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All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

The Delta x B = 0 Constraint Versus Minimization of Numerical Errors in MHD Simulations

The MHD equations are a system of non-strictly hyperbolic conservation laws. The non-convexity of the inviscid flux vector resulted in corresponding Jacobian matrices with undesirable properties. It has previously been shown by Powell et al. (1995) that an 'almost' equivalent MHD system in non-conservative form can be derived. This non-conservative system has a better conditioned eigensystem. Aside from Powell et al., the MHD equations can be derived from basic principles in either conservative or non-conservative form. The Delta x B = 0 constraint of the MHD equations is only an initial condition constraint, it is very different from the incompressible Navier-Stokes equations in which the divergence condition is needed to close the system (i.e., to have the same number of equations and the same number of unknown). In the MHD formulations, if Delta x B = 0 initially, all one needs is to construct appropriate numerical schemes that preserve this constraint at later time evolutions. In other words, one does not need the Delta x B condition to close the MHD system. We formulate our new scheme together with the Cargo & Gallice (1997) form of the MHD approximate Riemann solver in curvilinear grids for both versions of the MHD equations. A novel feature of our new method is that the well-conditioned eigen-decomposition of the non-conservative MHD equations is used to solve the conservative equations. This new feature of the method provides well-conditioned eigenvectors for the conservative formulation, so that correct wave speeds for discontinuities are assured. The justification for using the non-conservative eigen-decomposition to solve the conservative equations is that our scheme has a better control of the numerical error associated with the divergence of the magnetic condition. Consequently, computing both forms of the equations with the same eigen-decomposition is almost equivalent. It will be shown that this approach, using the non-conservative eigensystem when solving the conservative equations, also works well in the context of standard shock-capturing schemes.

Yee, H. C.↗
NASA NTRS2002

The Delta(dot) B = O Constraint vs. Minimization of Numerical Errors in MHD Simulations

The MHD equations are a system of non-strictly hyperbolic conservation laws. The non-convexity of the inviscid flux vector resulted in corresponding Jacobian matrices with undesirable properties. On the other hand, the MHD equations can be derived from basic principles in either conservative or non-conservative form. The non-conservative system has a better conditioned eigensystem. The Delta(dot)B = 0 constraint of the A4HD equations is only an initial condition constraint. One does not need the Delta(dot)B condition to close the MHD system. We formulate our new low dissipative high order scheme together with the Cargo & Gallice (1997) form of the MHD approximate Riemann solver in curvilinear grids for both versions of the MHD equations. A novel feature of our new method is that the well-conditioned eigen-decomposition of the non-conservative MHD equations is used to solve the conservative equations. This new feature of the method provides well-conditioned eigenvectors for the conservative formulation, so that correct wave speeds for discontinuities are assured. The justification for using the non-conservative eigen-decomposition to solve the conservative equations is that our scheme has a better control of the numerical error associated with the Delta(dot)B condition. Consequently, computing both forms of the equations with the same eigen-decomposition is almost equivalent. It will be shown that this approach, using the non-conservative eigensystem when solving the conservative equations, also works well in the context of standard shock-capturing schemes.

Yee, H. C.↗
NASA NTRSDate not supplied

A Moving Discontinuous Galerkin Method with Interface Condition Enforcement for Reacting Hypersonic Flows

The necessity of enforcing conservation in computational elements or cells (element conservation) for discontinuous solutions is well understood and respected for solving conservation laws in computational fluid dynamics (CFD). In contrast, interface conservation, where the conservation across cell interfaces is enforced, is long ignored, and yet is also ruled and required by the underlying physics just like element conservation. Violation of the interface conservation across discontinuities is the root cause why an exact discontinuous solution can never be achieved in shock capturing methods. The interface conservation is examined and explored in this talk. Moving discontinuous Galerkin (MDG) finite element method with interface conservation enforcement (MDG-ICE) [1],[2] are then presented for solving compressible flow problems with discontinuities based on the observation that the interface conservation can only be satisfied, only when mesh interfaces are aligned with discontinuities. In the MDG-ICE formulation, both conservative quantities and grid geometry are considered as independent variables. A space-time DG formulation is used to solve the multi-material compressible Euler equations in the standard discontinuous solution space and the discrete grid geometry is solved using a variational formulation in a continuous space. A self-adaptive Levenberg-Marquardt method is utilized to solve the resulting over-determined system of nonlinear equations arising from the MDG-ICE formulation. A number of numerical experiments for a variety of flow problems are conducted to assess the accuracy and performance of the MDG-ICE method. Numerical results obtained indicate that the MDG-ICE method is able to deliver the designed order of both h- and p-convergence even for discontinuous solutions, and detect all types of interfaces, via interface condition enforcement and satisfy, via grid movement, the compressible Euler equations and the associated interface condition.

Discontinuous Galekin↗
DOE OSTI2026

Axisymmetric hydrodynamics in numerical relativity: treating coordinate singularity, artificial heating and modeling MHD instabilities

Two-dimensional axisymmetric simulations of binary neutron star (BNS) merger remnant are a cheap alternative to 3D simulations. To maintain realism for secular timescales, simulations must avoid accumulated errors from drifts in conserved quantities and artificial heating, and they must model turbulent transport in a way that remains plausible throughout the evolution. It is also crucial to avoid numerical artifacts due to the polar coordinate axis singularity. Methods that behave well near the axis often break flux-conservative form of the hydrodynamic equations, resulting in significant drifts in conserved quantities. We present a flux-conservative scheme that maintains smoothness near the axis without sacrificing conservative formulation of the equations or incurring drifts in conserved global quantities. We compare the numerical performance of different treatments of the hydrodynamic equations when evolving a hypermassive neutron star resembling the remnant of a BNS merger. These simulations demonstrate that the new scheme combines the axis smoothness of non-conservative methods with the mass and angular momentum conservation of other conservative methods on $\sim 10^2$ ms timescales of viscous and neutrino-driven evolution. Because fluid profiles remain smooth in the remnant interior, it is possible to remove artificial heating by evolving the entropy density. We show how physical heating and cooling terms can be easily calculated from source terms of the conservative evolution variables and demonstrate our implementation. Finally, we discuss and implement improvements to the effective viscosity scheme to better model the effect of magnetohydrodynamic instabilities as the remnant evolves.

axisymmetry↗
DOE OSTI2020

Intersection-distribution-based remapping between arbitrary meshes for staggered multi-material arbitrary Lagrangian-Eulerian hydrodynamics

In this paper, we present a new intersection-distribution-based remapping method between arbitrary polygonal meshes for indirect staggered multi-material arbitrary Lagrangian-Eulerian hydrodynamics. All cell-centered material quantities are conservatively remapped using intersections between the Lagrangian (old, source) mesh and the rezoned (new, target) mesh. The new nodal masses are obtained by conservative distribution of all material masses in each new cell to the cell's corners and then collecting those corner masses at new nodes. This distribution is done using a local constrained optimization approach for each cell in the new mesh. In order to remap nodal momentum we first define cell-centered momentum for each cell in the old mesh, conservatively remap this to the new mesh and then conservatively distribute the new zonal momentum to each cell's bounding nodes, again using local constrained optimization. Our method also conserves total energy by applying a new nodal kinetic energy correction that relies on a process similar to that used for remapping nodal mass and momentum. Cell-centered kinetic energy is computed, conservatively remapped and then distributed to nodes. The discrepancy between this conservatively remapped and actual nodal kinetic energy is then conservatively distributed to the internal energies of the materials in the cells surrounding each node. Unlike conventional cell-based corrections of this type, this new nodal kinetic energy correction has not been observed to drive material internal energy negative in any of our testing. Unlike flux based remapping, our new intersection-distribution method can be applied to remapping between source and target meshes that are arbitrarily different, which provides superior flexibility in the rezoning strategy. Our method is accurate, essentially conservative and essentially bounds preserving.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Contrasting modes of macro and microsynteny evolution in a eukaryotic subphylum

Examination of the changes in order and arrangement of homologous genes is key for understanding the mechanisms of genome evolution in eukaryotes. Previous comparisons between eukaryotic genomes have revealed considerable conservation across species that diverged hundreds of millions of years ago (e.g., vertebrates, bilaterian animals, and filamentous fungi). However, understanding how genome organization evolves within and between eukaryotic major lineages remains underexplored. We analyzed high-quality genomes of 120 representative budding yeast species (subphylum Saccharomycotina) spanning ~400 million years of eukaryotic evolution to examine how their genome organization evolved and to compare it with the evolution of animal and plant genome organization. We, in this study, found that the decay of both macrosynteny (the conservation of homologous chromosomes) and microsynteny (the conservation of local gene content and order) was strongly associated with evolutionary divergence across budding yeast major clades. However, although macrosynteny decayed very fast, within ~100 million years, the microsynteny of many genes—especially genes in metabolic clusters (e.g., in the GAL gene cluster)—was much more deeply conserved both within major clades and across the subphylum. We further found that when genomes with similar evolutionary divergence times were compared, budding yeasts had lower macrosynteny conservation than animals and filamentous fungi but higher conservation than angiosperms. In contrast, budding yeasts had levels of microsynteny conservation on par with mammals, whereas angiosperms exhibited very low conservation. Our results provide new insight into the tempo and mode of the evolution of gene and genome organization across an entire eukaryotic subphylum.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

A Perturbative Solution for Nonlinear Stratified Upwelling over a Frictional Slope

Abstract A perturbative solution of simplified primitive equations for nonlinear weakly stratified upwelling over a frictional slope is found that resolves the vertical structure of velocity fields and can satisfy Ertel’s potential vorticity conservation in the stratified inviscid interior. The solution uses assumptions consistent with the model proposed by Lentz and Chapman, including a steady-state, constant cross-shore density gradient, no alongshore gradients, laterally inviscid, and consideration of cross-shore advection of alongshore momentum. The solution resolves the vertical structure of velocity fields (including subsurface maxima of compensational flow, not resolved by Lentz and Chapman) and can satisfy Ertel’s potential vorticity conservation in the stratified inviscid interior. The dynamics are similar to Lentz and Chapman; bottom stress balances alongshore wind stress in a homogeneous density ocean and is replaced by nonlinear cross-shore transport of alongshore momentum as the Burger number (S=αN/f, whereα,N, andfare the bottom slope, buoyancy frequency, Coriolis frequency, respectively) increases. When the solution uses the empirical relation between cross-shore and vertical density gradients proposed by Lentz and Chapman, vorticity conservation is not satisfied and the nonlinear momentum transport estimated by the solution linearly increases withS, asymptotically matching Lentz and Chapman forS< 1. When the solution conserves interior potential vorticity, the momentum transport is proportional toS 2 forS< 1 and is in better agreement with numerical simulations.

Oceanography↗
DOE OSTI2026

Rethinking the soil core microbiome

The concept of a core microbiome emerged from host-associated research to describe microbial members or functions conserved across clearly defined spatial, temporal, and biological boundaries. In soil- and plant-associated microbiome research, however, the term has increasingly shifted toward analytically defined subsets selected using study-specific thresholds or criteria. Synthesizing recent literature and cross-site analyses of bioenergy crop field soils, we show that the original biological meaning of the core microbiome has been blurred by dataset-specific analytical criteria. Taxa designated as ‘core’ were highly sensitive to methodological choices and often reflected explanatory value rather than conserved biological membership. Moreover, many studies that identify taxonomic ‘core’ members interpret their significance in functional terms, suggesting that functional conservation may be the biological interest. Taxonomic conservation may not be the most biologically meaningful target in highly heterogeneous soil and rhizosphere systems, where functional conservation may persist despite taxonomic turnover. Accordingly, ‘core microbiome’ should be reserved for microbial components explicitly demonstrated to be conserved across defined spatial, temporal, and environmental dimensions and linked to conserved ecological functions, while taxa selected for explanatory value are better described as ‘explanatory subsets of taxa’. Greater terminological precision will improve cross-study comparability and strengthen ecological inference in plant–soil microbiome research.

bioenergy crops↗
DOE OSTI2023

Virtual Time III, Part 1: Unified Virtual Time Synchronization for Parallel Discrete Event Simulation

Algorithms for synchronization of parallel discrete event simulation have historically been divided between conservative methods that require lookahead but not rollback, and optimistic methods that require rollback but not lookahead. In this paper we present a new approach in the form of a framework called Unified Virtual Time (UVT) that unifies the two approaches, combining the advantages of both within a single synchronization theory. Whenever timely lookahead information is available, a logical process (LP) executes conservatively using an irreversible event handler. When lookahead information is not available the LP does not block, as it would in a classical conservative execution, but instead executes optimistically using a reversible event handler. The switch from conservative to optimistic synchronization and back is decided on an event-by-event basis by the simulator, transparently to the model code. UVT treats conservative synchronization algorithms as optional accelerators for an underlying optimistic synchronization algorithm, enabling the speed of conservative execution whenever it is applicable, but otherwise falling back on the generality of optimistic execution. We describe UVT in a novel way, based on fundamental invariants, monotonicity requirements, and synchronization rules. UVT permits zero-delay messages and pays careful attention to tie-handling using superposition. We prove that under fairly general conditions a UVT simulation always makes progress in virtual time. This is Part 1 of a trio of papers describing the UVT framework for PDES, mixing conservative and optimistic synchronization and integrating throttling control.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

A New Approach for a Wider Class of Entropy Split Methods for Compressible Gas Dynamics and MHD

The high order entropy split methods of Sjögreen & Yee [1, 2] by entropy splitting of the compressible Euler (inviscid) flux derivatives for a thermally-perfect gas are based on Harten’s entropy function [3, 4, 5]. Their derivation takes advantage of the homogeneity property of Euler flux, symmetrizable Euler flux derivatives and energy-norm stability in conjunction with high order classical spatial central, DRP (dispersion relation-preserving) [6, 7, 8] or Padé (compact) spatial discretizations [9] with summation-by-parts (SBP) operators [10]. Our entropy split methods have been proven entropy conserving and stable [1, 11, 12]. Our proofs do not rely on a two-point numerical flux, but rather only a linear difference operator is required to derive these methods. To extend the entropy split method for the MHD, we used the Godunov symmetrizable non-conservative MHD form [12, 13, 14]. These high order entropy split methods not only preserve certain physical properties of the chosen governing equations but are also known to either improve numerical stability, and/or minimize aliasing errors in long time integration of turbulent flow computations without the aid of added numerical dissipation. In our previous published work, extensive error norm comparison with grid refinement was performed to show the high accuracy performance of these methods. These studies also showed how well the entropy split methods conserve the entropy, momentum and mass, and preserve the kinetic energy for long time integration of the various flows [1, 2, 12, 13, 14]. The objective of the present work is to use a new approach to obtain a wider class of entropy split methods consisting of a two-point numerical flux portion and a non-conservative portion in such a way that the homogeneity property of the compressible Euler flux is not required. For high order classical spatial central, DRP (dispersion relation-preserving) or Padé (compact) spatial discretizations, this new approach can be proven to be entropy conservative with conservative spatial dsicretizations while at the same time allowing a wider class of symmetrizable inviscid flux derivatives. We also use this generalization to derive an entropy split scheme that is entropy conserving for the equations of MHD without the homogeneity property using the Godunov symmetrizable ideal MHD formulation [15].

High Order Physical Preserving Methods↗
DOE OSTI2023

Assessment of Potential Dose and Environmental Impacts from Proposed Testing at the INL National Security Test Range

This assessment uses screening-level models to calculate potential environmental impacts from proposed tests at two locations at the Idaho National Laboratory (INL) National Security Test Range (NSTR) site. Proposed tests could be conducted using 11 different radioactive material types that include K 2 O, LaBr 3 , KBr, Cu, Zr, F, Ga, Ga 2 O 3 , NaNO 2 , Ga-68, and Tc-99m. The tests could potentially release radioactive material to the atmosphere and radionuclides and other contaminants to the soil, which could leach into the unsaturated zone and migrate to the aquifer. Atmospheric transport of radionuclides to potential human receptors and time-integrated air concentrations were calculated with a Gaussian plume model and three years of hourly meteorological data. Potential surface-soil impacts were calculated with the computer program mixing-cell model (MCM). Groundwater impacts were calculated with the computer programs MCM and GWSCREEN. Radiological doses from potential atmospheric releases were calculated for public receptors off the INL Site and for workers at nearby INL facilities. Results were compared to regulatory dose limits. Maximum potential groundwater concentrations were estimated in the aquifer below the NSTR site and compared to drinking water standards or risk-based screening levels for resident tap water. Soil concentrations were calculated and compared to risk-based screening levels for workers and potential future residents. All impacts were estimated based on the assumption that 12 tests are conducted annually using all 11 material types for 15 years. This document provides the resources to enable a subject matter expert in the field of environmental assessments to replicate the modeling and calculations. The methodology and parameters are presented in the text. All electronic files, including computer-code input, output, executable files, batch files, scripts, and spreadsheet files, are contained in a zip file that can be accessed by selecting “Additional Information” (select Native File) in the INL Electronic Document Management System (EDMS). It is highly unlikely the test scenarios evaluated in this ECAR will adversely impact human health based on comparisons of calculated dose and concentration against regulatory standards and risk-based screening levels. Conservative estimates of dose to workers and the public from atmospheric transport of possible radionuclide releases are far below federal radiation protection standards. Conservative estimates of potential contaminant concentrations in groundwater are less than federal drinking water standards or screening levels. Predicted radionuclide concentrations in surface soils are below risk-based screening levels, except for Ge-68 (material Ga-68) for the worker. The Ge-68 soil concentration can be made less than the worker PRG, if the number of annual tests using Ga-68 is reduced from 12 to 6. However, the sum of ratios still exceeds one because of the high K-40 ratio. If the EF of the worker (number of days the worker is in the contaminated testing area) is reduced from 225 days/yr (default value for full time worker) to 112 days/yr, the Ge-68 ratio is less than one and the sum of ratios is less than one. Actual radiation doses and groundwater and surface-soil concentrations are likely to be much less than those calculated because of the conservative assumptions and parameters employed in the modeling. For example, atmospheric-transport calculations assume the entire inventory of each material type is readily released to the atmosphere and no plume deposition, depletion, or radioactive decay occurs during transport. The calculations also assume the same meteorological conditions (e.g., wind velocity, wind direction, stability class) that produce the maximum 95th percentile concentration (i.e., concentration representing the 95th percentile of a distribution of concentrations derived from 3 years of hourly meteorological data) at each receptor location are the same for all 12 tests during the year, and each receptor is assumed to be present during all 12 tests. The surface-soil assessment assumes the entire inventory of each test is deposited in the top 5 cm of soil. No atmospheric dispersal is assumed, and the radionuclides are subject only to leaching and radioactive decay. The groundwater-pathway modeling is conservative in that it is one-dimensional in the unsaturated zone (no lateral spreading/dilution) and assumes the entire inventory of contaminants infiltrates into the ground at the same location for every test. This is especially conservative for particulate radionuclides because they would have to dissolve or corrode first and some would be dispersed into the atmosphere. The groundwater receptor is also assumed to consume water directly from a hypothetical well positioned in the location of maximum concentration. In addition, conservative degradation rates were used, and volatilization was not considered for the nonradradioactive chemicals modeled. And finally, the calculations assume all 12 tests will be performed at the same place at both locations, and all 11 radioactive material types will be used for each test. This is conservative because it is anticipated that no more than two material types will be used per test.

99 GENERAL AND MISCELLANEOUS↗
NASA NTRS1991

Choice of velocity variables for complex flow computation

The issue of adopting the velocity components as dependent velocity variables for the Navier-Stokes flow computations is investigated. The viewpoint advocated is that a numerical algorithm should preferably honor both the physical conservation law in differential form and the geometric conservation law in discrete form. With the use of Cartesian velocity vector, the momentum equations in curvilinear coordinates can retain the full conservation-law form and satisfy the physical conservation laws. With the curvilinear velocity components, source terms appear in differential equations and hence the full conservation law form can not be retained. In discrete expressions, algorithms based on the Cartesian components can satisfy the geometric conservation-law form for convection terms but not for viscous terms; those based on the curvilinear components, on the other hand, cannot satisfy the geometric conservation-law form for either convection or viscous terms. Several flow solutions for domain with 90 and 360 degree turnings are presented to illustrate the issues of using the Cartesian velocity components and the staggered grid arrangement.

Shyy, W.↗