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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Potential quantum advantage for simulation of fluid dynamics

Numerical simulation of turbulent fluid dynamics needs to either parametrize turbulence—which introduces large uncertainties—or explicitly resolve the smallest scales—which is prohibitively expensive. Here, we provide evidence through analytic bounds and numerical studies that a potential quantum speedup can be achieved to simulate fluid dynamics using quantum computing. Specifically, we provide a lattice Boltzmann formulation of fluid dynamics for which we give evidence that low-order Carleman linearization is much more accurate than previously believed for these systems. This is achieved via a combination of reformulating the Navier-Stokes nonlinearity (u·$\triangledown$u) to lattice-Boltzmann nonlinearity (u 2 ) and accurately linearizing the dynamical equations, which effectively trades nonlinearity for additional degrees of freedom that add negligible expense in the quantum solver. Based on this, we apply a quantum algorithm for simulating the Carleman-linearized lattice Boltzmann equation and provide evidence that its cost scales logarithmically with system size compared with polynomial scaling in the best known classical algorithms. In this paper, we suggest that a quantum advantage may exist for simulating fluid dynamics, paving the way for simulating nonlinear multiscale transport phenomena in a wide range of disciplines using quantum computing.

42 ENGINEERING↗
DOE OSTI2020

A fast implicit solver for semiconductor models in one space dimension

Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in semiconductor devices under a low-density assumption. At each implicit time step, the discretized system is formulated as a fixed-point problem, which can then be solved with a variety of methods. A key algorithmic component in all the approaches considered here is a recently developed sweeping algorithm for Vlasov-Poisson systems. A synthetic acceleration scheme has been implemented to accelerate the convergence of iterative solvers by using the solution to a drift-diffusion equation as a preconditioner. The performance of four iterative solvers and their accelerated variants has been compared on problems modeling semiconductor devices with various electron mean-free-path.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

Implicit solvers for unstructured meshes

Implicit methods were developed and tested for unstructured mesh computations. The approximate system which arises from the Newton linearization of the nonlinear evolution operator is solved by using the preconditioned GMRES (Generalized Minimum Residual) technique. Three different preconditioners were studied, namely, the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over relaxation (SSOR). The preconditioners were optimized to have good vectorization properties. SSOR and ILU were also studied as iterative schemes. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also studied. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Venkatakrishnan, V.↗
DOE OSTI2023

Development of a continuous synthesis process for carbamazepine using validated in-line Raman spectroscopy and kinetic modelling for disturbance simulation

Mitigation of failure modes in the continuous synthesis (CS) of a drug substance (DS) has the potential to widen the adoption of continuous manufacturing (CM) technologies by the pharmaceutical industry. Here, this work demonstrates the development of a robust continuous process for the synthesis of carbamazepine (CBZ), an essential medicine as per the World Health Organization (WHO), facilitated by kinetic modelling and monitored by in-line Raman spectroscopy. Accurate kinetic modelling and the use of validated process analytical technology (PAT) models for quantitative measurement were found to play an important role in developing CS of drug substances. Kinetic data for the formation of CBZ from iminostilbene (ISB) were collected by batch reaction sampling and high-performance liquid chromatography (HPLC) analysis. A non-linear solver and iterative method was applied to determine two sets of Arrhenius parameters simultaneously for the reaction system by minimizing the standard error of the model fit. The start-up and dynamic equilibrium stages for the CS of CBZ using a continuous stirred tank reactor (CSTR) were modelled based on the batch kinetic data and employed to optimize conversion and simulate process disturbances. An in-line Raman spectroscopy method was successfully developed, validated, and integrated to determine the concentrations of CBZ and ISB within the operating range for the CS. The CS kinetic model was evaluated experimentally from startup to dynamic equilibrium over 10 residence times with monitoring by HPLC and in-line Raman spectroscopy. The developed kinetic model in tandem with in-line Raman spectroscopy successfully predicted disturbances due to changes in process variables and can serve as a useful tool in the future design of advanced process control strategies for the continuous synthesis of CBZ.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2016

An Inviscid Decoupled Method for the Roe FDS Scheme in the Reacting Gas Path of FUN3D

An approach is described to decouple the species continuity equations from the mixture continuity, momentum, and total energy equations for the Roe flux difference splitting scheme. This decoupling simplifies the implicit system, so that the flow solver can be made significantly more efficient, with very little penalty on overall scheme robustness. Most importantly, the computational cost of the point implicit relaxation is shown to scale linearly with the number of species for the decoupled system, whereas the fully coupled approach scales quadratically. Also, the decoupled method significantly reduces the cost in wall time and memory in comparison to the fully coupled approach. This work lays the foundation for development of an efficient adjoint solution procedure for high speed reacting flow.

Thompson, Kyle B.↗
NASA NTRS2018

High-resolution Wave Propagation Method for Stratified Flows

The implementation of the multidimensional f-waves Riemann solver for the time-dependent, three-dimensional, nonhydrostatic, meso- and microscale atmospheric flows is described in detail. The Riemann solver employs flux-based wave decomposition (f-waves) for the calculation of Godunov fluxes in which the flux differences are written directly as the linear combination of the right eigenvectors of the hyperbolic system. The scheme incorporates the source term due to gravity without introducing discretization errors which is an important property in the context of atmospheric flows. The resulting flow solver is conservative, accurate, stable, and well-balanced. The implementation of the solver is evaluated using benchmark test cases for atmospheric dynamics.

Riemann problem↗
NASA NTRS1989

Parallel linear equation solvers for finite element computations

The overall objective of this research is to develop efficient methods for the solution of linear and nonlinear systems of equations on parallel and supercomputers, and to apply these methods to the solution of problems in structural analysis. Attention has been given so far only to linear equations. The methods considered for the solution of the stiffness equation Kx=f have been Choleski factorization and the conjugate gradient iteration with SSOR and Incomplete Choleski preconditioning. More detail on these methods will be given on subsequent slides. These methods have been used to solve for the static displacements for the mast and panel focus problems in conjunction with the CSM testbed system based on NICE/SPAR.

Ortega, James M.↗
NASA NTRS1991

Implicit solvers for unstructured meshes

Implicit methods for unstructured mesh computations are developed and tested. The approximate system which arises from the Newton-linearization of the nonlinear evolution operator is solved by using the preconditioned generalized minimum residual technique. These different preconditioners are investigated: the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over-relaxation (SSOR). The preconditioners have been optimized to have good vectorization properties. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also investigated. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Venkatakrishnan, V.↗
NASA NTRS1992

Aerodynamic shape optimization via sensitivity analysis on decomposed computational domains

Direct and iterative method considered to be most applicable to large systems of linear equations arising in discrete sensitivity analysis are assessed. Based on a single-domain grid, computations are performed using a banded matrix solver and an iterative solver, the generalized minimum residual (GMRES) method. The banded matrix solver is found to be generally the most economical method for those applications where the number of right-hand sides is large (i.e., a large number of design variables or a large number of adjoint vectors). For systems of equations that are too large to be solved by direct methods, an approach is proposed whereby the computational domain is divided into small subdomains, and each subdomain is solved separately.

Eleshaky, Mohamed E.↗
NASA NTRS2001

Multigrid approaches to non-linear diffusion problems on unstructured meshes

The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.

Mavriplis, Dimitri J.↗
DOE OSTI2023

Combining Sparse Approximate Factorizations with Mixed-precision Iterative Refinement

The standard LU factorization-based solution process for linear systems can be enhanced in speed or accuracy by employing mixed-precision iterative refinement. Most recent work has focused on dense systems. We investigate the potential of mixed-precision iterative refinement to enhance methods for sparse systems based on approximate sparse factorizations. In doing so, we first develop a new error analysis for LU- and GMRES-based iterative refinement under a general model of LU factorization that accounts for the approximation methods typically used by modern sparse solvers, such as low-rank approximations or relaxed pivoting strategies. We then provide a detailed performance analysis of both the execution time and memory consumption of different algorithms, based on a selected set of iterative refinement variants and approximate sparse factorizations. Our performance study uses the multifrontal solver MUMPS, which can exploit block low-rank factorization and static pivoting. We evaluate the performance of the algorithms on large, sparse problems coming from a variety of real-life and industrial applications showing that mixed-precision iterative refinement combined with approximate sparse factorization can lead to considerable reductions of both the time and memory consumption.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Milestone 49 Report: Batched Sparse LA Phase 5 Implementation

Batched sparse linear algebra operations in general, and solvers in particular, have become the major algorithmic development activity and foremost performance engineering effort in the numerical software libraries work on modern hardware with accelerators such as GPUs. Many applications, ECP and non-ECP alike, require simultaneous solutions of many small linear systems of equations that are structurally sparse in one form or another. In order to move towards high hardware utilization levels, it is important to provide these applications with appropriate interface designs to be both functionally efficient and performance portable and give full access to the appropriate batched sparse solvers running on modern hardware accelerators prevalent across DOE supercomputing sites since the inception of ECP. To this end, we present here a summary of recent advances on the interface designs in use by HPC software libraries supporting batched sparse linear algebra and the development of sparse batched kernel codes for solvers and preconditioners. We also address the potential interoperability opportunities to keep the corresponding software portable between the major hardware accelerators from AMD, Intel, and NVIDIA, while maintaining the appropriate disclosure levels conforming to the active NDA agreements. The presented interface specifications include a mix of batched band, sparse iterative, and sparse direct solvers with their accompanying functionality that is already required by the application codes or we anticipated to be needed in the near future. This report summarizes progress in Kokkos Kernels and the xSDK libraries MAGMA, Ginkgo, hypre, PETSc, and SuperLU.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1988

Newton solution of inviscid and viscous problems

The application of Newton iteration to inviscid and viscous airfoil calculations is examined. Spatial discretization is performed using upwind differences with split fluxes. The system of linear equations which arises as a result of linearization in time is solved directly using either a banded matrix solver or a sparse matrix solver. In the latter case, the solver is used in conjunction with the nested dissection strategy, whose implementation for airfoil calculations is discussed. The boundary conditions are also implemented in a fully implicit manner, thus yielding quadratic convergence. Complexities such as the ordering of cell nodes and the use of a far field vortex to correct freestream for a lifting airfoil are addressed. Various methods to accelerate convergence and improve computational efficiency while using Newton iteration are discussed. Results are presented for inviscid, transonic nonlifting and lifting airfoils and also for laminar viscous cases.

Venkatakrishnan, V.↗
DOE OSTI2024

Sparse Linear Solvers for Large-scale Electromagnetic Transient Simulations

Linear solvers form the basis for electromagnetic transient (EMT) simulations. There is a need to speed up EMT simulations as larger regions are analyzed using EMT simulations. For the same, the performance of linear solvers plays an important role. Exploiting the sparsity of the matrices generated in EMT simulations could assist with speed-up. Scalability is also crucial as power grids expand, demanding solutions capable of accommodating the increasing system size. Recent studies from the North American Electric Reliability Corporation (NERC) increasingly emphasize that EMT simulation models of the power grid will grow larger with the inclusion of power electronics components. Parallelisms in sparsity patterns exploit modern central processing units (CPUs), multi-core CPUs, and graphics processing units (GPUs) architectures in sparse solver designs. Therefore, this paper explores publicly available existing linear solvers and investigates their efficiency in large-scale power grid simulations. A large-scale power grid is developed by increasing the size of the IEEE 39 bus test system to up to 39000 bus systems.

Hsu, Kuan-Chieh↗
NASA NTRS1994

Performance issues for iterative solvers in device simulation

Due to memory limitations, iterative methods have become the method of choice for large scale semiconductor device simulation. However, it is well known that these methods still suffer from reliability problems. The linear systems which appear in numerical simulation of semiconductor devices are notoriously ill-conditioned. In order to produce robust algorithms for practical problems, careful attention must be given to many implementation issues. This paper concentrates on strategies for developing robust preconditioners. In addition, effective data structures and convergence check issues are also discussed. These algorithms are compared with a standard direct sparse matrix solver on a variety of problems.

Fan, Qing↗
DOE OSTI2021

Pyomo.GDP: an ecosystem for logic based modeling and optimization development

We present three core principles for engineering-oriented integrated modeling and optimization tool sets—intuitive modeling contexts, systematic computer-aided reformulations, and flexible solution strategies—and describe how new developments in Pyomo.GDP for Generalized Disjunctive Programming (GDP) advance this vision. We describe a new logical expression system implementation for Pyomo.GDP allowing for a more intuitive description of logical propositions. The logical expression system supports automated reformulation of these logical constraints to linear constraints. We also describe two new logic-based global optimization solver implementations built on Pyomo.GDP that exploit logical structure to avoid “zero-flow” numerical difficulties that arise in nonlinear network design problems when nodes or streams disappear. These new solvers also demonstrate the capability to link to external libraries for expanded functionality within an integrated implementation. We present these new solvers in the context of a flexible array of solution paths available to GDP models. Finally, we present results on a new library of GDP models demonstrating the value of multiple solution approaches.

42 ENGINEERING↗
DOE OSTI2024

Towards exascale for wind energy simulations

We examine large-eddy-simulation modeling approaches and computational performance of two open-source computational fluid dynamics codes for the simulation of atmospheric boundary layer flows that are of direct relevance to wind energy production. The first code, NekRS, is a high-order, unstructured-grid, spectral element code. The second code, AMR-Wind, is a second-order, block-structured, finite-volume code with adaptive mesh refinement capabilities. The objective of this study is to co-develop these codes in order to improve model fidelity and performance for each. These features will be critical for running ABL-based applications such as wind farm analysis on advanced computing architectures. To this end, we investigate the performance of NekRS and AMR-Wind on the Oak Ridge Leadership Facility supercomputers Summit, using 4 to 800 nodes (24 to 4,800 NVIDIA V100 GPUs), and Crusher, the testbed for the Frontier exascale system, using 18 to 384 Graphics Compute Dies on AMD MI250X GPUs. We compare strong- and weak-scaling capabilities, linear solver performance, and time to solution. We also identify leading inhibitors to parallel scaling.

17 WIND ENERGY↗