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At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Higher-order accurate Osher schemes with application to compressible boundary layer stability

Two fourth order accurate Osher schemes are presented which maintain higher order accuracy on nonuniform grids. They use either a conservative finite difference or finite volume discretization. Both methods are successfully used for direct numerical simulations of flat plate boundary layer instability at different Mach numbers. Results of growth rates of Tollmien-Schlichting waves compare well with direct simulations of incompressible flow and for compressible flow with results obtained by solving the parabolic stability equations.

Vandervegt, J. J. W.↗
NASA NTRS1990

Numerical simulation of rarefied gas flow through a slit

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas from one reservoir to another through a two-dimensional slit. The cases considered are for hard vacuum downstream pressure, finite pressure ratios, and isobaric pressure with thermal diffusion, which are not well established in spite of the simplicity of the flow field. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, three kinds of collision sampling techniques, the time counter (TC) method, the null collision (NC) method, and the no time counter (NTC) method, are used.

Keith, Theo G., Jr.↗
NASA NTRS1985

A computer analysis program for interfacing thermal and structural codes

A software package has been developed to transfer three-dimensional transient thermal information accurately, efficiently, and automatically from a heat transfer analysis code to a structural analysis code. The code is called three-dimensional TRansfer ANalysis Code to Interface Thermal and Structural codes, or 3D TRANCITS. TRANCITS has the capability to couple finite difference and finite element heat transfer analysis codes to linear and nonlinear finite element structural analysis codes. TRANCITS currently supports the output of SINDA and MARC heat transfer codes directly. It will also format the thermal data output directly so that it is compatible with the input requirements of the NASTRAN and MARC structural analysis codes. Other thermal and structural codes can be interfaced using the transfer module with the neutral heat transfer input file and the neutral temperature output file. The transfer module can handle different elemental mesh densities for the heat transfer analysis and the structural analysis.

Thompson, R. L.↗
NASA NTRS1985

A computer analysis program for interfacing thermal and structural codes

A software package has been developed to transfer three-dimensional transient thermal information accurately, efficiently, and automatically from a heat transfer analysis code to a structural analysis code. The code is called three-dimensional TRansfer ANalysis Code to Interface Thermal and Structural codes, or 3D TRANCITS. TRANCITS has the capability to couple finite difference and finite element heat transfer analysis codes to linear and nonlinear finite element structural analysis codes. TRANCITS currently supports the output of SINDA and MARC heat transfer codes directly. It will also format the thermal data output directly so that it is compatible with the input requirements of the NASTRAN and MARC structural analysis codes. Other thermal and structural codes can be interfaced using the transfer module with the neutral heat transfer input file and the neutral temperature output file. The transfer module can handle different elemental mesh densities for the heat transfer analysis and the structural analysis.

Thompson, R. L.↗
NASA NTRS1992

FDDO and DSMC analyses of rarefied gas flow through 2D nozzles

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas expanding through a two-dimensional nozzle and into a surrounding low-density environment. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, the variable hard sphere model is used as a molecular model and the no time counter method is employed as a collision sampling technique. The results of both the FDDO and the DSMC methods show good agreement. The FDDO method requires less computational effort than the DSMC method by factors of 10 to 40 in CPU time, depending on the degree of rarefaction.

Chung, Chan-Hong↗
NASA NTRS1995

Large-eddy simulation of flow past a circular cylinder

Some of the most challenging applications of large-eddy simulation are those in complex geometries where spectral methods are of limited use. For such applications more conventional methods such as finite difference or finite element have to be used. However, it has become clear in recent years that dissipative numerical schemes which are routinely used in viscous flow simulations are not good candidates for use in LES of turbulent flows. Except in cases where the flow is extremely well resolved, it has been found that upwind schemes tend to damp out a significant portion of the small scales that can be resolved on the grid. Furthermore, it has been found that even specially designed higher-order upwind schemes that have been used successfully in the direct numerical simulation of turbulent flows produce too much dissipation when used in conjunction with large-eddy simulation. The objective of the current study is to perform a LES of incompressible flow past a circular cylinder at a Reynolds number of 3900 using a solver which employs an energy-conservative second-order central difference scheme for spatial discretization and compare the results obtained with those of Beaudan & Moin (1994) and with the experiments in order to assess the performance of the central scheme for this relatively complex geometry.

Mittal, R.↗
DOE OSTI2021

Butterfly Factorization Via Randomized Matrix-Vector Multiplications

This paper presents an adaptive randomized algorithm for computing the butterfly factorization of an m × n matrix with m ≈ n provided that both the matrix and its transpose can be rapidly applied to arbitrary vectors. The resulting factorization is composed of O(log n) sparse factors, each containing O(n) nonzero entries. The factorization can be attained using O(n 3/2 log n) computation and O(n log n) memory resources. Furthermore, the proposed algorithm can be implemented in parallel and can apply to matrices with strong or weak admissibility conditions arising from surface integral equation solvers as well as multi-frontal-based finite-difference, finite-element, or finite-volume solvers. A distributed-memory parallel implementation of the algorithm demonstrates excellent scaling behavior.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Sparse Approximate Multifrontal Factorization with Butterfly Compression for High-Frequency Wave Equations

In this work, we present a fast and approximate multifrontal solver for large-scale sparse linear systems arising from finite-difference, finite-volume or finite-element discretization of high-frequency wave equations. The proposed solver leverages the butterfly algorithm and its hierarchical matrix extension for compressing and factorizing large frontal matrices via graph-distance guided entry evaluation or randomized matrix-vector multiplication-based schemes. Complexity analysis and numerical experiments demonstrate $\mathcal{O}(N\log^2 N)$ computation and $\mathcal{O}(N)$ memory complexity when applied to an $N\times N$ sparse system arising from 3D high-frequency Helmholtz and Maxwell problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part I: the Linear Setting

Fully implicit Runge--Kutta (IRK) methods have many desirable properties as time integration schemes in terms of accuracy and stability, but high-order IRK methods are not commonly used in practice with numerical PDEs due to the difficulty of solving the stage equations. This paper introduces a theoretical and algorithmic preconditioning framework for solving the systems of equations that arise from IRK methods applied to linear numerical PDEs (without algebraic constraints). Additionally, this framework also naturally applies to discontinuous Galerkin discretizations in time. Under quite general assumptions on the spatial discretization that yield stable time integration, the preconditioned operator is proven to have condition number bounded by a small, order-one constant, independent of the spatial mesh and time-step size, and with only weak dependence on number of stages/polynomial order; for example, the preconditioned operator for 10th-order Gauss IRK has condition number less than two, independent of the spatial discretization and time step. The new method can be used with arbitrary existing preconditioners for backward Euler-type time-stepping schemes and is amenable to the use of three-term recursion Krylov methods when the underlying spatial discretization is symmetric. The new method is demonstrated to be effective on various high-order finite-difference and finite element discretizations of linear parabolic and hyperbolic problems, demonstrating fast, scalable solution of up to 10th-order accuracy. The new method consistently outperforms existing block preconditioning approaches, and in several cases, the new method can achieve 4th-order accuracy using Gauss integration with roughly half the number of preconditioner applications and wallclock time as required using standard diagonally IRK methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1972

Analysis of the transient response of shell structures by numerical methods.

This paper examines some basic considerations underlying dynamic shell response analysis and the impact of these considerations upon the practical aspects of solution by numerical methods. Emphasis is placed on the solution of linear problems. The present states of development of the finite difference and finite element methods are reviewed, and techniques for the treatment of temporal variation are discussed. An examination is made of the frequency parameters characteristic of thin shell theory, applied excitations, and spatial mesh geometries, and the significance of these parameters with respect to computational convergence is illustrated.

Geers, T. L.↗
NASA NTRS1978

Numerical spatial marching techniques for estimating duct attenuation and source pressure profiles

A numerical method was developed that could predict the pressure distribution of a ducted source from far field pressure inputs. Using an initial value formulation, the two-dimensional homogeneous Helmholtz wave equation (no steady flow) was solved using explicit marching techniques. The Von Neumann method was used to develop relationships which describe how sound frequency and grid spacing effect numerical stability. At the present time, stability considerations limit the approach to high frequency sound. Sample calculations for both hard and soft wall ducts compare favorably to known boundary value solutions. In addition, assuming that reflections in the duct are small, this initial value approach was successfully used to determine the attenuation of a straight soft wall duct. Compared to conventional finite difference or finite element boundary value approaches, the numerical marching technique is orders of magnitude shorter in computation time and required computer storage and can be easily employed in problems involving high frequency sound.

Baumeister, K. J.↗
NASA NTRS1978

Numerical spatial marching techniques for estimating duct attenuation and source pressure profiles

A numerical method is developed that could predict the pressure distribution of a ducted source from far-field pressure inputs. Using an initial value formulation, the two-dimensional homogeneous Helmholtz wave equation (no steady flow) is solved using explicit marching techniques. The Von Neumann method is used to develop relationships which describe how sound frequency and grid spacing effect numerical stability. At the present time, stability considerations limit the approach to high frequency sound. Sample calculations for both hard and soft wall ducts compare favorably to known boundary value solutions. In addition, assuming that reflections in the duct are small, this initial value approach is successfully used to determine the attenuation of a straight soft wall duct. Compared to conventional finite difference or finite element boundary value approaches, the numerical marching technique is orders of magnitude shorter in computation time and required computer storage and can be easily employed in problems involving high frequency sound.

Baumeister, K. J.↗
NASA NTRS1979

Computer analysis of shells of revolution using asymptotic results

It is suggested that asymptotic results for the behavior of thin shells can be incorporated in a general computer code for the analysis of a complex shell structure. The advantage when compared to existing finite difference or finite element codes is a substantial reduction in computational labor with the capability of working to a specified level of accuracy. A reduction in user preparation time and dependance on user judgment is also gained, since mesh spacing can be internally generated. The general theory is described in this paper, as well as the implementation in the computer code FAST 1 (Functional Algorithm for Shell Theory) for the analysis of the general axisymmetric shell structure with axisymmetric loading.

Steele, C. R.↗
NASA NTRS1980

Numerical techniques in linear duct acoustics

Both finite difference and finite element analyses of small amplitude (linear) sound propagation in straight and variable area ducts with flow, as might be found in a typical turboject engine duct, muffler, or industrial ventilation system, are reviewed. Both steady state and transient theories are discussed. Emphasis is placed on the advantages and limitations associated with the various numerical techniques. Examples of practical problems are given for which the numerical techniques have been applied.

Baumeister, K. J.↗
NASA NTRS1979

Spectral methods for problems in complex geometries

Techniques that permit the efficient application of spectral methods to solve problems in nearly arbitrary geometries are presented. These methods were found to be viable alternatives to finite difference and finite element processes. The spectral methods applied are extensions of the standard techniques of separation of variables to the solution of arbitrarily complicated problems.

Orszag, S. A.↗
NASA NTRS1980

Numerical techniques in linear duct acoustics - A status report

A review is presented covering both finite difference and finite element analysis of small amplitude (linear) sound propagation in straight and variable area ducts with flow, as might be found in a typical turbojet engine duct, muffer, or industrial ventilation system. Both 'steady' state and transient theories are discussed. Emphasis is placed on the advantages and limitations associated with the various numerical techniques. Examples of practical problems are given for which the numerical techniques have been applied.

Baumeister, K. J.↗