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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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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Numerical solutions of the complete Navier-Stokes equations

The physical phenomena within supersonic flows that sustain chemical reactions are investigated. An earlier study to develop accurate physical models for supersonic reacting flowfields focused on 2-D laminar shear layers. The objective is to examine the mixing and subsequent combustion within turbulent reacting shear layers. To conduct this study, a computer program has been written to solve the axisymmetric Reynolds averaged Navier-Stokes equations. The numerical method uses a cell-centered finite volume approach and a Runge Kutta time stepping scheme. The Reynolds averaged equations are closed using the eddy viscosity concept. Several zero-equation models have been tested by making calculations for an H2-air nonreacting coaxial jet flow. Comparisons made with experimental data show that Cohen's eddy viscosity model provides best agreement. The finite rate chemistry model used in the study of 2-D laminar shear layers is incorporated into the computer program and data is compared from a recent experiment performed at NASA Langley.

Hassan, H. A.↗
NASA NTRS1990

Global simulation of the solar wind-magnetosphere interaction - The importance of its numerical validity

This paper examines the global interaction of the solar wind with the geomagnetic field, using a newly developed three-dimensional high-precision MHD simulation code which employs the fourth-order Runge-Kutta-Gill scheme in time and the direct finite-difference method in space, and which allows much less numerical error than the conventional code. The simulation reveals in detail the formation processes of the magnetosphere and the bow shock, as well as the plasma sheet formation process. It is shown that, contrary to the conventional understanding, no Kelvin-Helmholtz instability occurs along the magnetopause in an ideal MHD.

Watanabe, K.↗
NASA NTRS2013

Spectral Element Method for the Simulation of Unsteady Compressible Flows

This work uses a discontinuous-Galerkin spectral-element method (DGSEM) to solve the compressible Navier-Stokes equations [1{3]. The inviscid ux is computed using the approximate Riemann solver of Roe [4]. The viscous fluxes are computed using the second form of Bassi and Rebay (BR2) [5] in a manner consistent with the spectral-element approximation. The method of lines with the classical 4th-order explicit Runge-Kutta scheme is used for time integration. Results for polynomial orders up to p = 15 (16th order) are presented. The code is parallelized using the Message Passing Interface (MPI). The computations presented in this work are performed using the Sandy Bridge nodes of the NASA Pleiades supercomputer at NASA Ames Research Center. Each Sandy Bridge node consists of 2 eight-core Intel Xeon E5-2670 processors with a clock speed of 2.6Ghz and 2GB per core memory. On a Sandy Bridge node the Tau Benchmark [6] runs in a time of 7.6s.

Diosady, Laslo Tibor↗
NASA NTRS1997

Solution of Aeroacoustic Problems by a Nonlinear, Hybrid Method

Category 1, problem 3 (scattering of sound by a sphere) and category 2, problem 1 (spherical source in a cylindrical duct subject to uniform flow) are solved in generalized coordinates using the nonlinear Euler equations together with nonreflecting boundary conditions. A temporally and spatially fourth-order accurate finite-difference, Runge-Kutta time-marching technique is employed for the near-field calculations and a Kirchhoff method is employed for the prediction of far-field sound. Computations are all performed on parallel processors using the data-parallel paradigm.

Oezyoeruek, Yusuf↗
NASA NTRS1992

Neural network error correction for solving coupled ordinary differential equations

A neural network is presented to learn errors generated by a numerical algorithm for solving coupled nonlinear differential equations. The method is based on using a neural network to correctly learn the error generated by, for example, Runge-Kutta on a model molecular dynamics (MD) problem. The neural network programs used in this study were developed by NASA. Comparisons are made for training the neural network using backpropagation and a new method which was found to converge with fewer iterations. The neural net programs, the MD model and the calculations are discussed.

Shelton, R. O.↗
NASA NTRS1986

An Euler aerodynamic method for leading-edge vortex flow simulation

The current capabilities and the future plans for a three dimensional Euler Aerodynamic Method are described. The basic solution algorithm is based on the finite volume, Runge-Kutta pseudo-time-stepping scheme of FLO-57. Several modifications to improve accuracy and computational efficiency were incorporated and others are being investigated. The computer code is used to analyze a cropped delta wing at 0.6 Mach number and an arrow wing at 0.85 Mach number. Computed aerodynamic parameters are compared with experimental data. In all cases, the configuration is impulsively started and no Kutta condition is applied at sharp edges. The results indicate that with additional development and validation, the present method will be a useful tool for engineering analysis of high speed aircraft.

Raj, P.↗
DOE OSTI2025

Sylvester-preconditioned adaptive-rank implicit time integrators for advection-diffusion equations with variable coefficients

Here, we consider the adaptive-rank integration of multi-dimensional time-dependent advection-diffusion partial differential equations (PDEs) with variable coefficients. We employ a standard finite-difference method for spatial discretization coupled with high-order diagonally implicit Runge-Kutta temporal schemes. The discrete equation is a generalized Sylvester equation (GSE), which we solve with a projection-based adaptive-rank algorithm structured around two key strategies: (i) constructing dimension-wise subspaces using a novel atypical extended Krylov strategy, and (ii) efficiently solving the basis coefficient matrix with a preconditioned GMRES solver. The low-rank decomposition is performed in 2D using SVD and with high-order SVD (HOSVD) in 3D to represent the tensor in a compressed Tucker format. For d-dimensional problems (here, d = 2 or 3), the computational complexity and memory storage of the approach are found numerically to scale as and $\mathscr{O}(Nr^2) + \mathscr{O} (r^{d+1})$ and $\mathscr{O}(Nr) + \mathscr{O} (r^{d})$, respectively, with the one-dimensional resolution and the maximal rank during the Krylov iteration (which we find to be largely independent of on our numerical examples). We present numerical examples that illustrate the advertised properties of the algorithm.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1984

On the solution of problems involving impact type loading

The response of beam and plate members to pulse and impact loading is investigated, and numerical methods are analyzed and compared. The equations of motion, the finite difference and finite element methods, the time integration/Runge-Kutta techniques, and material modeling are discussed in detail. It is found that both the finite difference and the finite element methods could be accurately employed to discretize the spatial variation in the displacements. Central differences or a fourth order Runge-Kutta algorithm could be used for the time integration. The total energy of the system would give the stability and accuracy of the solution. Results showed that the finite element method provided better efficiency in obtaining accurate solution than the finite difference method when a scalar processor is used. However, the finite difference method was more efficient on the vector processor. Therefore, the most efficient method of solution depends on the type of computer present for the analysis.

Moyer, E. T., Jr.↗
NASA NTRS1989

Finite element computation of hypersonic flow past a complete body

The finite element method was applied to compressible flows past complete blunt bodies in a first attempt to use the method to model hypersonic flow past re-entry vehicles. A Runge-Kutta time marching scheme was utilized and was found to adequately handle the bow shock and downstream wake. Adaptive refinement was successively applied to the flow field grid, and improvement in solution accuracy was observed. The results reported in this paper include the flow past a circular cylinder at Mach 3, and the flow in the plane of symmetry for the flow past a sphere at Mach 10.

Hommel, Mark↗
DOE OSTI2020

An error-controlled adaptive time-stepping method for particle advancement in coupled CFD-DEM simulations

Coupled Computational-Fluid-Dynamics (CFD) and Discrete-Element-Method (DEM) models provide an accurate description of multiphase physical systems where a solid granular particle phase exists in an underlying gaseous continuous medium. The time integration of the granular phase in these simulations is typically handled using an explicit scheme with a constant time-step among all particles that is invariant in time to resolve inter-particle collisions. A locally third-order accurate adaptive time integration technique for particles that employs an embedded locally second-order scheme for error determination is presented in this work. The particle time-step size is dynamically adapted based on solution error, thus leading to significant savings in computational time. The efficacy of our scheme is quantified using four test cases of varying complexity (binary collision, homogeneous cooling system, fluidized bed and hopper discharge). The adaptive time-stepping method exhibits improved performance (~ 2–3 times in most of the cases studied) compared to three commonly used non-adaptive time-step methods (first-order Euler-explicit, second-order Adams-Bashforth and third-order Runge-Kutta schemes), while maintaining the same level of accuracy and parallel scalability.

42 ENGINEERING↗
DOE OSTI2024

A high-order explicit Runge-Kutta approximation technique for the shallow water equations

Here, we introduce a high-order space–time approximation of the Shallow Water Equations with sources that is invariant-domain preserving (IDP), well-balanced with respect to rest states, and employs a novel explicit Runge–Kutta (ERK) introduced in Ern and Guermond (SIAM J. Sci. Comput. 44(5), A3366–A3392, 2022) for systems of non-linear conservation equations. The resulting method is then numerically illustrated through verification and validation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Time-dependent density functional theory with the orthogonal projector augmented wave method

The projector augmented wave (PAW) method of Blöchl linearly maps smooth pseudo wavefunctions to the highly oscillatory all-electron DFT orbitals. Compared to norm-conserving pseudopotentials (NCPP), PAW has the advantage of lower kinetic energy cutoffs and larger grid spacing at the cost of having to solve for non-orthogonal wavefunctions. We earlier developed orthogonal PAW (OPAW) to allow the use of PAW when orthogonal wavefunctions are required. In OPAW, the pseudo wavefunctions are transformed through the efficient application of powers of the PAW overlap operator with essentially no extra cost compared to NCPP methods. Previously, we applied OPAW to DFT. Here, we take the first step to make OPAW viable for post-DFT methods by implementing it in real-time time-dependent (TD) DFT. Using fourth-order Runge–Kutta for the time-propagation, we compare calculations of absorption spectra for various organic and biological molecules and show that very large grid spacings are sufficient, 0.6–0.7 bohr in OPAW-TDDFT rather than the 0.4–0.5 bohr used in traditional NCPP-TDDFT calculations. This reduces the memory and propagation costs by around a factor of 3. Our method would be directly applicable to any post-DFT methods that require time-dependent propagations such as the GW approximation and the Bethe–Salpeter equation.

Chemistry↗
NASA NTRS1994

An assessment of the adaptive unstructured tetrahedral grid, Euler Flow Solver Code FELISA

A three-dimensional solution-adaptive Euler flow solver for unstructured tetrahedral meshes is assessed, and the accuracy and efficiency of the method for predicting sonic boom pressure signatures about simple generic models are demonstrated. Comparison of computational and wind tunnel data and enhancement of numerical solutions by means of grid adaptivity are discussed. The mesh generation is based on the advancing front technique. The FELISA code consists of two solvers, the Taylor-Galerkin and the Runge-Kutta-Galerkin schemes, both of which are spacially discretized by the usual Galerkin weighted residual finite-element methods but with different explicit time-marching schemes to steady state. The solution-adaptive grid procedure is based on either remeshing or mesh refinement techniques. An alternative geometry adaptive procedure is also incorporated.

Djomehri, M. Jahed↗
NASA NTRS1986

Influence of numerical dissipation in computing supersonic vortex-dominated flows

Steady supersonic vortex-dominated flows are solved using the unsteady Euler equations for conical and three-dimensional flows around sharp- and round-edged delta wings. The computational method is a finite-volume scheme which uses a four-stage Runge-Kutta time stepping with explicit second- and fourth-order dissipation terms. The grid is generated by a modified Joukowski transformation. The steady flow solution is obtained through time-stepping with initial conditions corresponding to the freestream conditions, and the bow shock is captured as a part of the solution. The scheme is applied to flat-plate and elliptic-section wings with a leading edge sweep of 70 deg at an angle of attack of 10 deg and a freestream Mach number of 2.0. Three grid sizes of 29 x 39, 65 x 65 and 100 x 100 have been used. The results for sharp-edged wings show that they are consistent with all grid sizes and variation of the artificial viscosity coefficients. The results for round-edged wings show that separated and attached flow solutions can be obtained by varying the artificial viscosity coefficients. They also show that the solutions are independent of the way time stepping is done. Local time-stepping and global minimum time-steeping produce same solutions.

Kandil, O. A.↗
NASA NTRS1988

A Navier-Stokes solver for cascade flows

A computer code for solving the Reynolds averaged full Navier-Stokes equations has been developed and applied using sheared H-type grids. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. The integration in time is based on an explicit four-stage Runge-Kutta scheme. Local time stepping, variable coefficient implicit residual smoothing, and a full multigrid method have been implemented to accelerate steady state calculations. Comparisons with experimental data show that the code is an accurate viscous solver and can give very good blade-to-blade predictions for engineering applications in less than 100 multigrid cycles on the finest mesh.

Arnone, A.↗
NASA NTRS1992

Direct numerical simulations of a spatially developing plane wake

In the present paper, direct numerical methods by which to simulate the spatially developing free shear flows in the transitional region are described and the numerical results of a spatially developing plane wake are presented. The incompressible time-dependent Navier-Stokes equations were solved using Pade finite difference approximations in the streamwise direction, a mapped pseudospectral Fourier method in the cross-stream direction, and a third-order compact Runge-Kutta scheme for time advancement. The unstable modes of the Orr-Sommerfeld equations were used to perturb the inlet of the wake. Statistical analyses were performed and some numerical results were compared with experimental measurements. When only the fundamental mode is forced, the energy spectra show amplification of the fundamental and its higher harmonics. In this case, unperturbed alternate vortices develop in the saturation region of the wake. The phase jitter around the fundamental frequency plays a critical role in generating vortices of random shape and spacing. Large- and small-scale distortions of the fundamental structure are observed. Pairing of vortices of the same sign is observed, as well as vortex coupling of vortices of the opposite sign.

Maekawa, Hiroshi↗
NASA NTRS1993

A Navier-Stokes solver for turbomachinery applications

A computer code for solving the Reynolds-averaged full Navier-Stokes equations has been developed and applied using H- and C-type grids. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. The integration in time is based on an explicit four-stage Runge-Kutta scheme. Local time stepping, variable coefficient implicit residual smoothing, and a full multigrid method have been implemented to accelerate steady-state calculations. A grid independence analysis is presented for a transonic rotor blade. Comparisons with experimental data show that the code is an accurate viscous solver and can give very good blade-to-blade predictions for engineering applications.

Arnone, A.↗
DOE OSTI2022

An immersed interface method for the 2D vorticity-velocity Navier-Stokes equations with multiple bodies

We present an immersed interface method for the vorticity-velocity form of the 2D Navier Stokes equations that directly addresses challenges posed by nonconvex immersed bodies, multiply connected domains, and the calculation of force distributions on immersed surfaces. The immersed interface method is re-interpreted as a polynomial extrapolation of flow quantities and boundary conditions into the immersed solid bodies, reducing computational cost and enabling simulations with nonconvex bodies that could not be discretized with previous immersed interface methods. In the flow, the vorticity transport equation is discretized using a conservative finite difference scheme and explicit Runge-Kutta time integration. The velocity reconstruction problem is transformed to a scalar Poisson equation that is discretized with conservative finite differences, and solved using an FFT-accelerated iterative algorithm. The use of conservative differencing throughout leads to exact enforcement of a discrete Kelvin's theorem, allowing for simulations with multiply connected domains and outflow boundaries that have challenged other immersed interface vortex methods. We also explore novel methods for recovering time-dependent pressure distributions on immersed bodies within a vorticity-based method and present a novel control volume formulation for recovering aerodynamic moments from only the vorticity and velocity fields. The method achieves second order spatial accuracy and third order temporal accuracy, and is validated on a variety of 2D flows in internal and free-space domains.

97 MATHEMATICS AND COMPUTING↗