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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 181 records · Page 10
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DOE OSTI2013

Liquid and liquid–gas flows at all speeds

All speed flows and in particular low Mach number flow algorithms are addressed for the numerical approximation of the Kapila et al. [1] multiphase flow model. This model is valid for fluid mixtures evolving in mechanical equilibrium but out of temperature equilibrium and is efficient for material interfaces computation separating miscible and non-miscible fluids. In this context, the interface is considered as a numerically diffused zone, captured as well as all present waves (shocks, expansion waves). The same flow model can be used to solve cavitating and boiling flows [2]. Many applications occurring with liquid–gas interfaces and cavitating flows involve a very wide range of Mach number, from 10{sup −3} to supersonic (and even hypersonic) conditions with respect to the mixture sound speed. It is thus important to address numerical methods free of restrictions regarding the Mach number. To do this, a preconditioned Riemann solver is built and embedded into the Godunov explicit scheme. It is shown that this method converges to exact solutions but needs too small time steps to be efficient. An implicit version is then derived, first in one dimension and second in the frame of 2D unstructured meshes. Two-phase flow preconditioning is then addressed in the frame of the Saurel et al. [3] algorithm. Modifications of the preconditioned Riemann solver are needed and detailed. Convergence of both single phase and two-phase numerical solutions are demonstrated with the help of single phase and two-phase steady nozzle flow solutions. Last, the method is illustrated by the computation of real cavitating flows in Venturi nozzles. Vapour pocket size and instability frequencies are reproduced by the model and method without using any adjustable parameter.

42 ENGINEERING↗
DOE OSTI2024

A collision-based hybrid method for the BGK equation

In this article, we apply the collision-based hybrid method introduced by Hauck and McClarren to the Boltzmann equation with the BGK operator and a hyperbolic scaling. An implicit treatment of the source term is used to handle stiffness associated with the BGK operator. Although it helps the numerical scheme become stable with a large time step size, it is still not obvious to achieve the desired order of accuracy due to the relationship between the size of the spatial cell and the mean free path. Without asymptotic preserving property, a very restricted grid size is required to resolve the mean free path, which is not practical. Our approaches are based on the noncollision-collision decomposition of the BGK equation. We introduce the arbitrary order of nodal discontinuous Galerkin (DG) discretization in space with a semi-implicit time-stepping method; we employ the backward Euler time integration for the uncollided equation and the 2nd order predictor-corrector scheme for the collided equation, i.e., both source terms in uncollided and collided equations are treated implicitly and only streaming term in the collided equation is solved explicitly. This improves the computational efficiency without the complexity of the numerical implementation. Numerical results are presented for various Knudsen numbers to present the effectiveness and accuracy of our hybrid method. Also, we compare the solutions of the hybrid and non-hybrid schemes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

A coupled ordinates method for solution acceleration of rarefied gas dynamics simulations

Non-equilibrium rarefied flows are frequently encountered in a wide range of applications, including atmospheric re-entry vehicles, vacuum technology, and microscale devices. Rarefied flows at the microscale can be effectively modeled using the ellipsoidal statistical Bhatnagar–Gross–Krook (ESBGK) form of the Boltzmann kinetic equation. Numerical solutions of these equations are often based on the finite volume method (FVM) in physical space and the discrete ordinates method in velocity space. However, existing solvers use a sequential solution procedure wherein the velocity distribution functions are implicitly coupled in physical space, but are solved sequentially in velocity space. This leads to explicit coupling of the distribution function values in velocity space and slows down convergence in systems with low Knudsen numbers. Furthermore, this also makes it difficult to solve multiscale problems or problems in which there is a large range of Knudsen numbers. In this paper, we extend the coupled ordinates method (COMET), previously developed to study participating radiative heat transfer, to solve the ESBGK equations. In this method, at each cell in the physical domain, distribution function values for all velocity ordinates are solved simultaneously. This coupled solution is used as a relaxation sweep in a geometric multigrid method in the spatial domain. Enhancements to COMET to account for the non-linearity of the ESBGK equations, as well as the coupled implementation of boundary conditions, are presented. The methodology works well with arbitrary convex polyhedral meshes, and is shown to give significantly faster solutions than the conventional sequential solution procedure. Acceleration factors of 5–9 are obtained for low to moderate Knudsen numbers on single processor platforms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

A new multi-energy neutrino radiation-hydrodynamics code in full general relativity and its application to the gravitational collapse of massive stars

We present a new multi-dimensional radiation-hydrodynamics code for massive stellar core-collapse in full general relativity (GR). Employing an M1 analytical closure scheme, we solve spectral neutrino transport of the radiation energy and momentum based on a truncated moment formalism. Regarding neutrino opacities, we take into account a baseline set in state-of-the-art simulations, in which inelastic neutrino–electron scattering, thermal neutrino production via pair annihilation, and nucleon–nucleon bremsstrahlung are included. While the Einstein field equations and the spatial advection terms in the radiation-hydrodynamics equations are evolved explicitly, the source terms due to neutrino–matter interactions and energy shift in the radiation moment equations are integrated implicitly by an iteration method. To verify our code, we first perform a series of standard radiation tests with analytical solutions that include the check of gravitational redshift and Doppler shift. A good agreement in these tests supports the reliability of the GR multi-energy neutrino transport scheme. We then conduct several test simulations of core-collapse, bounce, and shock stall of a 15M{sub ⊙} star in the Cartesian coordinates and make a detailed comparison with published results. Our code performs quite well to reproduce the results of full Boltzmann neutrino transport especially before bounce. In the postbounce phase, our code basically performs well, however, there are several differences that are most likely to come from the insufficient spatial resolution in our current 3D-GR models. For clarifying the resolution dependence and extending the code comparison in the late postbounce phase, we discuss that next-generation Exaflops class supercomputers are needed at least.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Downwinding for preserving strong stability in explicit integrating factor Runge-Kutta methods

Here strong stability preserving (SSP) Runge-Kutta methods are desirable when evolving in time problems that have discontinuities or sharp gradients and require nonlinear non-inner-product stability properties to be satisfied. Unlike the case for L 2 linear stability, implicit methods do not significantly alleviate the time-step restriction when the SSP property is needed. For this reason, when handling problems with a linear component that is stiff and a nonlinear component that is not, SSP integrating factor Runge-Kutta methods may offer an attractive alternative to traditional time-stepping methods. The strong stability properties of integrating factor Runge-Kutta methods where the transformed problem is evolved with an explicit SSP Runge-Kutta method with non-decreasing abscissas was recently established. However, these methods typically have smaller SSP coefficients (and therefore a smaller allowable time-step) than the optimal SSP Runge-Kutta methods, which often have some decreasing abscissas. In this work, we consider the use of downwinded spatial operators to preserve the strong stability properties of integrating factor Runge-Kutta methods where the Runge-Kutta method has some decreasing abscissas. We present the SSP theory for this approach and present numerical evidence to show that such an approach is feasible and performs as expected. However, we also show that in some cases the integrating factor approach with explicit SSP Runge-Kutta methods with non-decreasing abscissas performs nearly as well, if not better, than with explicit SSP Runge-Kutta methods with downwinding. In conclusion, while the downwinding approach can be rigorously shown to guarantee the SSP property for a larger timestep, in practice using the integrating factor approach by including downwinding as needed with optimal explicit SSP Runge-Kutta methods does not necessarily provide significant benefit over using explicit SSP Runge-Kutta methods with non-decreasing abscissas.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Conservative tightly-coupled simulations of stochastic multiscale systems

Multiphysics problems often involve components whose macroscopic dynamics is driven by microscopic random fluctuations. The fidelity of simulations of such systems depends on their ability to propagate these random fluctuations throughout a computational domain, including subdomains represented by deterministic solvers. When the constituent processes take place in nonoverlapping subdomains, system behavior can be modeled via a domain-decomposition approach that couples separate components at the interfaces between these subdomains. Its coupling algorithm has to maintain a stable and efficient numerical time integration even at high noise strength. We propose a conservative domain-decomposition algorithm in which tight coupling is achieved by employing either Picard's or Newton's iterative method. Coupled diffusion equations, one of which has a Gaussian white-noise source term, provide a computational testbed for analysis of these two coupling strategies. Fully-converged (“implicit”) coupling with Newton's method typically outperforms its Picard counterpart, especially at high noise levels. This is because the number of Newton iterations scales linearly with the amplitude of the Gaussian noise, while the number of Picard iterations can scale superlinearly. At large time intervals between two subsequent inter-solver communications, the solution error for single-iteration (“explicit”) Picard's coupling can be several orders of magnitude higher than that for implicit coupling. Increasing the explicit coupling's communication frequency reduces this difference, but the resulting increase in computational cost can make it less efficient than implicit coupling at similar levels of solution error, depending on the communication frequency of the latter and the noise strength. This trend carries over into higher dimensions, although at high noise strength explicit coupling may be the only computationally viable option.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Explicit integration with GPU acceleration for large kinetic networks

We demonstrate the first implementation of recently-developed fast explicit kinetic integration algorithms on modern graphics processing unit (GPU) accelerators. Taking as a generic test case a Type Ia supernova explosion with an extremely stiff thermonuclear network having 150 isotopic species and 1604 reactions coupled to hydrodynamics using operator splitting, we demonstrate the capability to solve of order 100 realistic kinetic networks in parallel in the same time that standard implicit methods can solve a single such network on a CPU. This orders-of-magnitude decrease in computation time for solving systems of realistic kinetic networks implies that important coupled, multiphysics problems in various scientific and technical fields that were intractable, or could be simulated only with highly schematic kinetic networks, are now computationally feasible.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

EXPLICIT-IMPLICIT SCHEME FOR RELATIVISTIC RADIATION HYDRODYNAMICS

We propose an explicit-implicit scheme for numerically solving special relativistic radiation hydrodynamic equations, which ensures a conservation of total energy and momentum (matter and radiation). In our scheme, zeroth and first moment equations of the radiation transfer equation are numerically solved without employing a flux-limited diffusion approximation. For an hyperbolic term, of which the timescale is the light crossing time when the flow velocity is comparable to the speed of light, is explicitly solved using an approximate Riemann solver. Source terms describing an exchange of energy and momentum between the matter and the radiation via the gas-radiation interaction are implicitly integrated using an iteration method. The implicit scheme allows us to relax the Courant-Friedrichs-Lewy condition in optically thick media, where heating/cooling and scattering timescales could be much shorter than the dynamical timescale. We show that our numerical code can pass test problems of one- and two-dimensional radiation energy transport, and one-dimensional radiation hydrodynamics. Our newly developed scheme could be useful for a number of relativistic astrophysical problems. We also discuss how to extend our explicit-implicit scheme to the relativistic radiation magnetohydrodynamics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

A regulatory perspective on the response function method for determining allowable content of a radioactive materials transportation package or storage cask - 15023

In order to simplify shielding design, there has been an increasingly use of a so-called dose rate response function method for determining the allowable contents in radioactive materials (including spent fuel) transportation package and spent fuel storage cask designs. In essence, this approach uses a pre-calculated dose rate at a given location outside the storage cask or transportation package for a given source inside the cask. It assumes that there is a one-to-one relationship between a source inside the cask and the dose rate outside the cask, i.e., a dose rate response function of a source. Thus, the allowable content is obtained by simply dividing the targeted dose rate by the response function. This method converts the complex particle transport problem into a simple arithmetic calculation. If used correctly and prudently, this approach can greatly simplify the shielding design of casks. However, the use of this method must demonstrate the validity of the assumption, that is, the nuclear physics property of the media through which the particle transverses must be similar to that used in computing the response function. Because of the assumptions and approximations, either implicitly or explicitly, made in the models for dose rate response functions, to assure safety the users should also consider the errors in the models and the bias and uncertainties associated with the code used to calculate the response function. This paper reviewed the advantages and some of the major potential pitfalls of this method from the regulatory perspective. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2017

Extreme scale unstructured adaptive CFD for aerodynamic flow control

Understanding the flow of fluid, either liquid or gas, through and around solid bodies has challenged man since the dawn of scientific inquiry. Many of the great minds of science and mathematics have progressively built up a hierarchy of fluid models since fluid flow impacts our lives in so many fundamental ways - from the early days of flow of water in viaducts to cities, to today's flight of planes. This chapter is concerned with the computational modeling of turbulent flow around aerodynamic bodies such as planes and wind turbines. In this case, viscous effects near the solid bodies create very thin boundary layers that yield highly anisotropic (gradients normal to the surface may be 10 6 larger than gradients along the surface) solutions to the governing non-linear partial differential equations (PDE); the Navier-Stokes equations. Furthermore, turbulent flows develop extremely broad ranges of length and time scales motivating the use of discretization methods capable of employing adaptivity and implicit time integration. The combination of these features - non-linear, anisotropy, adaptivity, and implicit - dramatically raise the complexity of the discretization, posing large challenges to efficient scalable parallel implementation. However, through careful design, the more complex algorithms can provide great reductions in computational cost relative to simpler methods (e.g., Cartesian grids with explicit time integration) that are easier to mate efficiently to hardware. In this chapter, we not only describe our approach but we also address the fact that while complex algorithms may never be as efficient flop-for-flop as simple methods, in the important measure of science-per-core-hour, they can still win big by making complex features like adaptivity and implicit methods as efficient and scalable as possible.

42 ENGINEERING↗
DOE OSTI2018

Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration

Plasmas with varying collisionalities occur in many applications, such as tokamak edge regions, where the flows are characterized by significant variations in density and temperature. While a kinetic model is necessary for weakly-collisional high-temperature plasmas, high collisionality in colder regions render the equations numerically stiff due to disparate time scales. In this study, we propose an implicit–explicit algorithm for such cases, where the collisional term is integrated implicitly in time, while the advective term is integrated explicitly in time, thus allowing time step sizes that are comparable to the advective time scales. This partitioning results in a more efficient algorithm than those using explicit time integrators, where the time step sizes are constrained by the stiff collisional time scales. Finally, we implement semi-implicit additive Runge–Kutta methods in COGENT, a high-order finite-volume gyrokinetic code and test the accuracy, convergence, and computational cost of these semi-implicit methods for test cases with highly-collisional plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Accuracy and efficiency in computing electrostatic potential for an ion channel model in layered dielectric/electrolyte media

This paper will investigate the numerical accuracy and efficiency in computing the electrostatic potential for a finite-height cylinder, used in an explicit/implicit hybrid solvation model for ion channel and embedded in a layered dielectric/electrolyte medium representing a biological membrane and ionic solvents. A charge locating inside the cylinder cavity, where ion channel proteins and ions are given explicit atomistic representations, will be influenced by the polarization field of the surrounding implicit dielectric/electrolyte medium. Two numerical techniques, a specially designed boundary integral equation method and an image charge method, will be investigated and compared in terms of accuracy and efficiency for computing the electrostatic potential. The boundary integral equation method based on the three-dimensional layered Green's functions provides a highly accurate solution suitable for producing a benchmark reference solution, while the image charge method is found to give reasonable accuracy and highly efficient and viable to use the fast multipole method for interactions of a large number of charges in the atomistic region of the hybrid solvation model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

General-relativistic Resistive Magnetohydrodynamics with Robust Primitive-variable Recovery for Accretion Disk Simulations

Recent advances in black hole astrophysics, particularly the first visual evidence of a supermassive black holeat the center of the galaxy M87 by the Event Horizon Telescope (EHT), and the detection of an orbiting “hot spot”nearby the event horizon of Sgr A* in the Galactic center by the Gravity Collaboration, require the developmentof novel numerical methods to understand the underlying plasma microphysics. Non-thermal emission related tosuch hot spots is conjectured to originate from plasmoids that form due to magnetic reconnection in thin currentlayers in the innermost accretion zone. Resistivity plays a crucial role in current sheet formation, magneticreconnection, and plasmoid growth in black hole accretion disks and jets. We included resistivity in the three-dimensional general-relativistic magnetohydrodynamics (GRMHD) codeBHACand present the implementationof an Implicit-Explicit scheme to treat the stiff resistive source terms of the GRMHD equations. The algorithmis tested in combination with adaptive mesh refinement to resolve the resistive scales and a constrained transportmethod to keep the magnetic field solenoidal. Several novel methods for primitive variable recovery, a key part inrelativistic magnetohydrodynamics codes, are presented and compared for accuracy, robustness, and efficiency.We propose a new inversion strategy that allows for resistive-GRMHD simulations of low gas-to-magneticpressure ratio and highly magnetized regimes as applicable for black hole accretion disks, jets, and neutron starmagnetospheres. We apply the new scheme to study the effect of resistivity on accreting black holes, accountingfor dissipative effects as reconnection

(magnetohydrodynamics:) MHD↗
DOE OSTI2017

Efficient algorithms and implementations of entropy-based moment closures for rarefied gases

We present efficient algorithms and implementations of the 35-moment system equipped with the maximum-entropy closure in the context of rarefied gases. While closures based on the principle of entropy maximization have been shown to yield very promising results for moderately rarefied gas flows, the computational cost of these closures is in general much higher than for closure theories with explicit closed-form expressions of the closing fluxes, such as Grad's classical closure. Following a similar approach as Garrett et al. (2015) , we investigate efficient implementations of the computationally expensive numerical quadrature method used for the moment evaluations of the maximum-entropy distribution by exploiting its inherent fine-grained parallelism with the parallelism offered by multi-core processors and graphics cards. We show that using a single graphics card as an accelerator allows speed-ups of two orders of magnitude when compared to a serial CPU implementation. To accelerate the time-to-solution for steady-state problems, we propose a new semi-implicit time discretization scheme. The resulting nonlinear system of equations is solved with a Newton type method in the Lagrange multipliers of the dual optimization problem in order to reduce the computational cost. Additionally, fully explicit time-stepping schemes of first and second order accuracy are presented. We investigate the accuracy and efficiency of the numerical schemes for several numerical test cases, including a steady-state shock-structure problem.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Error estimates of finite difference methods for the Dirac equation in the massless and nonrelativistic regime

We present four frequently used finite difference methods and establish the error bounds for the discretization of the Dirac equation in the massless and nonrelativistic regime, involving a small dimensionless parameter 0 < ε &NestedLessLess; 1 inversely proportional to the speed of light. In the massless and nonrelativistic regime, the solution exhibits rapid motion in space and is highly oscillatory in time. Specifically, the wavelength of the propagating waves in time is at O(ε), while in space, it is at O(1) with the wave speed at O(ε -1 ). We adopt one leap-frog, two semi-implicit, and one conservative Crank-Nicolson finite difference methods to numerically discretize the Dirac equation in one dimension and establish rigorously the error estimates which depend explicitly on the time step τ, mesh size h, and the small parameter ε. The error bounds indicate that, to obtain the “correct” numerical solution in the massless and nonrelativistic regime, i.e., 0 < ε &NestedLessLess; 1, all these finite difference methods share the same ε-scalability as time step τ = O(ε 3/2 ) and mesh size h = O(ε 1/2 ). A large number of numerical results are reported to verify the error estimates.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Simulation of crumpled sheets via alternating quasistatic and dynamic representations

In this work, we present a method for simulating the large-scale deformation and crumpling of thin, elastoplastic sheets. Motivated by the physical behavior of thin sheets during crumpling, two different formulations of the governing equations of motion are used: (1) a quasistatic formulation that effectively describes smooth deformations, and (2) a fully dynamic formulation that captures large changes in the sheet's velocity. The former is a differential-algebraic system of equations integrated implicitly in time, while the latter is a set of ordinary differential equations (ODEs) integrated explicitly. We adopt a hybrid integration scheme to adaptively alternate between the quasistatic and dynamic representations as appropriate. Further, we demonstrate the capacity of this method to effectively simulate a variety of crumpling phenomena. Finally, we show that statistical properties, notably the accumulation of creases under repeated loading, as well as the area distribution of facets, are consistent with experimental observations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

New implicitly solvable potential produced by second order shape invariance

The procedure proposed recently by Bougie et al. (2010) to study the general form of shape invariant potentials in one-dimensional Supersymmetric Quantum Mechanics (SUSY QM) is generalized to the case of Higher Order SUSY QM with supercharges of second order in momentum. A new shape invariant potential is constructed by this method. It is singular at the origin, it grows at infinity, and its spectrum depends on the choice of connection conditions in the singular point. The corresponding Schrödinger equation is solved explicitly: the wave functions are constructed analytically, and the energy spectrum is defined implicitly via the transcendental equation which involves Confluent Hypergeometric functions. - Highlights: • New potential with 2nd order irreducible shape invariance was constructed. • The connection conditions at the singularity of potential were obtained. • The explicit expressions for all wave functions were derived. • The implicit equation for the energy spectrum was obtained.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗