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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 1: Analysis description

A new computer code was developed to solve the two-dimensional or axisymmetric, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 1 is the Analysis Description, and describes in detail the governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models.

Towne, Charles E.↗
NASA NTRS1997

A Three-Dimensional Linearized Unsteady Euler Analysis for Turbomachinery Blade Rows

A three-dimensional, linearized, Euler analysis is being developed to provide an efficient unsteady aerodynamic analysis that can be used to predict the aeroelastic and aeroacoustic responses of axial-flow turbo-machinery blading.The field equations and boundary conditions needed to describe nonlinear and linearized inviscid unsteady flows through a blade row operating within a cylindrical annular duct are presented. A numerical model for linearized inviscid unsteady flows, which couples a near-field, implicit, wave-split, finite volume analysis to a far-field eigenanalysis, is also described. The linearized aerodynamic and numerical models have been implemented into a three-dimensional linearized unsteady flow code, called LINFLUX. This code has been applied to selected, benchmark, unsteady, subsonic flows to establish its accuracy and to demonstrate its current capabilities. The unsteady flows considered, have been chosen to allow convenient comparisons between the LINFLUX results and those of well-known, two-dimensional, unsteady flow codes. Detailed numerical results for a helical fan and a three-dimensional version of the 10th Standard Cascade indicate that important progress has been made towards the development of a reliable and useful, three-dimensional, prediction capability that can be used in aeroelastic and aeroacoustic design studies.

Montgomery, Matthew D.↗
NASA NTRS1999

Development of a Linearized Unsteady Euler Analysis with Application to Wake/Blade-Row Interactions

A three-dimensional, linearized, Euler analysis is being developed to provide a comprehensive and efficient unsteady aerodynamic analysis for predicting the aeroacoustic and aeroelastic responses of axial-flow turbomachinery blading. The mathematical models needed to describe nonlinear and linearized, inviscid, unsteady flows through a blade row operating within a cylindrical annular duct are presented in this report. A numerical model for linearized inviscid unsteady flows, which couples a near-field, implicit, wave-split, finite volume analysis to far-field eigen analyses, is also described. The linearized aerodynamic and numerical models have been implemented into the three-dimensional unsteady flow code, LINFLUX. This code is applied herein to predict unsteady subsonic flows driven by wake or vortical excitations. The intent is to validate the LINFLUX analysis via numerical results for simple benchmark unsteady flows and to demonstrate this analysis via application to a realistic wake/blade-row interaction. Detailed numerical results for a three-dimensional version of the 10th Standard Cascade and a fan exit guide vane indicate that LINFLUX is becoming a reliable and useful unsteady aerodynamic prediction capability that can be applied, in the future, to assess the three-dimensional flow physics important to blade-row, aeroacoustic and aeroelastic responses.

Verdon, Joseph M.↗
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.↗
NASA NTRS1990

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 2: User's guide

A new computer code was developed to solve the two-dimensional or axisymmetric, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 2 is the User's Guide, and describes the program's general features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

Towne, Charles E.↗
NASA NTRS1990

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference

A new computer code was developed to solve the 2-D or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating-direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 3 is the Programmer's Reference, and describes the program structure, the FORTRAN variables stored in common blocks, and the details of each subprogram.

Towne, Charles E.↗
NASA NTRS1993

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 1: Analysis description

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. The governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models are described in detail.

Towne, Charles E.↗
NASA NTRS1993

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 1: Analysis description

A computer code called Proteus 3D has been developed to solve the three dimensional, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort has been to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation have been emphasized. The governing equations are solved in generalized non-orthogonal body-fitted coordinates by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. It describes in detail the governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models.

Towne, Charles E.↗
NASA NTRS1993

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 2: User's guide

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the User's Guide, and describes the program's features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

Towne, Charles E.↗
NASA NTRS1993

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 2: User's guide

A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This User's Guide describes the program's features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

Towne, Charles E.↗
NASA NTRS1993

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference

A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.

Towne, Charles E.↗
NASA NTRS1993

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 3: Programmer's reference

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.

Towne, Charles E.↗
DOE OSTI2025

Ten-moment fluid modeling of the Weibel instability

We investigate the one-dimensional non-relativistic Weibel instability through the capture of anisotropic pressure tensor dynamics using an implicit 10-moment fluid model that employs the electromagnetic Darwin approximation. The results obtained from the 10-moment model are compared with an implicit particle-in-cell simulation. The linear growth rates obtained from the numerical simulations are in good agreement with the theoretical fluid and kinetic dispersion relations. The fluid dispersion relations are derived using Maxwell’s equations and the Darwin approximation. We also show that the magnetohydrodynamic approximation can be used to model the Weibel instability if one accounts for an anisotropic pressure tensor and unsteady terms in the generalised Ohm’s law. In addition, we develop a preliminary theory for the saturation magnetic field strength of the Weibel instability, showing good agreement with the numerical results.

Kuldinow, D. A. (ORCID:0000000319730196)↗
NASA NTRS1995

An Adaptive Semi-Implicit Scheme for Simulations of Unsteady Viscous Compressible Flows

A numerical scheme for simulation of unsteady, viscous, compressible flows is considered. The scheme employs an explicit discretization of the inviscid terms of the Navier-Stokes equations and an implicit discretization of the viscous terms. The discretization is second order accurate in both space and time. Under appropriate assumptions, the implicit system of equations can be decoupled into two linear systems of reduced rank. These are solved efficiently using a Gauss-Seidel method with multigrid convergence acceleration. When coupled with a solution-adaptive mesh refinement technique, the hybrid explicit-implicit scheme provides an effective methodology for accurate simulations of unsteady viscous flows. The methodology is demonstrated for both body-fitted structured grids and for rectangular (Cartesian) grids.

Steinthorsson, Erlendur↗
NASA NTRS1997

Computational Considerations for the Simulation of Discontinuous Flows

The numerical study of aeroacoustic problems places stringent demands on the choice of a computational algorithm, because it requires the ability to propagate disturbances of small amplitude and short wavelength. The demands are particularly high when shock waves are involved, because the chosen algorithm must also resolve discontinuities in the solution. In a previous work the capabilities and deficiencies of shock-capturing methods for aeroacoustic problems were demonstrated using a high-order essentially nonoscillatory (ENO) numerical method. It was shown that first-order results are obtained when simulating time-dependent flows with discontinuities. The present study reaffirms this conclusion by comparing the ENO results with those obtained using a conventional linear scheme. A sixth-order-accurate compact implicit finite difference scheme is used to investigate various discontinuous flows. The design order of accuracy is achieved in the smooth regions of a steady-state, quasi-one-dimensional Euler test case, as well as in the time-dependent Burgers' equation. However, in the unsteady Euler sound-shock interaction, first-order results are obtained downstream of the shock. A comparison is made between the linear and nonlinear results, noting the advantages of each method. A discontinuous linear model problem is then used to identify the cause of the first-order results. Here, the nature of the solution error is quantified as being predominantly a numerical phase shift, and a post-processing procedure is demonstrated which increases the solution accuracy downstream of the discontinuity to second-order.

Carpenter Mark H.↗
NASA NTRS1981

Development of an unsteady aerodynamic analysis for finite-deflection subsonic cascades

An unsteady potential flow analysis, which accounts for the effects of blade geometry and steady turning, was developed to predict aerodynamic forces and moments associated with free vibration or flutter phenomena in the fan, compressor, or turbine stages of modern jet engines. Based on the assumption of small amplitude blade motions, the unsteady flow is governed by linear equations with variable coefficients which depend on the underlying steady low. These equations were approximated using difference expressions determined from an implicit least squares development and applicable on arbitrary grids. The resulting linear system of algebraic equations is block tridiagonal, which permits an efficient, direct (i.e., noniterative) solution. The solution procedure was extended to treat blades with rounded or blunt edges at incidence relative to the inlet flow.

Verdon, J. M.↗
NASA NTRS1987

Efficient solutions to the Euler equations for supersonic flow with embedded subsonic regions

A line Gauss-Seidel (LGS) relaxation algorithm in conjunction with a one-parameter family of upwind discretizations of the Euler equations in two dimensions is described. Convergence of the basic algorithm to the steady state is quadratic for fully supersonic flows and is linear for other flows. This is in contrast to the block alternating direction implicit methods (either central or upwind differenced) and the upwind biased relaxation schemes, all of which converge linearly, independent of the flow regime. Moreover, the algorithm presented herein is easily coupled with methods to detect regions of subsonic flow embedded in supersonic flow. This allows marching by lines in the supersonic regions, converging each line quadratically, and iterating in the subsonic regions, and yields a very efficient iteration strategy. Numerical results are presented for two-dimensional supersonic and transonic flows containing oblique and normal shock waves which confirm the efficiency of the iteration strategy.

Walters, Robert W.↗
DOE OSTI2020

A fast implicit solver for semiconductor models in one space dimension

Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in semiconductor devices under a low-density assumption. At each implicit time step, the discretized system is formulated as a fixed-point problem, which can then be solved with a variety of methods. A key algorithmic component in all the approaches considered here is a recently developed sweeping algorithm for Vlasov-Poisson systems. A synthetic acceleration scheme has been implemented to accelerate the convergence of iterative solvers by using the solution to a drift-diffusion equation as a preconditioner. The performance of four iterative solvers and their accelerated variants has been compared on problems modeling semiconductor devices with various electron mean-free-path.

97 MATHEMATICS AND COMPUTING↗