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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

The multi-assumption architecture and testbed (MAAT v1.0): R code for generating ensembles with dynamic model structure and analysis of epistemic uncertainty from multiple sources

Abstract. Here, computer models are ubiquitous tools used to represent systems across many scientific and engineering domains. For any given system, many computer models exist, each built on different assumptions and demonstrating variability in the ways in which these systems can be represented. This variability is known as epistemic uncertainty, i.e. uncertainty in our knowledge of how these systems operate. Two primary sources of epistemic uncertainty are (1) uncertain parameter values and (2) uncertain mathematical representations of the processes that comprise the system. Many formal methods exist to analyse parameter-based epistemic uncertainty, while process-representation-based epistemic uncertainty is often analysed post hoc, incompletely, informally, or is ignored. In this model description paper we present the multi-assumption architecture and testbed (MAAT v1.0) designed to formally and completely analyse process-representation-based epistemic uncertainty. MAAT is a modular modelling code that can simply and efficiently vary model structure (process representation), allowing for the generation and running of large model ensembles that vary in process representation, parameters, parameter values, and environmental conditions during a single execution of the code. MAAT v1.0 approaches epistemic uncertainty through sensitivity analysis, assigning variability in model output to processes (process representation and parameters) or to individual parameters. In this model description paper we describe MAAT and, by using a simple groundwater model example, verify that the sensitivity analysis algorithms have been correctly implemented. The main system model currently coded in MAAT is a unified, leaf-scale enzyme kinetic model of C 3 photosynthesis. In the Appendix we describe the photosynthesis model and the unification of multiple representations of photosynthetic processes. The numerical solution to leaf-scale photosynthesis is verified and examples of process variability in temperature response functions are provided. For rapid application to new systems, the MAAT algorithms for efficient variation of model structure and sensitivity analysis are agnostic of the specific system model employed. Therefore MAAT provides a tool for the development of novel or toy models in many domains, i.e. not only photosynthesis, facilitating rapid informal and formal comparison of alternative modelling approaches.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Multilevel Graph Partitioning for Three-Dimensional Discrete Fracture Network Flow Simulations

We present a topology-based method for mesh-partitioning in three-dimensional discrete fracture network (DFN) simulations that takes advantage of the intrinsic multi-level nature of a DFN. DFN models are used to simulate flow and transport through low-permeability fractured media in the subsurface by explicitly representing fractures as discrete entities. The governing equations for flow and transport are numerically integrated on computational meshes generated on the interconnected fracture networks. Modern high-fidelity DFN simulations require high-performance computing on multiple processors where performance and scalability depends partially on obtaining a high-quality partition of the mesh to balance work-loads and minimize communication across all processors. The discrete structure of a DFN naturally lends itself to various graph representations, which can be thought of as coarse-scale representations of the computational mesh. Using this concept, we develop two applications of the multilevel graph partitioning algorithm to partition the mesh of a DFN. In the first, we project a partition of the graph based on the DFN topology onto the mesh of the DFN and in the second, this DFN-based projection is used as the initial condition for further partitioning refinement of the mesh. We compare the performance of these methods with standard multi-level graph partitioning using graph-based metrics (cut, imbalance, partitioning time), computational-based metrics (FLOPS, iterations, solver time), and total run time. The DFN-based and the mesh-based partitioning methods are comparable in terms of the graph-based metrics, but the time required to obtain the partition is several orders of magnitude faster using the DFN-based partitions. The computation-based metrics show comparable performance between both methods so, in combination, the DFN-based partitions are several orders of magnitude faster than the mesh-based partition. Furthermore, the method which uses the DFN-partition solution as the initial condition of the mesh partition provided cut and imbalance values that were close to the mesh-based partition but in a fraction of the time. In turn, this hybrid method outperformed both of the other methods in terms of the total run time.

58 GEOSCIENCES↗
DOE OSTI2011

Framework for discrete-time quantum walks and a symmetric walk on a binary tree

We formulate a framework for discrete-time quantum walks, motivated by classical random walks with memory. We present a specific representation of the classical walk with memory 2, on which this is based. The framework has no need for coin spaces, it imposes no constraints on the evolution operator other than unitarity, and is unifying of other approaches. As an example we construct a symmetric discrete-time quantum walk on the semi-infinite binary tree. The generating function of the amplitude at the root is computed in closed form, as a function of time and the initial level n in the tree, and we find the asymptotic and a full numerical solution for the amplitude. It exhibits a sharp interference peak and a power-law tail, as opposed to the exponentially decaying tail of a broadly peaked distribution of the classical symmetric random walk on a binary tree. The probability peak is orders of magnitude larger than it is for the classical walk (already at small n). The quantum walk shows a polynomial algorithmic speedup in n over the classical walk, which we conjecture to be of the order 2/3, based on strong trends in data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Impact of bowtie filter and object position on the two-dimensional noise power spectrum of a clinical MDCT system

Purpose: Noise characteristics of clinical multidetector CT (MDCT) systems can be quantified by the noise power spectrum (NPS). Although the NPS of CT has been extensively studied in the past few decades, the joint impact of the bowtie filter and object position on the NPS has not been systematically investigated. This work studies the interplay of these two factors on the two dimensional (2D) local NPS of a clinical CT system that uses the filtered backprojection algorithm for image reconstruction. Methods: A generalized NPS model was developed to account for the impact of the bowtie filter and image object location in the scan field-of-view (SFOV). For a given bowtie filter, image object, and its location in the SFOV, the shape and rotational symmetries of the 2D local NPS were directly computed from the NPS model without going through the image reconstruction process. The obtained NPS was then compared with the measured NPSs from the reconstructed noise-only CT images in both numerical phantom simulation studies and experimental phantom studies using a clinical MDCT scanner. The shape and the associated symmetry of the 2D NPS were classified by borrowing the well-known atomic spectral symbols s, p, and d, which correspond to circular, dumbbell, and cloverleaf symmetries, respectively, of the wave function of electrons in an atom. Finally, simulated bar patterns were embedded into experimentally acquired noise backgrounds to demonstrate the impact of different NPS symmetries on the visual perception of the object. Results: (1) For a central region in a centered cylindrical object, an s-wave symmetry was always present in the NPS, no matter whether the bowtie filter was present or not. In contrast, for a peripheral region in a centered object, the symmetry of its NPS was highly dependent on the bowtie filter, and both p-wave symmetry and d-wave symmetry were observed in the NPS. (2) For a centered region-ofinterest (ROI) in an off-centered object, the symmetry of its NPS was found to be different from that of a peripheral ROI in the centered object, even when the physical positions of the two ROIs relative to the isocenter were the same. (3) The potential clinical impact of the highly anisotropic NPS, caused by the interplay of the bowtie filter and position of the image object, was highlighted in images of specific bar patterns oriented at different angles. The visual perception of the bar patterns was found to be strongly dependent on their orientation. Conclusions: The NPS of CT depends strongly on the bowtie filter and object position. Even if the location of the ROI with respect to the isocenter is fixed, there can be different symmetries in the NPS, which depend on the object position and the size of the bowtie filter. For an isolated off-centered object, the NPS of its CT images cannot be represented by the NPS measured from a centered object.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Designing a Framework for Solving Multiobjective Simulation Optimization Problems

Multiobjective simulation optimization (MOSO) problems are optimization problems with multiple conflicting objectives, where evaluation of at least one of the objectives depends on a black-box numerical code or real-world experiment, which we refer to as a simulation. Whereas an extensive body of research is dedicated to developing new algorithms and methods for solving these and related problems, it is challenging and time-consuming to integrate these techniques into real-world production-ready solvers. This is partly because of the diversity and complexity of modern state-of-the-art MOSO algorithms and methods and partly because of the complexity and specificity of many real-world problems and their corresponding computing environments. The complexity of this problem is only compounded when introducing potentially complex and/or domain-specific surrogate-modeling techniques, problem formulations, design spaces, and data acquisition functions. Here, this paper carefully surveys the current state of the art in MOSO algorithms, techniques, and solvers, as well as problem types and computational environments where MOSO is commonly applied. We then present several key challenges in the design of a parallel multiobjective simulation optimization framework (ParMOO) and how they have been addressed. Finally, we provide two case studies demonstrating how customized ParMOO solvers can be quickly built and deployed to solve real-world MOSO problems.

engineering design optimization↗
DOE OSTI2010

The application of quaternions and other spatial representations to the reconstruction of re-entry vehicle motion.

The analysis of spacecraft kinematics and dynamics requires an efficient scheme for spatial representation. While the representation of displacement in three dimensional Euclidean space is straightforward, orientation in three dimensions poses particular challenges. The unit quaternion provides an approach that mitigates many of the problems intrinsic in other representation approaches, including the ill-conditioning that arises from computing many successive rotations. This report focuses on the computational utility of unit quaternions and their application to the reconstruction of re-entry vehicle (RV) motion history from sensor data. To this end they will be used in conjunction with other kinematic and data processing techniques. We will present a numerical implementation for the reconstruction of RV motion solely from gyroscope and accelerometer data. This will make use of unit quaternions due to their numerical efficacy in dealing with the composition of many incremental rotations over a time series. In addition to signal processing and data conditioning procedures, algorithms for numerical quaternion-based integration of gyroscope data will be addressed, as well as accelerometer triangulation and integration to yield RV trajectory. Actual processed flight data will be presented to demonstrate the implementation of these methods.

47 OTHER INSTRUMENTATION↗
DOE OSTI2019

Parallel-In-Time Multigrid with Adaptive Spatial Coarsening for The Linear Advection and Inviscid Burgers Equations

We apply a multigrid reduction-in-time (MGRIT) algorithm to hyperbolic partial differential equations in one spatial dimension. This study is motivated by the observation that sequential time-stepping is a computational bottleneck when attempting to implement highly concurrent algorithms; thus parallel-in-time methods are desirable. MGRIT adds parallelism by using a hierarchy of successively coarser temporal levels to accelerate the solution on the finest level. In the case of explicit time-stepping, spatial coarsening is a suitable approach to ensure that stability conditions are satisfied on all levels, and it may be useful for implicit time-stepping by producing cheaper multigrid cycles. Unfortunately, uniform spatial coarsening results in extremely slow convergence when the wave speed is near zero, even if only locally. We present an adaptive spatial coarsening strategy that addresses this issue for the variable coefficient linear advection equation and the inviscid Burgers equation using first-order explicit or implicit time-stepping methods. Serial numerical results show this method offers significant improvements over uniform coarsening and is convergent for the inviscid Burgers equation with and without shocks. Parallel scaling tests on up to 128K cores indicate that run-time improvements over serial time-stepping strategies are possible when spatial parallelism alone saturates, and that scalability is robust for oscillatory solutions which change on the scale of the grid spacing.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

A pencil beam approach to proton computed tomography

Purpose: A new approach to proton computed tomography (pCT) is presented. In this approach, protons are not tracked one-by-one but a beam of particles is considered instead. The elements of the pCT reconstruction problem (residual energy and path) are redefined on the basis of this new approach. An analytical image reconstruction algorithm applicable to this scenario is also proposed. Methods: The pencil beam (PB) and its propagation in matter were modeled by making use of the generalization of the Fermi–Eyges theory to account for multiple Coulomb scattering (MCS). This model was integrated into the pCT reconstruction problem, allowing the definition of the mean beam path concept similar to the most likely path (MLP) used in the single-particle approach. A numerical validation of the model was performed. The algorithm of filtered backprojection along MLPs was adapted to the beam-by-beam approach. The acquisition of a perfect proton scan was simulated and the data were used to reconstruct images of the relative stopping power of the phantom with the single-proton and beam-by-beam approaches. The resulting images were compared in a qualitative way. Results: The parameters of the modeled PB (mean and spread) were compared to Monte Carlo results in order to validate the model. For a water target, good agreement was found for the mean value of the distributions. As far as the spread is concerned, depth-dependent discrepancies as large as 2%–3% were found. For a heterogeneous phantom, discrepancies in the distribution spread ranged from 6% to 8%. The image reconstructed with the beam-by-beam approach showed a high level of noise compared to the one reconstructed with the classical approach. Conclusions: The PB approach to proton imaging may allow technical challenges imposed by the current proton-by-proton method to be overcome. In this framework, an analytical algorithm is proposed. Further work will involve a detailed study of the performances and limitations of this approach in terms of image quality. The paper shows how to account for the MCS in the reconstruction step with this new approach when an analytical reconstruction algorithm is used.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Application of High Performance Computing for Studying Cyclic Variability in Dilute Internal Combustion Engines

Combustion instabilities in dilute internal combustion engines are manifest in cyclic variability (CV) in engine performance measures such as integrated heat release or shaft work. Understanding the factors leading to CV is important in model-based control, especially with high dilution where experimental studies have demonstrated that deterministic effects can become more prominent. Observation of enough consecutive engine cycles for significant statistical analysis is standard in experimental studies but is largely wanting in numerical simulations because of the computational time required to compute hundreds or thousands of consecutive cycles. We have proposed and begun implementation of an alternative approach to allow rapid simulation of long series of engine dynamics based on a low-dimensional mapping of ensembles of single-cycle simulations which map input parameters to output engine performance. This paper details the use Titan at the Oak Ridge Leadership Computing Facility to investigate CV in a gasoline direct-injected spark-ignited engine with a moderately high rate of dilution achieved through external exhaust gas recirculation. The CONVERGE™ CFD software was used to perform single-cycle simulations with imposed variations of operating parameters and boundary conditions selected according to a sparse grid sampling of the parameter space. Using an uncertainty quantification technique, the sampling scheme is chosen similar to a design of experiments grid but uses algorithms designed to minimize the number of samples required to achieve a desired degree of accuracy. The simulations map input parameters to output metrics of engine performance for a single cycle, and by mapping over a large parameter space, results can be interpolated from within that space. This interpolation scheme forms the basis for a low-dimensional ‘metamodel’ (or model of a model) which can be used to mimic the dynamical behavior of corresponding high-dimensional simulations. Simulations of high-EGR spark-ignition combustion cycles within a parametric sampling grid were performed and analyzed statistically, and sensitivities of the physical factors leading to high CV are presented. With these results, the prospect of producing low-dimensional metamodels to describe engine dynamics at any point in the parameter space will be discussed. Additionally, modifications to the methodology to account for nondeterministic effects in the numerical solution environment are proposed.

Finney, Charles E. A.↗
DOE OSTI2019

Early Career Award: An Enabling Computational Framework for Uncertainty Assimilation and Propagation in Complex PDE Systems: Sparse and Low-rank Techniques (Final Report)

This project aims to develop a set of new theories, algorithms, and computational tools that enable ultra-scalable representation and propagation of high-dimensional uncertainties to circumvent the issue of curse-of-dimensionality. The research components are motivated by the fact that highly scalable algorithms are needed to achieve exascale performance for uncertainty quantification and predictive simulation at extreme scales. Although these developments are generic and applicable to a wide range of high-dimensional, complex, stochastic, partial-differential-equation (PDE) systems, this research effort will focus on predictive simulation of high-energy-density lithium batteries. To create knowledge about the precise failure mechanisms of these batteries and ultimately predict their performance and reliability, a truly data-driven, multi-scale, multi-physics framework is needed that allows studying (i) dominant sources of uncertainty in the governing physical models at all scales of relevance and (ii) the interface between the interchanging physics and scales. The impact of the planned mathematical and numerical advancements in prediction of high-dimensional uncertain systems will be broad across areas of engineering and science such as climate modeling, fusion energy, combustion, and nanoscience, among others.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2010

A Multigrid Framework for SN Discretizations of the Boltzmann Transport Equation with Application to Spatially Unstructured Grids

The space-angle multiple/semi-coarsening multigrid methods of [3] for S n discretizations of the Boltzmann transport equation was developed assuming rediscretizations of the streaming collision operators on the coarser spatial grids. These rediscretized operators are directly used in the kernels of the spatial coarse-level scalar flux integral equations, which undergo the multigrid process. Since the computation is essentially performed on these integral equations, it appears that the multigrid procedure is applied directly to the finest level scalar flux integral equation, rather than to the finest level S n system. However, this procedure is actually applied implicitly to the finest level S n system, though it would be beneficial to directly relate the multiple/semi-coarsening methods to the full S n system: being able to relate the multigrid procedure directly to the full S n system will lead to a general framework that can help guide the development of multigrid algorithms for more general S n discretization settings, such as when spatial rediscretization of the integral equation kernel can not be applied. In this latter case, applying an operator-dependent Galerkin coarsening procedure to the integral operator is difficult, if not realizable, because the kernel is dense and often given by its action of numerically sweeping over all the streaming-collision operators. In this paper, we develop and analyze such a multigrid framework for the S n system. We further relate this framework to a multigrid scheme that directly coarsens the scalar flux integral equation using a Galerkin coarsening approach. For this approach, we show that an intricate operator-dependent Galerkin coarsening procedure may not be needed. In particular, this paper develops a Galerkin-principle framework for S n discretizations of the Boltzmann equation, of which the analysis shows that simple interpolation operators can be used to coarsen the integral equations operators arising from the space-angle multiple/semi-coarsening methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Three-dimensional simulation of unstable gravity-driven infiltration of water into a porous medium

Infiltration of water in dry porous media is subject to a powerful gravity-driven instability. Although the phenomenon of unstable infiltration is understood, its description using continuum mathematical models has posed a significant challenge for several decades. The classical model of water flow in the unsaturated flow, the Richards equation, is unable to reproduce the instability. In this work, we present a computational study of a model of unsaturated flow in porous media that extends the Richards equation and is capable of predicting the instability and captures the key features of gravity fingering quantitatively. The extended model is based on a phase-field formulation and is fourth-order in space. The new model poses a set of challenges for numerical discretizations, such as resolution of evolving interfaces, stiffness in space and time, treatment of singularly perturbed equations, and discretization of higher-order spatial partial–differential operators. We develop a numerical algorithm based on Isogeometric Analysis, a generalization of the finite element method that permits the use of globally-smooth basis functions, leading to a simple and efficient discretization of higher-order spatial operators in variational form. We highlight the accuracy, efficiency and robustness of our method with several examples in two and three dimensions in both homogeneous and strongly heterogeneous media. We simulate, for the first time, unstable gravity-driven infiltration in three dimensions, and confirm that the new theory reproduces the fundamental features of water infiltration into a porous medium. Our findings are consistent with classical experimental observations that demonstrate a transition from stable to unstable fronts depending on the infiltration flux.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Towards Automated Reasoning Chains for Verification of LLM-Generated Scientific Code

With the rise of Large Language Model (LLM) generated code, including in domains like scientific computing, ensuring not only syntactical, but also mathematical correctness, has become a critical task. Traditional formal methods approaches often struggle with the ambiguity of floating-point code, and full symbolic execution is extremely costly and limited. We propose a chain-of-reasoning approach that iteratively lifts basic semantics from code into the SPIRAL system and then establishes numerical equivalency to the desired mathematical operation. Here, we leverage the ample mathematical knowledge already formalized in SPIRAL to enable the system to recognize not just different implementations of the same algorithm but fully separate approaches to solving the given problem. The chain establishes tight error bounds on the output of given code with respect to the true continuous solution it approximates, quantifying all sources of error. We demonstrate this approach by establishing the correctness of a pseudospectral solver for a simple 1-dimensional Poisson problem.

Oschatz, Quentin [Carnegie Mellon University,Pitts↗
DOE OSTI2025

Analog Systems for Edge Optimization

Over the past decade, analog computing has the subject of substantial research interest providing a path toward improved computational efficiency in the post-Dennard era. Analog matrix vector multiplication (MVM) accelerators provide a popular approach given the ubiquity of MVM operations in numerous applications. However, historically analog computing systems can struggle with applications requiring high precision due to the inherent susceptibility of these systems to analog non-idealities. Therefore, prior work on analog systems has focused either on applications known to be tolerant of limited precision (e.g., neural network inference), or using expensive techniques to emulate high-precision using many analog MVM operations. In this work, we propose an alternative approach. Motivated by recent advances in inexact nonlinear solvers and optimizers, we explore the potential of co-designing optimization algorithms which can take full advantage of the fundamentally inexact analog MVM operations. To enable these co-designed algorithms we also develop a general mathematical theory of the precision and energy efficiency of analog operations, and a new system architecture for tightly-coupled analog and digital computation. Finally, we examine the applicability of analog computing to a wider class of symmetric positive definite systems and find potential in using analog operations as a sparse approximate inverse preconditioner. With these core innovations, this project provides a path toward effectively implementing optimization algorithms on power-constrained autonomous and semi-autonomous systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Simulating Fracture Sealing by Granular LCM Particles in Geothermal Drilling

Lost circulation occurs when the returned fluid is less than what is pumped into the well due to loss of fluid to pores or fractures. A lost-circulation event is a common occurrence in a geothermal well. Typical geothermal reservoirs are often under-pressured and have larger fracture apertures. A severe lost-circulation event is costly and may lead to stuck pipe, well instability, and well abandonment. One typical treatment is adding lost-circulation materials (LCMs) to seal fractures. Conventional LCMs fail to properly seal fractures because their mechanical limit is exceeded at elevated temperatures. In this paper, parametric studies in numerical simulations are conducted to better understand different thermal effects on the sealing mechanisms of LCMs. The computational fluid dynamics (CFDs) and the discrete element method (DEM) are coupled to accurately capture the true physics of sealing by granular materials. Due to computational limits, the traditional Eulerian–Eulerian approach treats solid particles as a group of continuum matter. With the advance of modern computational power, particle bridging is achievable with DEM to track individual particles by modeling their interactive forces between each other. Particle–fluid interactions can be modeled by coupling CFD algorithms. Fracture sealing capability is investigated by studying the effect of four individual properties including fluid viscosity, particle size, friction coefficient, and Young’s modulus. It is found that thermally degraded properties lead to inefficient fracture sealing.

15 GEOTHERMAL ENERGY↗
DOE OSTI2019

Unified Geometric Multigrid Algorithm for Hybridized High-Order Finite Element Methods

In this paper, we consider a standard elliptic partial differential equation and propose a geometric multigrid algorithm based on Dirichlet-to-Neumann (DtN) maps for hybridized high-order finite element methods. The proposed unified approach is applicable to any locally conservative hybridized finite element method including multinumerics with different hybridized methods in different parts of the domain. For these methods, the linear system involves only the unknowns residing on the mesh skeleton, and constructing intergrid transfer operators is therefore not trivial. The key to our geometric multigrid algorithm is the physics-based energy-preserving intergrid transfer operators which depend only on the fine scale DtN maps. Thanks to these operators, we completely avoid upscaling of parameters and no information regarding subgrid physics is explicitly required on coarse meshes. Moreover, our algorithm is agglomeration-based and can straightforwardly handle unstructured meshes. We perform extensive numerical studies with hybridized mixed methods, hybridized discontinuous Galerkin methods, weak Galerkin methods, and hybridized versions of interior penalty discontinuous Galerkin methods on a range of elliptic problems including subsurface flow through highly heterogeneous porous media. We compare the performance of different smoothers and analyze the effect of stabilization parameters on the scalability of the multigrid algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

An Eulerian Vlasov-Fokker–Planck algorithm for spherical implosion simulations of inertial confinement fusion capsules

Here, we present a numerical algorithm that enables a phase-space adaptive Eulerian Vlasov–Fokker–Planck (VFP) simulation of inertial confinement fusion (ICF) capsule implosions. The approach relies on extending a recent mass, momentum, and energy conserving phase-space moving-mesh adaptivity strategy to spherical geometry. In configuration space, we employ a mesh motion partial differential equation (MMPDE) strategy while, in velocity space, the mesh is expanded/contracted and shifted with the plasma’s evolving temperature and drift velocity. The mesh motion is dealt with by transforming the underlying VFP equations into a computational (logical) coordinate, with the resulting inertial terms carefully discretized to ensure conservation. To deal with the spatial and temporally varying dynamics in a spherically imploding system, we have developed a novel nonlinear stabilization strategy for MMPDE in the configuration space. The strategy relies on a nonlinear optimization procedure that optimizes between mesh quality and the volumetric rate change of the mesh to ensure both accuracy and stability of the solution. Implosions of ICF capsules are driven by several boundary conditions: (1) an elastic moving wall boundary; (2) a time-dependent Maxwellian Dirichlet boundary; and (3) a pressure-driven Lagrangian boundary. Of these, the pressure-driven Lagrangian boundary driver is new to our knowledge. The implementation of our strategy is verified through a set of test problems, including the Guderley and Van-Dyke implosion problems — the first-ever reported using a Vlasov–Fokker–Planck model.

1D2V↗
DOE OSTI2023

Direct implicit and explicit energy-conserving particle-in-cell methods for modeling of capacitively coupled plasma devices

Achieving large-scale kinetic modeling is a crucial task for the development and optimization of modern plasma devices. With the trend of decreasing pressure in applications, such as plasma etching, kinetic simulations are necessary to self-consistently capture the particle dynamics. The standard, explicit, electrostatic, momentum-conserving particle-in-cell method suffers from restrictive stability constraints on spatial cell size and temporal time step, requiring resolution of the electron Debye length and electron plasma period, respectively. This results in a very high computational cost, making the technique prohibitive for large volume device modeling. We investigate the direct implicit algorithm and the explicit energy conserving algorithm as alternatives to the standard approach, both of which can reduce computational cost with a minimal (or controllable) impact on results. These algorithms are implemented into the well-tested EDIPIC-2D and LTP-PIC codes, and their performance is evaluated via 2D capacitively coupled plasma discharge simulations. The investigation reveals that both approaches enable the utilization of cell sizes larger than the Debye length, resulting in a reduced runtime, while incurring only minor inaccuracies in plasma parameters. The direct implicit method also allows for time steps larger than the electron plasma period; however, care must be taken to avoid numerical heating or cooling. It is demonstrated that by appropriately adjusting the ratio of cell size to time step, it is possible to mitigate this effect to an acceptable level.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗