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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 991 records · Page 55
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

A fast Euler solver for steady flows

A numerical technique to solve the Euler equations for steady, two-dimensional flows is presented. The technique extends to two-dimensional problems a formulation which was found to be extremely efficient for one-dimensional flows. Generalized Riemann variables are defined along two families of orthogonal coordinates, and integrated separately, sweeping back and forth alternatively along coordinate lines. The technique is second-order accurate and converges very rapidly. In addition, each step requires a minimal number of operations. Preliminary results for subsonic and transonic shockless flows are presented and discussed.

Moretti, G.↗
NASA NTRS1987

A parallelized elliptic solver for reacting flows

A modified Newton algorithm for the solution of nonlinear elliptic boundary value problems via finite discretization methods is presented. A serial implementation of this algorithm which has recently been applied successfully to the computation of an axisymmetric over-ventilated subsonic laminar methane-air jet diffusion flame is described. Parallel implementation issues and a complexity theory are presented. Included as well are actual performance data for model systems obtained on the Intel Hypercube and a discussion of its implications for modeling realistic systems.

Keyes, David E.↗
NASA NTRS1991

An implicit three-dimensional Navier-Stokes solver for compressible flow

A three-dimensional numerical method based on the lower-upper symmetric-Gauss-Seidel implicit scheme in conjunction with the flux-limited dissipation model is developed for solving the compressible Navier-Stokes equations. A new computer code which is based on this method requires only 9 microsec per grid-point per iteration on a single processor of a Cray YMP computer and executes at the sustained rate of 170 MFLOPS. A reduction of 4 orders of magnitude in the residual for a high Reynolds number flow using 230 K grid points is obtained in 24 minutes. The computational results compare well with available experimental data.

Yoon, Seokkwan↗
NASA NTRS2017

Geometrically Flexible and Efficient Flow Analysis of High Speed Vehicles Via Domain Decomposition, Part 1: Unstructured-Grid Solver for High Speed Flows

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. This paper describes the key numerical methods and techniques that were found to be required to robustly obtain accurate solutions to hypersonic flows on non-hex-dominant unstructured grids. The methods and techniques described include: an augmented stencil, weighted linear least squares, cell-average gradient method, a robust multidimensional cell-average gradient-limiter process that is consistent with the augmented stencil of the cell-average gradient method and a cell-face gradient method that contains a cell skewness sensitive damping term derived using hyperbolic diffusion based concepts. A data-parallel matrix-based symmetric Gauss-Seidel point-implicit scheme, used to solve the governing equations, is described and shown to be more robust and efficient than a matrix-free alternative. In addition, a y+ adaptive turbulent wall boundary condition methodology is presented. This boundary condition methodology is deigned to automatically switch between a solve-to-the-wall and a wall-matching-function boundary condition based on the local y+ of the 1st cell center off the wall. The aforementioned methods and techniques are then applied to a series of hypersonic and supersonic turbulent flat plate unit tests to examine the efficiency, robustness and convergence behavior of the implicit scheme and to determine the ability of the solve-to-the-wall and y+ adaptive turbulent wall boundary conditions to reproduce the turbulent law-of-the-wall. Finally, the thermally perfect, chemically frozen, Mach 7.8 turbulent flow of air through a scramjet flow-path is computed and compared with experimental data to demonstrate the robustness, accuracy and convergence behavior of the unstructured-grid solver for a realistic 3-D geometry on a non-hex-dominant grid.

White, Jeffery A.↗
NASA NTRS1988

3-D plume flow computations with an upwind solver

In the present study multi-nozzle plume flows are computed with a three-dimensional, Navier-Stokes solver. Numerical simulations are performed with the flux-split, two-factor, time symptotic, viscous flow solver. The two factor splitting provides a stable three-dimensional solution procedure under ideal-gas assumptions. Viscous, ideal-gas solutions for a thin lip symmetrical nozzle are compared with experimental and numerical solutions. Computed solutions to axisymmetric and three-dimensional, multi-nozzle problems at various altitudes and flight conditions demonstrate flow field complexity and three-dimensional effects.

Venkatapathy, Ethiraj↗
DOE OSTI2018

A scalable geometric multigrid solver for nonsymmetric elliptic systems with application to variable-density flows

A geometric multigrid algorithm is introduced for solving nonsymmetric linear systems resulting from the discretization of the variable density Navier–Stokes equations on nonuniform structured rectilinear grids and high-Reynolds number flows. The restriction operation is defined such that the resulting system on the coarser grids is symmetric, thereby allowing for the use of efficient smoother algorithms. To achieve an optimal rate of convergence, the sequence of interpolation and restriction operations are determined through a dynamic procedure. A parallel partitioning strategy is introduced to minimize communication while maintaining the load balance between all processors. To test the proposed algorithm, we consider two cases: 1) homogeneous isotropic turbulence discretized on uniform grids and 2) turbulent duct flow discretized on stretched grids. Testing the algorithm on systems with up to a billion unknowns shows that the cost varies linearly with the number of unknowns. This O (N) behavior confirms the robustness of the proposed multigrid method regarding ill-conditioning of large systems characteristic of multiscale high-Reynolds number turbulent flows. The robustness of our method to density variations is established by considering cases where density varies sharply in space by a factor of up to 104, showing its applicability to two-phase flow problems. Strong and weak scalability studies are carried out, employing up to 30,000 processors, to examine the parallel performance of our implementation. Excellent scalability of our solver is shown for a granularity as low as 104 to 105 unknowns per processor. At its tested peak throughput, it solves approximately 4 billion unknowns per second employing over 16,000 processors with a parallel efficiency higher than 50%.

Computer Science↗
DOE OSTI2021

The curled wake model: a three-dimensional and extremely fast steady-state wake solver for wind plant flows

Abstract. Wind turbine wake models typically require approximations, such as wake superposition and deflection models, to accurately describe wake physics. However, capturing the phenomena of interest, such as the curled wake and interaction of multiple wakes, in wind power plant flows comes with an increased computational cost. To address this, we propose a new hybrid method that uses analytical solutions with an approximate form of the Reynolds-averaged Navier–Stokes equations to solve the time-averaged flow over a wind plant. We compare results from the solver to supervisory control and data acquisition data from the Lillgrund wind plant obtaining wake model predictions which are generally within 1 standard deviation of the mean power data. We perform simulations of flow over the Columbia River Gorge to demonstrate the capabilities of the model in complex terrain. We also apply the solver to a case with wake steering, which agreed well with large-eddy simulations. This new solver reduces the time – and therefore the related cost – it takes to simulate a steady-state wind plant flow (on the order of seconds using one core). Because the model is computationally efficient, it can also be used for different applications including wake steering for wind power plants and layout optimization.

17 WIND ENERGY↗
DOE OSTI2022

An aggregation-based nonlinear multigrid solver for two-phase flow and transport in porous media

A nonlinear multigrid solver for two-phase flow and transport in a mixed fractional-flow velocity-pressure-saturation formulation is proposed. The solver, which is under the framework of the full approximation scheme (FAS), extends our previous work on nonlinear multigrid for heterogeneous diffusion problems. The coarse spaces in the multigrid hierarchy are constructed by first aggregating degrees of freedom, and then solving some local flow problems. The mixed formulation and the choice of coarse spaces allow us to assemble the coarse problems without visiting finer levels during the solving phase, which is crucial for the scalability of multigrid methods. Specifically, a natural generalization of the upwind flux can be evaluated directly on coarse levels using the precomputed coarse flux basis vectors. We find that the resulting solver is applicable to problems discretized on general unstructured grids. The performance of the proposed nonlinear multigrid solver in comparison with the standard single level Newton's method is demonstrated through challenging numerical examples. It is observed that the proposed solver is robust for highly nonlinear problems and clearly outperforms Newton's method in the case of high Courant-Friedrichs-Lewy (CFL) numbers.

58 GEOSCIENCES↗
NASA NTRS2012

OVERSMART Reporting Tool for Flow Computations Over Large Grid Systems

Structured grid solvers such as NASA's OVERFLOW compressible Navier-Stokes flow solver can generate large data files that contain convergence histories for flow equation residuals, turbulence model equation residuals, component forces and moments, and component relative motion dynamics variables. Most of today's large-scale problems can extend to hundreds of grids, and over 100 million grid points. However, due to the lack of efficient tools, only a small fraction of information contained in these files is analyzed. OVERSMART (OVERFLOW Solution Monitoring And Reporting Tool) provides a comprehensive report of solution convergence of flow computations over large, complex grid systems. It produces a one-page executive summary of the behavior of flow equation residuals, turbulence model equation residuals, and component forces and moments. Under the automatic option, a matrix of commonly viewed plots such as residual histograms, composite residuals, sub-iteration bar graphs, and component forces and moments is automatically generated. Specific plots required by the user can also be prescribed via a command file or a graphical user interface. Output is directed to the user s computer screen and/or to an html file for archival purposes. The current implementation has been targeted for the OVERFLOW flow solver, which is used to obtain a flow solution on structured overset grids. The OVERSMART framework allows easy extension to other flow solvers.

Kao, David L.↗
DOE OSTI2025

FreeMHD: Validation and verification of the open-source, multi-domain, multi-phase solver for electrically conductive flows

The extreme heat fluxes in the divertor region of tokamaks may require an alternative to solid plasma-facing components, for the extraction of heat and the protection of the surrounding walls. Flowing liquid metals are proposed as an alternative, but raise additional challenges that require investigation and numerical simulations. Free surface designs are desirable for plasma-facing components, but steady flow profiles and surface stability must be ensured to limit undesirable interactions with the plasma. Previous studies have mainly used steady-state, 2D, or simplified models for internal flows and have not been able to adequately model free-surface liquid metal (LM) experiments. Therefore, FreeMHD has been recently developed as an open-source magnetohydrodynamics (MHD) solver for free-surface electrically conductive flows subject to a strong external magnetic field. The FreeMHD solver computes incompressible free-surface flows with multi-region coupling for the investigation of MHD phenomena involving fluid and solid domains. The model utilizes the finite-volume OpenFOAM framework under the low magnetic Reynolds number approximation. FreeMHD is validated using analytical solutions for the velocity profiles of closed channel flows with various Hartmann numbers and wall conductance ratios. Next, experimental measurements are then used to verify FreeMHD, through a series of cases involving dam breaking, 3D magnetic fields, and free-surface LM flows. These results demonstrate that FreeMHD is a reliable tool for the design of LM systems under free surface conditions at the reactor scale. Furthermore, it is flexible, computationally inexpensive, and can be used to solve fully 3D transient MHD flows.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1991

Eigenvalue calculation procedure for an Euler/Navier-Stokes solver with application to flows over airfoils

A Lanczos procedure is presently applied to a Navier-Stokes (N-S) solver for eigenvalues and eigenvectors associated with the small-perturbation analysis of the N-S equations' finite-difference representation for airfoil flows; the matrix used is very large, sparse, real, and nonsymmetric. The Lanczos procedure is shown to furnish complete spectral information for the eigenvalues, as required for transient-stability analysis of N-S solvers.

Mahajan, Aparajit J.↗
NASA NTRS1989

Numerical simulation of flow over a hypersonic aircraft using an explicit upwind PNS solver

A hypersonic flow field over a generic airplane configuration is simulated by solving the Parabolized Navier-Stokes (PNS) equations. The finite difference solution of the PNS equations is calculated using a noniterative space marching, explicit, upwind scheme recently developed by the authors. Special gridding techniques are used which allowed the sharp changes in surface geometry of the airplane configuration to be modelled without smoothing of corners. Comparisons of the PNS results to a solution of the Navier-Stokes equations demonstrates a good agreement of the numerical results in approximately 1/6 of the cpu time. This paper demonstrates that the explicit upwind algorithm for solving the PNS equations is an efficient method for simulating hypersonic flow fields about complete airplane configurations and should be considered as an alternative to solving the Navier-Stokes equations for flow fields where the PNS equations are valid.

Korte, John J.↗
DOE OSTI2016

New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards’ equation

We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioning strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. Furthermore, we show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.

58 GEOSCIENCES↗
NASA NTRS1987

Supersonic flow computations over aerospace configurations using an Euler marching solver

For fully supersonic flows, an efficient strategy for obtaining numerical solutions is to employ space marching techniques. A full potential marching technique, known as the SIMP code and capable of handling such embedded subsonic regions, has achieved some success analyzing low supersonic Mach number flows. The extension of the full potential approach to the Euler equation which model the exact nonlinear inviscid gas dynamic flow processes is presented. Within the assumption of an inviscid flow, such an Euler marching solver can be applied to a wide class of shocked flows including the hypersonic range. The intent is to maintain some of the basic features of the full potential SIMP code within the Euler solver in dealing with geometry input, gridding techniques, and input/output routines including post processing of results. An Euler marching code known as EMTAC was developed. Results obtained for a variety of configurations involving canard, wing, horizontal tail, flow-through inlet, and fuselage using both the EMTAC and SIMP codes are reported. For shocked cases satisfying the isentropic assumption, the EMTAC and SIMP codes produced practically the same results. In terms of execution time, the EMTAC code is slower.

Szema, Kuo-Yen↗
DOE OSTI2025

Limitations of Fault-Tolerant Quantum Linear System Solvers for Quantum Power Flow

Quantum computers hold promise for solving problems intractable for classical computers, especially those with high time or space complexity. Practical quantum advantage can be said to exist for such problems when the end-to-end time for solving such a problem using a classical algorithm exceeds that required by a quantum algorithm. Reducing the power flow (PF) problem into a linear system of equations allows for the formulation of quantum PF (QPF) algorithms, which are based on solving methods for quantum linear systems such as the Harrow-Hassidim-Lloyd (HHL) algorithm. Speedup from using QPF algorithms is often claimed to be exponential when compared to classical PF solved by state-of-the-art algorithms. Here, we investigate the potential for practical quantum advantage in solving QPF compared to classical methods on gate-based quantum computers. Notably, this paper does not present a new QPF solving algorithm but scrutinizes the end-to-end complexity of the QPF approach, providing a nuanced evaluation of the purported quantum speedup in this problem. Our analysis establishes a best-case bound for the HHL-based quantum power flow complexity, conclusively demonstrating that the HHL-based method has higher runtime complexity compared to the classical algorithm for solving the direct current power flow (DCPF) and fast decoupled load flow (FDLF) problem. Notably, our analysis and conclusions can be extended to any quantum linear system solver with rigorous performance guarantees, based on the known complexity lower bounds for this problem. Additionally, we establish that for potential practical quantum advantage (PQA) to exist it is necessary to consider DCPF-type problems with a very narrow range of condition number values and readout requirements.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2023

Optimal Power Flow Derived Sparse Linear Solver Benchmarks

Due to the changing nature of the power grid, it is increasingly important to be able to solve a high-fidelity optimal power-flow models on large power networks. This high-fidelity problem, called AC Optimal Power Flow (ACOPF), is a nonlinear, nonconvex optimization problem. One of the few reliable ways of solving such a problem is interior point methods. These methods result in sparse linear systems where the coefficient matrix is symmetric, indefinite and nearly always ill-conditioned. As such, they are particularly challenging for sparse linear solvers and represent a considerable computational bottleneck in solving the ACOPF problem. In this paper, we introduce a repository of linear systems captured from ACOPF problems when solved by the open-source optimizer IPOPT. These matrices are meant to be used as a test suite for sparse linear solver development.

97 MATHEMATICS AND COMPUTING↗