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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

Two-Dimensional Ffowcs Williams/Hawkings Equation Solver

FWH2D is a Fortran 90 computer program that solves a two-dimensional (2D) version of the equation, derived by J. E. Ffowcs Williams and D. L. Hawkings, for sound generated by turbulent flow. FWH2D was developed especially for estimating noise generated by airflows around such approximately 2D airframe components as slats. The user provides input data on fluctuations of pressure, density, and velocity on some surface. These data are combined with information about the geometry of the surface to calculate histories of thickness and loading terms. These histories are fast-Fourier-transformed into the frequency domain. For each frequency of interest and each observer position specified by the user, kernel functions are integrated over the surface by use of the trapezoidal rule to calculate a pressure signal. The resulting frequency-domain signals are inverse-fast-Fourier-transformed back into the time domain. The output of the code consists of the time- and frequency-domain representations of the pressure signals at the observer positions. Because of its approximate nature, FWH2D overpredicts the noise from a finite-length (3D) component. The advantage of FWH2D is that it requires a fraction of the computation time of a 3D Ffowcs Williams/Hawkings solver.

Lockard, David P.↗
NASA NTRS1981

An implicit marching procedure for the treatment of supersonic flow fields using the conservative full potential equation

A new aerodynamic prediction technique based on the conservative full potential equation is developed for the treatment of supersonic flow fields. This new technique bridges the gap between simplistic linear theory methods and complex Euler solvers. A novel local density linearization concept and a second order accurate retarded density scheme, both producing the correct artificial viscosity, are introduced in developing an implicit marching scheme for solving the scalar phi. The method produces results that compare well with Euler solvers and requires an order of magnitude less computer time and significantly less computer memory over existing nonlinear codes. The scalar phi formulation can be extended to handle subsonic pockets in the marching direction and also is suitable for developing inverse procedures where the shape corresponding to a prescribed loading is sought.

Shankar, V.↗
NASA NTRS2003

Aerodynamic Shape Optimization Using Hybridized Differential Evolution

An aerodynamic shape optimization method that uses an evolutionary algorithm known at Differential Evolution (DE) in conjunction with various hybridization strategies is described. DE is a simple and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems. Various hybridization strategies for DE are explored, including the use of neural networks as well as traditional local search methods. A Navier-Stokes solver is used to evaluate the various intermediate designs and provide inputs to the hybrid DE optimizer. The method is implemented on distributed parallel computers so that new designs can be obtained within reasonable turnaround times. Results are presented for the inverse design of a turbine airfoil from a modern jet engine. (The final paper will include at least one other aerodynamic design application). The capability of the method to search large design spaces and obtain the optimal airfoils in an automatic fashion is demonstrated.

Madavan, Nateri K.↗
NASA NTRS2009

The a(4) Scheme-A High Order Neutrally Stable CESE Solver

The CESE development is driven by a belief that a solver should (i) enforce conservation laws in both space and time, and (ii) be built from a nondissipative (i.e., neutrally stable) core scheme so that the numerical dissipation can be controlled effectively. To provide a solid foundation for a systematic CESE development of high order schemes, in this paper we describe a new high order (4-5th order) and neutrally stable CESE solver of a 1D advection equation with a constant advection speed a. The space-time stencil of this two-level explicit scheme is formed by one point at the upper time level and two points at the lower time level. Because it is associated with four independent mesh variables (the numerical analogues of the dependent variable and its first, second, and third-order spatial derivatives) and four equations per mesh point, the new scheme is referred to as the a(4) scheme. As in the case of other similar CESE neutrally stable solvers, the a(4) scheme enforces conservation laws in space-time locally and globally, and it has the basic, forward marching, and backward marching forms. Except for a singular case, these forms are equivalent and satisfy a space-time inversion (STI) invariant property which is shared by the advection equation. Based on the concept of STI invariance, a set of algebraic relations is developed and used to prove the a(4) scheme must be neutrally stable when it is stable. Numerically, it has been established that the scheme is stable if the value of the Courant number is less than 1/3

Chang, Sin-Chung↗
NASA NTRS1996

A PDE Sensitivity Equation Method for Optimal Aerodynamic Design

The use of gradient based optimization algorithms in inverse design is well established as a practical approach to aerodynamic design. A typical procedure uses a simulation scheme to evaluate the objective function (from the approximate states) and its gradient, then passes this information to an optimization algorithm. Once the simulation scheme (CFD flow solver) has been selected and used to provide approximate function evaluations, there are several possible approaches to the problem of computing gradients. One popular method is to differentiate the simulation scheme and compute design sensitivities that are then used to obtain gradients. Although this black-box approach has many advantages in shape optimization problems, one must compute mesh sensitivities in order to compute the design sensitivity. In this paper, we present an alternative approach using the PDE sensitivity equation to develop algorithms for computing gradients. This approach has the advantage that mesh sensitivities need not be computed. Moreover, when it is possible to use the CFD scheme for both the forward problem and the sensitivity equation, then there are computational advantages. An apparent disadvantage of this approach is that it does not always produce consistent derivatives. However, for a proper combination of discretization schemes, one can show asymptotic consistency under mesh refinement, which is often sufficient to guarantee convergence of the optimal design algorithm. In particular, we show that when asymptotically consistent schemes are combined with a trust-region optimization algorithm, the resulting optimal design method converges. We denote this approach as the sensitivity equation method. The sensitivity equation method is presented, convergence results are given and the approach is illustrated on two optimal design problems involving shocks.

Borggaard, Jeff↗
NASA NTRS1994

Steady potential solver for unsteady aerodynamic analyses

Development of a steady flow solver for use with LINFLO was the objective of this report. The solver must be compatible with LINFLO, be composed of composite mesh, and have transonic capability. The approaches used were: (1) steady flow potential equations written in nonconservative form; (2) Newton's Method; (3) implicit, least-squares, interpolation method to obtain finite difference equations; and (4) matrix inversion routines from LINFLO. This report was given during the NASA LeRC Workshop on Forced Response in Turbomachinery in August of 1993.

Hoyniak, Dan↗
NASA NTRS1995

An unstructured-grid software system for solving complex aerodynamic problems

A coordinated effort has been underway over the past four years to elevate unstructured-grid methodology to a mature level. The goal of this endeavor is to provide a validated capability to non-expert users for performing rapid aerodynamic analysis and design of complex configurations. The Euler component of the system is well developed, and is impacting a broad spectrum of engineering needs with capabilities such as rapid grid generation and inviscid flow analysis, inverse design, interactive boundary layers, and propulsion effects. Progress is also being made in the more tenuous Navier-Stokes component of the system. A robust grid generator is under development for constructing quality thin-layer tetrahedral grids, along with a companion Navier-Stokes flow solver. This paper presents an overview of this effort, along with a perspective on the present and future status of the methodology.

Frink, Neal T.↗
NASA NTRS1995

Inverse Design of Nacelles Using Multi-Block Navier Stokes Codes

The objective of this work is to reshape a nacelle to achieve a specified nacelle pressure distribution. The nacelle may be either isolated or installed on an airplane. There are no restrictions on the attitude (toe, incidence, and roll) and position of the nacelle. The design algorithm is coupled to two different multi-block 3-D Navier Stokes flow solvers. The coupling between design and analysis is automated to the point where the design proceeds with minimal user input.

Naik, D. A.↗
NASA NTRS1989

A multigrid and upwind viscous flow solver on 3-D embedded and overlapped grids

A numerically efficient method is presented for solving the three-dimensional governing equations of the viscous compressible flow about complex configurations with topologically different components. The physical domain is decomposed into regions for which the grid generation is relatively simple and virtually with no significant restrictions. The Navier-Stokes equations are solved by an implicit, approximately factored, upwind, finite-volume scheme. The block inversions and the diagonalized scalar inversions of the coefficient matrices are modified to allow the holes created in the computational domain by the embedded and overlapped grids. The convergence is accelerated by a multigrid algorithm despite the existence of such holes. The solution for s supersonic flow past a blunt-nose-cylinder at high angle-of-attack is obtained using a C-O grid embedded in a global Cartesian grid.

Baysal, Oktay↗
NASA NTRS2013

ISSM: Ice Sheet System Model

In order to have the capability to use satellite data from its own missions to inform future sea-level rise projections, JPL needed a full-fledged ice-sheet/iceshelf flow model, capable of modeling the mass balance of Antarctica and Greenland into the near future. ISSM was developed with such a goal in mind, as a massively parallelized, multi-purpose finite-element framework dedicated to ice-sheet modeling. ISSM features unstructured meshes (Tria in 2D, and Penta in 3D) along with corresponding finite elements for both types of meshes. Each finite element can carry out diagnostic, prognostic, transient, thermal 3D, surface, and bed slope simulations. Anisotropic meshing enables adaptation of meshes to a certain metric, and the 2D Shelfy-Stream, 3D Blatter/Pattyn, and 3D Full-Stokes formulations capture the bulk of the ice-flow physics. These elements can be coupled together, based on the Arlequin method, so that on a large scale model such as Antarctica, each type of finite element is used in the most efficient manner. For each finite element referenced above, ISSM implements an adjoint. This adjoint can be used to carry out model inversions of unknown model parameters, typically ice rheology and basal drag at the ice/bedrock interface, using a metric such as the observed InSAR surface velocity. This data assimilation capability is crucial to allow spinning up of ice flow models using available satellite data. ISSM relies on the PETSc library for its vectors, matrices, and solvers. This allows ISSM to run efficiently on any parallel platform, whether shared or distrib- ISSM: Ice Sheet System Model NASA's Jet Propulsion Laboratory, Pasadena, California uted. It can run on the largest clusters, and is fully scalable. This allows ISSM to tackle models the size of continents. ISSM is embedded into MATLAB and Python, both open scientific platforms. This improves its outreach within the science community. It is entirely written in C/C++, which gives it flexibility in its design, and the power/speed that C/C++ allows. ISSM is svn (subversion) hosted, on a JPL repository, to facilitate its development and maintenance. ISSM can also model propagation of rifts using contact mechanics and mesh splitting, and can interface to the Dakota software. To carry out sensitivity analysis, mesh partitioning algorithms are available, based on the Scotch, Chaco, and Metis partitioners that ensure equal area mesh partitions can be done, which are then usable for sampling and local reliability methods.

Larour, Eric↗
NASA NTRS2001

UNIPASS for AvSP? A Broader View

UNIPASS is a general-purpose probabilistic computer program consisting of three major modules, including preprocessor, solver and postprocessor. UNIPASS contains a user-friendly Graphical User Interface (GUI), numerous state-of-the-art probabilistic analysis techniques, a large library of statistical distributions and a function module with a large library of support functions that can easily define any complex limit-state function in a scripting FORTRAN-like syntax format. Its inverse probability analysis and sensitivities analysis capabilities make it a powerful design aid in any product cycle. Its precise numerical analysis engine is accurate enough to push the failure probabilities of a design to well below 10 (exp -50). UNIPASS is equipped with advanced artificial intelligence that is designed to handle systems with an essentially unlimited number of random variables with ease and efficiency. Its modular arrangement allows you to tailor an analysis to the desired level of accuracy and efficiency. The depth and comprehensiveness of UNIPASS are built upon the decades of experience and expertise of industry leaders including Boeing Aircraft, NASA and the DoD. Its rich content also makes UNIPASS a valuable instructional tool for random processes and probabilistic mechanics. The topics include: 1) Reliability in AvSP; 2) Role of UNIPASS in AvSP; and 3) Examples. This paper is in viewgraph form.

Wu, N. Eva↗
NASA NTRS1991

Hierarchically parallelized constrained nonlinear solvers with automated substructuring

This paper develops a parallelizable multilevel constrained nonlinear equation solver. The substructuring process is automated to yield appropriately balanced partitioning of each succeeding level. Due to the generality of the procedure, both sequential, partially and fully parallel environments can be handled. This includes both single and multiprocessor assignment per individual partition. Several benchmark examples are presented. These illustrate the robustness of the procedure as well as its capacity to yield significant reductions in memory utilization and calculational effort due both to updating and inversion.

Padovan, J.↗
NASA NTRS1998

Euler Calculations at Off-Design Conditions for an Inlet of Inward Turning RBCC-SSTO Vehicle

The inviscid performance of an inward turning inlet design is calculated computationally for the first time. Hypersonic vehicle designs based on the inward turning inlets have been shown analytically to have increased effective specific impulse and lower heat load than comparably designed vehicles with two-dimensional inlets. The inward turning inlets are designed inversely from inviscid stream surfaces of known flow fields. The computational study is performed on a Mach 12 inlet design to validate the performance predicted by the design code (HAVDAC) and calculate its off-design Mach number performance. The three-dimensional Euler equations are solved for Mach 4, 8, and 12 using a software package called SAM, which consists of an unstructured mesh generator (SAMmesh), a three-dimensional unstructured mesh flow solver (SAMcfd), and a CAD-based software (SAMcad). The computed momentum averaged inlet throat pressure is within 6% of the design inlet throat pressure. The mass-flux at the inlet throat is also within 7 % of the value predicted by the design code thereby validating the accuracy of the design code. The off-design Mach number results show that flow spillage is minimal, and the variation in the mass capture ratio with Mach number is comparable to an ideal 2-D inlet. The results from the inviscid flow calculations of a Mach 12 inward turning inlet indicate that the inlet design has very good on and off-design performance which makes it a promising design candidate for future air-breathing hypersonic vehicles.

Takashima, N.↗
NASA NTRS1987

A transputer based finite element solver

The feasibility of performing FEM structural-mechanics analyses on transputer systems is investigated experimentally. Transputers are programmable microprocessors equipped with local memory and point-to-point communication links; they can be joined in a large concurrent system via a programming language which supports distributed processing; this permits parallel processing at relatively low hardware cost. The computational tasks required by FEM programs are reviewed; the hardware (one PC, one master transputer, and 12 slave transputers) employed in the test calculations is described; and results demonstrating the speed and efficiency of the transputer array in assembling a global stiffness matrix and performing Gauss-Jordan matrix inversion are presented in graphs. It is predicted that larger transputer networks could approach the power of supercomputers at minicomputer costs.

Favenesi, J. A.↗
NASA NTRS1994

Hierarchically Parallelized Constrained Nonlinear Solvers with Automated Substructuring

This paper develops a parallelizable multilevel multiple constrained nonlinear equation solver. The substructuring process is automated to yield appropriately balanced partitioning of each succeeding level. Due to the generality of the procedure,_sequential, as well as partially and fully parallel environments can be handled. This includes both single and multiprocessor assignment per individual partition. Several benchmark examples are presented. These illustrate the robustness of the procedure as well as its capability to yield significant reductions in memory utilization and calculational effort due both to updating and inversion.

Padovan, Joe↗
NASA NTRS1993

Using parallel banded linear system solvers in generalized eigenvalue problems

Subspace iteration is a reliable and cost effective method for solving positive definite banded symmetric generalized eigenproblems, especially in the case of large scale problems. This paper discusses an algorithm that makes use of two parallel banded solvers in subspace iteration. A shift is introduced to decompose the banded linear systems into relatively independent subsystems and to accelerate the iterations. With this shift, an eigenproblem is mapped efficiently into the memories of a multiprocessor and a high speed-up is obtained for parallel implementations. An optimal shift is a shift that balances total computation and communication costs. Under certain conditions, we show how to estimate an optimal shift analytically using the decay rate for the inverse of a banded matrix, and how to improve this estimate. Computational results on iPSC/2 and iPSC/860 multiprocessors are presented.

Zhang, Hong↗
NASA NTRS1986

Viscous compressible flow direct and inverse computation and illustrations

An algorithm for laminar and turbulent viscous compressible two dimensional flows is presented. For the application of precise boundary conditions over an arbitrary body surface, a body-fitted coordinate system is used in the physical plane. A thin-layer approximation of tne Navier-Stokes equations is introduced to keep the viscous terms relatively simple. The flow field computation is performed in the transformed plane. A factorized, implicit scheme is used to facilitate the computation. Sample calculations, for Couette flow, developing pipe flow, an isolated airflow, two dimensional compressor cascade flow, and segmental compressor blade design are presented. To a certain extent, the effective use of the direct solver depends on the user's skill in setting up the gridwork, the time step size and the choice of the artificial viscosity. The design feature of the algorithm, an iterative scheme to correct geometry for a specified surface pressure distribution, works well for subsonic flows. A more elaborate correction scheme is required in treating transonic flows where local shock waves may be involved.

Yang, T. T.↗
NASA NTRS1995

A Hybrid Parallel Preconditioning Algorithm For CFD

A new hybrid preconditioning algorithm will be presented which combines the favorable attributes of incomplete lower-upper (ILU) factorization with the favorable attributes of the approximate inverse method recently advocated by numerous researchers. The quality of the preconditioner is adjustable and can be increased at the cost of additional computation while at the same time the storage required is roughly constant and approximately equal to the storage required for the original matrix. In addition, the preconditioning algorithm suggests an efficient and natural parallel implementation with reduced communication. Sample calculations will be presented for the numerical solution of multi-dimensional advection-diffusion equations. The matrix solver has also been embedded into a Newton algorithm for solving the nonlinear Euler and Navier-Stokes equations governing compressible flow. The full paper will show numerous examples in CFD to demonstrate the efficiency and robustness of the method.

Barth,Timothy J.↗