Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “coarse-grid.”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2

Stable Machine‐Learning Parameterization of Subgrid Processes in a Comprehensive Atmospheric Model Learned From Embedded Convection‐Permitting Simulations

Modern climate projections often suffer from inadequate spatial and temporal resolution due to computational limitations, resulting in inaccurate representations of sub-grid processes. A promising technique to address this is the multiscale modeling framework (MMF), which embeds a kilometer-resolution cloud-resolving model (CRM) within each atmospheric column of a host climate model to replace traditional convection and cloud parameterizations. Machine learning offers a unique opportunity to make MMF more accessible by emulating the embedded CRM and reducing its substantial computational cost. Although many studies have demonstrated proof-of-concept success of achieving stable hybrid simulations, it remains a challenge to achieve near operational-level success with real geography and comprehensive variable emulation that includes, for example, explicit cloud condensate coupling. In this study, we present a stable hybrid model capable of integrating for at least 5 years with near operational-level complexity, including coarse-grid geography, seasonality, explicit cloud condensate and wind predictions, and land coupling. Our model demonstrates skillful online performance, achieving a 5-year zonal mean tropospheric temperature bias within 2 K, water vapor bias within 1 g/kg, and a precipitation root mean square error of 0.96 mm/day. Key factors contributing to our online performance include an expressive U-Net architecture and physical thermodynamic constraints for microphysics. With microphysical constraints mitigating unrealistic cloud formation, our work is the first to demonstrate realistic multi-year cloud condensate climatology under the MMF framework. Despite these advances, online diagnostics reveal persistent biases in certain regions, highlighting the need for innovative strategies to further optimize online performance.

Hu, Zeyuan [NVIDIA Corporation, Santa Clara, CA (U↗

Parallel-in-Time Solution of Scalar Nonlinear Conservation Laws

Here, we consider the parallel-in-time solution of scalar nonlinear conservation laws in one spatial dimension. The equations are discretized in space with a conservative finite-volume method using weighted essentially nonoscillatory (WENO) reconstructions, and in time with high-order explicit Runge–Kutta methods. The solution of the global, discretized space-time problem is sought via a nonlinear iteration that uses a novel linearization strategy in cases of nondifferentiable equations. Under certain choices of discretization and algorithmic parameters, the nonlinear iteration coincides with Newton’s method, although, more generally, it is a preconditioned residual correction scheme. At each nonlinear iteration, the linearized problem takes the form of a certain discretization of a linear conservation law over the space-time domain in question. An approximate parallel-in-time solution of the linearized problem is computed with a single multigrid reduction-in-time (MGRIT) iteration; however, any other effective parallel-in-time method could be used in its place. The MGRIT iteration employs a novel coarse-grid operator that is a modified conservative semi-Lagrangian discretization and generalizes those we have developed previously for nonconservative scalar linear hyperbolic problems. Numerical tests are performed for the inviscid Burgers and Buckley–Leverett equations. For many test problems, the solver converges in just a handful of iterations with a convergence rate independent of mesh resolution, including problems with (interacting) shocks and rarefactions.

97 MATHEMATICS AND COMPUTING↗

Limitations of Bin and Bulk Microphysics in Reproducing the Observed Spatial Structure of Light Precipitation

Abstract Coarse-gridded atmospheric models often account for subgrid-scale variability by specifying probability distribution functions (PDFs) of process rate inputs such as cloud and rainwater mixing ratios ( q c and q r , respectively). PDF parameters can be obtained from numerous sources: in situ observations, ground- or space-based remote sensing, or fine-scale modeling such as large-eddy simulation (LES). LES is appealing to constrain PDFs because it generates large sample sizes, can simulate a variety of cloud regimes/case studies, and is not subject to the ambiguities of observations. However, despite the appeal of using model output for parameterization development, it has not been demonstrated that LES satisfactorily reproduces the observed spatial structure of microphysical fields. In this study, the structure of observed and modeled microphysical fields are compared by applying bifractal analysis, an approach that quantifies variability across spatial scales, to simulations of a drizzling stratocumulus field that span a range of domain sizes, drop concentrations (a proxy for mesoscale organization), and microphysics schemes (bulk and bin). Simulated q c closely matches observed estimates of bifractal parameters that measure smoothness and intermittency. There are major discrepancies between observed and simulated q r properties, though, with bulk simulated q r consistently displaying the bifractal properties of observed clouds (smooth, minimally intermittent) rather than rain while bin simulations produce q r that is appropriately intermittent but too smooth. These results suggest fundamental limitations of bulk and bin schemes to realistically represent higher-order statistics of the observed rain structure.

54 ENVIRONMENTAL SCIENCES↗

Parallel-in-Time Integration for Nonlinear Hyperbolic Problems (Final Report)

The work for the subcontract was situated in the area of parallel-in-time integration for hyperbolic partial differential equations (PDEs). Parallel-in-time integration is an active area of research due to its ability to enable faster numerical simulations for applications throughout many areas of science. Over the past two decades, much progress has been made in this area; however, this progress has largely been limited to diffusion-dominated PDEs, with some recent success in scalar linear hyperbolic PDEs. Given the ubiquity of numerical simulations of hyperbolic PDEs throughout the sciences, in particular, nonlinear hyperbolic systems, there is a strong need to develop efficient parallel-in-time techniques for hyperbolic problems beyond simple scalar and linear cases, which is the main topic of this subcontract. The main focus of the work was to further develop and perfect coarse-grid operators for the Multigrid Reduction-inTime (MGRIT) method applied to hyperbolic PDEs that were recently proposed in PhD thesis, based on a modified semi-Lagrangian approach.

97 MATHEMATICS AND COMPUTING↗

Non-Intrusive Parallel-in-Time Solvers for Partial Differential Equations (Final Report)

Many time-dependent problems and simulations are often modeled using Partial Differential Equations. Traditional modeling approaches that use sequential time-stepping are reaching a bottleneck in optimizing efficiency. The Center of Applied Science and Computing at Lawrence Livermore National Laboratory extensively works on parallelizing these algorithms to leverage the increasing computational power from the growing number of processors in computer hardware. In particular, they aim to design non-intrusive algorithms that can generalize to a variety of problems and sizes without requiring additional information from or modifications on the original problems. Multigrid Reduction in Time (MGRIT) is a parallel-in-time algorithm that is designed to be non-intrusive. This project focuses on increasing the efficiency of MGRIT by approximating the coarse-grid operator using machine learning approaches as a means to find the most non-intrusive, or general, solution.

97 MATHEMATICS AND COMPUTING↗

Convergence acceleration of viscous flow computations

A multiple-grid convergence acceleration technique introduced for application to the solution of the Euler equations by means of Lax-Wendroff algorithms is extended to treat compressible viscous flow. Computational results are presented for the solution of the thin-layer version of the Navier-Stokes equations using the explicit MacCormack algorithm, accelerated by a convective coarse-grid scheme. Extensions and generalizations are mentioned.

Johnson, G. M.↗

Multiple-grid convergence acceleration of viscous and inviscid flow computations

A multiple-grid algorithm for use in efficiently obtaining steady solution to the Euler and Navier-Stokes equations is presented. The convergence of a simple, explicit fine-grid solution procedure is accelerated on a sequence of successively coarser grids by a coarse-grid information propagation method which rapidly eliminates transients from the computational domain. This use of multiple-gridding to increase the convergence rate results in substantially reduced work requirements for the numerical solution of a wide range of flow problems. Computational results are presented for subsonic and transonic inviscid flows and for laminar and turbulent, attached and separated, subsonic viscous flows. Work reduction factors as large as eight, in comparison to the basic fine-grid algorithm, were obtained. Possibilities for further performance improvement are discussed.

Johnson, G. M.↗

Spectral multigrid methods for elliptic equations 2

A detailed description of spectral multigrid methods is provided. This includes the interpolation and coarse-grid operators for both periodic and Dirichlet problems. The spectral methods for periodic problems use Fourier series and those for Dirichlet problems are based upon Chebyshev polynomials. An improved preconditioning for Dirichlet problems is given. Numerical examples and practical advice are included.

Zang, T. A.↗

Multiple-grid convergence acceleration of viscous and inviscid flow computations

A multiple-grid algorithm for use in efficiently obtaining steady solution to the Euler and Navier-Stokes equations is presented. The convergence of a simple, explicit fine-grid solution procedure is accelerated on a sequence of successively coarser grids by a coarse-grid information propagation method which rapidly eliminates transients from the computational domain. This use of multiple-gridding to increase the convergence rate results is substantially reduced work requirements for the numerical solution of a wide range of flow problems. Computational results are presented for subsonic and transonic inviscid flows and for laminar and turbulent, attached and separated, subsonic viscous flows. Work reduction factors as large as eight, in comparison to the basic fine-grid algorithm, were obtained. Possibilities for further performance improvement are discussed. Previously announced in STAR as N83-21847

Johnson, G. M.↗

Spectral multigrid methods for elliptic equations II

A detailed description of spectral multigrid methods is provided. This includes the interpolation and coarse-grid operators for both periodic and Dirichlet problems. The spectral methods for periodic problems use Fourier series and those for Dirichlet problems are based upon Chebyshev polynomials. An improved preconditioning for Dirichlet problems is given. Numerical examples and practical advice are included.

Zang, T. A.↗

Multigrid method for nearly singular and slightly indefinite problems

This paper deals with nearly singular, possibly indefinite problems for which the usual multigrid solvers converge very slowly or even diverge. The main difficulty is related to some badly approximated smooth functions which correspond to eigenfunctions with nearly zero eigenvalues. A correction to the usual coarse-grid equations is derived, both in the correction scheme and in the full approximation scheme. The performance of the new algorithm using this correction is essentially as that of usual multigrid for definite problems.

Brandt, A.↗

Euler solutions using an implicit multigrid technique

A coarse-grid correction algorithm has been implemented into an implicit upwind Euler solver and tested for transonic airfoil problems. The Euler solver uses split-flux formulation and penta-diagonal scalar equations, respectively, for the explicit and implicit operators. The multigrid sequence starts at the fine grid level, then steps down to each coarse grid level to smooth error components using implicit operators. Estimate of residuals can be obtained by two approaches, which differ in the level where the residuals are collected. Both approaches will lead to a work reduction factor of 12 for a Mach 0.75 flow at 2 degrees incidence on a 65x26 grid. The work reduction factor is found to increase proportional to the number of grid levels.

Li, Chien-Peng↗

Multigrid method for nearly singular and slightly indefinite problems

This paper deals with nearly singular, possibly indefinite problems for which the usual multigrid solvers converge very slowly or even diverge. The main difficulty is related to some badly approximated smooth functions which correspond to eigenfunctions with nearly zero eigenvalues. A correction to the usual coarse-grid equations is derived, both in the correction scheme and in the full approximation scheme. The performance of the new algorithm using this correction is essentially as that of usual multigrid for definite problems.

Brandt, A.↗

Navier-Stokes computation of flow around a round-edged double-delta wing

Computations of three-dimensional vortical flows over a thin round-edged double-delta wing with an aspect ratio of 2.05 are performed using an implicit upwind-relaxation finite-difference scheme. The effects of grid and angle of attack on the Navier-Stokes computations are studied. Coarse-grid calculations can not predict the detailed structures of the vortical flowfields for lack of grid resolution. On the contrary, fine-grid computations show that key features of vortex formation, interaction, and breakdown are simulated. Furthermore, computed lift coefficients and spanswise surface static pressure distributions are in good agreement with the experimental data up to alpha = 25 deg.

Hsu, C.-H.↗

Solution of the Neumann pressure problem in general orthogonal coordinates using the multigrid technique

The multigrid (MG) technique has been advanced for use with Neumann boundary-value problems in clustered curvilinear orthogonal coordinates. This comprises an important step in the analysis of incompressible flow using the velocity-pressure formulation of the Navier-Stokes equations. The finite-difference representation of the problem and the formulation of the restriction and coarse-grid correction operators are examined in detail. Maintaining consistency between these and the integral constraint associated with the Neumann problem is found to be critical for the success of the MG technique. The influence of the smoothing operator is examined by employing Gauss-Seidel, alternating-direction implicit, and strongly implicit techniques. The MG procedure enhances the efficiency of fine-grid solutions of the Neumann problem by a factor of 3 to 14, depending on the type of smoothing operator employed and the values of the problem parameters.

Ghia, U.↗

Supercomputer applications in gas turbine flowfield simulation

The numerical simulation of the unsteady three-dimensional viscous flow in a gas turbine stage is considered. Results from a three-dimensional time-accurate Navier-Stokes simulation of rotor-stator interaction in an axial turbine stage are presented. The present study uses a fine grid in the spanwise direction to better resolve the complex three-dimensional flowfield, and complements earlier reported coarse-grid calculations. Several different features of the flowfield are analyzed and compared to earlier calculations and to experimental data whenever possible. Computer animation techniques are used to visualize various unsteady three-dimensional features of the flow. The results demonstrate the capabilities of current computing hardware in obtaining accurate simulations of unsteady flows in turbomachines.

Madavan, Nateri K.↗

Large-Eddy Simulation of Turbulent Wall-Pressure Fluctuations

Large-eddy simulations of a turbulent boundary layer with Reynolds number based on displacement thickness equal to 3500 were performed with two grid resolutions. The computations were continued for sufficient time to obtain frequency spectra with resolved frequencies that correspond to the most important structural frequencies on an aircraft fuselage. The turbulent stresses were adequately resolved with both resolutions. Detailed quantitative analysis of a variety of statistical quantities associated with the wall-pressure fluctuations revealed similar behavior for both simulations. The primary differences were associated with the lack of resolution of the high-frequency data in the coarse-grid calculation and the increased jitter (due to the lack of multiple realizations for averaging purposes) in the fine-grid calculation. A new curve fit was introduced to represent the spanwise coherence of the cross-spectral density.

Singer, Bart A.↗

On Some Numerical Dissipation Schemes

Several schemes for introducing an artificial dissipation into a central difference approximation to the Euler and Navier Stokes equations are considered. The focus of the paper is on the convective upwind and split pressure (CUSP) scheme, which is designed to support single interior point discrete shock waves. This scheme is analyzed and compared in detail with scalar dissipation and matrix dissipation (MATD) schemes. Resolution capability is determined by solving subsonic, transonic, and hypersonic flow problems. A finite-volume discretization and a multistage time-stepping scheme with multigrid are used to compute solutions to the flow equations. Numerical solutions are also compared with either theoretical solutions or experimental data. For transonic airfoil flows the best accuracy on coarse meshes for aerodynamic coefficients is obtained with a simple MATD scheme. The coarse-grid accuracy for the original CUSP scheme is improved by modifying the limiter function used with the scheme, giving comparable accuracy to that obtained with the MATD scheme. The modifications reduce the background dissipation and provide control over the regions where the scheme can become first order.

Swanson, R. C.↗