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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

ZND Verification Tests for Reactive Burn Models in FLAG

The ZND theory, named after Zeldovich, von Neumann, and Doering, provides a simple model for one-dimensional ideal steady-state detonation. It assumes that the detonation wave front starts with a shock that is a discontinuous jump and is followed by a finite-length reaction zone. Reactive burn (also called reactive flow) models are based on ZND theory, as they model the shock initiation and detonation process with a finite reaction rate. The ZND wave propagation test is essentially the only available test case where an analytic solution exists for verification of reactive burn models in numerical codes. However, there are extensions and variants of the ZND test that have been devised for verification of multidimensional flows. The objective of this work is to provide verification of the reactive burn models currently implemented in the Lagrangian hydrocode FLAG and investigate the influence of mesh resolution, artificial viscosity models, and the Arbitrary Lagrangian-Eulerian (ALE) Euler relaxer on the simulation results. The burn models of interest are the Wescott-Stewart-Davis (WSD) model, the Scaled Uniform Reactive Flow (SURF) model (specifically with the SURFplus model extension), and the Arrhenius shock temperature state dependent WSD (AWSD) model. Previously, Ralph Menikoff has used ZND tests for verification of the SURF and SURFplus models in the Eulerian hydrocode xRAGE. The ZND tests here are somewhat different than the approach by Menikoff. In particular, we use a piston-driven ZND detonation wave (via a prescribed constant velocity boundary condition) in a Lagrangian framework whereas Menikoff had a ZND wave followed by a invariant rarefaction wave. The xRAGE simulations were carried out on uniform grids and adaptive mesh refinement (AMR) grids. Although AMR was recently implemented in FLAG and now fully functional for 2D simulations, it will not be evaluated with ZND tests at this time. Some work has been done previously for validating the reactive burn models in FLAG. For example, the validation studies of SURF with shock-to-detonation (SDT) tests, cylinder tests, and gap-stick tests. Further validation of the AWSD, WSD, and SURF models is described in for SDT, multi-shock, cylinder, and corner-turning tests. Recently, a large parameter study with approximately twenty SDT tests was performed to validate the AWSD, WSD, SURF, and SURFplus models while also investigating mesh resolution and artificial viscosity settings. To the best of our knowledge, the current work represents the first documented verification of these burn models in FLAG. The reader should note that many of the tables and figures in this report use units of cm/g/µs, which are the default units for FLAG. However, some lengths and velocities are expressed in µm and mm/µs, respectively, which are typical units for detonation analyses.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2025

Multi-material ALE remap with interface sharpening using high-order matrix-free finite element methods

The arbitrary Lagrangian-Eulerian (ALE) technique involves remapping field quantities from a Lagrangian mesh to an optimized mesh in a conservative, accurate and bounds-preserving manner. For methods based on arbitrary order finite elements, as described in a reference, material volume fractions are advected in pseudo-time using flux-corrected transport (FCT) without any form of interface reconstruction. In practice, this can lead to excessive propagation of small volume fractions throughout the domain. In addition, this method requires assembly of a global advection matrix to compute the bounds-preserving low-order FCT solution. In this work, we introduce a new approach for ALE remap using a high-order matrix-free technique which incorporates a flux modification to sharpen material interfaces in a conservative manner. Our approach begins with computing a bounds-preserving low-order solution to the ALE remap equations at the element level. We then compute a sharp interface solution (not guaranteed to be bounds-preserving) which comes from solving an augmented version of the ALE remap equations with a conservative flux modification which acts to sharpen material volume fractions based on their gradients and transport directions. Using the sharp interface solution, we make global corrections to the bounds-preserving solution while maintaining preservation of bounds. By blending with the sharpened solution at the global level we are able to globally conserve mass without hindering the remap pseudo-time step. This new interface-aware ALE remap method is based entirely on partial assembly techniques where globally assembled matrix operators are no longer needed, resulting in a globally matrix-free FCT method for multi-material, multi-field ALE remap with high performance on GPU architectures. We present results of our new remap method on 1D, 2D and 3D benchmarks and describe the algorithmic tailoring for GPU architectures that was developed.

Vargas, Arturo [Lawrence Livermore National Labora↗
DOE OSTI2021

DRACO: An Overview [Slides]

DRACO (Diffusion ReACtiOn) is a diffusion and chemistry code designed to: 1) Operate on 3D with an unstructured grid defining an arbitrary geometry of interacting parts. 2) Generate its own meshes and use meshes created by other software. 3)Model the transport of any number of diffusing quantities: Concentrations, pressures, temperature, etc. 4) Allow diffusion coefficients to depend in an arbitrary way on concentration, temperature, position, time, etc. 5) Model general chemistry between concentrations with arbitrary reaction rates. 6) Allow arbitrary initial conditions, boundary conditions, and sources/sinks. 7) Allow all of the above to be specified by the user.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

High-Order Mesh r-Adaptivity with Tangential Relaxation and Guaranteed Mesh Validity

High-order meshes are crucial for achieving optimal convergence rates in curvilinear domains, preserving symmetry, and aligning with key flow features in moving mesh simulations [1], but their quality is challenging to control. In prior work, we have developed techniques based on Target-Matrix Optimization Paradigm (TMOP) to adapt a given high-order mesh to the geometry and solution of the partial differential equation (PDE) [2, 3]. Here, we extend this framework to address two key gaps in the literature for highorder mesh 𝑟-adaptivity. First, we introduce tangential relaxation on curved surfaces using solely the discrete mesh representation, eliminating the need for access to underlying geometry (e.g., CAD model). Second, we ensure a continuously positive Jacobian determinant throughout the domain. This determinant positivity is essential for using the high-order mesh resulting from 𝑟-adaptivity with arbitrary quadrature schemes in simulations. The proposed approach is demonstrated to be robust using a variety of numerical experiments.

Mathematics and Computing↗
NASA NTRS1979

A fast, conservative algorithm for solving the transonic full-potential equation

A fast, fully implicit approximate factorization (AF) algorithm designed to solve the conservative transonic full-potential equation in either two or three dimensions is described. The algorithm uses an upwind bias of the density coefficient for stability in supersonic regions. This provides an effective upwind difference of the streamwise terms for any orientation of the velocity vector (i.e., 'rotated differencing'), and thereby greatly enhances the reliability of the present algorithm. A numerical transformation is used to establish an arbitrary body-fitted finite-difference mesh. Computed results for both airfoils and simplified wings demonstrate substantial improvement in convergence speed for the new algorithm relative to standard successive-line overrelaxation algorithms.

Holst, T. L.↗
NASA NTRS1992

A finite element formulation for scattering from electrically large 2-dimensional structures

A finite element formulation is given using the scattered field approach with a fictitious material absorber to truncate the mesh. The formulation includes the use of arbitrary approximation functions so that more accurate results can be achieved without any modification to the software. Additionally, non-polynomial approximation functions can be used, including complex approximation functions. The banded system that results is solved with an efficient sparse/banded iterative scheme and as a consequence, large structures can be analyzed. Results are given for simple cases to verify the formulation and also for large, complex geometries.

Ross, Daniel C.↗
NASA NTRS1980

Fast, Conservative Algorithm for Solving the Transonic Full-Potential Equation

A fast, fully implicit approximate factorization algorithm designed to solve the conservative, transonic, full-potential equation in either two or three dimensions is described. The algorithm uses an upwind bias of the density coefficient for stability in supersonic regions. This provides an effective upwind difference of the streamwise terms for any orientation of the velocity vector (i.e., rotated differencing), thereby greatly enhancing the reliability of the present algorithm. A numerical transformation is used to establish an arbitrary body-fitted, finite-difference mesh. Computed results for both airfoils and simplified wings demonstrate substantial improvement in convergence speed for the new algorithm relative to standard successive-line over-relaxation algorithms.

Holst, Terry L.↗
NASA NTRS1993

Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics

Most of the recently proposed computational methods for solving partial differential equations on multiprocessor architectures stem from the 'divide and conquer' paradigm and involve some form of domain decomposition. For those methods which also require grids of points or patches of elements, it is often necessary to explicitly partition the underlying mesh, especially when working with local memory parallel processors. In this paper, a family of cost-effective algorithms for the automatic partitioning of arbitrary two- and three-dimensional finite element and finite difference meshes is presented and discussed in view of a domain decomposed solution procedure and parallel processing. The influence of the algorithmic aspects of a solution method (implicit/explicit computations), and the architectural specifics of a multiprocessor (SIMD/MIMD, startup/transmission time), on the design of a mesh partitioning algorithm are discussed. The impact of the partitioning strategy on load balancing, operation count, operator conditioning, rate of convergence and processor mapping is also addressed. Finally, the proposed mesh decomposition algorithms are demonstrated with realistic examples of finite element, finite volume, and finite difference meshes associated with the parallel solution of solid and fluid mechanics problems on the iPSC/2 and iPSC/860 multiprocessors.

Farhat, Charbel↗
NASA NTRS1996

Preconditioning Operators on Unstructured Grids

We consider systems of mesh equations that approximate elliptic boundary value problems on arbitrary (unstructured) quasi-uniform triangulations and propose a method for constructing optimal preconditioning operators. The method is based upon two approaches: (1) the fictitious space method, i.e., the reduction of the original problem to a problem in an auxiliary (fictitious) space, and (2) the multilevel decomposition method, i.e., the construction of preconditioners by decomposing functions on hierarchical meshes. The convergence rate of the corresponding iterative process with the preconditioner obtained is independent of the mesh step. The preconditioner has an optimal computational cost: the number of arithmetic operations required for its implementation is proportional to the number of unknowns in the problem. The construction of the preconditioning operators for three dimensional problems can be done in the same way.

Nepomnyaschikh, S. V.↗
NASA NTRS1983

TAS: A Transonic Aircraft/Store flow field prediction code

A numerical procedure has been developed that has the capability to predict the transonic flow field around an aircraft with an arbitrarily located, separated store. The TAS code, the product of a joint General Dynamics/NASA ARC/AFWAL research and development program, will serve as the basis for a comprehensive predictive method for aircraft with arbitrary store loadings. This report described the numerical procedures employed to simulate the flow field around a configuration of this type. The validity of TAS code predictions is established by comparison with existing experimental data. In addition, future areas of development of the code are outlined. A brief description of code utilization is also given in the Appendix. The aircraft/store configuration is simulated using a mesh embedding approach. The computational domain is discretized by three meshes: (1) a planform-oriented wing/body fine mesh, (2) a cylindrical store mesh, and (3) a global Cartesian crude mesh. This embedded mesh scheme enables simulation of stores with fins of arbitrary angular orientation.

Thompson, D. S.↗
DOE OSTI2022

Agglomeration-based geometric multigrid solvers for compact discontinuous Galerkin discretizations on unstructured meshes

Here, we present a geometric multigrid solver for the Compact Discontinuous Galerkin method through building a hierarchy of coarser meshes using a simple agglomeration method which handles arbitrary element shapes and dimensions. The method is easily extendable to other discontinuous Galerkin discretizations, including the Local DG method and the Interior Penalty method. We demonstrate excellent solver performance for Poisson's equation, provided a flux formulation is used for the operator coarsening and a suitable switch function chosen for the numerical fluxes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Modeling the Interaction of Laser-Produced Proton Beams with Matter

A major goal of this project is to significantly increase our understanding of isochoric heating of matter using laser produced proton beams, and the associated high energy density (HED) and warm dense matter (WDM) regimes generated. This will benefit research fields such as planetary science, fusion energy, plasma physics, and material science. For example, it will enhance our understanding of WDM properties of iron and silica under conditions encountered in planetary interiors and diagnostic components in fusion devices exposed to high fluxes of energetic plasma ions. The project is motivated by recent experiments that irradiated Si targets with proton beams generated by the 20 TW-laser at the SLAC MEC end-station. The HED/WDM states are probed using the 50 fs hard X-rays available in the 3rd harmonic of the LCLS. As part of this project, results from the phase contrast X-ray imaging, which shows the generation of compression waves that produces rear surface spallation, are compared with results from the 3D multi-physics multi- material code, PISALE, that combines Arbitrary Lagrangian-Eulerian (ALE) hydrodynamics with Adaptive Mesh Refinement (AMR). This comparison required modifications to several physics models in the PISALE (Pacific Island Structured-AMR with ALE) code. An important aspect of this project is the continued training of graduate students in HED physics and in conducting complex multiphysics simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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↗
NASA NTRS1985

Adaptive mesh solution for supersonic conical flow in a rectilinear inlet

Solutions for the inviscid and viscous supersonic conical flow in a complete rectilinear inlet consisting of four planes intersecting at arbitrary wedge and sweep angles are obtained. To compute the flow on a specially constructed mesh, a three-dimensional flow solver ARC3D is used. It is shown that a single-pass mesh re-adaptation procedure can be used to obtain improved shock capture without the necessity of modifying the flow code, provided that the flow solver works in curvilinear coordinates and is restartable. Results computed by the method show good agreement with experimental measurements and previous calculations.

Kerlick, G. D.↗
NASA NTRS1980

Boundary-fitted coordinate systems for arbitrary computational regions

The method of Smith and Wiegel was used to generate meshes for mixer lobes and subsonic inlets that are compatible with flow analysis codes requiring a boundary fitted coordinate system. Successful application of this mesh generator required development of procedures to distribute the mesh points along the boundaries, to regulate the dependence of the connecting function to the local boundary slope, to concentrate the mesh into regions of special interest, and to modify the mesh grid so that it possessed a smooth progression of cell metrics and cell volumes in all directions. The method of Smith and Wiegel when coupled with the extensions mentioned above has proven to be easy to use and control for the inlet and mixer lobe geometries investigated.

Kowalski, E. J.↗
NASA NTRS1988

Adaptive mesh generation for viscous flows using Delaunay triangulation

A method for generating an unstructured triangular mesh in two dimensions, suitable for computing high Reynolds number flows over arbitrary configurations is presented. The method is based on a Delaunay triangulation, which is performed in a locally stretched space, in order to obtain very high aspect ratio triangles in the boundary layer and the wake regions. It is shown how the method can be coupled with an unstructured Navier-Stokes solver to produce a solution adaptive mesh generation procedure for viscous flows.

Mavriplis, Dimitri J.↗
NASA NTRS1988

Adaptive mesh generation for viscous flows using Delaunay triangulation

A method for generating an unstructured triangular mesh in two dimensions, suitable for computing high Reynolds number flows over arbitrary configurations is presented. The method is based on a Delaunay triangulation, which is performed in a locally stretched space, in order to obtain very high aspect ratio triangles in the boundary layer and the wake regions. It is shown how the method can be coupled with an unstructured Navier-Stokes solver to produce a solution adaptive mesh generation procedure for viscous flows.

Mavriplis, Dimitri J.↗
NASA NTRS1990

Adaptive mesh generation for viscous flows using Delaunay triangulation

A method for generating an unstructured triangular mesh in two dimensions, suitable for computing high Reynolds number flows over arbitrary configurations is presented. The method is based on a Delaunay triangulation, which is performed in a locally stretched space, in order to obtain very high aspect ratio triangles in the boundary layer and the wake regions. It is shown how the method can be coupled with an unstructured Navier-Stokes solver to produce a solution adaptive mesh generation procedure for viscous flows.

Mavriplis, Dimitri J.↗