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NASA NTRS1992

Optimal matrix approximants in structural identification

Problems of model correlation and system identification are central in the design, analysis, and control of large space structures. Of the numerous methods that have been proposed, many are based on finding minimal adjustments to a model matrix sufficient to introduce some desirable quality into that matrix. In this work, several of these methods are reviewed, placed in a modern framework, and linked to other previously known ideas in computational linear algebra and optimization. This new framework provides a point of departure for a number of new methods which are introduced here. Significant among these is a method for stiffness matrix adjustment which preserves the sparsity pattern of an original matrix, requires comparatively modest computational resources, and allows robust handling of noisy modal data. Numerical examples are included to illustrate the methods presented herein.

Beattie, C. A.↗

NASA NTRS1998

Spurious Numerical Oscillations in Numerical Simulation of Supersonic Flows Using Shock Capturing Schemes

The numerical simulation of transitional and turbulent processes in hypersonic boundary layers often involves a physical process of a shock-disturbance wave interaction in complex two-dimensional and three-dimensional flow fields. For such simulations, it is required that there be a high order of accuracy in capturing both the shock and the small disturbances. The purpose of this paper is to evaluate the viability of using high order shock capturing schemes to track small disturbances in a multi-dimensional steady hypersonic flow. The numerical methods that are to be studied are the Total Variation Diminishing (TVD) scheme, and Essentially Non-Oscillatory (ENO) scheme. This paper shows that the presence of numerical oscillations in the flow field solution may drastically hinder any attempt at tracking the propagation of any physical disturbances. It has been found that the numerical oscillations that exist for shock capturing methods may be significant enough to pollute a flow field containing small physical disturbances. The effects of the refinement of the grid do not reduce the oscillations, but rather they decrease the wavelength of the oscillations. It is shown that by aligning the shock with the grid, the amplitude of these spurious oscillations may be greatly reduced.

Lee, Theodore K.↗

NASA NTRS1993

Three-dimensional magnetotail equilibria by numerical relaxation techniques

Consideration is given to a numerical method to iteratively approach 3D magnetostatic force equilibria, with modeling emphasis on the development of a suitable model of the earth's magnetotail, including a portion of the inner magnetosphere, i.e., on models which violate the 'tail approximation' commonly employed in analytical models. The numerical approach is compared to methods developed for laboratory plasma physics. The method is applied to the magnetotail outside of 10 R(E), using Tsyganenko's (1987) model for the quiet magnetosphere as an initial condition. The changes of the magnetic field necessary to yield an equilibrium configuration and the resulting distribution of the self-consistently derived pressure are discussed. It is shown that a self-consistent magnetotail equilibrium based on a close approximation to Tsyganenko's requires a region 1 type current system, which is not present in the initial configuration.

Hesse, Michael↗

DOE OSTI2014

Quantifying the Combined Effect of Radiation Therapy and Hyperthermia in Terms of Equivalent Dose Distributions

Purpose: To develop a method to quantify the therapeutic effect of radiosensitization by hyperthermia; to this end, a numerical method was proposed to convert radiation therapy dose distributions with hyperthermia to equivalent dose distributions without hyperthermia. Methods and Materials: Clinical intensity modulated radiation therapy plans were created for 15 prostate cancer cases. To simulate a clinically relevant heterogeneous temperature distribution, hyperthermia treatment planning was performed for heating with the AMC-8 system. The temperature-dependent parameters α (Gy{sup −1}) and β (Gy{sup −2}) of the linear–quadratic model for prostate cancer were estimated from the literature. No thermal enhancement was assumed for normal tissue. The intensity modulated radiation therapy plans and temperature distributions were exported to our in-house-developed radiation therapy treatment planning system, APlan, and equivalent dose distributions without hyperthermia were calculated voxel by voxel using the linear–quadratic model. Results: The planned average tumor temperatures T90, T50, and T10 in the planning target volume were 40.5°C, 41.6°C, and 42.4°C, respectively. The planned minimum, mean, and maximum radiation therapy doses were 62.9 Gy, 76.0 Gy, and 81.0 Gy, respectively. Adding hyperthermia yielded an equivalent dose distribution with an extended 95% isodose level. The equivalent minimum, mean, and maximum doses reflecting the radiosensitization by hyperthermia were 70.3 Gy, 86.3 Gy, and 93.6 Gy, respectively, for a linear increase of α with temperature. This can be considered similar to a dose escalation with a substantial increase in tumor control probability for high-risk prostate carcinoma. Conclusion: A model to quantify the effect of combined radiation therapy and hyperthermia in terms of equivalent dose distributions was presented. This model is particularly instructive to estimate the potential effects of interaction from different treatment modalities.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2014

On the possibility of detecting local refractive index changes in optically transparent objects by means of a point nanoantenna attached to a fibre microaxicon

It is shown theoretically that the use of the spectral registration of the dipole local plasmon resonance (DLPR) displacement in a single spherical gold nanoantenna, placed near the surface of a homogeneous dielectric medium, allows the mapping of extremely small variations (to 5 × 10{sup -4}) of the refractive index (RI) of this medium. Using the quasi-static approximation, we have developed an analytic model that allows evaluation of the spectral displacement of the nanoantenna DLPR depending on the variation in the medium refractive index. The point probe based on a fibre microaxicon with a gold spherical nanoantenna attached to its top is proposed that allows practical implementation of the developed RI scanning method. Numerical calculations of the probe characteristics using the time-domain finite-difference method are presented, and it is shown that for the case of a gold spherical nanoantenna of small size, comparable with the skin layer thickness in gold, the relative spectral shift value is in good agreement with the results obtained by using the developed analytic model. (laser applications and other topics in quantum electronics)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1969

Variational approach to the gradient method - Theory and numerical experiments

Analytical approach to gradient method within framework of Bolza problem of variational calculus, using linearized differential and isoperimetric constraints

Miele, A.↗

NASA NTRS1987

Parallel Algorithm Solves Coupled Differential Equations

Numerical methods adapted to concurrent processing. Algorithm solves set of coupled partial differential equations by numerical integration. Adapted to run on hypercube computer, algorithm separates problem into smaller problems solved concurrently. Increase in computing speed with concurrent processing over that achievable with conventional sequential processing appreciable, especially for large problems.

Hayashi, A.↗

NASA NTRS1990

A multiblock multigrid method for the solution of the three-dimensional Euler equations

A general multiblock, multigrid method for the solution of the Euler equations has been developed. Two types of numerical methods were investigated, van Leer's flux-vector-splitting and Roe's flux-difference-splitting, with MUSCL type differencing used in both methods. An explicit two-step method and a multi-stage Runge-Kutta method have been tested. Results are presented for test cases of a channel flow, nozzle exhaust flow, and a transonic wing.

Cannizzaro, Frank E.↗

DOE OSTI2016

IMPLEMENTATION AND VALIDATION OF A FULLY IMPLICIT ACCUMULATOR MODEL IN RELAP-7

This paper presents the implementation and validation of an accumulator model in RELAP-7 under the framework of preconditioned Jacobian free Newton Krylov (JFNK) method, based on the similar model used in RELAP5. RELAP-7 is a new nuclear reactor system safety analysis code being developed at the Idaho National Laboratory (INL). RELAP-7 is a fully implicit system code. The JFNK and preconditioning methods used in RELAP-7 is briefly discussed. The slightly modified accumulator model is summarized for completeness. The implemented model was validated with LOFT L3-1 test and benchmarked with RELAP5 results. RELAP-7 and RELAP5 had almost identical results for the accumulator gas pressure and water level, although there were some minor difference in other parameters such as accumulator gas temperature and tank wall temperature. One advantage of the JFNK method is its easiness to maintain and modify models due to fully separation of numerical methods from physical models. It would be straightforward to extend the current RELAP-7 accumulator model to simulate the advanced accumulator design.

Accumulator↗

DOE OSTI2016

Implementation and validation of a fully implicit accumulator model in RELAP-7

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2019

thornado-hydro: towards discontinuous Galerkin methods for supernova hydrodynamics

The toolkit for high-order neutrino-radiation hydrodynamics (thornado) is being developed for simulations of core-collapse supernovae (CCSNe) and related problems. Current capabilities in thornado include solvers for the Euler equations — in non-relativistic and special relativistic limits — and the two-moment model of neutrino transport. The spatial discretization in thornado is based on the discontinuous Galerkin (DG) method, which is receiving increased attention from the computational astrophysics community. In this paper, we provide an overview of the numerical methods for the Euler equations in thornado, and present some encouraging preliminary numerical results from a set of basic tests in one and two spatial dimensions.

Endeve, Eirik↗

NASA NTRS1989

An Approximate Model for the Performance and Acoustic Predictions of Counterrotating Propeller Configurations

An approximate method was developed to analyze and predict the acoustics of a counterrotating propeller configuration. The method employs the analytical techniques of Lock and Theodorsen as described by Davidson to predict the steady performance of a counterrotating configuration. Then, a modification of the method of Lesieutre is used to predict the unsteady forces on the blades. Finally, the steady and unsteady loads are used in the numerical method of Succi to predict the unsteady acoustics of the propeller. The numerical results are compared with experimental acoustic measurements of a counterrotating propeller configuration by Gazzaniga operating under several combinations of advance ratio, blade pitch, and number of blades. In addition, a constant-speed commuter-class propeller configuration was designed with the Davidson method and the acoustics analyzed at three advance ratios. Noise levels and frequency spectra were calculated at a number of locations around the configuration. The directivity patterns of the harmonics in both the horizontal and vertical planes were examined, with the conclusion that the noise levels of the even harmonics are relatively independent of direction whereas the noise levels of the odd harmonics are extremely dependent on azimuthal direction in the horizontal plane. The equations of Succi are examined to explain this behavior.

Denner, Brett William↗

DOE OSTI2015

Wave propagation in anisotropic elastic materials and curvilinear coordinates using a summation-by-parts finite difference method

We develop a fourth order accurate finite difference method for solving the three-dimensional elastic wave equation in general heterogeneous anisotropic materials on curvilinear grids. The proposed method is an extension of the method for isotropic materials, previously described in the paper by Sjögreen and Petersson (2012) [11]. The method we proposed discretizes the anisotropic elastic wave equation in second order formulation, using a node centered finite difference method that satisfies the principle of summation by parts. The summation by parts technique results in a provably stable numerical method that is energy conserving. Also, we generalize and evaluate the super-grid far-field technique for truncating unbounded domains. Unlike the commonly used perfectly matched layers (PML), the super-grid technique is stable for general anisotropic material, because it is based on a coordinate stretching combined with an artificial dissipation. Moreover, the discretization satisfies an energy estimate, proving that the numerical approximation is stable. We demonstrate by numerical experiments that sufficiently wide super-grid layers result in very small artificial reflections. Applications of the proposed method are demonstrated by three-dimensional simulations of anisotropic wave propagation in crystals.

58 GEOSCIENCES↗

DOE OSTI2022

Enriched immersed boundary method (EIBM) for interface-coupled multi-physics and applications to convective conjugate heat transfer

It is challenging to develop numerical methods that simultaneously maintain accuracy of resolving boundary conditions and mesh flexibility to handle the interface in interface-coupled multi-physics problems involving large property discontinuity. On the one hand, boundary-fitted methods possess high accuracy in capturing the interfacial phenomenon but involve complicated volumetric mesh generation, mesh-motion, and even re-meshing procedures. On the other hand, immersed boundary methods (IBM) provide mesh flexibility but sometimes suffer from inferior interface representations, leading to poor enforcement of boundary conditions. This paper presents an enriched immersed boundary method (EIBM) to overcome this challenge and demonstrates its efficacy in conjugate heat transfer, a representative example in interface-coupled multi-physics systems that have implications for many industrial processes. Further, the core technique of the method is to enhance IBM’s accuracy of the fluid–solid interface by enriching the degrees of freedom of the cut elements to enforce temperature and flux compatibilities and resolve all the physical unknowns on the background mesh to simplify the volumetric mesh generation. We implement the EIBM under the framework of a variational multiscale formulation for coupled Navier–Stokes and thermodynamics equations. The enriched DoFs enable better enforcement of temperature and flux compatibilities with large conductivity ratios across the fluid–solid interface. At the same time, the immersed nature of the proposed method still attains mesh flexibility. The EIBM’s accuracy is thoroughly evaluated through a set of examples, ranging from benchmark problems with analytical solutions to real-world cooling processes of a moving metallic structure with complex geometry.

42 ENGINEERING↗

NASA NTRS1992

Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method

A lattice Boltzmann model is presented which gives the complete Navier-Stokes equation and may provide an efficient parallel numerical method for solving various fluid problems. The model uses the single-time relaxation approximation and a particular Maxwell-type distribution. The model eliminates exactly (1) the non-Galilean invariance caused by a density-dependent coefficient in the convection term and (2) a velocity-dependent equation of state.

Chen, Hudong↗

DOE OSTI2018

On the convergence and convergence order of finite volume gradient schemes for oblique derivative boundary value problems

This work is an improvement of the previous note (Bradji in: Fuhrmann et al., Finite volumes for complex applications VII–methods, theoretical aspects. Proceedings of the FVCA 7, Berlin, 2014) which dealt with the convergence analysis of a finite volume scheme for the Poisson’s equation with a linear oblique derivative boundary condition. The formulation of the finite volume scheme given in Bradji (in: Fuhrmann et al., Finite volumes for complex applications VII–methods, theoretical aspects. Proceedings of the FVCA 7, Berlin, 2014) involves the discrete gradient introduced recently in Eymard et al. (IMA J Numer Anal 30(4):1009–1043, 2010). In this paper, we consider the convergence analysis of finite volume schemes involving the discrete gradient of Eymard et al. (IMA J Numer Anal 30(4):1009–1043, 2010) for elliptic and parabolic equations with linear oblique derivative boundary conditions. Linear oblique derivative boundary conditions arise for instance in the study of the motion of water in a canal, cf. Lesnic (Commun Numer Methods Eng 23(12):1071–1080, 2007). We derive error estimates in several norms which allow us to get error estimates for the approximations of the exact solutions and its first derivatives. In particular, we provide an error estimate between the gradient of the exact solutions and the discrete gradient of the approximate solutions. Convergence of the family of finite volume approximate solutions towards the exact solution under weak regularity assumption is also investigated. In the case of parabolic equations with oblique derivative boundary conditions, we develop a new discrete a priori estimate result. The proof of this result is based on the use of a discrete mean Poincaré–Wirtinger inequality. Thanks to the stated a priori estimate and to a comparison with an appropriately chosen auxiliary finite volume scheme, we derive the convergence results. This work can be viewed as a continuation of the previous work (Bradji and Gallouët in Int J Finite Vol 3(2):1–35, 2006) where a convergence analysis for a finite volume scheme, based on the admissible mesh of Eymard et al. (In: Ciarlet and Lions, Handbook of numerical analysis, North-Holland, Amsterdam, 2000), for the Poisson’s equation with a linear oblique derivative boundary conditions is given. The obtained convergence results do not require any relation between the mesh sizes of the spatial and time discretizations. Some numerical tests are presented for both elliptic and parabolic equations. In particular, we present three methods to compute the discrete solution.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Numerical modeling of hydrogen mixing in a direct-injection engine fueled with gaseous hydrogen

Hydrogen is considered as one of the most promising options to achieve effective decarbonization of the energy and transportation sectors. As such, it has recently been receiving increasing attention because of its promising potential as an energy carrier for advanced energy and propulsion systems. With a focus on internal combustion engines, direct injection (DI) of gaseous hydrogen during the compression stroke offers great potential for high engine efficiency and specific power while reducing the risk of backfiring and pre-ignition issues. Therefore, many experimental and numerical efforts have recently been dedicated to understanding the physical and chemical behaviors of hydrogen in engine during mixing and combustion. This study focuses on computational fluid dynamics (CFD) modeling of the hydrogen DI process in a hydrogen optical research engine. Under the conditions studied, gaseous hydrogen is injected into the combustion chamber via a centrally located single-hole injector at a pressure of 100 bar. Two configurations, namely low-and high-tumble, are investigated to understand the impact of different in-cylinder flow patterns on the fuel-air mixture preparation. Simulations are carried out using the commercial CFD software CONVERGE. Here, the in-cylinder turbulence is modeled with an unsteady Reynolds-averaged Navier-Stokes (URANS) formulation closed by the renormalization group (RNG) k-ε model. Several numerical methods and model constants, including but not limited to turbulent Schmidt number, are evaluated. The numerical results are systematically compared against experimental measurements of velocity and hydrogen concentration fields on the vertical center plane to assess the performance of the CFD model, unveil the physics of hydrogen mixing, and establish best practices for modeling hydrogen DI under relatively high injection pressure conditions.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2025

Evaluation of Flow Routing on the Unstructured Voronoi Meshes in Earth System Modeling

Flow routing is a fundamental process of Earth System Models' (ESMs) river component. Traditional flow routing models rely on Cartesian rectangular meshes, which exhibit limitations, particularly when coupled with unstructured mesh-based ocean components. They also lack the support for regionally refined models. While previous studies have highlighted the potential benefits of unstructured meshes for flow routing, their widespread application and comprehensive evaluation within ESMs remain limited. This study extends the river component of the Energy Exascale Earth System Model to unstructured Voronoi meshes. We evaluated the model's performance in simulating river discharge and water depth across three watersheds spanning the Arctic, temperate, and tropical regions. The results show that while providing several benefits, unstructured mesh-based flow routing can achieve comparable performance to structured mesh-based routing, and their difference is often less than 10%. Although the unstructured mesh-based method could address several existing limitations, this research also shows that additional improvements in the numerical method are needed to fully exploit the advantages of unstructured mesh for hydrologic and ESMs.

54 ENVIRONMENTAL SCIENCES↗