress the limit-cycle oscillation. The active control model is based on state feedback and the control law is established using pole placement techniques. The control law is based on the feedback of two states: the roll-angle and roll velocity. The primary model of the computational applications consists of a 80 deg swept, sharp edged, delta wing at 30 deg angle of attack in a freestream of Mach number 0.1 and Reynolds number of 0.4 x 10(exp 6). With a limit-cycle roll amplitude of 41.1 deg, the control model is applied, and the results show that within one and one half cycles of oscillation, the wing roll amplitude and velocity are brought to zero.

Kandil, Osama A.↗
NASA NTRS1997

CFD Analysis and Design Optimization Using Parallel Computers

A versatile and efficient multi-block method is presented for the simulation of both steady and unsteady flow, as well as aerodynamic design optimization of complete aircraft configurations. The compressible Euler and Reynolds Averaged Navier-Stokes (RANS) equations are discretized using a high resolution scheme on body-fitted structured meshes. An efficient multigrid implicit scheme is implemented for time-accurate flow calculations. Optimum aerodynamic shape design is achieved at very low cost using an adjoint formulation. The method is implemented on parallel computing systems using the MPI message passing interface standard to ensure portability. The results demonstrate that, by combining highly efficient algorithms with parallel computing, it is possible to perform detailed steady and unsteady analysis as well as automatic design for complex configurations using the present generation of parallel computers.

Martinelli, Luigi↗
NASA NTRS1986

A second-order accurate kinetic-theory-based method for inviscid compressible flows

An upwind method for the numerical solution of the Euler equations is presented. This method, called the kinetic numerical method (KNM), is based on the fact that the Euler equations are moments of the Boltzmann equation of the kinetic theory of gases when the distribution function is Maxwellian. The KNM consists of two phases, the convection phase and the collision phase. The method is unconditionally stable and explicit. It is highly vectorizable and can be easily made total variation diminishing for the distribution function by a suitable choice of the interpolation strategy. The method is applied to a one-dimensional shock-propagation problem and to a two-dimensional shock-reflection problem.

Deshpande, Suresh M.↗
NASA NTRS1987

Adaptive finite element methods for high-speed compressible flows

An adaptive finite element algorithm for solving the unsteady Euler equations is described. The finite element algorithm is based on a Taylor/Galerkin formulation and uses a very fast and efficient data structure to refine and unrefine the grid in order to optimize the approximation. A general version of the method which can be applied to moving grids with sliding interfaces is given, and results for a transient supersonic calculation of rotor-stator interaction are presented.

Oden, J. T.↗
NASA NTRS1991

Diagonal implicit multigrid solution of compressible turbulent flows

The Caughey (1988) multigrid diagonal implicit algorithm for Euler equations is extended to solve the two-dimensional thin layer Navier-Stokes equations for turbulent transonic flows. To further accelerate convergence to a steady state, the implicit scheme is used within the multigrid method. Results are presented for transonic flows past airfoils, and the flow-field results are compared with other computational data and experiments demonstrating the accuracy of the method.

Varma, R. R.↗
NASA NTRS1990

Two-dimensional Euler and Navier-Stokes Time accurate simulations of fan rotor flows

Two numerical methods are presented which describe the unsteady flow field in the blade-to-blade plane of an axial fan rotor. These methods solve the compressible, time-dependent, Euler and the compressible, turbulent, time-dependent, Navier-Stokes conservation equations for mass, momentum, and energy. The Navier-Stokes equations are written in Favre-averaged form and are closed with an approximate two-equation turbulence model with low Reynolds number and compressibility effects included. The unsteady aerodynamic component is obtained by superposing inflow or outflow unsteadiness to the steady conditions through time-dependent boundary conditions. The integration in space is performed by using a finite volume scheme, and the integration in time is performed by using k-stage Runge-Kutta schemes, k = 2,5. The numerical integration algorithm allows the reduction of the computational cost of an unsteady simulation involving high frequency disturbances in both CPU time and memory requirements. Less than 200 sec of CPU time are required to advance the Euler equations in a computational grid made up of about 2000 grid during 10,000 time steps on a CRAY Y-MP computer, with a required memory of less than 0.3 megawords.

Boretti, A. A.↗
NASA NTRS1985

Algorithms for the Euler and Navier-Stokes equations for supercomputers

The steady state Euler and Navier-Stokes equations are considered for both compressible and incompressible flow. Methods are found for accelerating the convergence to a steady state. This acceleration is based on preconditioning the system so that it is no longer time consistent. In order that the acceleration technique be scheme-independent, this preconditioning is done at the differential equation level. Applications are presented for very slow flows and also for the incompressible equations.

Turkel, E.↗
NASA NTRS1985

Algorithms for the Euler and Navier-Stokes equations for supercomputers

The steady state Euler and Navier-Stokes equations are considered for both compressible and incompressible flow. Methods are found for accelerating the convergence to a steady state. This acceleration is based on preconditioning the system so that it is no longer time consistent. In order that the acceleration technique be scheme-independent, this preconditioning is done at the differential equation level. Applications are presented for very slow flows and also for the incompressible equations.

Turkel, E.↗
NASA NTRS1996

Refinement Of Hexahedral Cells In Euler Flow Computations

Topologically Independent Grid, Euler Refinement (TIGER) computer program solves Euler equations of three-dimensional, unsteady flow of inviscid, compressible fluid by numerical integration on unstructured hexahedral coordinate grid refined where necessary to resolve shocks and other details. Hexahedral cells subdivided, each into eight smaller cells, as needed to refine computational grid in regions of high flow gradients. Grid Interactive Refinement and Flow-Field Examination (GIRAFFE) computer program written in conjunction with TIGER program to display computed flow-field data and to assist researcher in verifying specified boundary conditions and refining grid.

Melton, John E.↗