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Results for “implicit and explicit algorithms”

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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113 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Towards Multifluid Multiphysics Continuum Plasma Simulation for Modeling Magnetically-driven Experiments on Z

Magnetically driven experiments supporting pulsed-power utilize a wide range of configurations, including wire-arrays, gas-puffs, flyer plates, and cylindrical liners. This experimental flexibility is critical to supporting radiation effects, dynamic materials, magneto-inertial-fusion (MIF), and basic high energy density laboratory physics (HEDP) efforts. Ultimately, the rate at which these efforts progress is limited by our understanding of the complex plasma physics of these systems. Our effort has been to begin to develop an advanced algorithmic structure and a R&D code implementation for a plasma physics simulation capability based on the five-moment multi-fluid / full-Maxwell plasma model. This model can be used for inclusion of multiple fluid species (e.g., electrons, multiple charge state ions, and neutrals) and allows for generalized collisional interactions between species, models for ionization/recombination, magnetized Braginskii collisional transport, dissipative effects, and can be readily extended to incorporate radiation transport physics. In the context of pulsed-power simulations this advanced model will help to allow SNL to computationally simulate the dense continuum regions of the physical load (e.g. liner implosions, flyer plates) as well as partial power-flow losses in the final gap region of the inner MITL. In this report we briefly summarize results of applying a preliminary version of this model in the context of verification type problems, and some initial magnetic implosion relevant prototype problems. The MIF relevant prototype problems include results from fully-implicit / implicit-explicit (IMEX) resistive MHD as well as full multifluid EM plasma formulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

A plasma–vacuum interface tracking algorithm for magnetohydrodynamic simulations of coaxial plasma accelerators

The resistive Magneto-hydrodynamic (MHD) model describes the behavior of a strongly ionized plasma in the presence of external electric and magnetic fields. For problems involving the plasma with an open boundary to very low pressure/vacuum regions, the continuum assumption is no longer valid in the entire domain of interest. For example, this is seen in a plasma accelerator where a dense plasma expands into a vacuum background. A common practice to deal with this issue is to assign small values of density and pressure to the vacuum regions and proceed to solve the continuum based MHD equations throughout the domain. We show that this approach fails to produce solutions consistent with the physics of the problem and can give rise to unacceptable artifacts such as spurious shocks. Here, we develop a plasma–vacuum interface tracking approach to mitigate this problem. The plasma–vacuum interface is tracked in a physically consistent manner and the MHD equations are solved only in the regions that contain the plasma. The interface tracking is achieved using a face-flux formulation derived from the theoretical solution to a 1D free expansion problem. Coupled with a threshold based approach, the interface tracking is implemented for both explicit and implicit time stepping frameworks on generalized unstructured grids. Simulations of magnetized thermal plasma jets expanding into a vacuum background indicate plume profiles devoid of the unphysical shock obtained using the small background density approach. In the context of resistive MHD simulations, the interface tracking approach overcomes the numerical stiffness induced by specifying a large background resistivity in the vacuum regions, resulting in significant wall-clock time gains.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Data-driven linear time advance operators for the acceleration of plasma physics simulation

In this study, we demonstrate the application of data-driven linear operator construction for time advance with a goal of accelerating plasma physics simulation. We apply dynamic mode decomposition (DMD) to data produced by the nonlinear SOLPS-ITER (Scrape-off Layer Plasma Simulator - International Thermonuclear Experimental Reactor) plasma boundary code suite in order to estimate a series of linear operators and monitor their predictive accuracy via online error analysis. We find that this approach defines when these dynamics can be represented by a sequence of approximate linear operators and is essential for providing consistent projections when compared to an unconstrained application. For linear diffusion and advection–diffusion fluid test problems, we construct and apply operators within explicit and implicit time advance schemes, demonstrating that stability can be robustly guaranteed in each case. We further investigate the use of the linear time advance operators within several integration methods including forward Euler, backward Euler, and the matrix exponential. The application of this method to simulation data from SOLPS-ITER, with varying levels of Markov chain Monte Carlo numerical noise, shows that constrained DMD operators yield a capability to identify, extract, and integrate a (slow) subset of the present timescales. Example applications show that for projected speedup factors of [Formula: see text], and [Formula: see text], a mean relative error of 3%, 5%, and 8% and maximum relative error less than 20% are achievable, which appears acceptable for typical SOLPS-ITER steady-state simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Efficient Multigrid Reduction-in-Time for Method-of-Lines Discretizations of Linear Advection

Parallel-in-time methods for partial differential equations (PDEs) have been the subject of intense development over recent decades, particularly for diffusion-dominated problems. It has been widely reported in the literature, however, that many of these methods perform quite poorly for advection-dominated problems. In this report we analyze the particular iterative parallel-in-time algorithm of multigrid reduction-in-time (MGRIT) for discretizations of constant-wave-speed linear advection problems. We focus on common method-of-lines discretizations that employ upwind finite differences in space and Runge-Kutta methods in time. Using a convergence framework we developed in previous work, we prove for a subclass of these discretizations that, if using the standard approach of rediscretizing the fine-grid problem on the coarse grid, robust MGRIT convergence with respect to CFL number and coarsening factor is not possible. This poor convergence and non-robustness is caused, at least in part, by an inadequate coarse-grid correction for smooth Fourier modes in space-time known as characteristic components. We propose an alternative coarse-grid operator that provides a better correction of these modes. This coarse-grid operator is related to previous work and uses a semi-Lagrangian discretization combined with an implicitly treated truncation error correction. Theory and numerical experiments show the proposed coarse-grid operator yields fast MGRIT convergence for many of the method-of-lines discretizations considered, including for both implicit and explicit discretizations of high order. Parallel results demonstrate speed-up over sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Scalable smoothing strategies for a geometric multigrid method for the immersed boundary equations

The immersed boundary (IB) method is a widely used approach to simulating fluid-structure interaction (FSI). Although explicit versions of the IB method can suffer from severe time step size restrictions, these methods remain popular because of their simplicity and generality. In prior work (Guy et al., Adv Comput Math, 2015), some of us developed a geometric multigrid preconditioner for a stable semi-implicit IB method under Stokes flow conditions; however, this solver methodology used a Vanka-type smoother that presented limited opportunities for parallelization. This work extends this Stokes-IB solver methodology by developing smoothing techniques that are suitable for parallel implementation. Specifically, we demonstrate that an additive version of the Vanka smoother can yield an effective multigrid preconditioner for the Stokes-IB equations, and we introduce an efficient Schur complement-based smoother that is also shown to be effective for the Stokes-IB equations. We investigate the performance of these solvers for a broad range of material stiffnesses, both for Stokes flows and flows at nonzero Reynolds numbers, and for thick and thin structural models. We show here that linear solver performance degrades with increasing Reynolds number and material stiffness, especially for thin interface cases. Nonetheless, the proposed approaches promise to yield effective solution algorithms, especially at lower Reynolds numbers and at modest-to-high elastic stiffnesses.

97 MATHEMATICS AND COMPUTING↗