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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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Parallelized POD-based suboptimal economic model predictive control of a state-constrained Boussinesq approximation

Motivated by an energy efficient building application, we want to optimize a quadratic cost functional subject to the Boussinesq approximation of the Navier-Stokes equations and to bilateral state and control constraints. Since the computation of such an optimal solution is numerically costly, we design an efficient strategy to compute a sub-optimal (but applicationally acceptable) solution with significantly reduced computational effort. We employ an economic Model Predictive Control (MPC) strategy to obtain a feedback control. The MPC sub-problems are based on a linear-quadratic optimal control problem subjected to mixed control and state constraints and a convection-diffusion equation, reduced with proper orthogonal decomposition. Finally, to solve each sub-problem, we apply a primal-dual active set strategy. The method can be fully parallelized, which enables the solution of large problems with real-world parameters.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Mixing model with multi-particle interactions for Lagrangian simulations of turbulent mixing

We report on the numerical study of the mixing volume model (MVM) for molecular diffusion in Lagrangian simulations of turbulent mixing problems. The MVM is based on the multi-particle interaction in a finite volume (mixing volume). A priori test of the MVM, based on the direct numerical simulations of planar jets, is conducted in the turbulent region and the interfacial layer between the turbulent and non-turbulent fluids. The results show that the MVM predicts well the mean effects of the molecular diffusion under various numerical and flow parameters. The number of the mixing particles should be large for predicting a value of the molecular diffusion term positively correlated to the exact value. The size of the mixing volume relative to the Kolmogorov scale η is important in the performance of the MVM. The scalar transfer across the turbulent/non-turbulent interface is well captured by the MVM especially with the small mixing volume. Furthermore, the MVM with multiple mixing particles is tested in the hybrid implicit large-eddy-simulation/Lagrangian-particle-simulation (LES–LPS) of the planar jet with the characteristic length of the mixing volume of O(100η). Despite the large mixing volume, the MVM works well and decays the scalar variance in a rate close to the reference LES. The statistics in the LPS are very robust to the number of the particles used in the simulations and the computational grid size of the LES. Both in the turbulent core region and the intermittent region, the LPS predicts a scalar field well correlated to the LES.

42 ENGINEERING↗
DOE OSTI2021

Non-Diffusive Volume Advection with A High Order Interface Reconstruction Method

We show that non-diffusive volume advection in two-dimensions is achieved with several benchmark problems using a newly developed high-order volume of fluids (VOF) interface reconstruction method. (1) A new VOF interface reconstruction method using circular/corner facets (linear facets are a degenerate case of arcs). We create a circular interface facet in each mixed zone by matching neighbor volume with a hybrid Newton’s-bisection method and the local solution is final. In the general case, the new VOF interface reconstruction has 3rd order accuracy and can be easily made seamless. The new method addresses intrinsic issues with Young’s method such as gaps between interface facets in the case of a curved interface, and inability to define curvature nor identify corners. (2) A non-diffusive volume advection scheme. In an ALE advection step, a well-defined interface can be carried over through a Lagrange step and used to compute volume distribution into a relaxed mesh. Then, an interface reconstruction step is performed to redefine the interface in the relaxed mesh. We must point out that the interface carried over is also a solution of interface reconstruction because all the volume fractions in the relaxed mesh are naturally matched. We provide an interface tracking method compatible with our reconstruction scheme, where it is granted to use the prior info as an initial guess to capture sub-mesh resolution features. As a result, we are able to treat multiple facets inside a single mixed cell and obtain highly accurate, non-diffusive solution for advection problems with rather coarse meshes. We show our solutions for two-dimensional incompressible flows with two materials with a) the X + O diagonal translation; b) the Zalesak rotational test; and c) the single vortex spiral test.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

fPINNs: Fractional Physics-Informed Neural Networks

Physics-informed neural networks (PINNs), introduced, are effective in solving integer-order partial differential equations (PDEs) based on scattered and noisy data. PINNs employ standard feedforward neural networks (NNs) with the PDEs explicitly encoded into the NN using automatic differentiation, while the sum of the mean-squared PDE residuals and the mean-squared error in initial-boundary conditions is minimized with respect to the NN parameters. Here we extend PINNs to fractional PINNs (fPINNs) to solve space-time fractional advection-diffusion equations (fractional ADEs), and we study systematically their convergence, hence explaining both fPINNs and PINNs for the first time. Specifically, we demonstrate their accuracy and effectiveness in solving multidimensional forward and inverse problems with forcing terms whose values are only known at randomly scattered spatio-temporal coordinates (black-box (BB) forcing terms). A novel element of the fPINNs is the hybrid approach that we introduce for constructing the residual in the loss function using both automatic differentiation for the integer-order operators and numerical discretization for the fractional operators. This approach bypasses the difficulties stemming from the fact that automatic differentiation is not applicable to fractional operators because the standard chain rule in integer calculus is not valid in fractional calculus. To discretize the fractional operators, we employ the Grünwald--Letnikov (GL) formula in one-dimensional fractional ADEs and the vector GL formula in conjunction with the directional fractional Laplacian in two- and three-dimensional fractional ADEs. We first consider the one-dimensional fractional Poisson equation and compare the convergence of the fPINNs against the finite difference method (FDM). We present the solution convergence using both the mean L 2 error as well as the standard deviation due to sensitivity to NN parameter initializations. Using different GL formulas we observe first-, second-, and third-order convergence rates for small size training sets but the error saturates for larger training sets. We explain these results by analyzing the four sources of numerical errors due to discretization, sampling, NN approximation, and optimization. The total error decays monotonically (below 10 –5 for a third-order GL formula) but it saturates beyond that point due to the optimization error. We also analyze the relative balance between discretization and sampling errors and observe that the sampling size and the number of discretization points (auxiliary points) should be comparable to achieve the highest accuracy. As we increase the depth of the NN up to certain value, the mean error decreases and the standard deviation increases, whereas the width has essentially no effect unless its value is either too small or too large. We next consider time-dependent fractional ADEs and compare white-box (WB) and BB forcing. We observe that for the WB forcing, our results are similar to the aforementioned cases; however, for the BB forcing fPINNs outperform FDM. Subsequently, we consider multidimensional time-, space-, and space-time-fractional ADEs using the directional fractional Laplacian and we observe relative errors of 10 –3 ~ 10 –4 . Lastly, we solve several inverse problems in one, two, and three dimensions to identify the fractional orders, diffusion coefficients, and transport velocities and obtain accurate results given proper initializations even in the presence of significant noise.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

1-D coupled surface flow and transport equations revisited via the physics-informed neural network approach

The de Saint-Venant equation (SVE) and advection–diffusion equation (ADE) are commonly employed to solve solute transport problems in surface water. In this work, we propose a mesh-free method based on the physics-informed neural network (PINN) to solve the one dimensional (1-D) SVE, ADE, and the coupled SVE and ADE (SVE-ADE) under various initial and boundary conditions. The PINN model extends the architecture of deep neural networks (DNNs) with implementation of loss function, which are additionally subject to constraints imposed by the physical laws of SVE and ADE, along with their initial and boundary conditions. In such a manner, PINNs can be quickly steered to the true solution while obeying the physical laws. The results of PINN model are compared with the analytical and/or numerical solutions under various conditions to investigate its accuracy and efficiency in solving the SVE, ADE, and SVE-ADE. Our results indicate PINN can accurately simulate the shock wave morphology and avoid numerical dissipation in unsteady flow condition. The PINN method outweighed traditional numerical methods in several aspects, including its ability to function with small amounts of data, no grid discretization, and random selection of sampling points, etc. Additionally, the PINN method is also suitable for solving inverse problems with sparse and noisy data. With 1% noise and 2000 initial and boundary condition points (N u ), the errors of the estimated flow rate (v) and diffusion coefficient (D) are 0.003% and 0.105%, respectively, which indicate the accuracy and robustness of the proposed method. Finally, our results indicate the capability and robustness of the proposed PINN methodology for solving multi-physics problems, irrespective of the presence of sparse and noisy data in the training dataset.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Stability of the Tonks–Langmuir discharge pre-sheath

The article formulates the stability problem of the plasma sheath in the Tonks–Langmuir discharge. Using the kinetic description of the ion gas, i.e., the stability of the potential shape in the quasi-neutral pre-sheath regarding the high and low frequency, the perturbations are investigated. The electrons are assumed to be Maxwell–Boltzmann distributed. Regarding high-frequency perturbations, the pre-sheath is shown to be stable. The stability problem regarding low-frequency perturbations can be reduced to an analysis of the “diffusion like” equation, which results in the instability of the potential distribution in the pre-sheath. By means of the Particle in Cell simulations, also the nonlinear stage of low frequency oscillations is investigated. Comparing the figure obtained with the figure for linear stage, one can find obvious similarity in the spatial-temporal behavior of the potential.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

A New Method for the Solution of Group Diffusion Equations

Here, the diffusion equations associated with the multigroup, multiregion problem are solved by expansions in eigenfunctions which are solutions of the Helmholtz equation. A determinantal criticality equation is exhibited in which the order of the determinant is independent of the number of groups and which can be solved without recourse to complicated computational procedures. Moreover, the need to fulfill explicitly the requirements that the flux and current associated with each neutron group be continuous across interfaces is eliminated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Stable low diffusion flux splitting schemes on unstructured meshes

Shock instabilities are shown to manifest in modern low-diffusion flux-vector splitting (FVS) schemes when used on unstructured meshes, or situations where shocks do not align with the mesh lines. These instabilities occur irrespective of the Mach number of the shock. Three types of dissipative mechanisms that suppress these instabilities are presented. These mechanisms are carefully designed in order to affect only problematic regions of the flux-splittings. The AUSM + and LDFSS schemes are stabilized using the proposed modifications. It is shown that the added dissipation improves the shock behavior of AUSM and LDFSS on unstructured meshes. It is also shown that the AUSM + -up scheme is prone to the “carbuncle” instability, a specific type of shock instability, when used on unstructured meshes. The modifications proposed in this work do not lead to carbuncle instabilities for the problems considered here. Furthermore, the modified schemes are shown to satisfy certain properties that are crucial for accurate shear layer computations, such as stationary contact preservation. Using benchmark problems, it is demonstrated that despite the diffusion added for stabilization, these schemes are not overly diffusive. Furthermore, due to these advantages, the modified FVS schemes presented here are promising candidates for high-speed compressible flow computations on unstructured meshes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Thermochemically-Informed Mass Transport Model for Zr in U-Zr Fuel

Recent improvements to the coupled Thermochimica-MOOSE/BISON code system have enabled efficient calculations of species transport based on direct evaluation of composition and temperature dependent chemical potentials of the species. This presents an alternative to the traditional approach to species transport in nuclear fuels, which has been to employ a diffusion formulation that combines concentration-gradient driven Fickian diffusion with a Soret term based on a heat of transport fit to experimental data. Here we describe the application of the coupled code system to the diffusion of Zr in U-Zr metallic fuel. New classes implemented in BISON to solve this problem are documented. The Zr concentration profile after 50 years of diffusion is found to be strongly dependent on the assumptions made pertaining how to mobility is calculated in multi-phase regions of the fuel element. Two assumptions are compared (simple averaging of mobilities and using the majority phase mobility), and good qualitative agreement with experimental measurements is obtained using the majority phase assumption.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2017

A high-order staggered meshless method for elliptic problems

Here, we present a new meshless method for scalar diffusion equations, which is motivated by their compatible discretizations on primal-dual grids. Unlike the latter though, our approach is truly meshless because it only requires the graph of nearby neighbor connectivity of the discretization points. This graph defines a local primal-dual grid complex with a virtual dual grid, in the sense that specification of the dual metric attributes is implicit in the method's construction. Our method combines a topological gradient operator on the local primal grid with a generalized moving least squares approximation of the divergence on the local dual grid. We show that the resulting approximation of the div-grad operator maintains polynomial reproduction to arbitrary orders and yields a meshless method, which attains $O(h^{m})$ convergence in both $L^2$- and $H^1$-norms, similar to mixed finite element methods. We demonstrate this convergence on curvilinear domains using manufactured solutions in two and three dimensions. Application of the new method to problems with discontinuous coefficients reveals solutions that are qualitatively similar to those of compatible mesh-based discretizations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

An information diffusion technique to assess integrated hazard risks

An integrated risk is a scene in the future associated with some adverse incident caused by multiple hazards. An integrated probability risk is the expected value of disaster. Due to the difficulty of assessing an integrated probability risk with a small sample, weighting methods and copulas are employed to avoid this obstacle. To resolve the problem, in this paper, we develop the information diffusion technique to construct a joint probability distribution and a vulnerability surface. Then, an integrated risk can be directly assessed by using a small sample. A case of an integrated risk caused by flood and earthquake is given to show how the suggested technique is used to assess the integrated risk of annual property loss.

58 GEOSCIENCES↗
DOE OSTI2019

ICAT: A numerical scheme to minimize numerical diffusion in advection-dispersion modeling and its application in identifying flow channeling

The advection-dispersion equation for scalar transport is essential for the numerical modeling of many fluid dynamics problems. However, solutions from numerical schemes always suffer from numerical diffusion and/or oscillation. In this study, we develop an Intra-Cell Advection Tracking (ICAT) scheme to minimize numerical diffusion and preserve monotonicity for advection-dispersion modeling. The key idea is to introduce “queues” in each discretized cell, and using a sequential transport rule and a flow distribution mechanism to track the scalar transport in these queues temporally and spatially. The capability and limitations of ICAT are first investigated through three test cases. Compared with the results obtained from other numerical schemes, the results from ICAT show substantially reduced numerical diffusion and agree better with analytical solutions. We also employ ICAT to simulate the transport process of a conservative tracer in a fracture with a highly heterogeneous aperture distribution. We report discrete flow channels in the fracture are better discerned by ICAT than by other numerical schemes, indicating the suitability of ICAT for modeling tracer transport in channelized flow fields.

15 GEOTHERMAL ENERGY↗
DOE OSTI2018

Nonlinear optimization for a tumor invasion PDE model

In this work, we introduce a methodology to approximate unknown parameters that appear on a non-linear reaction–diffusion model of tumor invasion. These equations consider that tumor-induced alteration of micro-environmental pH furnishes a mechanism for cancer invasion. A coupled system reaction–diffusion explaining this model is given by three partial differential equations for the non-dimensional spatial distribution and temporal evolution of the density of normal tissue, the neoplastic tissue growth and the excess concentration of H{sup +} ions. The tumor model parameters have a corresponding biological meaning: the reabsorption rate, the destructive influence of H{sup +} ions in the healthy tissue, the growth rate of tumor tissue and the diffusion coefficient. We propose to solve the direct problem using the Finite Element Method (FEM) and minimize an appropriate functional including both the real data (obtained via in-vitro experiments and fluorescence ratio imaging microscopy) and the numerical solution. The gradient of the functional is computed by the adjoint method.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SOLAR MODELS WITH NEW LOW METAL ABUNDANCES

In the past decade, the photospheric abundances of the Sun had been revised several times by many observers. The standard solar models constructed with the new low-metal abundances disagree with helioseismic results and detected neutrino fluxes. The solar model problem has puzzled some stellar physicists for more than 10 years. Rotation, enhanced diffusion, convection overshoot, and magnetic fields are used to reconcile the new abundances with helioseismology. The too low helium subsurface abundance in enhanced diffusion models can be improved by the mixing caused by rotation and magnetic fields. The problem of the depth of the convective zone in rotating models can be resolved by convection overshoot. Consequently, the Asplund–Grevesse–Sauval rotation model including overshooting (AGSR) reproduces the seismically inferred sound-speed and density profiles and the convection zone depth as well as the Grevesse and Sauval model computed before. But this model fails to reproduce the surface helium abundance, which is 0.2393 (2.6 σ away from the seismic value), and neutrino fluxes. The magnetic model called AGSM keeps the agreement of the AGSR and improves the prediction of the surface helium abundance. The observed separation ratios r {sub 02} and r {sub 13} are reasonably reproduced by AGSM. Moreover, neutrino fluxes calculated by this model are not far from the detected neutrino fluxes and the predictions of previous works.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

A block-spectral adaptive H-/$p$-refinement strategy for shock-dominated problems

An adaptive H-/p-refinement strategy using a novel sensor is devised and tested in a block-spectral compressible Euler code equipped with adaptive-mesh refinement (AMR) and high-order flux-reconstruction numerics. At each Gauss quadrature point (or solution point) within each spectral block (or mesh element) the discrete velocity jump ΔU = ∂U/∂y 1 Δy 1 + ∂V/∂y 2 Δy 2 + ∂W/∂y 3 Δy 3 is calculated and normalized by the local speed of sound, a. Here, the grid spacing, Δx i , is calculated in each direction as the distance between auxiliary Gauss-Lobatto points, staggered relative to the solution points. The polynomial order is increased from p = 0 to p = p max in regions of weak compression, (ΔU/a) crit < ΔU/a < 0 and kept at p = p max in regions of flow expansion ΔU/a ≥ 0, while staying at the H = 0 base mesh level. Regions experiencing strong compressions, i.e. ΔU/a < (ΔU/a) crit , are H-refined up to H = H max where H max is applied at the location of maximum compression, ΔU/a = min(ΔU/a) in the domain, while keeping p = 0 to guarantee robustness and monotonicity of the solution in the H refined region. The critical value of (ΔU/a) crit = -0.06 is found to effectively separate smooth and non-smooth solution regions, supported by a 1D detonation initiation test case in ideal gas and a shock-to-detonation transition in high explosives. Using this value, the Sod shock tube, Shu-Osher problem, double Mach reflection and a 2D detonation in a high-explosive are simulated with the proposed adaptive H-/p-refinement. In the Sod shock tube case, p-refinement resolves the (weak) contact discontinuity while H-refinement enhances the grid resolution in the shock exploiting the monotonicity of the p = 0 reconstruction. For the Shu-Osher problem, p-refinement captures the small-scale oscillations trailing the shock that would be otherwise attenuated, while H-refinement triggered by the ΔU-sensor appropriately tracks the shock. In the double Mach reflection problem, H-refinement confines the numerical diffusion around the reflected shock while p-refinement recaptures many physical features trailing the shock. Finally, in the 2D high-explosive detonation case, H-refinement follows the leading shock and resolves the curvature of the detonation wave, while p-refinement adds resolution to the trailing reaction zone. Finally, the proposed methodology is tested in a detonation-wave propagation test case in high-explosives with numerical predictions comparing favorably against experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

A spectral analysis of the domain decomposed Monte Carlo method for linear systems

The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear oper- ator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approxi- mation and the mean chord approximation are applied to estimate the leakage frac- tion of random walks from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem in numerical experiments to test the models for symmetric operators with spectral qualities similar to light water reactor problems. We find, in general, the derived approximations show good agreement with random walk lengths and leakage fractions computed by the numerical experiments.

97 MATHEMATICS AND COMPUTING↗