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All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Linearized Aeroelastic Solver Applied to the Flutter Prediction of Real Configurations

A fast-running unsteady aerodynamics code, LINFLUX, was previously developed for predicting turbomachinery flutter. This linearized code, based on a frequency domain method, models the effects of steady blade loading through a nonlinear steady flow field. The LINFLUX code, which is 6 to 7 times faster than the corresponding nonlinear time domain code, is suitable for use in the initial design phase. Earlier, this code was verified through application to a research fan, and it was shown that the predictions of work per cycle and flutter compared well with those from a nonlinear time-marching aeroelastic code, TURBO-AE. Now, the LINFLUX code has been applied to real configurations: fans developed under the Energy Efficient Engine (E-cubed) Program and the Quiet Aircraft Technology (QAT) project. The LINFLUX code starts with a steady nonlinear aerodynamic flow field and solves the unsteady linearized Euler equations to calculate the unsteady aerodynamic forces on the turbomachinery blades. First, a steady aerodynamic solution is computed for given operating conditions using the nonlinear unsteady aerodynamic code TURBO-AE. A blade vibration analysis is done to determine the frequencies and mode shapes of the vibrating blades, and an interface code is used to convert the steady aerodynamic solution to a form required by LINFLUX. A preprocessor is used to interpolate the mode shapes from the structural dynamics mesh onto the computational fluid dynamics mesh. Then, LINFLUX is used to calculate the unsteady aerodynamic pressure distribution for a given vibration mode, frequency, and interblade phase angle. Finally, a post-processor uses the unsteady pressures to calculate the generalized aerodynamic forces, eigenvalues, an esponse amplitudes. The eigenvalues determine the flutter frequency and damping. Results of flutter calculations from the LINFLUX code are presented for (1) the E-cubed fan developed under the E-cubed program and (2) the Quiet High Speed Fan (QHSF) developed under the Quiet Aircraft Technology project. The results are compared with those obtained from the TURBO-AE code. A graph of the work done per vibration cycle for the first vibration mode of the E-cubed fan is shown. It can be seen that the LINFLUX results show a very good comparison with TURBO-AE results over the entire range of interblade phase angle. The work done per vibration cycle for the first vibration mode of the QHSF fan is shown. Once again, the LINFLUX results compare very well with the results from the TURBOAE code.

Reddy, Tondapu S.↗
NASA NTRS1991

Parallel-vector computation for linear structural analysis and non-linear unconstrained optimization problems

Several parallel-vector computational improvements to the unconstrained optimization procedure are described which speed up the structural analysis-synthesis process. A fast parallel-vector Choleski-based equation solver, pvsolve, is incorporated into the well-known SAP-4 general-purpose finite-element code. The new code, denoted PV-SAP, is tested for static structural analysis. Initial results on a four processor CRAY 2 show that using pvsolve reduces the equation solution time by a factor of 14-16 over the original SAP-4 code. In addition, parallel-vector procedures for the Golden Block Search technique and the BFGS method are developed and tested for nonlinear unconstrained optimization. A parallel version of an iterative solver and the pvsolve direct solver are incorporated into the BFGS method. Preliminary results on nonlinear unconstrained optimization test problems, using pvsolve in the analysis, show excellent parallel-vector performance indicating that these parallel-vector algorithms can be used in a new generation of finite-element based structural design/analysis-synthesis codes.

Nguyen, D. T.↗
NASA NTRS1993

The block adaptive multigrid method applied to the solution of the Euler equations

In the present study, a scheme capable of solving very fast and robust complex nonlinear systems of equations is presented. The Block Adaptive Multigrid (BAM) solution method offers multigrid acceleration and adaptive grid refinement based on the prediction of the solution error. The proposed solution method was used with an implicit upwind Euler solver for the solution of complex transonic flows around airfoils. Very fast results were obtained (18-fold acceleration of the solution) using one fourth of the volumes of a global grid with the same solution accuracy for two test cases.

Pantelelis, Nikos↗
NASA NTRS2001

A Parallel Multigrid Solver for Viscous Flows on Anisotropic Structured Grids

This paper presents an efficient parallel multigrid solver for speeding up the computation of a 3-D model that treats the flow of a viscous fluid over a flat plate. The main interest of this simulation lies in exhibiting some basic difficulties that prevent optimal multigrid efficiencies from being achieved. As the computing platform, we have used Coral, a Beowulf-class system based on Intel Pentium processors and equipped with GigaNet cLAN and switched Fast Ethernet networks. Our study not only examines the scalability of the solver but also includes a performance evaluation of Coral where the investigated solver has been used to compare several of its design choices, namely, the interconnection network (GigaNet versus switched Fast-Ethernet) and the node configuration (dual nodes versus single nodes). As a reference, the performance results have been compared with those obtained with the NAS-MG benchmark.

Prieto, Manuel↗
NASA NTRS1994

Technical report series on global modeling and data assimilation. Volume 2: Direct solution of the implicit formulation of fourth order horizontal diffusion for gridpoint models on the sphere

High order horizontal diffusion of the form K Delta(exp 2m) is widely used in spectral models as a means of preventing energy accumulation at the shortest resolved scales. In the spectral context, an implicit formation of such diffusion is trivial to implement. The present note describes an efficient method of implementing implicit high order diffusion in global finite difference models. The method expresses the high order diffusion equation as a sequence of equations involving Delta(exp 2). The solution is obtained by combining fast Fourier transforms in longitude with a finite difference solver for the second order ordinary differential equation in latitude. The implicit diffusion routine is suitable for use in any finite difference global model that uses a regular latitude/longitude grid. The absence of a restriction on the timestep makes it particularly suitable for use in semi-Lagrangian models. The scale selectivity of the high order diffusion gives it an advantage over the uncentering method that has been used to control computational noise in two-time-level semi-Lagrangian models.

Max J. Suarez↗
NASA NTRS1999

An Adaptive Unstructured Grid Method by Grid Subdivision, Local Remeshing, and Grid Movement

An unstructured grid adaptation technique has been developed and successfully applied to several three dimensional inviscid flow test cases. The approach is based on a combination of grid subdivision, local remeshing, and grid movement. For solution adaptive grids, the surface triangulation is locally refined by grid subdivision, and the tetrahedral grid in the field is partially remeshed at locations of dominant flow features. A grid redistribution strategy is employed for geometric adaptation of volume grids to moving or deforming surfaces. The method is automatic and fast and is designed for modular coupling with different solvers. Several steady state test cases with different inviscid flow features were tested for grid/solution adaptation. In all cases, the dominant flow features, such as shocks and vortices, were accurately and efficiently predicted with the present approach. A new and robust method of moving tetrahedral "viscous" grids is also presented and demonstrated on a three-dimensional example.

Pirzadeh, Shahyar Z.↗
NASA NTRSDate not supplied

Porting OVERFLOW CFD Code to GPUs: To Hackathons and Beyond!

OVERFLOW is an overset, structured computational fluid dynamics (CFD) code written in Fortran which is widely used in the government, industry, and academia. Over the last several years the OVERFLOW developers have been working to port miniapps based on computationally expensive parts of OVERFLOW to run on GPUs, primarily using OpenACC. This effort started at our first hackathon in 2019 and since then the OVERFLOW team has attended two additional hackathons (virtually). These hackathon environments have provided a great place to collaborate with others and learn from experts. These learning experiences enabled porting two miniapps to run effectively on NVIDIA GPUs using OpenACC. The first miniapp focused on motifs found in the solver itself and the final ported version runs three times fast ona single V100 compared to a 40 core, dual-socket Intel Skylake node. The speed up in this solverminiapp required multiple design changes including increasing the amount of parallelism available and the amount of work performed in each kernel. The second miniapp focused on overset MPI communication, also saw significant speedups over the CPU implementation using a CUDA-aware MPI implementation through OpenACC. This presentation will discuss our experience at the hackathons, our process of porting the miniapps to run on the GPUs, and several lessons learned throughout.

OpenACC↗
NASA NTRS2011

Fast Numerical Methods for the Design of Layered Photonic Structures with Rough Interfaces

Modified boundary conditions (MBC) and a multilayer approach (MA) are proposed as fast and efficient numerical methods for the design of 1D photonic structures with rough interfaces. These methods are applicable for the structures, composed of materials with arbitrary permittivity tensor. MBC and MA are numerically validated on different types of interface roughness and permittivities of the constituent materials. The proposed methods can be combined with the 4x4 scattering matrix method as a field solver and an evolutionary strategy as an optimizer. The resulted optimization procedure is fast, accurate, numerically stable and can be used to design structures for various applications.

Komarevskiy, Nikolay↗
NASA NTRS1987

A general method for dynamic analysis of structures overview

The presented research deals with the development of a dynamic analysis method for structural systems. The modeling approach is essentially a finite element method in the sense that the structure is divided into n elements. An element is defined as any structural unit whose degree of freedom (dofs) can be categorized as either interface or non-interface dofs. An element could be a fundamental unit such as a rod, a beam, a plate etc., or it could be an entire structural component. Furthermore, the parameters for the element could be distributed or lumped. The choice of elements is totally arbitrary and is a matter of user convenience. In particular, issues of accuracy and convergence do not enter on the level of example that bookkeeping is reduced to a minimum. Each element is modeled using a set of interface constraint modes (ICM) combined with a set of interface restrained normal models (IRNM). The next step is the solution of the system eigenvalue problem. The procedure calls for the sequential solution of a number of small eigenvalue problems based on a truncation principle for IRNM. In addition, the form of these eigenvalue problems is very simple such that an escalator type of eigenvalue problem solver can be used which is extremely cost-effective and fast.

Engels, Remi C.↗
NASA NTRS1993

The development and application of the self-adaptive grid code, SAGE

The multidimensional self-adaptive grid code, SAGE, has proven to be a flexible and useful tool in the solution of complex flow problems. Both 2- and 3-D examples given in this report show the code to be reliable and to substantially improve flowfield solutions. Since the adaptive procedure is a marching scheme the code is extremely fast and uses insignificant CPU time compared to the corresponding flow solver. The SAGE program is also machine and flow solver independent. Significant effort was made to simplify user interaction, though some parameters still need to be chosen with care. It is also difficult to tell when the adaption process has provided its best possible solution. This is particularly true if no experimental data are available or if there is a lack of theoretical understanding of the flow. Another difficulty occurs if local features are important but missing in the original grid; the adaption to this solution will not result in any improvement, and only grid refinement can result in an improved solution. These are complex issues that need to be explored within the context of each specific problem.

Davies, Carol B.↗
NASA NTRS2018

Solar Sail Transfers from Invariant Objects to L5 Periodic Orbits

The rising interest in a mission to the Sun-Earth L5 point for heliophysics or Trojan asteroid search and the development of solar sails has opened the question of using solar radiation pressure for such a mission. Different solar sail trajectories to the Sun-Earth L5 point are constructed. Different invariant objects in the neighbourhood of Earth are considered for departure: equilibrium points, families of periodic orbits and their associated invariant manifold. Using a multi-objective genetic algorithm, differential correction and the optimal control solver PSOPT the transfers are obtained. The approach followed results in fast solar sail transfers which can be used for the preliminary design of a mission to the Sun-Earth L5 point.

Fernandez, Alvaro↗
NASA NTRS1994

Accelerated panel methods using the fast multipole method

Panel methods are commonly used in computational fluid dynamics for the solution of potential flow problems. The methods are a numerical technique based on the surface distribution of singularity elements. The solution is the process of finding the strength of the singularity elements distributed over the body's surface. This process involves the solution of the matrix problem Pq = p' for a set of unknowns q. The Fast Multipole Method is used to directly compute q without using matrix solvers. The algorithm works in O(N) time for N points, a great improvement over standard matrix solvers. In panel methods, the surface of a body is divided into a series of quadrilateral panels. The methods involve the computation of the influence of all other panels on each individual panel. The influence is based on the surface distribution, though this can be approximated by the area for distant panels. An alternative approximation, though with arbitrary accuracy, is to develop a multipole expansion about the center of the panel to describe the effect of a given panel on distant points in space. The expansion is based on the moments of the panel, thus allow the use of various surface distributions without changing the basic algorithm, just the computation of the various moments. The expansions are then manipulated in a tree walk to develop Taylor series expansions about a point in space which describe the effect of all distant panels on any point within a volume of convergence. The effect of near panels then needs to be computed directly, but the effect of all distant panels can be computed by simply evaluating the resulting expansion. The Fast Multipole Method has been applied to panel methods for the solution of source and doublet distributions. A major feature of the algorithm is that the algorithm does not change to derive the potential and velocity for sources and doublets. The same expansions can be used for both sources and doublets. Since the velocity is related to the potential, and the doublet potential is related to the z-component of the source velocity, all values can be derived from the same expansion by taking a series of partial derivatives. This requires more expansion terms to be kept since terms are lost in the process of taking partial derivatives. Thus to maintain accuracy for the doublet computation, more terms are required than if just evaluating for sources. The resulting Fast Multipole code should then parallelize better than classical panel methods due to the locality of data dependencies found in the Fast Multipole Method. Theoretically the parallelized code should execute in O(log N) time with O(N) processors, though this is not practical. Ongoing work includes implementing the parallel accelerated panel method, including methods to improve the load balancing of the problem by taking advantage of the known geometry of panels, and to encorporate sensitivity analysis into the algorithm.

Leathrum, James F., Jr.↗
NASA NTRS2022

Whistler Waves Generated by Nongyrotropic and Gyrotropic Electron Beams During Asymmetric Guide Field Reconnection

Using a two-dimensional particle-in-cell simulation of asymmetric reconnection with a guide field whose strength is 0.3 times the reconnecting magnetic field, we study electron distribution functions and wave intensities in the diffusion region, focusing on the electron diffusion region (EDR). Wave activities with frequencies below the electron cyclotron frequency are observed, and these are whistler waves propagating almost anti-parallel to the magnetic field. The waves are concentrated near the magnetospheric separatrix away from the X line, but the wave activity also spreads through the EDR near the X line. The reconnection outflows are asymmetric in the outflow direction in the magnetospheric side, and the wave intensity is stronger in the side of the faster electron outflow. We study the whistler waves using the fast Fourier transform, analyses of electron velocity distribution functions, and the dispersion solver calculation. Along the magnetospheric separatrix in the stronger outflow side, highly anisotropic electron beams exist with super-Alfvénic drift speeds. The dispersion analysis shows that there are two modes: a temperature anisotropy mode and a beam mode. Outside the EDR, the whistler wave intensity is highest near the separatrix, but the wave intensity decreases if we move away from the separatrix toward the magnetic neutral line because of the increase in the electron population near zero parallel velocity. In the EDR, in the velocity plane perpendicular to the magnetic field, ring/crescent electron distribution functions are observed. Near the X-line, the wave power is enhanced where nongyrotropic electrons contribute to increase the perpendicular temperature anisotropy.

magnetic reconnection↗
NASA NTRS1991

Nonequilibrium radiative heating prediction method for aeroassist flowfields with coupling to flowfield solvers

A method for predicting radiation adsorption and emission coefficients in thermochemical nonequilibrium flows is developed. The method is called the Langley optimized radiative nonequilibrium code (LORAN). It applies the smeared band approximation for molecular radiation to produce moderately detailed results and is intended to fill the gap between detailed but costly prediction methods and very fast but highly approximate methods. The optimization of the method to provide efficient solutions allowing coupling to flowfield solvers is discussed. Representative results are obtained and compared to previous nonequilibrium radiation methods, as well as to ground- and flight-measured data. Reasonable agreement is found in all cases. A multidimensional radiative transport method is also developed for axisymmetric flows. Its predictions for wall radiative flux are 20 to 25 percent lower than those of the tangent slab transport method, as expected, though additional investigation of the symmetry and outflow boundary conditions is indicated. The method was applied to the peak heating condition of the aeroassist flight experiment (AFE) trajectory, with results comparable to predictions from other methods. The LORAN method was also applied in conjunction with the computational fluid dynamics (CFD) code LAURA to study the sensitivity of the radiative heating prediction to various models used in nonequilibrium CFD. This study suggests that radiation measurements can provide diagnostic information about the detailed processes occurring in a nonequilibrium flowfield because radiation phenomena are very sensitive to these processes.

Hartung, Lin C.↗
NASA NTRS1994

Radiation and scattering from printed antennas on cylindrically conformal platforms

The goal was to develop suitable methods and software for the analysis of antennas on cylindrical coated and uncoated platforms. Specifically, the finite element boundary integral and finite element ABC methods were employed successfully and associated software were developed for the analysis and design of wraparound and discrete cavity-backed arrays situated on cylindrical platforms. This work led to the successful implementation of analysis software for such antennas. Developments which played a role in this respect are the efficient implementation of the 3D Green's function for a metallic cylinder, the incorporation of the fast Fourier transform in computing the matrix-vector products executed in the solver of the finite element-boundary integral system, and the development of a new absorbing boundary condition for terminating the finite element mesh on cylindrical surfaces.

Kempel, Leo C.↗
NASA NTRS2000

LSENS, The NASA Lewis Kinetics and Sensitivity Analysis Code

A general chemical kinetics and sensitivity analysis code for complex, homogeneous, gas-phase reactions is described. The main features of the code, LSENS (the NASA Lewis kinetics and sensitivity analysis code), are its flexibility, efficiency and convenience in treating many different chemical reaction models. The models include: static system; steady, one-dimensional, inviscid flow; incident-shock initiated reaction in a shock tube; and a perfectly stirred reactor. In addition, equilibrium computations can be performed for several assigned states. An implicit numerical integration method (LSODE, the Livermore Solver for Ordinary Differential Equations), which works efficiently for the extremes of very fast and very slow reactions, is used to solve the "stiff" ordinary differential equation systems that arise in chemical kinetics. For static reactions, the code uses the decoupled direct method to calculate sensitivity coefficients of the dependent variables and their temporal derivatives with respect to the initial values of dependent variables and/or the rate coefficient parameters. Solution methods for the equilibrium and post-shock conditions and for perfectly stirred reactor problems are either adapted from or based on the procedures built into the NASA code CEA (Chemical Equilibrium and Applications).

Radhakrishnan, K.↗
NASA NTRS2016

An Immersed Boundary Method for Solving the Compressible Navier-Stokes Equations with Fluid Structure Interaction

An immersed boundary method for the compressible Navier-Stokes equation and the additional infrastructure that is needed to solve moving boundary problems and fully coupled fluid-structure interaction is described. All the methods described in this paper were implemented in NASA's LAVA solver framework. The underlying immersed boundary method is based on the locally stabilized immersed boundary method that was previously introduced by the authors. In the present paper this method is extended to account for all aspects that are involved for fluid structure interaction simulations, such as fast geometry queries and stencil computations, the treatment of freshly cleared cells, and the coupling of the computational fluid dynamics solver with a linear structural finite element method. The current approach is validated for moving boundary problems with prescribed body motion and fully coupled fluid structure interaction problems in 2D and 3D. As part of the validation procedure, results from the second AIAA aeroelastic prediction workshop are also presented. The current paper is regarded as a proof of concept study, while more advanced methods for fluid structure interaction are currently being investigated, such as geometric and material nonlinearities, and advanced coupling approaches.

Equations↗
NASA NTRS1992

A finite element: Boundary integral method for electromagnetic scattering

A method that combines the finite element and boundary integral techniques for the numerical solution of electromagnetic scattering problems is presented. The finite element method is well known for requiring a low order storage and for its capability to model inhomogeneous structures. Of particular emphasis in this work is the reduction of the storage requirement by terminating the finite element mesh on a boundary in a fashion which renders the boundary integrals in convolutional form. The fast Fourier transform is then used to evaluate these integrals in a conjugate gradient solver, without a need to generate the actual matrix. This method has a marked advantage over traditional integral equation approaches with respect to the storage requirement of highly inhomogeneous structures. Rectangular, circular, and ogival mesh termination boundaries are examined for two-dimensional scattering. In the case of axially symmetric structures, the boundary integral matrix storage is reduced by exploiting matrix symmetries and solving the resulting system via the conjugate gradient method. In each case several results are presented for various scatterers aimed at validating the method and providing an assessment of its capabilities. Important in methods incorporating boundary integral equations is the issue of internal resonance. A method is implemented for their removal, and is shown to be effective in the two-dimensional and three-dimensional applications.

Collins, J. D.↗