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Results for “Finite Difference Methods”

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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Interface learning in fluid dynamics: Statistical inference of closures within micro–macro-coupling models

Many complex multiphysics systems in fluid dynamics involve using solvers with varied levels of approximations in different regions of the computational domain to resolve multiple spatiotemporal scales present in the flow. The accuracy of the solution is governed by how the information is exchanged between these solvers at the interface and several methods have been devised for such coupling problems. In this article, we construct a data-driven model by spatially coupling a microscale lattice Boltzmann method (LBM) solver and macroscale finite difference method (FDM) solver for reaction-diffusion systems. The coupling between the micro-macro solvers has one to many mapping at the interface leading to the interface closure problem, and we propose a statistical inference method based on neural networks to learn this closure relation. The performance of the proposed framework in a bifidelity setting partitioned between the FDM and LBM domain shows its promise for complex systems where analytical relations between micro-macro solvers are not available.

42 ENGINEERING↗
DOE OSTI2015

Convergence analysis of two-node CMFD method for two-group neutron diffusion eigenvalue problem

In this paper, the nonlinear coarse-mesh finite difference method with two-node local problem (CMFD2N) is proven to be unconditionally stable for neutron diffusion eigenvalue problems. The explicit current correction factor (CCF) is derived based on the two-node analytic nodal method (ANM2N), and a Fourier stability analysis is applied to the linearized algorithm. It is shown that the analytic convergence rate obtained by the Fourier analysis compares very well with the numerically measured convergence rate. It is also shown that the theoretical convergence rate is only governed by the converged second harmonic buckling and the mesh size. It is also noted that the convergence rate of the CCF of the CMFD2N algorithm is dependent on the mesh size, but not on the total problem size. This is contrary to expectation for eigenvalue problem. The novel points of this paper are the analytical derivation of the convergence rate of the CMFD2N algorithm for eigenvalue problem, and the convergence analysis based on the analytic derivations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Mathematical Simulation of the Migration of Radionuclides in a Soil Medium Under Nonisothermal Conditions with Account for Catalytic Microparticles and Nonlinear Processes

The problem of mathematical simulation of the vertical migration of radionuclides in a catalytic porous medium under nonisothermal conditions is considered. A numerical solution of the corresponding one-dimensional nonlinear boundary-value problem is obtained by the finite difference method. Numerical experiments are carried out and their analysis is made.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

A higher order approximate static condensation method for multi-material diffusion problems

The paper studies an approximate static condensation method for the diffusion problem with discontinuous diffusion coefficients. The method allows for a general polygonal mesh which is unfitted to the material interfaces. Moreover, the interfaces can be discontinuous across the mesh edges as typical for numerical reconstructions using the volume or moment-of-fluid methods. We apply a mimetic finite difference method to solve local diffusion problems and use P 1 (mortar) edge elements to couple local problems into the global system. The condensation process and the properties of the resulting algebraic system are discussed. It is demonstrated that the method is second order accurate on smooth solutions and performs well for problems with high contrast in diffusion coefficients. Experiments also show the robustness with respect to position of the material interfaces against the underlying mesh.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Calculating Control Rod Differential Worth Using Adjoint-Weighted Method

Recently, there are more and more research on using Monte Carlo method to calculate reactor important parameters. Control rod worth is one of the important parameters as it can determine the critical control rod position. There are two presentations of the control rod worth for utilization purpose, integral and differential. The former is the total reactivity change, while the latter is the reactivity change caused by per unit movement. In Monte Carlo calculation, differential control rod worth of a particular position is estimated by finite difference of reactivity between a small gap divided by gap distance. Though easy to implemented, the problem of this approach lies in that too large gap will enlarge error between 'differential' and 'difference', while too small gap will be disturbed by error caused by random fluctuation. Monte Carlo perturbation theory has been used to calculate the k{sub eff} sensitivity to certain parameters for a long time. By calculating the differential coefficient along with the k{sub eff}, this method is quite time-consuming and relatively accurate compared to finite difference method. Nevertheless, most of perturbation research focus on the perturbation of nuclide density or nuclear data. For geometrical perturbation, limited research was done before. Takahashi estimated the k{sub eff} sensitivity to reflector movement of pulsed fast reactor. MCNP6 used adjoint-weighted method for Godiva, Zeus and uranium oxyfluoride solution container benchmarks. This paper tries to apply the perturbation method to the determination of control rod differential worth. In this paper, based on RMC, a continuous-energy Reactor Monte Carlo transport code, Iterated Fission Probability method (IFP) is researched to calculate control rod differential worth on assembly level. IFP was originally developed by Hurwitz, and has been adopted by most of Monte Carlo code to compute adjoint-weighted parameters. This paper is organized with four parts. The first is introduction. Adjoint-weighted method is introduced in the second part. Problem 4 of benchmark from CASL is built to verify the method. Conclusion is given in final part.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2018

Calculation of Energy States of Excitons in Square Quantum Wells

The ground and excited energy states of excitons in single square GaAs-based quantum wells are found by the numerical solution of the three-dimensional Schrödinger equation. This equation is obtained within the envelope-function formalism from the exciton energy operator using the spherical approximation of the Luttinger Hamiltonian. Precise results for the exciton states are achieved by the finite-difference method. The radiative decay rates of the calculated states are also determined.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method

The Molecular Beam Epitaxial model is derived from the variation of a free energy, that consists of either a fourth order Ginzburg–Landau double well potential or a nonlinear logarithmic potential in terms of the gradient of a height function. One challenge in solving the MBE model numerically is how to develop proper temporal discretization for the nonlinear terms in order to preserve energy stability at the time-discrete level. In this paper, we resolve this issue by developing a first and second order time-stepping scheme based on the “Invariant Energy Quadratization” (IEQ) method. The novelty is that all nonlinear terms are treated semi-explicitly, and the resulted semi-discrete equations form a linear system at each time step. Moreover, the linear operator is symmetric positive definite and thus can be solved efficiently. We then prove that all proposed schemes are unconditionally energy stable. The semi-discrete schemes are further discretized in space using finite difference methods and implemented on GPUs for high-performance computing. Various 2D and 3D numerical examples are presented to demonstrate stability and accuracy of the proposed schemes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Orbital Advection with Magnetohydrodynamics and Vector Potential

Orbital advection is a significant bottleneck in disk simulations, and a particularly tricky one when used in connection with magnetohydrodynamics. We have developed an orbital advection algorithm suitable for the induction equation with magnetic potential. The electromotive force is split into advection and shear terms, and we find that we do not need an advective gauge since solving the orbital advection implicitly precludes the shear term from canceling the advection term. We prove and demonstrate the third order in time accuracy of the scheme. The algorithm is also suited to non-magnetic problems. Benchmarked results of (hydrodynamical) planet–disk interaction and of the magnetorotational instability are reproduced. We include detailed descriptions of the construction and selection of stabilizing dissipations (or high-frequency filters) needed to generate practical results. The scheme is self-consistent, accurate, and elegant in its simplicity, making it particularly efficient for straightforward finite-difference methods. As a result of the work, the algorithm is incorporated in the public version of the Pencil Code, where it can be used by the community.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Numerical Modeling of Ultra Wideband Combined Antennas

With the help of a program we developed, based on the finite difference method in the time domain, we have investigated the characteristics of ultra wideband combined antennas in detail. The antennas were developed to radiate bipolar pulses with durations in the range 0.5–3 ns. Data obtained by numerical modeling are compared with the data of experimental studies on antennas and have been used in the synthesis of electromagnetic pulses with maximum field strength.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

The Interface Influence in TiN/SiN{sub x} Multilayer Nanocomposite Under Irradiation

The paper focuses on studying the kinetics of radiation-induced point defects formed in TiN/SiN{sub x} multilayer nanocomposites with account of their generation, diffusion recombination, and the influence of sinks functioning as interfaces. In order to describe the kinetics in nanocrystalline TiN and amorphous SiN{sub x} phases, a finite-difference method is used to solve the system of balance kinetic equations for absolute defect concentrations depending on the spatiotemporal variables. A model of the disclination-dislocation interface structure is used to study the absorption of radiation-induced point defects on the boundaries in created stress fields. It is shown that the interface effectively absorbs point defects in these phases of TiN/SiN{sub x} multilayer nanocomposite, thereby reducing their amount within the space between phases. This behavior of point defects partially explains a mechanism of the radiation resistance in this type of nanocomposites.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2019

Miniband formation engineering in GaN/AlN superlattices with constant total effective length

In this work, we study the miniband formation procedure in GaN/AlN constant total effective length superlattices by means of the subband energy calculations. We calculate the transmission coefficients and miniband structures of the systems by means of the transfer matrix and finite difference methods, respectively. The miniband structures obtained by using these methods confirm each other. Here, we observe a nonlinear miniband gap behavior as the number of wells changes. Now, we can tune the width of each miniband and minigap by means of the number of wells and the total effective length of the system. By using the strategy of fixing the total length of the system and optimizing the number of layers inside it, we can find the same miniband widths as the usual superlattice (fixing the well width, not the total system length). However, in the earlier case (our proposal), fabrication of the device may need fewer amounts of the material and may lead to smaller device sizes, because we fixed the total system length.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Semi-numerical solution to a fractal telegraphic dual-porosity fluid flow model

We present a semi-numerical solution to a fractal telegraphic dual-porosity fluid flow model. It combines Laplace transform and finite difference schemes. The Laplace transform handles the time variable whereas the finite difference method deals with the spatial coordinate. This semi-numerical scheme is not restricted by space discretization and allows the computation of a solution at any time without compromising numerical stability or the mass conservation principle. Our formulation results in a non-analytically-solvable second-order differential equation whose spatial discretization yields a tridiagonal linear algebraic system. Moreover, we describe comparisons between semi-numerical and semi-analytical solutions for particular cases. Results agree well with those from semi-analytic solutions. Furthermore, we expose a parametric analysis from the coupled model in order to show the effects of relevant parameters on pressure profiles and flow rates for the case where neither analytic nor semi-analytic solutions are available.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Ion temperature and gas pressure effects on the magnetized sheath dynamics during plasma immersion ion implantation

Here, a collisional magnetized plasma with finite ion temperature is considered to examine the effects of the ion temperature and gas pressure on the plasma-sheath dynamics. We use the two-fluid model of plasma-sheath where the nonlinear equations of a dynamic sheath are solved using a full implicit scheme of finite difference method along with some convenient initial and boundary conditions at the plasma center and target. It is found that the ion temperature only has a significant effect on the characteristics of low voltage sheath, while the gas pressure (collision rate) seriously affects the dynamic characteristics of the low and high voltage plasma-sheath. One can see, increasing the ion temperature in low voltage plasma-sheath causes to increase the temporal curve of the ion dose and the ion impact energy on the target, reduces the temporal curve of the sheath width, and has no any effect on the temporal curve of the ion incident angle on the target. However, rising the gas pressure in low and high voltage plasma-sheath reduces all of these temporal curves.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Extreme sensitivity of higher-order interatomic force constants and thermal conductivity to the energy surface roughness of exchange-correlation functionals

In this Letter, we report that the fourth-order interatomic force constants (4th-IFCs) are significantly sensitive to the energy surface roughness of exchange-correlation (XC) functionals in density functional theory calculations. This sensitivity, which is insignificant for the second- (2nd-) and third-order (3rd-) IFCs, varies for different functionals in different materials and can cause misprediction of thermal conductivity by several times of magnitude. As a result, when calculating the 4th-IFCs using the finite difference method, the atomic displacement needs to be taken large enough to overcome the energy surface roughness, in order to accurately predict phonon lifetime and thermal conductivity. We demonstrate this phenomenon on a benchmark material (Si), a high-thermal conductivity material (BAs), and a low thermal conductivity material (NaCl). For Si, we find that the LDA, PBE, and PBEsol XC functionals are all smooth to the 2nd- and 3rd-IFCs but all rough to the 4th-IFCs. This roughness can lead to a prediction of nearly one order of magnitude lower thermal conductivity. For BAs, all three functionals are smooth to the 2nd- and 3rd-IFCs, and only the PBEsol XC functional is rough for the 4th-IFCs, which leads to a 40% underestimation of thermal conductivity. For NaCl, all functionals are smooth to the 2nd- and 3rd-IFCs but rough to the 4th-IFCs, leading to a 70% underprediction of thermal conductivity at room temperature. In conclusion, with these observations, we provide general guidance on the calculation of 4th-IFCs for an accurate thermal conductivity prediction.

42 ENGINEERING↗
DOE OSTI2018

Numerical investigation on two-fluid model (micropolar-Newtonian) for pulsatile flow of blood in a tapered arterial stenosis with radially variable magnetic field and core fluid viscosity

In the present study, an unsteady two-fluid model of blood through a tapered arterial stenosis with variable viscosity in the presence of variable magnetic field has been investigated. In this model, blood in the core region is assumed to be micropolar and plasma in the peripheral layer as Newtonian. Finite difference method is employed in solving the governing equations. The solutions for velocity, flow rate, wall shear stress and flow resistance are computed numerically. A comparison between the velocity profiles obtained by the present study and the experimental data is made and a good agreement between them is found. The model is used to study the effect of parameters such as taper angle, radially variable viscosity, hematocrit, the coupling number, the micropolar parameter, magnetic field and plasma layer thickness on physiologically important parameters such as wall shear stress distribution in the stenotic region and flow resistance. The results in the case of constant magnetic field and variable magnetic field are compared to study the effects of magnetic field on the flow of blood. It is found that the magnitudes of wall shear stress and flow resistance are higher in the case of variable magnetic field. It is important to note that the flow resistance is higher for magneto-micropolar fluid than the micropolar fluid. The wall shear stress decreases with increasing hematocrit parameter whereas flow resistance increases with hematocrit when the applied pressure gradient is held fixed. The model clearly shows the situation of a patient with a tapered arterial stenosis under feverish condition. Due care has been taken to compare the present theoretical results with the existing ones including experimental results and good agreement between them has been observed both qualitatively and quantitatively.

42 ENGINEERING↗
DOE OSTI2017

Interaction between two conducting spheres in weakly ionized collisional plasma

Charging of two conducting spheres in a weakly ionized collisional plasma flow is considered. The spheres are arranged along the flow, and the plasma is assumed to consist of two ion species with the charges equal in magnitude but opposite in sign. The problem is analyzed with allowance for the external electric field, charging of the spheres due to the sedimentation of plasma ions on them, the fields of the sphere charges, the space charge field, and the processes of recombination and molecular diffusion. The interaction between the spheres and plasma is studied by numerically solving a time-dependent problem in a bispherical coordinate system by the finite difference method. The steady-state values of the sphere charges and the distributions of the space charge and ion densities in the ambient plasma are found as functions of the plasma parameters and the distance between the spheres. The electrostatic forces acting on the spheres are determined, and the effects of the external field, the space charge fields, and the fields of the sphere charges are comparatively analyzed. It is shown that, for the considered plasma parameters, the main electrostatic effect in the interaction between two spheres is their mutual approach in the external field due to the difference in their charges (one sphere catches up with the other). Due to the friction force with the neutral gas, this mutual approach is much slower than all other processes in the system. For widely spaced spheres, the results coincide with the solution obtained previously for a solitary sphere.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Semi-analytical sensitivity analysis for nonlinear transient problems

Efficient analytical sensitivity computations are essential elements of gradient-based optimization schemes; however, they can be difficult to implement. This implementation issue is often resolved by adopting the semi-analytical method which exhibits the efficiency of the analytical methods and the ease of implementation of the finite difference method. However, care must be taken as semi-analytical sensitivities may exhibit errors due to truncation and round-off. Additional errors are introduced if the convergence tolerance of the primal analysis is not sufficiently small. This paper gives a general overview and some new developments of the analytical and semi-analytical sensitivity analyses for nonlinear steady-state, transient, and dynamic problems. We discuss the restrictive assumptions, accuracy, and consistency of these methods. Both adjoint and direct differentiation methods are studied. Numerical examples are provided.

42 ENGINEERING↗
DOE OSTI2017

A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part I: Model problem analysis

A stable partitioned algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and rigid bodies. This added-mass partitioned (AMP) algorithm remains stable, without sub-iterations, for light and even zero mass rigid bodies when added-mass and viscous added-damping effects are large. The scheme is based on a generalized Robin interface condition for the fluid pressure that includes terms involving the linear acceleration and angular acceleration of the rigid body. Added mass effects are handled in the Robin condition by inclusion of a boundary integral term that depends on the pressure. Added-damping effects due to the viscous shear forces on the body are treated by inclusion of added-damping tensors that are derived through a linearization of the integrals defining the force and torque. Added-damping effects may be important at low Reynolds number, or, for example, in the case of a rotating cylinder or rotating sphere when the rotational moments of inertia are small. In this second part of a two-part series, the general formulation of the AMP scheme is presented including the form of the AMP interface conditions and added-damping tensors for general geometries. A fully second-order accurate implementation of the AMP scheme is developed in two dimensions based on a fractional-step method for the incompressible Navier-Stokes equations using finite difference methods and overlapping grids to handle the moving geometry. Here, the numerical scheme is verified on a number of difficult benchmark problems.

97 MATHEMATICS AND COMPUTING↗