Search NASA⌕ Search

SEARCH · Search NASA

Results for “implicit method”

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 1,387 records · Page 77

The space-time solution element method: A new numerical approach for the Navier-Stokes equations

This paper is one of a series of papers describing the development of a new numerical method for the Navier-Stokes equations. Unlike conventional numerical methods, the current method concentrates on the discrete simulation of both the integral and differential forms of the Navier-Stokes equations. Conservation of mass, momentum, and energy in space-time is explicitly provided for through a rigorous enforcement of both the integral and differential forms of the governing conservation laws. Using local polynomial expansions to represent the discrete primitive variables on each cell, fluxes at cell interfaces are evaluated and balanced using exact functional expressions. No interpolation or flux limiters are required. Because of the generality of the current method, it applies equally to the steady and unsteady Navier-Stokes equations. In this paper, we generalize and extend the authors' 2-D, steady state implicit scheme. A general closure methodology is presented so that all terms up through a given order in the local expansions may be retained. The scheme is also extended to nonorthogonal Cartesian grids. Numerous flow fields are computed and results are compared with known solutions. The high accuracy of the scheme is demonstrated through its ability to accurately resolve developing boundary layers on coarse grids. Finally, we discuss applications of the current method to the unsteady Navier-Stokes equations.

Scott, James R.↗

Transient two-dimensional heat transfer through a composite body with application to deicing of aircraft components

Nine different numerical methods are examined for their ability to model the process of the melting and removal of ice from an airfoil using electrothermal heaters. A technique is presented for modeling the phase change which assumes a phase for each node. The technique allows solvers such as Alternating Direction Implicit, Alternating Direction Explicit, and Strongly Implicit Procedure to find a solution which can then be iterated to find the correct phase of each node. Comparisons made for a standard deicer pad comprised of five layers showed the ADI method to be superior to the other methods considered.

Wright, W. B.↗

An integrated model-driven method for in-treatment upper airway motion tracking using cine MRI in head and neck radiation therapy

Purpose: For the first time, MRI-guided radiation therapy systems can acquire cine images to dynamically monitor in-treatment internal organ motion. However, the complex head and neck (H&N) structures and low-contrast/resolution of on-board cine MRI images make automatic motion tracking a very challenging task. In this study, the authors proposed an integrated model-driven method to automatically track the in-treatment motion of the H&N upper airway, a complex and highly deformable region wherein internal motion often occurs in an either voluntary or involuntary manner, from cine MRI images for the analysis of H&N motion patterns. Methods: Considering the complex H&N structures and ensuring automatic and robust upper airway motion tracking, the authors firstly built a set of linked statistical shapes (including face, face-jaw, and face-jaw-palate) using principal component analysis from clinically approved contours delineated on a set of training data. The linked statistical shapes integrate explicit landmarks and implicit shape representation. Then, a hierarchical model-fitting algorithm was developed to align the linked shapes on the first image frame of a to-be-tracked cine sequence and to localize the upper airway region. Finally, a multifeature level set contour propagation scheme was performed to identify the upper airway shape change, frame-by-frame, on the entire image sequence. The multifeature fitting energy, including the information of intensity variations, edge saliency, curve geometry, and temporal shape continuity, was minimized to capture the details of moving airway boundaries. Sagittal cine MR image sequences acquired from three H&N cancer patients were utilized to demonstrate the performance of the proposed motion tracking method. Results: The tracking accuracy was validated by comparing the results to the average of two manual delineations in 50 randomly selected cine image frames from each patient. The resulting average dice similarity coefficient (93.28% ± 1.46%) and margin error (0.49 ± 0.12 mm) showed good agreement between the automatic and manual results. The comparison with three other deformable model-based segmentation methods illustrated the superior shape tracking performance of the proposed method. Large interpatient variations of swallowing frequency, swallowing duration, and upper airway cross-sectional area were observed from the testing cine image sequences. Conclusions: The proposed motion tracking method can provide accurate upper airway motion tracking results, and enable automatic and quantitative identification and analysis of in-treatment H&N upper airway motion. By integrating explicit and implicit linked-shape representations within a hierarchical model-fitting process, the proposed tracking method can process complex H&N structures and low-contrast/resolution cine MRI images. Future research will focus on the improvement of method reliability, patient motion pattern analysis for providing more information on patient-specific prediction of structure displacements, and motion effects on dosimetry for better H&N motion management in radiation therapy.

60 APPLIED LIFE SCIENCES↗

High-Order Preconditioners for Modern Computing Architectures: Line-Based Discontinuous Galerkin Method on GPUs

The goals of our project are to be able to overcome issues that plague computing in modern architecture such as limited memory bandwidth, badly conditioned Jacobians, and restrictive time steps. We begin by describing the line-based discontinuous Galerkin (line DG) method for a scalar two-dimensional problem. Line DG has been shown to provide a significant increase in sparsity for Jacobian matrix, especially in the diagonal block elements. In addition to this, the implicit time integration scheme helps alleviate the time step restriction but requires solving a (potentially badly conditioned) linear system. We can precondition the linear system to facilitate the solution. Since we want to solve the system on the GPU, the increase in sparsity from the line DG method is helpful to alleviate the memory issue. We successfully implemented a computation of the Jacobian on the CPU and are currently working on the GPU implementation. Finally, I discuss how this opportunity to intern at Lawrence Livermore National Laboratory through the National Science Foundation Mathematical Sciences Graduate Internship has affected my personal and professional growth.

97 MATHEMATICS AND COMPUTING↗

Iterative PNS method for attached flows with upstream influence

A stable global-iteration procedure is developed by utilizing successive sweeps, from inflow to outflow boundaries, of a parabolized Navier-Stokes code for attached, steady supersonic flow. It is shown that the procedure converges in about ten or fewer iterations, and allows for the upstream influence within the subsonic region of a supersonic boundary layer. An implicit forward difference is employed in the subsonic region to evaluate the pressure-gradient term in the streamwise momentum equation. The pressure-gradient term is normally approximated in standard single-sweep parabolized methods, suppressing the upstream influence. The iterative results obtained demonstrate the validity of the single-sweep method for weak interactions. For hypersonic viscous interaction on a flat plate at a Mach number of 5.8, it is found that the single-sweep method has a small error that vanishes as the Reynolds number of the flow is increased. However, the skin friction has an error of about 10 percent for low Reynolds numbers and for hot wall conditions. The application of this method to laminar two-dimensional flow over weak expansion and compression corners shows that the pressure and skin friction results in the vicinity of the expansion corner compare favorably with a time-dependent Navier-Stokes numerical solution.

Rakich, J. V.↗

The halo light-cone catalogues of ABACUSSUMMIT

We describe a method for generating halo catalogues on the light-cone using the AbacusSummit suite of N-body simulations. The main application of these catalogues is the construction of realistic mock galaxy catalogues and weak lensing maps on the sky. Our algorithm associates the haloes from a set of coarsely spaced snapshots with their positions at the time of light-cone crossing by matching halo particles to on-the-fly light-cone particles. It then records the halo and particle information into an easily accessible product, which we call the AbacusSummit halo light-cone catalogues. Our recommended use of this product is in the halo mass regime of M halo > 2.1 x 10 11 M ⊙ h -1 for the base resolution simulations, i.e. haloes containing at least 100 particles, where the interpolated halo properties are most reliable. To test the validity of the obtained catalogues, we perform various visual inspections and consistency checks. In particular, we construct galaxy mock catalogues of emission-line galaxies (ELGs) at z ~ 1 by adopting a modified version of the AbacusHOD script, which builds on the standard halo occupation distribution (HOD) method by including various extensions. We find that the multipoles of the autocorrelation function are consistent with the predictions from the full-box snapshot, implicitly validating our algorithm. In addition, we compute and output CMB convergence maps and find that the auto- and cross-power spectrum agrees with the theoretical prediction at the sub-per-cent level.

79 ASTRONOMY AND ASTROPHYSICS↗

A Characteristic-Based Spectral Element Method for Moving-Domain Problems

Here, we introduce a characteristic-based numerical procedure for simulating incompressible flows in domains with moving boundaries. Our approach utilizes an operator-integration-factor splitting technique to help produce an efficient and stable numerical scheme. Using the spectral element method and an arbitrary Lagrangian-Eulerian formulation, we explore flows where the convective acceleration effects are non-negligible. Several examples, ranging from laminar to turbulent flows, are considered. Comparisons with a standard, semi-implicit time-stepping procedure illustrate the improved performance of our scheme.

97 MATHEMATICS AND COMPUTING↗

A machine learning approach to predict metabolic pathway dynamics from time-series multiomics data

New synthetic biology capabilities hold the promise of dramatically improving our ability to engineer biological systems. However, a fundamental hurdle in realizing this potential is our inability to accurately predict biological behavior after modifying the corresponding genotype. Kinetic models have traditionally been used to predict pathway dynamics in bioengineered systems, but they take significant time to develop, and rely heavily on domain expertise. Here, we show that the combination of machine learning and abundant multiomics data (proteomics and metabolomics) can be used to effectively predict pathway dynamics in an automated fashion. The new method outperforms a classical kinetic model, and produces qualitative and quantitative predictions that can be used to productively guide bioengineering efforts. This method systematically leverages arbitrary amounts of new data to improve predictions, and does not assume any particular interactions, but rather implicitly chooses the most predictive ones.

59 BASIC BIOLOGICAL SCIENCES↗

Large eddy simulation of atmospheric boundary layer flow over complex terrain in comparison with RANS simulation and on-site measurements under neutral stability condition

Large eddy simulation (LES) of the atmospheric boundary layer (ABL) flow over complex terrain is presented with a validation using meteorological tower (met-tower) data through an improved neutral stability sampling approach. The proposed stability sampling procedure includes a condition based on the most-likely occurrence time-periods of the neutral ABL and reduces the variabilities of the conditional wind statistics calculated at the met-towers in comparison to our previous work. The ABL flow simulations are carried out over a potential wind site with a prominent hill based using the OpenFOAM-based simulator for on/off-shore wind farm applications by applying the Lagrangian-averaged scale-invariant dynamic sub-grid scale turbulence model. A low-dissipative scale-selective discretization scheme for the non-linear convection term in the LES governing equation is adopted implicitly to ensure both the second-order accuracy and bounded solution. The LES inflow is generated through a precursor method with a “tiling” approach based on the flow driving parameters obtained from a corresponding Reynolds-averaged Navier–Stokes (RANS) simulation. Overall, the averaged wind velocity profiles predicted by the LES approach at all met-tower locations show a similar tendency as the RANS results, which are also in reasonable agreement with the met-tower data. An obvious difference in wind speed standard deviation profiles is seen between LES and RANS, especially at regions downstream of the hill edge, where the LES shows under-predicted results at the highest measurement levels in comparison to the tower data. The computational costs of the LES are found to be about 20 times higher than the RANS simulations.

Energy & Fuels↗

Kinetic Learning vo.1

New synthetic biology capabilities hold the promise of dramatically improving our ability to engineer biological systems. However, a fundamental hurdle in realizing this potential is our inability to accurately predict biological behavior after modifying the corresponding genotype. Kinetic models have traditionally been used to predict pathway dynamics in bioengineered systems, but they take significant time to develop, and rely heavily on domain expertise. This software implements a method to effectively predict pathway dynamics in an automated fashion using a combination of machine learning and abundant multiomics data (proteomics and metabolomics). The new method outperforms a classical kinetic model, and produces qualitative and quantitative predictions that can be used to productively guide bioengineering efforts. This method systematically leverages arbitrary amounts of new data to improve predictions, and does not assume any particular interactions, but rather implicitly chooses the most predictive ones.

Martin, HectorGarcia↗

Nonlinear seismic analysis of a reactor structure impact between core components

The seismic analysis of the FFTF-PIOTA (Fast Flux Test Facility-Postirradiation Open Test Assembly), subjected to a horizontal DBE (Design Base Earthquake) is presented. The PIOTA is the first in a set of open test assemblies to be designed for the FFTF. Employing the direct method of transient analysis, the governing differential equations describing the motion of the system are set up directly and are implicitly integrated numerically in time. A simple lumped-nass beam model of the FFTF which includes small clearances between core components is used as a "driver" for a fine mesh model of the PIOTA. The nonlinear forces due to the impact of the core components and their effect on the PIOTA are computed.

Hill, R. G.↗

Transonic flow analysis for rotors. Part 2: Three-dimensional, unsteady, full-potential calculation

A numerical method is presented for calculating the three-dimensional unsteady, transonic flow past a helicopter rotor blade of arbitrary geometry. The method solves the full-potential equations in a blade-fixed frame of reference by a time-marching implicit scheme. At the far-field, a set of first-order radiation conditions is imposed, thus minimizing the reflection of outgoing wavelets from computational boundaries. Computed results are presented to highlight radial flow effects in three dimensions, to compare surface pressure distributions to quasi-steady predictions, and to predict the flow field on a swept-tip blade. The results agree well with experimental data for both straight- and swept-tip blade geometries.

Chang, I. C.↗

Unsteady Euler solution of transonic helicopter rotor flow

A new time-accurate Euler method is presented for calculating the transonic flow over a lifting or nonlifting rotor blade in both hover and forward flight. The approach is to solve the conservative Euler equations in a rotor-fixed frame of reference using a finite-volume method. The discretized equations are solved by using a Runge-Kutta multistage scheme with a new higher-order implicit residual smoothing procedure. Preliminary results were compared with wind-tunnel data. In all the cases considered, good agreement was found with experimental data.

Chang, I-Chung↗

A multi-block multigrid method for the solution of the Euler and Navier-Stokes equations for three-dimensional flows

A multi-block multigrid method for the solution of the three-dimensional Euler and Navier-Stokes equations is presented. The basic flow solver is a cell-vertex method which employs central-difference spatial approximations and Runge-Kutta time stepping. The use of local time stepping, implicit residual smoothing, multigrid techniques, and variable-coefficient numerical smoothing results in an efficient and robust scheme. The multi-block strategy places the block loop within the Runge-Kutta loop such that accuracy and convergence are not affected by block boundaries. This has been verified by comparing the results of one- and two-block calculations in which the two-block grid is generated by splitting the one-block grid. Results are presented for both Euler and Navier-Stokes computations of wings and wing-fuselage combinations.

Atkins, H. L.↗

Simultaneous use of Ground Reflection and Lateral Attenuation Noise Models

Ground reflections and lateral attenuation due to refraction and scattering are two effects of acoustic propagation that can strongly influence noise received by an observer. Software that predicts community aviation noise can be reliant on ground reflection models to predict noise at receivers. However, empirical lateral attenuation models often include the influence of ground reflections implicitly, so a double-bookkeeping error can exist if one is used together with a reflection model. An accounting method that reconciles this bookkeeping issue for the Chien and Soroka reflection model and a Society of Automotive Engineers lateral attenuation model is presented. Importance to emerging supersonic civil aircraft is discussed.

noise↗

Simultaneous Use of Ground Reflection and Lateral Attenuation Noise Models

Ground reflections and lateral attenuation due to refraction and scattering are two effects of acoustic propagation that can strongly influence noise received by an observer. Software that predicts community aviation noise can be reliant on ground reflection models to predict noise at receivers. However, empirical lateral attenuation models often include the influence of ground reflections implicitly, so a double-bookkeeping error can exist if one is used together with a reflection model. An accounting method that reconciles this bookkeeping issue for the Chien and Soroka reflection model and a Society of Automotive Engineers lateral attenuation model is presented. Importance to emerging supersonic civil aircraft is discussed.

noise↗

Multigrid for hypersonic viscous two- and three-dimensional flows

The use of a multigrid method with central differencing to solve the Navier-Stokes equations for hypersonic flows is considered. The time dependent form of the equations is integrated with an explicit Runge-Kutta scheme accelerated by local time stepping and implicit residual smoothing. Variable coefficients are developed for the implicit process that removes the diffusion limit on the time step, producing significant improvement in convergence. A numerical dissipation formulation that provides good shock capturing capability for hypersonic flows is presented. This formulation is shown to be a crucial aspect of the multigrid method. Solutions are given for two-dimensional viscous flow over a NACA 0012 airfoil and three-dimensional flow over a blunt biconic.

Turkel, E.↗

Transonic solutions of the Euler equations by the finite volume method

An investigation is conducted of the time-accurate convergence of representative transonic flows to a steady state under given constraints of time-accuracy. Factored explicit and implicit difference operators are used to accelerate the calculations. Attention is given to flow at a Mach number of 1.35 past a circular cylinder and supersonic flow past a NACA 0012 airfoil for three different Mach numbers. Questions of transonic wave behavior are considered along with the equations of motion and the characteristics of the mesh network.

Rizzi, A.↗