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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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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Multigrid Acceleration of Time-Accurate DNS of Compressible Turbulent Flow

An efficient scheme for the direct numerical simulation of 3D transitional and developed turbulent flow is presented. Explicit and implicit time integration schemes for the compressible Navier-Stokes equations are compared. The nonlinear system resulting from the implicit time discretization is solved with an iterative method and accelerated by the application of a multigrid technique. Since we use central spatial discretizations and no artificial dissipation is added to the equations, the smoothing method is less effective than in the more traditional use of multigrid in steady-state calculations. Therefore, a special prolongation method is needed in order to obtain an effective multigrid method. This simulation scheme was studied in detail for compressible flow over a flat plate. In the laminar regime and in the first stages of turbulent flow the implicit method provides a speed-up of a factor 2 relative to the explicit method on a relatively coarse grid. At increased resolution this speed-up is enhanced correspondingly.

Broeze, Jan↗
DOE OSTI2024

DG-IMEX method for a two-moment model for radiation transport in the $\mathscr{O}$($v$/$c$) limit

Here, we consider neutral particle systems described by moments of a phase-space density and propose a realizability-preserving numerical method to evolve a spectral two-moment model for particles interacting with a background fluid moving with nonrelativistic velocities. The system of nonlinear moment equations, with special relativistic corrections to $\mathscr{O}$($v$/$c$), expresses a balance between phase-space advection and collisions and includes velocity-dependent terms that account for spatial advection, Doppler shift, and angular aberration. The model is conservative for the correct $\mathscr{O}$($v$/$c$) Eulerian-frame number density and is consistent, to $\mathscr{O}$($v$/$c$), with Eulerian-frame energy and momentum conservation. This model is closely related to the one promoted by Lowrie et al. and similar to models currently used to study transport phenomena in large-scale simulations of astrophysical environments. The proposed numerical method is designed to preserve moment realizability, which guarantees that the moments correspond to a nonnegative phase-space density. The realizability-preserving scheme consists of the following key components: (i) a strong stability-preserving implicit-explicit (IMEX) time-integration method; (ii) a discontinuous Galerkin (DG) phase-space discretization with carefully constructed numerical uxes; (iii) a realizability-preserving implicit collision update; and(iv) a realizability-enforcing limiter. In time integration, nonlinearity of the moment model necessitates solution of nonlinear equations, which we formulate as fixed-point problems and solve with tailored iterative solvers that preserve moment realizability with guaranteed global convergence. We also analyze the simultaneous Eulerian-frame number and energy conservation properties of the semi-discrete DG scheme and propose a "spectral redistribution" scheme that promotes Eulerian-frame energy conservation. Through numerical experiments, we demonstrate the accuracy and robustness of this DG-IMEX method and investigate its Eulerian-frame energy conservation properties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

The Peridigm Meshfree Peridynamics Code

Abstract Peridigm is a meshfree peridynamics code written in C++ for use on large-scale parallel computers. It was originally developed at Sandia National Laboratories and is currently managed as an open-source, community driven software project. Its primary features include bond-based, state-based, and non-ordinary state-based constitutive models, bond failure laws, contact, and support for explicit and implicit time integration. To date, Peridigm has been used primarily by methods developers focused on solid mechanics and material failure. Peridigm utilizes foundational software components from Sandia’s Trilinos project and was designed for extensibility. This paper provides an overview of the solution methods implemented in Peridigm , a discussion of its software infrastructure, and demonstrates the use of Peridigm for the solution of several example problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

FIERRO V.X

FIERRO is a modern C++ code intended to simulate quasi-static solid mechanics problems and transient, compressible material dynamic problems with Lagrangian methods, which have meshes with constant mass elements that move with the material. FIERRO is designed to aid a) material model research that has historically been done using commercial implicit and explicit finite element codes, b) numerical methods research, and c) computer science research. FIERRO supports user developed material models that adhere to several industry standard formats by using a C++ to Fortran interface to couple the model to the numerical solvers. FIERRO is built on the ELEMENTS library that supports a diverse suite of element types, including high-order elements, and quadrature rules. The mesh class within the ELEMENTS library is designed for efficient calculations on unstructured meshes and to minimize memory usage. FIERRO is designed to readily accommodate a range of numerical methods including continuous finite element, finite volume, and discontinuous Galerkin methods. FIERRO is designed to support explicit and implicit time integration methods. FIERRO only supports a single material in an element. No physical data exists within the code.

Morgan, Nathaniel↗
NASA NTRS1979

Finite element methodology for transient conduction/forced-convection thermal analysis

Finite element methodology for steady state thermal analysis of convectively cooled structures has been extended for transient analysis. The finite elements are based on representing the fluid passages by fluid bulk-temperature nodes and fluid-solid interface nodes. The formulation of the finite element equations for a typical flow passage is based on the weighted residual method with upwind weighting functions. Computer implementation of the convective finite element methodology using explicit and implicit time integration algorithms is described. Accuracy and efficiency of the methodology is evaluated by comparisons with analytical solutions and finite-difference lumped-parameter analyses. The comparative analyses demonstrate that finite element conduction/conduction methodology may be used to predict transient temperatures with an accuracy equal or superior to the lumped-parameter finite-difference method.

Thornton, E. A.↗
NASA NTRS1983

Mixed time integration schemes for transient conduction forced-convection analysis

A partition procedure for forced-convection conduction transient problems is presented. Mixed time partitions are defined wherein coupled conduction force-matrix equations are discretized using an implicit integration method, followed by derivation of a mixed time integration technique. Explicit-implicit and explicit-explicit partitions are performed for a stability analysis for transient conditions, e.g., those found in an actively air-cooled engine and airframe structure.

Liu, W. K.↗
NASA NTRS1983

A new explicit method for the numerical solution of parabolic differential equations

A new method is derived for solving parabolic partial differential equations arising in transient heat conduction or in boundary-layer flows. The method is based on a combination of the modified differential quadrature (MDQ) method with the rational Runge-Kutta time-integration scheme. It is fully explicit, requires no matrix inversion, and is stable for any time-step for the heat equations. Burgers equation and the one- and two-dimensional heat equations are solved to demonstrate the accuracy and efficiency of the proposed algorithm. The present method is found to be very accurate and efficient when results are compared with analytic solutions.

Satofuka, N.↗
DOE OSTI2021

A scalable exponential-DG approach for nonlinear conservation laws: With application to Burger and Euler equations

In this work, we propose an Exponential DG framework for partial differential equations. We decompose 7 governing equations into linear and nonlinear parts to which we apply the discontinuous Galerkin 8 (DG) spatial discretization. In particular, we construct the linear part using Jacobian that effectively 9 capture stiff characteristics in the system. The former is integrated analytically, whereas the latter 10 is approximated. This approach i) is stable with a large Courant number (Cr > 1); ii) supports 11 high-order solutions both in time and space; iii) is computationally favorable compared to IMEX 12 DG methods with no preconditioner; iv) becomes comparable to explicit RKDG methods on uniform 13 mesh and beneficial on non-uniform grid for Euler equations; v) is scalable in a modern massively 14 parallel computing architecture due to its explicit nature of exponential time integrators and com15 pact communication stencil of DG method. Numerical results demonstrate the performance of our 16 proposed methods through various examples. We also discuss the stability and convergence analysis 17 for our exponential DG scheme in the context of Burgers equation.

42 ENGINEERING↗
DOE OSTI2021

Implicit-Explicit Multirate Infinitesimal GARK Methods

This work focuses on the development of a new class of high-order accurate methods for multirate time integration of systems of ordinary differential equations. Unlike other recent work in this area, the proposed methods support mixed implicit-explicit (IMEX) treatment of the slow time scale. In addition to allowing this slow time scale flexibility, the proposed methods utilize a so-called infinitesimal formulation for the fast time scale through definition of a sequence of modified “fast" initial-value problems that may be solved using any viable algorithm. We name the proposed class as implicit-explicit multirate infinitesimal generalized-structure additive Runge--Kutta (IMEX-MRI-GARK) methods. In addition to defining these methods, we prove that they may be viewed as specific instances of GARK methods and derive a set of order conditions on the IMEX-MRI-GARK coefficients to guarantee both third and fourth order accuracy for the overall multirate method. Additionally, we provide three specific IMEX-MRI-GARK methods, two of order three and one of order four. We conclude with numerical simulations on two multirate test problems, demonstrating the methods' predicted convergence rates and comparing their efficiency against both legacy IMEX multirate schemes and recent third and fourth order implicit MRI-GARK methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

An immersed interface method for the 2D vorticity-velocity Navier-Stokes equations with multiple bodies

We present an immersed interface method for the vorticity-velocity form of the 2D Navier Stokes equations that directly addresses challenges posed by nonconvex immersed bodies, multiply connected domains, and the calculation of force distributions on immersed surfaces. The immersed interface method is re-interpreted as a polynomial extrapolation of flow quantities and boundary conditions into the immersed solid bodies, reducing computational cost and enabling simulations with nonconvex bodies that could not be discretized with previous immersed interface methods. In the flow, the vorticity transport equation is discretized using a conservative finite difference scheme and explicit Runge-Kutta time integration. The velocity reconstruction problem is transformed to a scalar Poisson equation that is discretized with conservative finite differences, and solved using an FFT-accelerated iterative algorithm. The use of conservative differencing throughout leads to exact enforcement of a discrete Kelvin's theorem, allowing for simulations with multiply connected domains and outflow boundaries that have challenged other immersed interface vortex methods. We also explore novel methods for recovering time-dependent pressure distributions on immersed bodies within a vorticity-based method and present a novel control volume formulation for recovering aerodynamic moments from only the vorticity and velocity fields. The method achieves second order spatial accuracy and third order temporal accuracy, and is validated on a variety of 2D flows in internal and free-space domains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Photochemically Induced Acousto-optics Fluid Simulations

PIAFS is a finite-difference code to solve the compressible Navier-Stokes equations with chemical heating on Cartesian grids. It models chemical reactions of air (oxygen and carbon dioxide) with ozone subject to radiation. It uses a high-order WENO spatial discretization and explicit Runge-Kutta time integration. It is capable of parallel simulations using MPI. The code is written in C/C++.

Oudin, AlbertineN [Lawrence Livermore National Lab↗
NASA NTRS1990

Explicit-implicit staggered procedure for multibody dynamics analysis

An explicit-implicit staggered time-integration procedure is presented for the solution of multibody dynamical equations involving large rotations and constraints. The algorithms adopts a two-stage modification of the central difference algorithm for integrating the translational coordinates and the angular velocity vector, and the midpoint implicit algorithm to solve the kinematical relation in terms of the Euler parameters for updating the angular orientations. The Lagrange multipliers to enforce the system constraints are obtained by implicitly integrating a parabolically regularized differential equation for the multipliers. The performance of the present procedure has been evaluated to applying the procedure to solve several sample problems. The results indicate that the procedure is robust in dealing with a variety of constraints and spatial kinematic motions, hence it is recommended for applications to general multibody dynamics analyses.

Park, K. C.↗
NASA NTRS1989

An unconditionally stable Runge-Kutta method for unsteady rotor-stator interaction

A quasi-three-dimensional analysis has been developed for unsteady rotor-stator interaction in turbomachinery. The analysis solves the unsteady Euler or thin-layer Navier-Stokes equations in a body-fitted coordinate system. It accounts for the effects of rotation, radius change, and stress-surface thickness. The Baldwin-Lomax eddy-viscosity model is used for turbulent flows. The equations are integrated in time using an explicit four-stage Runge-Kutta scheme with a constant time step. Implicit residual smoothing is used to increase the stability limit of the time-accurate computations. The scheme is described, and stability and accuracy analyses are given.

Chima, Rodrick V.↗
NASA NTRS1993

Three-dimensional unstructured grid Euler method applied to turbine blades

Flow through a turbine annular cascade is calculated using a three-dimensional Euler method based on unstructured tetrahedral meshes. The equations are integrated in time using an explicit Runge-Kutta time-stepping scheme. The inviscid flux terms are discretized using a cell-centered finite-volume formulation with upwind flux-difference splitting. The tetrahedral meshes around the turbine blade are generated using an advancing-front technique with forced geometric periodicity between the blades. Good agreement is obtained between the present calculation and the experiment for both surface pressure distribution and flow behavior in the passage between the blades, demonstrating the capability of the present methodology for turbomachinery flow applications.

Kwon, Oh J.↗
DOE OSTI2020

Implicit fast sweeping method for hyperbolic systems of conservation laws

Implicit time-accurate methods are often used to integrate stiff problems where explicit schemes impose severe time step restrictions. This paper presents an efficient numerical framework based on the Fast Sweeping Method (FSM) for solving linear and nonlinear hyperbolic systems of conservation laws. The solution at each discrete location is computed by sweeping the numerical domain in several predetermined directions that follow the causality of the characteristic families. The use of a fractional step strategy eliminates the need for a solution selection criterion while one-sided stencils limit the number of sweeps to at most 2 d for d space dimensions. This work focuses on the first-order implicit upwind method since it constitutes the building block for high-order conservative schemes. For problems where the degree of stiffness evolves over time, implicit-explicit hybridization can be accomplished with the same algorithm by simply switching the stencil at each time level. As opposed to traditional implicit solvers, the sweeping method does not require a local time linearization of the fluxes thereby preserving the nonlinear stability properties of the original implicit scheme. It also avoids the large computational and memory requirements associated with solving large block-diagonal systems of equations. Here, a series of one- and two-dimensional test cases are presented for the inviscid Burgers' equation and the reactive Euler equations. The results indicate that the implicit FSM can allow a major reduction in the number of time steps even in the presence of discontinuous solution profiles.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

One-sweep moment-based semi-implicit-explicit integration for gray thermal radiation transport

Thermal radiation transport (TRT) is a time dependent, high dimensional partial integro-differential equation. In practical applications such as inertial confinement fusion, TRT is coupled to other physics such as hydrodynamics, plasmas, etc., and the timescales one is interested in capturing are often much slower than the radiation timescale. As a result, TRT is treated implicitly, and due to its stiffness and high dimensionality, is often a dominant computational cost in multiphysics simulations. Here we develop a new approach for implicit-explicit (IMEX) integration of gray TRT in the deterministic SN setting, which requires only one sweep per stage, with the simplest first-order method requiring only one sweep per time step. The partitioning of equations is done via a moment-based high-order low-order formulation of TRT, where the streaming operator and first two moments are used to capture the asymptotic stiff regimes of the streaming limit and diffusion limit. Absorption-reemission is treated explicitly, and although stiff, is sufficiently damped by the implicit solve that we achieve stable accurate time integration without incorporating the coupling of the high order and low order equations implicitly. Due to nonlinear coupling of the high-order and low-order equations through temperature-dependent opacities, to facilitate IMEX partitioning and higher-order methods, we use a semi-implicit integration approach amenable to nonlinear partitions. In conclusion, results are demonstrated on thick Marshak and crooked pipe benchmark problems, demonstrating orders of magnitude improvement in accuracy and wallclock compared with the standard first-order implicit integration typically used.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Implicit–explicit multirate infinitesimal stage-restart methods

Implicit–Explicit (IMEX) methods are flexible numerical time integration methods which solve an initial-value problem (IVP) that is split into stiff and nonstiff processes with the goal of lower computational costs than a purely implicit or explicit approach. A complementary form of flexible IVP solvers are multirate infinitesimal methods for problems split into fast- and slow-changing dynamics, that solve a multirate IVP by evolving a sequence of “fast” IVPs using any suitably accurate algorithm. This article introduces a new class of high-order implicit–explicit multirate methods that are designed for multirate IVPs in which the slow-changing dynamics are further split in an IMEX fashion. This new class, which we call implicit–explicit multirate infinitesimal stage-restart (IMEX-MRI-SR), both improves upon the previous implicit–explicit multirate infinitesimal generalized-structure additive Runge Kutta (IMEX-MRI-GARK) methods by allowing for far easier creation of new embedded methods, and extends multirate exponential Runge Kutta (MERK) methods by allowing the fast-changing dynamics to be nonlinear and the methods to be implicit. We leverage GARK theory to derive conditions for orders of accuracy up to four, and we provide second- and third-order accurate example methods, which are the first known embedded MRI methods with IMEX structure. We then perform numerical simulations demonstrating convergence rates and computational performance in both fixed-step and adaptive-step settings.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
NASA NTRS1991

Multigrid for hypersonic viscous two- and three-dimensional flows

The use of a multigrid method with central differencing to solve the Navier-Stokes equations for hypersonic flows is considered. The time dependent form of the equations is integrated with an explicit Runge-Kutta scheme accelerated by local time stepping and implicit residual smoothing. Variable coefficients are developed for the implicit process that removes the diffusion limit on the time step, producing significant improvement in convergence. A numerical dissipation formulation that provides good shock capturing capability for hypersonic flows is presented. This formulation is shown to be a crucial aspect of the multigrid method. Solutions are given for two-dimensional viscous flow over a NACA 0012 airfoil and three-dimensional flow over a blunt biconic.

Turkel, E.↗