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Results for “multiscale numerical 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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Spatial intratumoral heterogeneity of proliferation in immunohistochemical images of solid tumors

Purpose: The interactions of neoplastic cells with each other and the microenvironment are complex. To understand intratumoral heterogeneity, subtle differences should be quantified. Main factors contributing to heterogeneity include the gradient ischemic level within neoplasms, action of microenvironment, mechanisms of intercellular transfer of genetic information, and differential mechanisms of modifications of genetic material/proteins. This may reflect on the expression of biomarkers in the context of prognosis/stratification. Hence, a rigorous approach for assessing the spatial intratumoral heterogeneity of histological biomarker expression with accuracy and reproducibility is required, since patterns in immunohistochemical images can be challenging to identify and describe. Methods: A quantitative method that is useful for characterizing complex irregular structures is lacunarity; it is a multiscale technique that exhaustively samples the image, while the decay of its index as a function of window size follows characteristic patterns for different spatial arrangements. In histological images, lacunarity provides a useful measure for the spatial organization of a biomarker when a sampling scheme is employed and relevant features are computed. The proposed approach quantifies the segmented proliferative cells and not the textural content of the histological slide, thus providing a more realistic measure of heterogeneity within the sample space of the tumor region. The aim is to investigate in whole sections of primary pancreatic neuroendocrine neoplasms (pNENs), using whole-slide imaging and image analysis, the spatial intratumoral heterogeneity of Ki-67 immunostains. Unsupervised learning is employed to verify that the approach can partition the tissue sections according to distributional heterogeneity. Results: The architectural complexity of histological images has shown that single measurements are often insufficient. Inhomogeneity of distribution depends not only on percentage content of proliferation phase but also on how the phase fills the space. Lacunarity curves demonstrate variations in the sampled image sections. Since the spatial distribution of proliferation in each case is different, the width of the curves changes too. Image sections that have smaller numerical variations in the computed features correspond to neoplasms with spatially homogeneous proliferation, while larger variations correspond to cases where proliferation shows various degrees of clumping. Grade 1 (uniform/nonuniform: 74%/26%) and grade 3 (uniform: 100%) pNENs demonstrate a more homogeneous proliferation with grade 1 neoplasms being more variant, while grade 2 tumor regions render a more diverse landscape (50%/50%). Hence, some cases show an increased degree of spatial heterogeneity comparing to others with similar grade. Whether this is a sign of different tumor biology and an association with a more benign/malignant clinical course needs to be investigated further. The extent and range of spatial heterogeneity has the potential to be evaluated as a prognostic marker. Conclusions: The association with tumor grade as well as the rationale that the methodology reflects true tumor architecture supports the technical soundness of the method. This reflects a general approach which is relevant to other solid tumors and biomarkers. Drawing upon the merits of computational biomedicine, the approach uncovers salient features for use in future studies of clinical relevance.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

A 1D–0D–3D coupled model for simulating blood flow and transport processes in breast tissue

In this work, we present mixed dimensional models for simulating blood flow and transport processes in breast tissue and the vascular tree supplying it. These processes are considered, to start from the aortic inlet to the capillaries and tissue of the breast. Large variations in biophysical properties and flow conditions exist in this system necessitating the use of different flow models for different geometries and flow regimes. In total, we consider four different model types. First, a system of 1D nonlinear hyperbolic partial differential equations (PDEs) is considered to simulate blood flow in larger arteries with highly elastic vessel walls. Second, we assign 1D linearized hyperbolic PDEs to model the smaller arteries with stiffer vessel walls. The third model type consists of ODE systems (0D models). It is used to model the arterioles and peripheral circulation. Finally, homogenized 3D porous media models are considered to simulate flow and transport in capillaries and tissue within the breast volume. Sink terms are used to account for the influence of the venous and lymphatic systems. Combining the four model types, we obtain two different 1D–0D–3D coupled models for simulating blood flow and transport processes: The first model results in a fully coupled 1D–0D–3D model covering the complete path from the aorta to the breast combining a generic arterial network with a patient specific breast network and geometry. The second model is a reduced one based on the separation of the generic and patient specific parts. The information from a calibrated fully coupled model is used as inflow condition for the patient specific sub-model allowing a significant computational cost reduction. Several numerical experiments are conducted to calibrate the generic model parameters and to demonstrate realistic flow simulations compared to existing data on blood flow in the human breast and vascular system. Moreover, we use two different breast vasculature and tissue data sets to illustrate the robustness of our reduced sub-model approach.

multiscale blood flow models↗
DOE OSTI2019

Multi-rate time integration on overset meshes

Overset meshes are an effective tool for the computational fluid dynamic simulation of problems with complex geometries or multiscale spatio-temporal features. When the maximum allowable timestep on one or more meshes is significantly smaller than on the remaining meshes, standard explicit time integrators impose inefficiencies for time-accurate calculations by requiring that all meshes advance with the smallest timestep. With the targeted use of multi-rate time integrators, separate meshes can be time-marched at independent rates to avoid wasteful computation while maintaining accuracy and stability. This work applies time-explicit multi-rate integrators to the simulation of the compressible Navier-Stokes equations discretized on overset meshes using summation-by-parts (SBP) operators and simultaneous approximation term (SAT) boundary conditions. We introduce a class of multi-rate Adams-Bashforth (MRAB) schemes that offer significant stability improvements and computational efficiencies for SBP-SAT methods. We present numerical results that confirm the efficacy of MRAB integrators, outline a number of implementation challenges, and demonstrate a reduction in computational cost enabled by MRAB. We also look at the use of our method in the setting of a large-scale distributed-memory parallel implementation where we discuss concerns involving load balancing and communication efficiency.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2003

Fractals and Spatial Methods for Mining Remote Sensing Imagery

The rapid increase in digital remote sensing and GIS data raises a critical problem -- how can such an enormous amount of data be handled and analyzed so that useful information can be derived quickly? Efficient handling and analysis of large spatial data sets is central to environmental research, particularly in global change studies that employ time series. Advances in large-scale environmental monitoring and modeling require not only high-quality data, but also reliable tools to analyze the various types of data. A major difficulty facing geographers and environmental scientists in environmental assessment and monitoring is that spatial analytical tools are not easily accessible. Although many spatial techniques have been described recently in the literature, they are typically presented in an analytical form and are difficult to transform to a numerical algorithm. Moreover, these spatial techniques are not necessarily designed for remote sensing and GIS applications, and research must be conducted to examine their applicability and effectiveness in different types of environmental applications. This poses a chicken-and-egg problem: on one hand we need more research to examine the usability of the newer techniques and tools, yet on the other hand, this type of research is difficult to conduct if the tools to be explored are not accessible. Another problem that is fundamental to environmental research are issues related to spatial scale. The scale issue is especially acute in the context of global change studies because of the need to integrate remote-sensing and other spatial data that are collected at different scales and resolutions. Extrapolation of results across broad spatial scales remains the most difficult problem in global environmental research. There is a need for basic characterization of the effects of scale on image data, and the techniques used to measure these effects must be developed and implemented to allow for a multiple scale assessment of the data before any useful process-oriented modeling involving scale-dependent data can be conducted. Through the support of research grants from NASA, we have developed a software module called ICAMS (Image Characterization And Modeling System) to address the need to develop innovative spatial techniques and make them available to the broader scientific communities. ICAMS provides new spatial techniques, such as fractal analysis, geostatistical functions, and multiscale analysis that are not easily available in commercial GIS/image processing software. By bundling newer spatial methods in a user-friendly software module, researchers can begin to test and experiment with the new spatial analysis methods and they can gauge scale effects using a variety of remote sensing imagery. In the following, we describe briefly the development of ICAMS and present application examples.

Lam, Nina↗
DOE OSTI2016

Generalization of mixed multiscale finite element methods with applications

Many science and engineering problems exhibit scale disparity and high contrast. The small scale features cannot be omitted in the physical models because they can affect the macroscopic behavior of the problems. However, resolving all the scales in these problems can be prohibitively expensive. As a consequence, some types of model reduction techniques are required to design efficient solution algorithms. For practical purpose, we are interested in mixed finite element problems as they produce solutions with certain conservative properties. Existing multiscale methods for such problems include the mixed multiscale finite element methods. We show that for complicated problems, the mixed multiscale finite element methods may not be able to produce reliable approximations. This motivates the need of enrichment for coarse spaces. Two enrichment approaches are proposed, one is based on generalized multiscale finte element metthods (GMsFEM), while the other is based on spectral element-based algebraic multigrid (rAMGe). The former one, which is called mixed GMsFEM, is developed for both Darcy’s flow and linear elasticity. Application of the algorithm in two-phase flow simulations are demonstrated. For linear elasticity, the algorithm is subtly modified due to the symmetry requirement of the stress tensor. The latter enrichment approach is based on rAMGe. The algorithm differs from GMsFEM in that both of the velocity and pressure spaces are coarsened. Due the multigrid nature of the algorithm, recursive application is available, which results in an efficient multilevel construction of the coarse spaces. Stability, convergence analysis, and exhaustive numerical experiments are carried out to validate the proposed enrichment approaches. iii

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

A micromorphically regularized Cam-clay model for capturing size-dependent anisotropy of geomaterials

Here we introduce a regularized anisotropic modified Cam-clay (MCC) model which captures the size-dependent anisotropic elastoplastic responses for clay, mudstone, shales, and sedimentary rock. By homogenizing the multiscale anisotropic effects induced by clay particle aggregate, clusters, peds, micro-fabric, and mineral contact across length scales, we introduce two distinctive anisotropic mechanisms for the MCC model at the material point and mesoscale levels. We first employ a mapping that links the anisotropic stress state to a fictitious isotropic principal stress-space to introduce anisotropy at the material point scale. Then, the mesoscale anisotropy is introduced via an anisotropic regularization mechanism. This anisotropic regularization mechanism is triggered by introducing gradient-dependence of the internal variables through a penalty method such that the resultant gradient-enhanced plastic flow may exhibit anisotropic responses non-coaxial to the stress gradient of the yield function. The influence of the size-dependent anisotropy on the formation of the shear band and the macroscopic responses of the effective media are analyzed in 2D and 3D numerical examples.

42 ENGINEERING↗
DOE OSTI2020

Bridging Scales to Model Reactive Diffusive Transport in Porous Media

Published by ECS. Two novel scale-bridging algorithms to model reaction-diffusion transport in porous media are presented. The algorithms are based on direct numerical simulations and couple the information of a micro-scale model, which accounts for the large field of view provided by micro X-ray computed tomography (X-ray CT), and a nano-scale model, which locally resolves transport in the fine structure extracted from nano X-ray CT. The micro-scale model is discretized in the through-plane direction into a 1D grid, where effective properties and internal boundaries are determined based on the results from the nano-scale model. The validated algorithms are used to examine transport of oxygen in precious group metal-free electrodes considering both zero- and first-order kinetics. Unlike conventional methods, the results show that the effective diffusivity is not a passive property but increases in regions where the reaction-rate coefficient is large. The proposed algorithms account for the multiscale coupling of reaction-diffusion transport and material microstructure, thus improving the predictions compared to conventional methods.

42 ENGINEERING↗
DOE OSTI2019

Phonon thermal conductance across GaN-AlN interfaces from first principles

The vibrational thermal conductances (G) across GaN-AlN interfaces are computed using a nonequilibrium Green's function formalism in the harmonic limit with bulk and interfacial interatomic force constants (IFCs) fully from density functional theory. Several numerical methods and supercell configurations are employed to examine the sensitivity of G to variances of IFCs. In particular, the effects of supercell size, the enforcement of symmetry constraints, and truncation of IFCs near the interface, and atomic relaxation on phonon transmission and conductance are explored. Our fully first-principles calculations are compared with common approximations and measured G values inferred from thermal conductivity measurements for GaN-AlN superlattices. Here, our calculated value, G~300MWm -2 K -1 , is nearly half that from measurements. This discrepancy is critically analyzed in terms of the physical assumptions of the calculations and the derivation of the experimental values. This work provides guidelines to determine “physically correct” sets of interfacial IFCs from first principles for thermal conductance calculations using minimal computational resources. It also contributes toward developing predictive calculations and a more complete picture of thermal conduction across interfaces, a step toward first-principles multiscale thermal transport.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Stochastic multiscale flux basis for Stokes-Darcy flows

Three algorithms are developed for uncertainty quantification in modeling coupled Stokes and Darcy flows. The porous media may consist of multiple regions with different properties. The permeability is modeled as a non-stationary stochastic variable, with its log represented as a sum of local Karhunen-Loève (KL) expansions. The problem is approximated by stochastic collocation on either tensor-product or sparse grids, coupled with a multiscale mortar mixed finite element method for the spatial discretization. A non-overlapping domain decomposition algorithm reduces the global problem to a coarse scale mortar interface problem, which is solved by an iterative solver, for each stochastic realization. In the traditional domain decomposition implementation, each subdomain solves a local Dirichlet or Neumann problem in every interface iteration. To reduce this cost, two additional algorithms based on deterministic or stochastic multiscale flux basis are introduced. The basis consists of the local flux (or velocity trace) responses from each mortar degree of freedom. It is computed for each subdomain independently before the interface iteration begins. The use of the multiscale flux basis avoids the need for subdomain solves on each iteration. The deterministic basis is computed at each stochastic collocation and used only at this realization. The stochastic basis is formed by further looping over all local realizations of a subdomain's KL region before the stochastic collocation begins. It is used over multiple realizations. Numerical tests are presented to illustrate the performance of the three algorithms, with the stochastic multiscale flux basis showing significant savings in computational cost compared to the other two algorithms.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2000

Fast Particle Methods for Multiscale Phenomena Simulations

We are developing particle methods oriented at improving computational modeling capabilities of multiscale physical phenomena in : (i) high Reynolds number unsteady vortical flows, (ii) particle laden and interfacial flows, (iii)molecular dynamics studies of nanoscale droplets and studies of the structure, functions, and evolution of the earliest living cell. The unifying computational approach involves particle methods implemented in parallel computer architectures. The inherent adaptivity, robustness and efficiency of particle methods makes them a multidisciplinary computational tool capable of bridging the gap of micro-scale and continuum flow simulations. Using efficient tree data structures, multipole expansion algorithms, and improved particle-grid interpolation, particle methods allow for simulations using millions of computational elements, making possible the resolution of a wide range of length and time scales of these important physical phenomena.The current challenges in these simulations are in : [i] the proper formulation of particle methods in the molecular and continuous level for the discretization of the governing equations [ii] the resolution of the wide range of time and length scales governing the phenomena under investigation. [iii] the minimization of numerical artifacts that may interfere with the physics of the systems under consideration. [iv] the parallelization of processes such as tree traversal and grid-particle interpolations We are conducting simulations using vortex methods, molecular dynamics and smooth particle hydrodynamics, exploiting their unifying concepts such as : the solution of the N-body problem in parallel computers, highly accurate particle-particle and grid-particle interpolations, parallel FFT's and the formulation of processes such as diffusion in the context of particle methods. This approach enables us to transcend among seemingly unrelated areas of research.

Koumoutsakos, P.↗
NASA NTRSDate not supplied

ICME for NASA Aerospace Applications: Batteries for Electric Aviation

NASA’s approach to computational materials modeling is detailed in the NASA Vision 2040 Roadmap for Multiscale Modeling and Simulation of Materials and Systems. This report is in the spirit of national initiatives such as the Material Genome Initiative (MGI), Integrated Computational Materials Engineering (ICME), and others. We utilize a combination of fundamental modeling, computational high-throughput screening, and data science methods, e.g., machine learning, are used to find innovative solutions to NASA or national technology challenges. Applications of interest are wide ranging from advanced alloys to batteries to coatings, among others. In this talk, we present three examples for recent work related to NASA applications. First, doping advanced sulfur battery cathodes with selenium boosts electrical conductivity important for electric aircraft applications. First principles calculations will be discussed that result in compositional design maps for these materials. Second, development of icephobic coatings is important to mitigate safety hazards associated with icing for aircraft. Molecular dynamics simulations are reported for ice-surface interfaces to understand adhesion mechanisms and help screen optimal ice-phobic coatings. Third, shape memory alloys have numerous applications as actuators, superelastic materials, etc. for aerospace. We report machine learning models that predict martensitic transition temperatures across a broad swath of compositional space.

John Lawson↗
DOE OSTI2025

A Performance Portable, Fully Implicit Landau Collision Operator with Batched Linear Solvers

Modern accelerators use hierarchical parallel programming models that enable massive multithreading within a processing element (PE), with multiple PEs per device driven by traditional processes. Batching is a technique for exposing PE-level parallelism in algorithms that have traditionally run on MPI processes or multiple threads within a single process. Opportunities for batching arise in, for example, kinetic discretizations of magnetized plasmas where collisions are advanced in velocity space at each spatial point independently. This paper builds on previous work on a high-performance, fully nonlinear, Landau collision operator by batching the linear solver, as well as batching the spatial point problems and adding new support for multiple grids for multiscale, multispecies problems. An anisotropic relaxation verification test that agrees well with previously published results and analytical models is presented. The performance results from NVIDIA A100 and AMD MI250X nodes are presented with hardware utilization analysis for each architecture. Finally, the entire implicit Landau operator time advance is implemented in Kokkos for performance portability, running entirely on the device and is available in the PETSc numerical library.

97 MATHEMATICS AND COMPUTING↗
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↗
DOE OSTI2022

Quantum-Accurate Multiscale Modeling of Shock Hugoniots, Ramp Compression Paths, Structural and Magnetic Phase Transitions, and Transport Properties in Highly Compressed Metals

Fully characterizing high energy density (HED) phenomena using pulsed power facilities (Z machine) and coherent light sources is possible only with complementary numerical modeling for design, diagnostic development, and data interpretation. The exercise of creating numerical tests, that match experimental conditions, builds critical insight that is crucial for the development of a strong fundamental understanding of the physics behind HED phenomena and for the design of next generation pulsed power facilities. The persistence of electron correlation in HED materials arising from Coulomb interactions and the Pauli exclusion principle is one of the greatest challenges for accurate numerical modeling and has hitherto impeded our ability to model HED phenomena across multiple length and time scales at sufficient accuracy. An exemplar is a ferromagnetic material like iron, while familiar and widely used, we lack a simulation capability to characterize the interplay of structure and magnetic effects that govern material strength, kinetics of phase transitions and other transport properties. Herein we construct and demonstrate the Molecular-Spin Dynamics (MSD) simulation capability for iron from ambient to earth core conditions, all software advances are open source and presently available for broad usage. These methods are multi-scale in nature, direct comparisons between high fidelity density functional theory (DFT) and linear-scaling MSD simulations is done throughout this work, with advancements made to MSD allowing for electronic structure changes being reflected in classical dynamics. Main takeaways for the project include insight into the role of magnetic spins on mechanical properties and thermal conductivity, development of accurate interatomic potentials paired with spin Hamiltonians, and characterization of the high pressure melt boundary that is of critical importance to planetary modeling efforts.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

A mechanistic damage model for solid oxide fuel cell ceramic materials - Part I: Constitutive modeling

A multiscale mechanistic damage model for solid oxide fuel cell (SOFC) ceramics that combines micromechanics of stiffness reduction due to material porosity change and microcracking with a continuum damage mechanics (CDM) description for the evolution of microcracks up to fracture is developed in this work. The model also accounts for volumetric swelling of the anode due to redox cycling. Porosity change and swelling during redox combined with normal operating thermomechanical loads could increase the stress, strain and damage distributions in SOFC stacks leading them to failure. The proposed model involves three governing parameters: (i) the porosity in terms of the pore or void volume fraction, (ii) material swelling magnitude prescribed at a given loading step, and (iii) the damage variable that describes microcracking caused by thermomechanical loads and swelling. Pores and microcracks in the ceramics are modeled as randomly distributed ellipsoidal inclusions with negligible stiffness by an Eshelby-Mori-Tanaka formulation combined with an inclusion orientation distribution method. Microcracking damage evolution is described by a CDM formulation. Volumetric swelling is treated in a similar way to thermal expansion in the constitutive relations. After validation and numerical checks, the damage model is used to analyze a simplified SOFC positive-electrode/electrolyte/negative-electrode (PEN) structure subjected a redox cycle in addition to thermomechanical loads experienced during normal operation of a SOFC stack.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2023

On the use of a multigrid-reduction-in-time algorithm for multiscale convergence of turbulence simulations

Simulations of turbulent flow present challenges in terms of accuracy and affordability on modern highly-parallel computer architectures. A multigrid-reduction-in-time algorithm is used to provide a framework for separately evolving different scales of turbulence and for parallelizing the temporal domain, thereby increasing the concurrency. It is hypothesized that the space–time locality of the small scales of turbulence can be used to circumvent difficulties in applying temporal multigrid to flows dominated by inertial physics. For algorithms that fall well short of spectral accuracy (fourth-order is used in this work) attention must be paid to the accuracy of features on scales transferred between multigrid levels. Numerical experiments were performed using implicit large-eddy simulation. Results from applying the approach to an infinite-Reynolds number Taylor–Green flow and a double-shear flow at a Reynolds number of 11650 provide strong evidence that the approach has merit. The multigrid-reduction-in-time framework can be used to parallelize the temporal domain of a high-Reynolds-number turbulent flow and permit independent convergence of different scales. Establishing this foundation allows for future research in reducing the wall-clock time to solve turbulent flows while retaining the same accuracy as sequential solvers. In conclusion, current performance results from parallelizing the temporal domain are not competitive with those from sequential-in-time methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

On the use of reverse Brownian motion to accelerate hybrid simulations

Multiscale and multiphysics simulations are two rapidly developing fields of scientific computing. Efficient coupling of continuum (deterministic or stochastic) constitutive solvers with their discrete (stochastic, particle-based) counterparts is a common challenge in both kinds of simulations. We focus on interfacial, tightly coupled simulations of diffusion that combine continuum and particle-based solvers. The latter employs the reverse Brownian motion (rBm), a Monte Carlo approach that allows one to enforce inhomogeneous Dirichlet, Neumann, or Robin boundary conditions and is trivially parallelizable. We discuss numerical approaches for improving the accuracy of rBm in the presence of inhomogeneous Neumann boundary conditions and alternative strategies for coupling the rBm solver with its continuum counterpart. Numerical experiments are used to investigate the convergence, stability, and computational efficiency of the proposed hybrid algorithm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A DG-IMEX Method for Two-moment Neutrino Transport: Nonlinear Solvers for Neutrino–Matter Coupling

Neutrino-matter interactions play an important role in core-collapse supernova (CCSN) explosions as they contribute to both lepton number and/or four-momentum exchange between neutrinos and matter, and thus act as the agent for neutrino-driven explosions. Due to the multiscale nature of neutrino transport in CCSN simulations, an implicit treatment of neutrino-matter interactions is desired, which requires solutions of coupled nonlinear systems in each step of the time integration scheme. In this paper we design and compare nonlinear iterative solvers for implicit systems with energy coupling neutrino-matter interactions commonly used in CCSN simulations. Specifically, we consider electron neutrinos and antineutrinos, which interact with static matter configurations through the Bruenn 85 opacity set. The implicit systems arise from the discretization of a nonrelativistic two-moment model for neutrino transport, which employs the discontinuous Galerkin (DG) method for phase-space discretization and an implicit-explicit (IMEX) time integration scheme. In the context of this DG-IMEX scheme, we propose two approaches to formulate the nonlinear systems — a coupled approach and a nested approach. For each approach, the resulting systems are solved with Anderson-accelerated fixedpoint iteration and Newton’s method. The performance of these four iterative solvers has been compared on relaxation problems with various degree of collisionality, as well as proto-neutron star deleptonization problems with several matter profiles adopted from spherically symmetric CCSN simulations. Here, numerical results suggest that the nested Anderson-accelerated fixed-point solver is more efficient than other tested solvers for solving implicit nonlinear systems with energy coupling neutrino-matter interactions.

79 ASTRONOMY AND ASTROPHYSICS↗