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At least 145 records · Page 8

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DOE OSTI2014

Fluid preconditioning for Newton–Krylov-based, fully implicit, electrostatic particle-in-cell simulations

A recent proof-of-principle study proposes an energy- and charge-conserving, nonlinearly implicit electrostatic particle-in-cell (PIC) algorithm in one dimension [9]. The algorithm in the reference employs an unpreconditioned Jacobian-free Newton–Krylov method, which ensures nonlinear convergence at every timestep (resolving the dynamical timescale of interest). Kinetic enslavement, which is one key component of the algorithm, not only enables fully implicit PIC as a practical approach, but also allows preconditioning the kinetic solver with a fluid approximation. This study proposes such a preconditioner, in which the linearized moment equations are closed with moments computed from particles. Effective acceleration of the linear GMRES solve is demonstrated, on both uniform and non-uniform meshes. The algorithm performance is largely insensitive to the electron–ion mass ratio. Numerical experiments are performed on a 1D multi-scale ion acoustic wave test problem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

A high-order discontinuous Galerkin method for fluid–structure interaction with efficient implicit–explicit time stepping

We present a high-order accurate scheme for coupled fluid–structure interaction problems. The fluid is discretized using a discontinuous Galerkin method on unstructured tetrahedral meshes, and the structure uses a high-order volumetric continuous Galerkin finite element method. Standard radial basis functions are used for the mesh deformation. The time integration is performed using a partitioned approach based on implicit–explicit Runge–Kutta methods. The resulting scheme fully decouples the implicit solution procedures for the fluid and the solid parts, which we perform using two separate efficient parallel solvers. We demonstrate up to fifth order accuracy in time on a non-trivial test problem, on which we also show that additional subiterations are not required. We solve a benchmark problem of a cantilever beam in a shedding flow, and show good agreement with other results in the literature. Finally, we solve for the flow around a thin membrane at a high angle of attack in both 2D and 3D, and compare with the results obtained with a rigid plate.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions

Here, we extend a recently proposed fully implicit PIC algorithm for the Vlasov–Darwin model in multiple dimensions (Chen and Chacón (2015) [1]) to curvilinear geometry. As in the Cartesian case, the approach is based on a potential formulation (Φ, A), and overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. Conservation theorems for local charge and global energy are derived in curvilinear representation, and then enforced discretely by a careful choice of the discretization of field and particle equations. Additionally, the algorithm conserves canonical-momentum in any ignorable direction, and preserves the Coulomb gauge ∇ • A = 0 exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with numerical experiments in mapped meshes in 1D-3V and 2D-3V.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

A scalable, fully implicit algorithm for the reduced two-field low-β extended MHD model

Here, we demonstrate a scalable fully implicit algorithm for the two-field low-β extended MHD model. This reduced model describes plasma behavior in the presence of strong guide fields, and is of significant practical impact both in nature and in laboratory plasmas. The model displays strong hyperbolic behavior, as manifested by the presence of fast dispersive waves, which make a fully implicit treatment very challenging. In this study, we employ a Jacobian-free Newton–Krylov nonlinear solver, for which we propose a physics-based preconditioner that renders the linearized set of equations suitable for inversion with multigrid methods. As a result, the algorithm is shown to scale both algorithmically (i.e., the iteration count is insensitive to grid refinement and timestep size) and in parallel in a weak-scaling sense, with the wall-clock time scaling weakly with the number of cores for up to 4096 cores. For a 4096 × 4096 mesh, we demonstrate a wall-clock-time speedup of ~6700 with respect to explicit algorithms. The model is validated linearly (against linear theory predictions) and nonlinearly (against fully kinetic simulations), demonstrating excellent agreement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

A fast implicit solver for semiconductor models in one space dimension

Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in semiconductor devices under a low-density assumption. At each implicit time step, the discretized system is formulated as a fixed-point problem, which can then be solved with a variety of methods. A key algorithmic component in all the approaches considered here is a recently developed sweeping algorithm for Vlasov-Poisson systems. A synthetic acceleration scheme has been implemented to accelerate the convergence of iterative solvers by using the solution to a drift-diffusion equation as a preconditioner. The performance of four iterative solvers and their accelerated variants has been compared on problems modeling semiconductor devices with various electron mean-free-path.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

On numerical energy conservation for an implicit particle-in-cell method coupled with a binary Monte-Carlo algorithm for Coulomb collisions

We report conventional particle-in-cell (PIC) methods suffer from enhanced numerical heating (explicit PIC) or cooling (semi-implicit PIC) when coupled with a binary Monte-Carlo algorithm for Coulomb collisions. In this work, a fully-implicit θ-PIC scheme (with adjustable time-biasing parameter 1/2 ≤ θ ≤) is considered. The discrete change in energy of a closed system after a time step for this scheme scales with (1/2 - θ)C θ , where C θ is a positive definite quantity that depends on the frequency spectrum of the energy in the fields. Collisions lead to additional energy in the field fluctuations associated with high-frequency light waves produced by a numerical Bremsstrahlung process, which can result in a large increase in the numerical cooling rate for θ > 1/2. However, for θ = 1/2, energy is exactly conserved. The energy in the field fluctuations on long time scales agrees with that calculated using the equipartition theorem for a classical system in thermodynamic equilibrium.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

A conservative implicit-PIC scheme for the hybrid kinetic-ion fluid-electron plasma model on curvilinear meshes

We report that the hybrid kinetic-ion fluid-electron plasma model is widely used to study challenging multi-scale problems in space and laboratory plasma physics. Here, a novel conservative scheme for this model employing implicit particle-in-cell techniques is extended to arbitrary coordinate systems via curvilinear maps from logical to physical space. The scheme features a fully non-linear electromagnetic formulation with a multi-rate time advance - including sub-cycling and orbit-averaging for the kinetic ions. By careful choice of compatible particle-based kinetic-ion and mesh-based fluid-electron discretizations in curvilinear coordinates, as well as particle-mesh interpolations and implicit midpoint time advance, the scheme is proven to conserve total energy for arbitrary curvilinear meshes. In the electrostatic limit, the method is also proven to conserve total momentum for arbitrary curvilinear meshes. Although momentum is not conserved for arbitrary curvilinear meshes in the electromagnetic case, it is for an important subset of Cartesian tensor-packed meshes. The scheme and its novel conservation properties are demonstrated for several challenging numerical problems using different curvilinear meshes, including a merging flux-rope simulation for a space weather application, and a helical m = 1 mode simulation for magnetic fusion energy application.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Local conservation of energy in fully implicit PIC algorithms

We consider the issue of strict, fully discrete local energy conservation for a whole class of fully implicit local-charge- and global-energy-conserving particle-in-cell (PIC) algorithms. Earlier studies demonstrated these algorithms feature strict global energy conservation. However, whether a local energy conservation theorem exists (in which the local energy update is governed by a flux balance equation at every mesh cell) for these schemes is unclear. In this study, we show that a local energy conservation theorem indeed exists. We begin our analysis with the 1D electrostatic PIC model without orbit-averaging, and then generalize our conclusions to account for orbit averaging, multiple dimensions, and electromagnetic models (Darwin). In all cases, a temporally, spatially, and particle-discrete local energy conservation theorem is shown to exist, proving that these formulations (as originally proposed in the literature), in addition to being locally charge conserving and globally energy conserving, are strictly locally energy conserving as well. In contrast to earlier proofs of local conservation in the literature, which only considered continuum time, our result is valid for the fully implicit time-discrete version of all models considered, including important features such as orbit averaging. We demonstrate the local-energy-conservation property numerically with a paradigmatic numerical example.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Asymptotic-preserving semi-implicit finite volume scheme for extended magnetohydrodynamics

A Finite Volume (FV) scheme is developed for solving the extended magnetohydrodynamic (XMHD) equations, yielding accurate results in the ideal, resistive, and Hall MHD limits. This is accomplished by first re-writing the XMHD equations such that it allows the algorithm to retain the use of ideal MHD Riemann solvers and the constrained transport method to preserve divergence-free magnetic fields. Incorporation of electron inertia and displacement current introduces additional numerical stiffness which motivates a semi-implicit FV scheme that re-formulates the XMHD model as a relaxation system. The equations are then advanced in time using an explicit 2nd-order Runge–Kutta scheme with operator splitting applied to the implicit source term updates at each sub-stage. For additional numerical stability, a density-dependent slope limiter is implemented to increase flux diffusivity at low density regions where non-ideal effects become significant. The algorithm is subsequently implemented in a scalable adaptive mesh refinement (AMR) framework. As the new algorithm retains many aspects of the ideal MHD formulations, it asymptotes naturally to the ideal MHD limit. Moreover, it shows promising results at the resistive and Hall MHD limits. This is verified against reference test problems for ideal, resistive and Hall MHD.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

On the use of finite difference matrix-vector products in Newton-Krylov solvers for implicit climate dynamics with spectral elements

Efficient solutions of global climate models require effectively handling disparate length and time scales. Implicit solution approaches allow time integration of the physical system with a step size governed by accuracy of the processes of interest rather than by stability of the fastest time scales present. Implicit approaches, however, require the solution of nonlinear systems within each time step. Usually, a Newton's method is applied to solve these systems. Each iteration of the Newton's method, in turn, requires the solution of a linear model of the nonlinear system. This model employs the Jacobian of the problem-defining nonlinear residual, but this Jacobian can be costly to form. If a Krylov linear solver is used for the solution of the linear system, the action of the Jacobian matrix on a given vector is required. In the case of spectral element methods, the Jacobian is not calculated but only implemented through matrix-vector products. The matrix-vector multiply can also be approximated by a finite difference approximation which may introduce inaccuracy in the overall nonlinear solver. In this paper, we review the advantages and disadvantages of finite difference approximations of these matrix-vector products for climate dynamics within the spectral element shallow water dynamical core of the Community Atmosphere Model.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2019

Evaluation of Implicit‐Explicit Additive Runge‐Kutta Integrators for the HOMME‐NH Dynamical Core

Abstract The nonhydrostatic High‐Order Method Modeling Environment (HOMME‐NH) atmospheric dynamical core supports acoustic waves that propagate significantly faster than the advective wind speed, thus greatly limiting the time step size that can be used with standard explicit time integration methods. Resolving acoustic waves is unnecessary for accurate climate and weather prediction. This numerical stiffness is addressed herein by considering implicit‐explicit additive Runge‐Kutta (ARK IMEX) methods that can treat the acoustic waves in a stable manner without requiring implicit treatment of nonstiff modes. Various ARK IMEX methods are evaluated for their efficiency in producing accurate solutions, ability to take large time step sizes, and sensitivity to grid cell length ratio. Both the gravity wave test and baroclinic instability test from the 2012 Dynamical Core Model Intercomparison Project are used to recommend 5 of the 27 ARK IMEX methods tested for use in HOMME‐NH.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Simulating Global Terrestrial Carbon and Nitrogen Biogeochemical Cycles With Implicit and Explicit Representations of Soil Microbial Activity

Abstract Nutrient limitation is widespread in terrestrial ecosystems. Accordingly, representations of nitrogen (N) limitation in land models typically dampen rates of terrestrial carbon (C) accrual, compared with C‐only simulations. These previous findings, however, rely on soil biogeochemical models that implicitly represent microbial activity and physiology. Here we present results from a biogeochemical model testbed that allows us to investigate how an explicit versus implicit representation of soil microbial activity, as represented in the MIcrobial‐MIneral Carbon Stabilization (MIMICS) and Carnegie‐Ames‐Stanford Approach (CASA) soil biogeochemical models, respectively, influence plant productivity, and terrestrial C and N fluxes at initialization and over the historical period. When forced with common boundary conditions, larger soil C pools simulated by the MIMICS model reflect longer inferred soil organic matter (SOM) turnover times than those simulated by CASA. At steady state, terrestrial ecosystems experience greater N limitation when using the MIMICS‐CN model, which also increases the inferred SOM turnover time. Over the historical period, however, warming‐induced acceleration of SOM decomposition over high latitude ecosystems increases rates of N mineralization in MIMICS‐CN. This reduces N limitation and results in faster rates of vegetation C accrual. Moreover, as SOM stoichiometry is an emergent property of MIMICS‐CN, we highlight opportunities to deepen understanding of sources of persistent SOM and explore its potential sensitivity to environmental change. Our findings underscore the need to improve understanding and representation of plant and microbial resource allocation and competition in land models that represent coupled biogeochemical cycles under global change scenarios.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

An implicit-explicit time splitting strategy for the far SOL plasma fluid model with DG-FEM discretization

We consider a far scrape-off layer (SOL) plasma fluid model of ions that is governed by a Braginskiitype model: a one-dimensional, nonlinear system of advection-diffusion equations coupled with a diffusion equation for neutral particles. Our motivation for studying this system arises from the coupling between the edge plasma and radio-frequency (RF) heating, where solving a far SOL plasma fluid model provides critical insights into edge plasma dynamics. Numerical simulations of plasma fluid models require advanced computational techniques to achieve both efficiency and accuracy, especially when resolving the boundary layer in magnetically confined plasmas. In this work, we propose an implicit-explicit time operator splitting strategy that allows for an efficient solution algorithm, where the diffusive terms are treated semi-implicitly requiring only a linear solve, while the advection part is handled explicitly using a strong-stability-preserving Runge-Kutta (SSP-RK3) scheme. This leads to a fully decoupled system in which the diffusion and advection sub-problems can be solved separately, simplifying the overall solution procedure and allowing for efficient parallelization, which is particularly relevant for exploring the impact of RF heating on the SOL plasma. The main challenge of the discretization is due to the strong coupling between diffusion and advection, particularly through the boundary conditions. This makes implementation of such a scheme in an accurate and stable manner nontrivial. We discuss in detail how to split the equations and manage boundary conditions to maintain stability and well-posedness for each subsystem. We also describe a spatial discretization approach, based on the discontinuous Galerkin finite element method (DG-FEM) and present numerical results for a one-dimensional system.

Burkovska, Olena [ORNL] (ORCID:0000000163101130)↗

DOE OSTI2013

An implicit logarithmic finite-difference technique for two dimensional coupled viscous Burgers’ equation

This article describes a new implicit finite-difference method: an implicit logarithmic finite-difference method (I-LFDM), for the numerical solution of two dimensional time-dependent coupled viscous Burgers’ equation on the uniform grid points. As the Burgers’ equation is nonlinear, the proposed technique leads to a system of nonlinear systems, which is solved by Newton's iterative method at each time step. Computed solutions are compared with the analytical solutions and those already available in the literature and it is clearly shown that the results obtained using the method is precise and reliable for solving Burgers’ equation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Derivation of a Markov state model of the dynamics of a protein-like chain immersed in an implicit solvent

A Markov state model of the dynamics of a protein-like chain immersed in an implicit hard sphere solvent is derived from first principles for a system of monomers that interact via discontinuous potentials designed to account for local structure and bonding in a coarse-grained sense. The model is based on the assumption that the implicit solvent interacts on a fast time scale with the monomers of the chain compared to the time scale for structural rearrangements of the chain and provides sufficient friction so that the motion of monomers is governed by the Smoluchowski equation. A microscopic theory for the dynamics of the system is developed that reduces to a Markovian model of the kinetics under well-defined conditions. Microscopic expressions for the rate constants that appear in the Markov state model are analyzed and expressed in terms of a temperature-dependent linear combination of escape rates that themselves are independent of temperature. Excellent agreement is demonstrated between the theoretical predictions of the escape rates and those obtained through simulation of a stochastic model of the dynamics of bond formation. Finally, the Markov model is studied by analyzing the eigenvalues and eigenvectors of the matrix of transition rates, and the equilibration process for a simple helix-forming system from an ensemble of initially extended configurations to mainly folded configurations is investigated as a function of temperature for a number of different chain lengths. For short chains, the relaxation is primarily single-exponential and becomes independent of temperature in the low-temperature regime. The profile is more complicated for longer chains, where multi-exponential relaxation behavior is seen at intermediate temperatures followed by a low temperature regime in which the folding becomes rapid and single exponential. It is demonstrated that the behavior of the equilibration profile as the temperature is lowered can be understood in terms of the number of relaxation modes or “folding pathways” that contribute to the evolution of the state populations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Implicit versus explicit momentum relaxation time solution for semiconductor nanowires

We discuss the necessity of the exact implicit Momentum Relaxation Time (MRT) solution of the Boltzmann transport equation in order to achieve reliable carrier mobility results in semiconductor nanowires. Firstly, the implicit solution for a 1D electron gas with a isotropic bandstructure is presented resulting in the formulation of a simple matrix system. Using this solution as a reference, the explicit approach is demonstrated to be inaccurate for the calculation of inelastic anisotropic mechanisms such as polar optical phonons, characteristic of III-V materials. Its validity for elastic and isotropic mechanisms is also evaluated. Finally, the implications of the MRT explicit approach inaccuracies on the total mobility of Si and III-V NWs are studied.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Stratification of drying particle suspensions: Comparison of implicit and explicit solvent simulations

We report that large scale molecular dynamics simulations are used to study drying suspensions of a binary mixture of large and small particles in explicit and implicit solvents. The solvent is first modeled explicitly and then mapped to a uniform viscous medium by matching the diffusion coefficients and the pair correlation functions of the particles. “Small-on-top” stratification of the particles, with an enrichment of the smaller ones at the receding liquid-vapor interface during drying, is observed in both models under the same drying conditions. With the implicit solvent model, we are able to model much thicker films and study the effect of the initial film thickness on the final distribution of particles in the dry film. Laslty, our results show that the degree of stratification is controlled by the Péclet number defined using the initial film thickness as the characteristic length scale. When the Péclet numbers of large and small particles are much larger than 1, the degree of “small-on-top” stratification is first enhanced and then weakens as the Péclet numbers are increased.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Verification of a fully implicit particle-in-cell method for the  v ∥ -formalism of electromagnetic gyrokinetics in the XGC code

A fully implicit particle-in-cell method for handling the v ∥ -formalism of electromagnetic gyrokinetics has been implemented in XGC. By choosing the v ∥ -formalism, here we avoid introducing the nonphysical skin terms in Ampère's law, which are responsible for the well-known “cancellation problem” in the p ∥ -formalism. The v ∥ -formalism, however, is known to suffer from a numerical instability when explicit time integration schemes are used due to the appearance of a time derivative in the particle equations of motion from the inductive component of the electric field. Here, using the conventional δf scheme, we demonstrate that our implicitly discretized algorithm can provide numerically stable simulation results with accurate dispersive properties. We verify the algorithm using a test case for shear Alfvén wave propagation in addition to a case demonstrating the ion temperature gradient-kinetic ballooning mode (ITG-KBM) transition. The ITG-KBM transition case is compared to results obtained from other δf gyrokinetic codes/schemes, whose verification has already been archived in the literature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗