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Results for “hyperbolic evolution equation”

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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7 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Mathematical modelling of the concave front in the adjacent high explosive detonation problem

This study presents an analysis of the transition-zone in adjacent high explosive (HE) detonation problems which uses a $D, 𝜅, \dot{D}$ relationship, where $D$ is the detonation front-normal velocity, 𝜅 is the detonation front curvature and $\dot{D}$ is the time derivative of detonation front-normal velocity. Our approach extends the traditional $(D, 𝜅)$ model to accurately predict the behaviour of both diverging and converging detonation shock fronts. Our findings affirm that a hyperbolic type of front evolution equation, enhanced with wave acceleration, provides a robust framework for modelling complex shock front dynamics in HE materials. This approach not only captures the natural effects of straightness and boundary slope jumps in the transition-zone but also bridges the gap between mathematical predictions and experimental observations, offering insights into the behaviour of both diverging and converging detonation propagations in a homogeneous HE.

acceleration↗
DOE OSTI2023

Evolution of the age-included nearest pair distribution in disperse multiphase flows

The age of the nearest particle pair is introduced as the difference between the current time and the most recent time when the nearest particle pair was formed. The evolution equation for the age-included nearest pair distribution function is derived. With the assumption of random destruction of the nearest particle pairs, the evolution equation predicts the exponential probability distribution of the ages of the nearest particle pairs. Particle-resolved numerical simulations with moving particles are performed to verify this prediction. The equation is then used to derive the evolution equation for the particle–fluid–particle (PFP) stress, which is known to be related to hyperbolicity of the two-fluid equations. It is found that the relaxation time of the age probability distribution is also the relaxation time for the PFP stress. Guided by the closure terms in the PFP stress evolution equation, we study kinematics of the nearest particle pairs in the particle-resolved simulations for flows caused by sedimentation of the particles with initially isotropic and homogeneous particle distributions. At the steady states, the particle Reynolds numbers are around 20. Anisotropy and inhomogeneity of particle distributions are seen to develop in these flows. The mean distances to the nearest particles and evolution of the distribution of the Voronoi cell volumes are studied. We also found the PFP stress is closely related to the changes in these inter-particle scale quantities.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Ameliorating the Courant-Friedrichs-Lewy condition in spherical coordinates: A double FFT filter method for general relativistic MHD in dynamical spacetimes

Numerical simulations of merging compact objects and their remnants form the theoretical foundation for gravitational wave and multimessenger astronomy. While Cartesian-coordinate-based adaptive mesh refinement is commonly used for simulations, spherical-like coordinates are more suitable for nearly spherical remnants and azimuthal flows due to lower numerical dissipation in the evolution of fluid angular momentum, as well as requiring fewer numbers of computational cells. However, the use of spherical coordinates to numerically solve hyperbolic partial differential equations can result in severe Courant-Friedrichs-Lewy (CFL) stability condition time step limitations, which can make simulations prohibitively expensive. This paper addresses this issue for the numerical solution of coupled spacetime and general relativistic magnetohydrodynamics evolutions by introducing a double fast Fourier transform (FFT) filter and implementing it within the fully message passing interface (mpi)-parallelized sphericalnr framework in the einstein toolkit. In conclusion, we demonstrate the effectiveness and robustness of the filtering algorithm by applying it to a number of challenging code tests, and show that it passes these tests effectively, demonstrating convergence while also increasing the time step significantly compared to unfiltered simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Nonlinear causality and strong hyperbolicity of baryon-rich Israel-Stewart hydrodynamics

We present the first set of fully-nonlinear, necessary and sufficient conditions guaranteeing causal evolution of the initial data for the Israel-Stewart hydrodynamic equations with shear and bulk viscosity coupled to a nonzero baryon current. These constraints not only provide nonlinear causality: they also (a) guarantee the existence of a locally well-posed evolution of the initial data (they enforce strong hyperbolicity) when excluding the endpoints of the bounds, (b) arise from purely algebraic constraints that make no underlying symmetry assumptions on the degrees of freedom and (c) propagate the relevant symmetries of the degrees of freedom over the entire evolution of the problem. Our work enforces a mathematically rigorous foundation for future studies of viscous relativistic hydrodynamics with baryon-rich matter including neutron star mergers and heavy-ion collisions.

Cordeiro, Ian [University of Illinois Urbana-Champ↗
DOE OSTI2020

Calibration of CDM-Based Creep Constitutive Model Using Accelerated Creep Test (ACT) Data

In conventional creep testing (CCT) a specimen is subject to constant load and temperature for a long-duration until creep rupture occurs. Conventional testing can be costly when considering the number of experiments needed to characterize the creep response of a material over a range of stress and temperature. To predict long-term creep-rupture properties, the time-temperature-stress superposition principle (TTSSP) approach has been employed where stress and/or temperature is applied at an elevated level; the result of which are extrapolated down to low stress and/or temperature conditions. These methods have been successful in predicting minimum-creep-strain-rate (MCSR) and stress-rupture (SR) but suffer from an inability to predict the creep deformation curve or account for changes in deformation mechanisms or aging that occurs at long-duration. An accelerated technique, termed the Stepped isostress method (SSM) allows the accelerated testing of materials to determine their creep deformation response. Unlike TTSSP tests, the SSM test employs a single specimen where the stress is periodically step increased until rupture. The SSM creep deformation curve is processed (time and strain shifted) to produce an accelerated creep deformation curve that represent the creep deformation curve at the initial stress level in SSM. A processing procedure for metals has yet to be developed. The research objective of this study is to develop a processing procedure for SSM test data using a creep-damage constitutive model. Triplicate SSM tests were conducted on Ni-based superalloy Inconel 718 at 650°C with stress being periodically increased until rupture. Triplicate CCT tests were conducted at the initial stress level of the SSM tests. The Sine-hyperbolic (Sinh) creep-damage model was employed in this study. The Sinh creep-damage constitutive model is based on coupled creep strain rate and damage evolution equations; where both rates are dependent on the current state of damage. Calibration is two-step: analytical and numerical optimization. Each stepped creep deformation curve is tackled quasi-analytically to determine MCSR and SR related material constants and accumulated damage. The damage accumulated at the end of each step was then passed onto subsequent steps to calibrate the MCSR, rupture prediction, and damage evolution. Numerical optimization was applied to optimize model constants involved in the creep strain constitutive equations in order to generate best-fitted Sinh creep deformation curves. The Sinh model predictions were compared to the SSM and CCT data. The Sinh model satisfactorily predicts the SSM data and thus the calibrated material constants provides a good estimate of rupture found in the CCT data. Calibration using SSM data reduces the number of tests needed to calibrate a model; significantly reducing costs. A single SSM test replaces numerous creep tests at different stresses.

36 MATERIALS SCIENCE↗
DOE OSTI2022

An adaptive scalable fully implicit algorithm based on stabilized finite element for reduced visco-resistive MHD

The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution methods for MHD are extremely challenging due to disparate time and length scales, strong hyperbolic phenomena, and nonlinearity. Additionally, therefore the development of scalable, implicit MHD algorithms and high-resolution adaptive mesh refinement strategies is of considerable importance. In this work, we develop a high-order stabilized finite-element algorithm for the reduced visco-resistive MHD equations based on the MFEM finite element library (mfem.org). The scheme is fully implicit, solved with the Jacobian-free Newton-Krylov (JFNK) method with a physics-based preconditioning strategy. Our preconditioning strategy is a generalization of the physics-based preconditioning methods in Chacón et al. (2002) to adaptive, stabilized finite elements. Algebraic multigrid methods are used to invert sub-block operators to achieve scalability. A parallel adaptive mesh refinement scheme with dynamic load-balancing is implemented to efficiently resolve the multi-scale spatial features of the system. Our implementation uses the MFEM framework, which provides arbitrary-order polynomials and flexible adaptive conforming and non-conforming meshes capabilities. Results demonstrate the accuracy, efficiency, and scalability of the implicit scheme in the presence of large scale disparity. The potential of the AMR approach is demonstrated on an island coalescence problem in the high Lundquist-number regime (≥ 10 7 ) with the successful resolution of plasmoid instabilities and thin current sheets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Causal explicit algorithm for heat conduction in a plasma

Hyperbolic heat conduction extends standard Spitzer-Harm heat conduction by including a term proportional to the time derivative of the heat flux. The new term arises from a kinetic derivation of the heat flux that includes higher order corrections. Here we present a causal explicit numerical algorithm for solving the nonlinear hyperbolic heat conduction equation in an unmagnetized plasma. The maximum stable timestep for the causal explicit algorithm scales linearly with the cell size, owing to the hyperbolic nature of the problem. This is in contrast to the quadratic scaling of the maximum stable timestep with the cell size for the parabolic forward time centered space algorithm. The favorable scaling of the timestep with the cell size enables a practical explicit implementation of heat conduction in high-performance massively parallel plasma codes. In particular, we have implemented the causal explicit algorithm in the laser plasma interaction code pF3D. We verify the CE algorithm and analyze its convergence rate by simulating a harmonic mode, which has an analytic solution within the context of the HHC model. We also compare simulations using the CE algorithm to those using the forward time centered space algorithm on a pair of test problems: evolution in time of a Gaussian temperature perturbation in a uniform plasma and heat transport in the presence of inverse bremsstrahlung heating by a Gaussian laser speckle.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗