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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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30 records · Page 2

Three-Dimensional Nacelle Aeroacoustics Code With Application to Impedance Education

A three-dimensional nacelle acoustics code that accounts for uniform mean flow and variable surface impedance liners is developed. The code is linked to a commercial version of the NASA-developed General Purpose Solver (for solution of linear systems of equations) in order to obtain the capability to study high frequency waves that may require millions of grid points for resolution. Detailed, single-processor statistics for the performance of the solver in rigid and soft-wall ducts are presented. Over the range of frequencies of current interest in nacelle liner research, noise attenuation levels predicted from the code were in excellent agreement with those predicted from mode theory. The equation solver is memory efficient, requiring only a small fraction of the memory available on modern computers. As an application, the code is combined with an optimization algorithm and used to reduce the impedance spectrum of a ceramic liner. The primary problem with using the code to perform optimization studies at frequencies above I1kHz is the excessive CPU time (a major portion of which is matrix assembly). The research recommends that research be directed toward development of a rapid sparse assembler and exploitation of the multiprocessor capability of the solver to further reduce CPU time.

Watson, Willie R.↗

Implementing abstract multigrid or multilevel methods

Multigrid methods can be formulated as an algorithm for an abstract problem that is independent of the partial differential equation, domain, and discretization method. In such an abstract setting, problems not arising from partial differential equations can be treated. A general theory exists for linear problems. The general theory was motivated by a series of abstract solvers (Madpack). The latest version was motivated by the theory. Madpack now allows for a wide variety of iterative and direct solvers, preconditioners, and interpolation and projection schemes, including user callback ones. It allows for sparse, dense, and stencil matrices. Mildly nonlinear problems can be handled. Also, there is a fast, multigrid Poisson solver (two and three dimensions). The type of solvers and design decisions (including language, data structures, external library support, and callbacks) are discussed. Based on the author's experiences with two versions of Madpack, a better approach is proposed. This is based on a mixed language formulation (C and FORTRAN + preprocessor). Reasons for not using FORTRAN, C, or C++ (individually) are given. Implementing the proposed strategy is not difficult.

Douglas, Craig C.↗

Modeling Sound Propagation Through Non-Axisymmetric Jets

A method for computing the far-field adjoint Green's function of the generalized acoustic analogy equations under a locally parallel mean flow approximation is presented. The method is based on expanding the mean-flow-dependent coefficients in the governing equation and the scalar Green's function in truncated Fourier series in the azimuthal direction and a finite difference approximation in the radial direction in circular cylindrical coordinates. The combined spectral/finite difference method yields a highly banded system of algebraic equations that can be efficiently solved using a standard sparse system solver. The method is applied to test cases, with mean flow specified by analytical functions, corresponding to two noise reduction concepts of current interest: the offset jet and the fluid shield. Sample results for the Green's function are given for these two test cases and recommendations made as to the use of the method as part of a RANS-based jet noise prediction code.

Leib, Stewart J.↗

Iterative solution techniques in boundary element analysis

Iterative techniques for the solution of the algebraic equations associated with the direct boundary element analysis (BEA) method are discussed. Continuum structural response analysis problems are considered, employing single- and multizone boundary element models with and without zone condensation. The impact on convergence rate and computer resource requirements associated with the sparse and blocked matrices, resulting in multizone BEA, is studied. Both conjugate gradient and generalized minimum residual preconditioned iterative solvers are applied for these problems and the performance of these algorithms is reported. Included is a quantification of the impact of the preconditioning utilized to render the boundary element matrices solvable by the respective iterative methods in a time competitive with direct methods.

Kane, J. H.↗

High-performance equation solvers and their impact on finite element analysis

The role of equation solvers in modern structural analysis software is described. Direct and iterative equation solvers which exploit vectorization on modern high-performance computer systems are described and compared. The direct solvers are two Cholesky factorization methods. The first method utilizes a novel variable-band data storage format to achieve very high computation rates and the second method uses a sparse data storage format designed to reduce the number of operations. The iterative solvers are preconditioned conjugate gradient methods. Two different preconditioners are included; the first uses a diagonal matrix storage scheme to achieve high computation rates and the second requires a sparse data storage scheme and converges to the solution in fewer iterations that the first. The impact of using all of the equation solvers in a common structural analysis software system is demonstrated by solving several representative structural analysis problems.

Poole, Eugene L.↗

High-performance equation solvers and their impact on finite element analysis

The role of equation solvers in modern structural analysis software is described. Direct and iterative equation solvers which exploit vectorization on modern high-performance computer systems are described and compared. The direct solvers are two Cholesky factorization methods. The first method utilizes a novel variable-band data storage format to achieve very high computation rates and the second method uses a sparse data storage format designed to reduce the number od operations. The iterative solvers are preconditioned conjugate gradient methods. Two different preconditioners are included; the first uses a diagonal matrix storage scheme to achieve high computation rates and the second requires a sparse data storage scheme and converges to the solution in fewer iterations that the first. The impact of using all of the equation solvers in a common structural analysis software system is demonstrated by solving several representative structural analysis problems.

Poole, Eugene L.↗

Time integration algorithms for the two-dimensional Euler equations on unstructured meshes

Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.

Slack, David C.↗

Application of direct solvers to unstructured meshes for the Euler and Navier-Stokes equations using upwind schemes

The application of Newton iteration to inviscid and viscous airfoil calculations on unstructured meshes is examined. A cell-centered finite volume scheme is employed on an unstructured mesh consisting of triangles. Roe's flux difference splitting scheme is used to compute the inviscid fluxes. Higher order accuracy is achieved by an interpolation procedure that makes use of auxiliary gradients. The efficient solution of the sparse linear system of equations which arises upon linearization in time is addressed. Results are presented for inviscid and viscous test cases. The complications which arise due to the introduction of nonlinear limiters are addressed.

Venkatakrishnan, V.↗

An incremental strategy for calculating consistent discrete CFD sensitivity derivatives

In this preliminary study involving advanced computational fluid dynamic (CFD) codes, an incremental formulation, also known as the 'delta' or 'correction' form, is presented for solving the very large sparse systems of linear equations which are associated with aerodynamic sensitivity analysis. For typical problems in 2D, a direct solution method can be applied to these linear equations which are associated with aerodynamic sensitivity analysis. For typical problems in 2D, a direct solution method can be applied to these linear equations in either the standard or the incremental form, in which case the two are equivalent. Iterative methods appear to be needed for future 3D applications; however, because direct solver methods require much more computer memory than is currently available. Iterative methods for solving these equations in the standard form result in certain difficulties, such as ill-conditioning of the coefficient matrix, which can be overcome when these equations are cast in the incremental form; these and other benefits are discussed. The methodology is successfully implemented and tested in 2D using an upwind, cell-centered, finite volume formulation applied to the thin-layer Navier-Stokes equations. Results are presented for two laminar sample problems: (1) transonic flow through a double-throat nozzle; and (2) flow over an isolated airfoil.

Korivi, Vamshi Mohan↗

Performance Optimization Methods for a Memory-Bound, Unstructured-Grid CFD Application on Massively Parallel GPU Platforms

Computational performance of the FUN3D unstructured-grid computational fluid dynamics (CFD) application on massively parallel GPU environments is memory-bound and highly dependent upon efficient reads from and atomic updates to the irregular cell-, edge-, and node-based data structures. In this talk, we present recent efforts into optimizing select performance-critical kernels on NVIDIA Tesla V100 and A100 GPUs and AMD CDNA MI100 GPUs. A novel use of L2 cache residency controls and asynchronous loads into on-chip shared memory are explored on the A100 GPU for the sparse iterative solver, which is dominated by mixed-precision, sparse matrix vector multiplication. Demonstrations show that these methods improve global memory bandwidth utilization by 13.5% on the A100 GPU. Several techniques are also presented that use registers and/or shared memory to facilitate array transposition and aggregation which combine to reduce the frequency and increase the cache efficiency of floating-point atomic updates to the irregular data structures. These methods are demonstrated to improve the kernel throughput by nearly 500% on select kernels on the AMD MI100 over atomic updates directly to global memory. Overall, both V100 and A100 GPUs outperformed the MI100 GPU on kernels dominated by double-precision atomic updates; however, the techniques demonstrated here reduced the performance gap and improved the MI100 performance.

GPU CPU unstructured CFD memory↗

Parallel Implicit Algorithms for CFD

The main goal of this project was efficient distributed parallel and workstation cluster implementations of Newton-Krylov-Schwarz (NKS) solvers for implicit Computational Fluid Dynamics (CFD.) "Newton" refers to a quadratically convergent nonlinear iteration using gradient information based on the true residual, "Krylov" to an inner linear iteration that accesses the Jacobian matrix only through highly parallelizable sparse matrix-vector products, and "Schwarz" to a domain decomposition form of preconditioning the inner Krylov iterations with primarily neighbor-only exchange of data between the processors. Prior experience has established that Newton-Krylov methods are competitive solvers in the CFD context and that Krylov-Schwarz methods port well to distributed memory computers. The combination of the techniques into Newton-Krylov-Schwarz was implemented on 2D and 3D unstructured Euler codes on the parallel testbeds that used to be at LaRC and on several other parallel computers operated by other agencies or made available by the vendors. Early implementations were made directly in Massively Parallel Integration (MPI) with parallel solvers we adapted from legacy NASA codes and enhanced for full NKS functionality. Later implementations were made in the framework of the PETSC library from Argonne National Laboratory, which now includes pseudo-transient continuation Newton-Krylov-Schwarz solver capability (as a result of demands we made upon PETSC during our early porting experiences). A secondary project pursued with funding from this contract was parallel implicit solvers in acoustics, specifically in the Helmholtz formulation. A 2D acoustic inverse problem has been solved in parallel within the PETSC framework.

Keyes, David E.↗

Implicit Formulation of Muscle Dynamics in OpenSim

Astronauts lose bone and muscle mass during spaceflight. Exercise countermeasure is the primary method for counteracting bone and muscle mass loss in space. New spacecraft exercise device concepts are currently being developed for the NASAs new crew exploration vehicle. The NASA Digital Astronaut Project (DAP) uses computational modeling to help determine if the new exercise devices will be effective as countermeasures. The NASA Digital Astronaut Project is developing the ability to utilize predictive simulation to provide insight into the change in kinematics and kinetics with a change in device and gravitational environment (1-g versus 0-g). For example, in space exercise the subject's body weight is applied in addition to the loads prescribed for musculoskeletal maintenance. How and where these loads are applied obviously directly impacts bone and tissue loads. Additionally, due to space vehicle structural requirements, exercise devices are often placed on vibration isolation systems. This changes the apparent impedance or stiffness of the device as seen by the user. Data collection under these conditions is often impractical and limited. Predictive modeling provides a means to have a virtual subject to test hypotheses. Predictive simulation provides a virtual subject for which we are able to perform studies such as sensitivity to device loading and vibration isolation without the need for laboratory kinematic or kinetic test data.Direct Collocation optimization provides an efficient means to perform task based optimization and predictive modeling. It is relatively straight forward to structure a physical exercise task in a Direct Collocation mathematical formulation: perform a motion such that you start at an initial pose, achieve a given amount of deflection i.e a squat, return to the initial pose, and minimize muscle activation cost. Direct Collocation is advantageous in that it does not require numerical integration to evaluate the objective function. Instead, the system dynamics are transformed to discrete time and the optimizer is constrained such that the solution is not considered to be a valid unless the dynamic equations are satisfied at all time points. The simulation and optimization are effectively done simultaneously. Due to the implicit integration, time steps can be more coarse than in a differential equation solver. In a gait scenario this means that that the model constraints and cost function are evaluated at 100 nodes in the gait cycle versus 10,000 integration steps in a variable-step forward dynamic simulation. Furthermore, no time is wasted on accurate simulations of movements that are far from the optimum. Constrained optimization algorithms require a Jacobian matrix that contains the partial derivatives of each of the dynamic constraints with respect to of each of the state and control variables at all time points. This is a large but sparse matrix. An implicit dynamics formulation requires computation of the dynamic residuals f as a function of the states x and their derivatives, and controls u:f(x, dxdt, u) 0If the dynamics of musculoskeletal system are formulated implicitly, the Jacobian elements are often available analytically, eliminating the need for numerical differentiation; this is obviously computationally advantageous. Additionally, implicit formulation of musculoskeletal dynamics do not suffer from singularities from low mass bodies, zero muscle activation, or other stiff system or

physical exercise↗