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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 289 records · Page 16

AWP: NASA's Aerosol Wind Profiler Coherent Doppler Wind Lidar

A new airborne coherent Doppler Wind Lidar (DWL) instrument has been implemented leveraging NASA's development of the 2-micron Wind-Space Pathfinder (Wind-SP) lidar transceiver. A technology development project, Wind-SP refined and demonstrated numerous components required for a coherent-detection space wind lidar instrument. Aerosol Wind Profiler (AWP) transitioned this transceiver into an airborne wind lidar capable of providing full 3-D wind vector retrievals. AWP operates with laser pulse energy and repetition rate combination required for high spatial and vertical resolution wind profiling from space. Operation from aircraft platforms will yield very strong signal return required for detailed process studies at <2km spatial and <100m vertical resolution under most conditions. AWP will serve as NASA’s wind calibration and validation instrument for future space-based wind observations over the coming decades, while also providing data supporting space wind lidar simulation studies. The AWP instrument is introduced and preliminary results from recent AWP demonstration flights are presented.

AWP↗

Three-dimensional checkerboard spin structure on a breathing pyrochlore lattice

The standard approach to realize a spin-liquid state is through magnetically frustrated states, relying on ingredients such as the lattice geometry, dimensionality, and magnetic interaction type of the spins. While Heisenberg spins on a pyrochlore lattice with only antiferromagnetic nearest-neighbor interactions are theoretically proven disordered, spins in real systems generally include longer-range interactions. The spatial correlations at longer distances typically stabilize a long-range order rather than enhancing a spin-liquid state. Both states can, however, be destroyed by short-range static correlations introduced by chemical disorder. Here, using disorder-free specimens with a clear long-range antiferromagnetic order, we refine the spin structure of the Heisenberg spinel ZnFe 2 O 4 through neutron magnetic diffraction. The unique wave vector (1, 0, $\frac{1}{2}$) leads to a spin structure that can be viewed as alternatively stacked ferromagnetic and antiferromagnetic tetrahedra in a three-dimensional checkerboard form. Stable coexistence of these opposing types of clusters is enabled by the bipartite breathing pyrochlore crystal structure, leading to a second-order phase transition at 10 K. The diffraction intensity of ZnFe 2 O 4 is an exact complement to the inelastic scattering intensity of several chromate spinel systems which are regarded as model classical spin liquids. Our results challenge this attribution, and suggest instead of the six-spin ring mode, spin excitations in chromate spinels are closely related to the (1, 0, $\frac{1}{2}$) type of spin order and the four-spin ferromagnetic cluster locally at one tetrahedron.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Convection-permitting hindcasting of diurnal variation of Mei-yu rainfall over East China with a global variable-resolution model

Two sets of 48-hr hindcast experiments for Mei-yu season using non-hydrostatic global variable-resolution model (MPAS-Atmosphere) with regional refinement at 4km resolution (V4km) and uniform 60km resolution (U60km) are first-time conducted to attempt at simulating the Mei-yu rainfall in 2015 over East China. The analysis focuses on the seasonal average of diurnal variation of precipitation amount (PA), intensity (PI), and frequency (PF). Both simulations reasonably reproduce the spatial distribution of PA. V4km is more skillful in simulating the spatial distributions and magnitudes of PF and PI. The diurnal cycle of Mei-yu rainfall shows a major early morning peak and a minor afternoon peak, contributed by precipitation during two sub-periods with distinct synoptic circulations. With strong Mei-yu in the first sub-period, the diurnal variation of PA is controlled by nocturnal southwesterly jet. V4km overestimates the morning peak mainly due to its bias in simulating boundary layer inertial oscillation. Although differences in PA between the simulations are small, U60km overestimates PF and underestimates PI. With weak Mei-yu in the second sub-period, the diurnal variation of PA is controlled by both synoptic circulation and local convection. At both resolutions, deviations in the large-scale circulation modulated by a few typhoons lead to positive biases in the morning peak of PA. After removing the typhoon impacts, V4km captures the observed diurnal cycle of PA well, while U60km significantly underestimates PA and PI particularly in the afternoon. Future studies focusing on advancing modeling of southwesterly jet and typhoons may further improve convection permitting simulation of Mei-yu rainfall.

Xu, Mingyue↗

High-Resolution Simulations of Geological CO 2 Injection: Application to the SPE11 Benchmark

Geological carbon sequestration (GCS) will play a critical role in decarbonization and in facilitating the transition to clean energy systems. Because CO 2 is highly mobile, ensuring its safe and permanent injection into subsurface geological formations involves monitoring over larger spatial domains and longer time periods than is typical for hydrocarbon reservoirs. This can benefit from simulation tools capable of modeling key CO 2 trapping mechanisms, particularly those optimized for speed and scalability on high-performance computing systems. Using isothermal versions of the SPE11B and SPE11C benchmark cases, we conduct a mesh refinement study simulating CO 2 injection into kilometer-scale rock formations at centimeter resolution with the GEOS open-source simulation framework. We focus on how mesh refinement improves the accuracy of convective mixing in both 2D and 3D simulations. The computational costs associated with achieving a converged solution highlight the need for predictive upscaling techniques. A systematic performance scaling analysis—including both central processing unit (CPU) and graphics processing unit (GPU) architectures—complements the “Results” section.

Geosciences↗

Refined interpretation of electron temperature response to neutral beam injection at DIII-D

Accurate particle and power deposition profiles of neutral beam injection (NBI) are essential to transport studies, and that information is usually acquired through Monte Carlo simulations with a given collisional model. The deposition process of the energetic beam particles leads to the informative electron temperature (T e ) evolution trajectory, which can be captured by electron cyclotron emission (ECE) system due to its good spatial and temporal resolution. Previously, some work has been done to interpret the T e responses to the pulsed NBI as a linear heating source with Fourier-based techniques, although that approach fell short when the fast ion slowing-down time becomes significant (~100 ms). It has been observed in DIII-D that the modulated NBI pulses (10–50 Hz) reduce local core T e values ~0.1 keV through cold electron dilution in high-T e (>2 keV) plasmas alongside accumulative heating. Here, a novel approach to interpret the T e response to NBI was developed by linearizing and modeling the detailed T e evolution trajectory using coherently averaged ECE data based on the different time scales of the terms in the local power and particle balance equations. The technique does not require absolute calibrations of ECE and is independent of collisional models. The resulting beam deposition profiles show good consistency and reasonable agreement with Monte Carlo calculations based on the atomic data from the Atomic Data and Analysis Structure (ADAS). Local electron density response measured by Thomson scattering (TS) also suggests the same features when the beam pulse is large enough for that diagnostic to resolve. The remaining discrepancies are also discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A high-resolution large-eddy simulation framework for wildland fire predictions using TensorFlow

Background: Wildfires are becoming more severe, so we need improved tools to predict them over a wide range of conditions and scales. One approach towards this goal entails the use of coupled fire/atmosphere modelling tools. Although significant progress has been made in advancing their physical fidelity, existing tools have not taken full advantage of emerging programming paradigms and computing architectures to enable high-resolution wildfire simulations. Aims: The aim of this study was to present a new framework that enables landscape-scale wildfire simulations with physical representation of combustion at an affordable cost. Methods: We developed a coupled fire/atmosphere simulation framework using TensorFlow, which enables efficient and scalable computations on Tensor Processing Units. Key Results: Simulation results for a prescribed fire were compared with experimental data. Predicted fire behavior and statistical analysis for fire spread rate, scar area, and intermittency showed overall reasonable agreement. Scalability analysis was performed, showing close to linear scaling. Conclusions: While mesh refinement was shown to have less impact on global quantities, such as fire scar area and spread rate, it benefits predictions of intermittent fire behavior, buoyancy-driven dynamics, and small-scale turbulent motion. Implications: This new simulation framework is efficient in capturing both global quantities and unsteady dynamics of wildfires at high spatial resolutions.

54 ENVIRONMENTAL SCIENCES↗

Numerical Analysis of Combustion Dynamics in a Full-Scale Rotating Detonation Rocket Engine using Large Eddy Simulations

Large eddy simulations (LES) using detailed chemistry and leveraging adaptive mesh refinement (AMR) are performed to gain insights into the combustion dynamics within a full-scale methane-oxygen non-premixed rotating detonation rocket engine (RDRE) employing impinging discrete injection schemes. In particular, a comparative analysis of two operating conditions corresponding to the same global equivalence ratio but different mass flow rates is carried out to investigate the resultant impact on detonation wave characteristics and RDRE global performance. Multiple co-rotating detonation waves with spatially-distributed wave structure and preferential alignment with the inner wall of the annulus (due to asymmetry in fuel distribution) are encountered under both conditions. Both cases exhibit pre-detonation deflagrative burning in the fill region, while one of the cases shows higher susceptibility to backflow into the feed plenums due to lower plenum pressures. Furthermore, heat release analysis shows that the thrust obtained from the RDRE is closely linked to the distribution of total heat release between detonative and deflagrative combustion. On the other hand, combustion efficiency is associated with the fraction of heat release occurring in fuel-rich versus fuel-lean regions within the RDRE.

33 ADVANCED PROPULSION SYSTEMS↗

Flow Characterization of the NASA Langley Unitary Plan Wind Tunnel, Test Section 2: Computational Results

This is an abstract for an invited paper at the AIAA Aviation Conference, June 2021. The work described here is part of an effort of coordinated experiments in the Unitary Plan Wind Tunnel (UPWT) facility at the NASA Langley Research Center (LaRC) and matching CFD simulations. The primary goal of the work is to assess the productivity and true predictive accuracy of CFD, absent any guidance from experiment, in the high supersonic speed range as compared to experiments performed at the NASA LaRC’s UPWT facility. This report concerns CFD simulation of the primary flow-path in the empty wind tunnel, including the settling chamber, nozzle, test section, and some of the tunnel downstream of the test section. The Mach number in the test section ranges from M~2.4 to M~4.6, and the required area ratio variation is achieved by translation of a nozzle block which constricts the area of a loosely S-shaped throat. Flow past protuberances in the settling chamber and into this S-bend throat are predicted by CFD to generate streamwise vorticity that may, or may not, persist through the throat and into the test section as coherent vortices. Some flow conditions are notably unsteady at frequencies well below those of turbulence, due to unsteady separated flow ahead of the nozzle block. The bulk flow moves at velocities ranging from 'walking speed' in the settling chamber to M~4.6 in the test section. Heat transfer to the settling chamber walls and buoyancy are significant at high Mach number. Subtle variations in surface curvature in the nozzle generate Mach waves that propagate into the test section. CFD of the empty tunnel serves two purposes. Firstly, the full-tunnel simulations are used to provide upstream boundary conditions for CFD of vehicle aerodynamics which are generally performed in a domain confined to the wind tunnel test section; these companion studies are addressed in other papers. Secondly, it is a challenging test for CFD to resolve all of the empty tunnel flow phenomena relevant to flow in the test section. It requires a more complete definition of geometry than was originally anticipated. In addition, it requires good spatial and temporal accuracy, and turbulence modeling that performs well on specific phenomena such as corner flows. The boundary conditions and solution algorithms must perform well from incompressible to almost hypersonic speeds. The final state of the pre-test CFD was a product of an iterative self-improvement process. The initial simulations of the empty tunnel were deficient in many respects, but hints to those deficiencies were recognized in the solutions, and remedies were implemented. Possible further improvements will be studied in the post-test phase when comparisons with experimental data are possible. The CFD was performed by five separate collaborative teams using four different flow solvers: FUN3D, Overflow, Star-CCM+ and USM3D. The level of effort of these teams varied significantly, but each made important contributions to the goals of the work. A concerted effort to use uncertainty quantification methods (UQ) in CFD is also a goal of this work. To this end, variations in CFD results due to grid refinement, turbulence modeling, and boundary conditions have been characterized. Code-to-code variation is another means of assessing CFD uncertainty. All CFD solvers predict similarity among the primary flow features; these include the variation of Mach number due to changes in Reynolds number, and the bulk flow angularity due to tunnel-wall curvature. All CFD solvers also predict similar trends in secondary flows, such as the downwash in the side-wall boundary layers. Three of the high-spatial resolution simulations give similar predictions of a complex secondary flow phenomena, streamwise vortices generated in the S-bend throat that persist into the side-wall boundary layers of the test section. Two of the highest-resolution simulations, run with the same turbulence model in different CFD solvers, gave encouragingly similar predictions of a complex tertiary flow phenomenon, small transient "sprites" of upwash flows, resulting from vortices that presumably originate in the separated flow near the leading edge of the nozzle block. While the CFD was done in a "blind pre-test" mode, requests from the experimental team for CFD results pertaining to unsteadiness and total temperature variations in the test section resulted in CFD runs that included a cooled wall in settling chamber. This then led to a change in the standard practice for running the Overflow results, which would not have occurred without this "release" of this experimental information. CFD was also used to guide some measurements. The paper will focus on establishing the consensus among CFD results and understanding differences among those results. Initial findings from the efforts to characterize CFD uncertainty have been done and will be included in the paper.

Robert Edward Childs↗

Electric Vehicle Charging Demand in the Chicago Metropolitan Area through 2030

This report outlines the collaborative efforts between Argonne National Laboratory and Exelon in advancing the Agent-Based Transportation Energy Analysis Model (ATEAM). Aligning with ComEd’s beneficial electrification plan, this study developed eight scenarios to access the temporal and spatial distribution of charging load and demand stemming from the widespread adoption of battery electric vehicles (BEV) adoption, augmented public charging infrastructure deployment, and increased multi-unit dwelling (MUD) charging availability. Enhancements to the ATEAM model encompassed the simulation of multiple days of travel behavior, estimation of total public charging infrastructure needs, user interface refinements, and output tracking at both vehicle and charging station levels. The total electricity consumption for residential and public charging to support over 800,000 BEVs in Chicago in 2029 is projected at approximately 10.2 GWh. Enhanced MUD home charging accessibility (70%) amplifies the home charging load in the study area by 1.5% compared to the baseline scenario (10%). The widespread adoption of BEVs reduces peak charging loads, owing to their inclusion across households with diverse income levels, thus fostering a more dispersed charging activity pattern. However, widespread BEV adoption increases the peak home charging load in areas with lower median household incomes, reflecting a higher BEV concentration in these locales and, subsequently, heightened peak charging demands. In the Widespread BEV adoption scenario, fewer census tracts exhibit elevated peak loads for combined home and public charging, indicating a more even distribution of charging demand across the study area. Predominantly, peak loads for combined charging—both home and public— occur between 2 p.m. and 10 p.m. across all scenarios, encompassing the majority of census tracts.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Clouds and the earth's radiant energy system (CERES) - Instrument design and development

Measurements of the earth's reflected shortwave and emitted longwave energy and of the effect of clouds on these quantities are planned using a refined version of the Earth Radiation Budget Experiment (ERBE) scanning instrument. The CERES instruments are being designed to accumulate earth radiance measurements with a repeatability of better than 0.5 percent over their five year life. Beginning in 1996, flights are planned on both polar and low earth orbit satellites to obtain the required temporal and spatial coverage. The design and development of CERES are discussed.

Kopia, Leonard P.↗

The X-Ray Lightcurve of Eta Carinae: Refinement of the Orbit and Evidence for Phase Dependent Mass Loss

We solve the RXTE X-ray lightcurve of the extremely luminous and massive star eta Carinae with a colliding wind emission model to refine the ground-based orbital elements. The sharp decline to X-ray minimum at the end of 1997 fixes the date of the last periastron passage at 1997.95 +/- 0.05, not 1998.13 as derived from ground-based radial velocities. This helps resolve a discrepancy between the ground-based radial velocities and spatially-resolved velocity measures obtained by STIS. The X-ray data are consistent with a mass function f(M) approx. = 1.5, lower than the value f(M) approx. = 7.5 previously reported, so that the masses of eta Carinae and the companion are M(sub eta) greater than or = 80 solar mass and M(sub c) approx. 30 solar mass respectively. In addition the X-ray data suggest that the mass loss rate from eta Carinae is generally less than 3 x 10(exp -4) solar mass/yr, about a factor of 5 lower than that derived from some observations in other wavebands. We could not match the duration of the X-ray minimum with any standard colliding wind model in which the wind is spherically symmetric and the mass loss rate is constant. However we show that we can match the variations around X-ray minimum if we include an increase of a factor of approx. 20 in the mass loss rate from eta Carinae for approximately 80 days following periastron. If real, this excess in M would be the first evidence of enhanced mass flow off the primary when the two stars are close (presumably driven by tidal interactions). Our interpretation of the X-ray data suggest that the ASCA and RXTE X-ray spectra near the X-ray minimum are significantly contaminated by unresolved hard emission (E greater than or = 2 keV) from sonic other nearby source, probably associated with scattering of tile colliding wind emission by circumstellar dust. Based on the X-ray fluxes the distance to n Carinae is 2300 pc with formal uncertainties of only approx. 10%.

Corcoran, M. F.↗

Quantitative Approach for the Accurate CFD Simulation of Hover in Turbulent Flow

Time-dependent Navier-Stokes simulations have been carried out for a V22 rotor in hover using an improved, low-diffusion, HLLE++ upwind algorithm in the OVERFLOW code. Emphasis is placed on lessons learned over the past decade regarding the effects of high-order spatial accuracy, grid resolution, and the use of detached eddy simulation in predicting the rotor performance, i.e., figure-of-merit (FM). A quick-start procedure is described together with a statistical measure of FM convergence that reduces hover computations by 5 times, similar in computational work for forward flight. Furthermore, Cartesian adaptive mesh refinement in the rotor wake revealed a complex turbulent flow with worm-like structures of various scales. These turbulent worms, found computationally more than a decade ago, have recently been observed in a separate German Aerospace Center (DLR) experiment. Moreover, adaptive mesh refinement has been used to resolve the tip-vortex to its correct physical size.

Neal M. Chaderjian↗

Dynamic measurement of bulk modulus of dielectric materials using a microwave phase shift technique

A microwave Doppler shift technique was developed for measuring the dynamic bulk modulus of dielectric materials such as solid propellants. The system has a demonstrated time resolution on the order of milliseconds and a theoretical spatial resolution of a few microns. Accuracy of the technique is dependent on an accurate knowledge of the wavelength of the microwave in the sample being tested. Such measurement techniques are discussed. Preliminary tests with two solid propellants, one non-aluminized and one containing 16% aluminum, yielded reasonable, reproducible results. It was concluded that with refinements the technique holds promise as a practical means for obtaining accurate dynamic bulk modulus data over a variety of transient conditions.

Barker, B. J.↗

Finite-volume application of high-order ENO schemes to two-dimensional boundary-value problems

Finite-volume applications of high-order accurate ENO schemes to two-dimensional boundary-value problems are studied. These schemes achieve high-order spatial accuracy, in smooth regions, by a piecewise polynomial approximation of the solution from cell averages. In addition, this spatial operation involves an adaptive stencil algorithm in order to avoid the oscillatory behavior that is associated with interpolation across steep gradients. High-order TVD Runge-Kutta methods are employed for time integration, thus making these schemes best suited for unsteady problems. Fifth- and sixth-order accurate applications are validated through a grid refinement study involving the solutions of scalar hyperbolic equations. A previously proposed extension for the Euler equations of gas dynamics is tested, including its application to solutions of boundary-value problems involving solid walls and curvilinear coordinates.

Casper, Jay↗

Multiplexed Holographic Data Storage in Bacteriorhodopsin

High density optical data storage, driven by the information revolution, remains at the forefront of current research areas. Much of the current research has focused on photorefractive materials (SBN and LiNbO3) and polymers, despite various problems with expense, durability, response time and retention periods. Photon echo techniques, though promising, are questionable due to the need for cryogenic conditions. Bacteriorhodopsin (BR) films are an attractive alternative recording medium. Great strides have been made in refining BR, and materials with storage lifetimes as long as 100 days have recently become available. The ability to deposit this robust polycrystalline material as high quality optical films suggests the use of BR as a recording medium for commercial optical disks. Our own recent research has demonstrated the suitability of BR films for real time spatial filtering and holography. We propose to fully investigate the feasibility of performing holographic mass data storage in BR. Important aspects of the problem to be investigated include various data multiplexing techniques (e.g. angle- amplitude- and phase-encoded multiplexing, and in particular shift-multiplexing), multilayer recording techniques, SLM selection and data readout using crossed polarizers for noise rejection. Systems evaluations of storage parameters, including access times, memory refresh constraints, erasure, signal-to-noise ratios and bit error rates, will be included in our investigations.

Mehrl, David J.↗

Determination of an Infrared Reference Frame

The mission of the European Space Agency's Hipparcos satellite was to provide high precision astrometric and photometric data for over 100,000 stars and somewhat lower precision data on over a million additional stars. These observations were made in the optical band (340 - 850 nm) and resulted in median precisions of better than 1 milli-arcsec (mas) in position and parallax and I mas/yr in proper motion. The Hipparcos frame is inertial within an estimated uncertainty of +/- 0.25 mas/yr. The other important wavelength band for astrometry has been the radio band. A reference frame has been defined based on absolute Very Long Baseline Interferometry (VLBI) positions of several hundreds of radio sources. There have been a number of projects to refine the link between the optical and radio reference frames. In recent years there has been increasing interest in the astrometry of infrared sources. For example, stars with circumstellar shells can be observed in both the optical and radio (e.g. SiO maser emission). The infrared emission from such sources is dominated by thermal dust emission. The spatial distribution of radiation in the three bands is expected to be quite different. In 1982 we proposed a number of infrared-selected sources (S(sub 10 micron) greater than or approx. equal to 100 J(sub y)) for inclusion in the Hipparcos Input Catalog. Most of those sources were observed, and in Sutton (1997) we report the optical astrometric results (position, proper motion, and parallax) for 87 such sources. These sources were selected to have reasonable agreement between infrared and optical positions, and so may be used as primary standards for future infrared astrometry. They are well distributed across the sky, but exhibit some bias towards the galactic plane and the northern hemisphere. We have also obtained a set of 1480 secondary standards (unpublished) A comparison between optical positions and 86 GHz SiO maser positions for 10 sources indicates coincidence at the 0.15 arcsec level, consistent with current uncertainties in the SiO positions. Improved measurements of the SiO maser positions are needed. VLBI data show that SiO maser spots can be distributed in broken rings of radii 10 - 30 mas, presumably centered on the stellar position. However the SiO flux may be distributed asymmetrically, in which case the flux-weighted center of the SiO emission can be different from the stellar position. We have also published a related paper on phase fluctuations in millimeter interferometry (Sutton and Hueckstaedt 1996). Radiometric monitoring of emission from atmospheric water vapor may be a method for correcting for such fluctuations. This is relevant to positional determinations at centimeter and millimeter wavelengths. The integration of visible, infrared, and radio astrometry is one of our principal goals.

Sutton, Edmund C.↗

CFD Predictions of Fluctuating Pressure Environments on NASA’s SLS Ascent Unsteady Aerodynamics Wind Tunnel Test

This paper details work that is being conducted on predicting fluctuating pressure environments on NASA launch vehicles using computational fluid dynamics (CFD). The accurate characterization of these aeroacoustics environments is necessary in the analysis of vehicle structural health and aerodynamic performance and in the vehicle design process. High-fidelity simulations of the unsteady flow over NASA’s SLS Ascent Unsteady Aerodynamics wind tunnel Test (AUAT) using the hybrid Reynolds-averaged Navier-Stokes (RANS)-large eddy simulations (LES) methodologies in Mississippi States’ Loci/CHEM solver are presented. The two available methods, Nelson-Nichols and dynamic hybrid RANS-LES (DHRL), are compared head-to-head on identical grids at two Mach numbers. At the high-subsonic Mach number, locally supersonic flow expanding over a shoulder induces a separation-reattachment system that is predicted poorly by the Nelson-Nichols method due to an under-prediction in unsteady content. The DHRL solution predicts the spatial extent and frequency domain response of this system well but under-predicts the peak noise levels due to a delay in the RANS-to-LES transition. At the low-supersonic Mach number, compression corner dynamics dominate the unsteady flow. While the Nelson Nichols solution captures this phenomenon well, another solution on a refined grid indicates that some model stress depletion is occurring. The DHRL solution again performs well at this Mach number and matches the wind tunnel data fairly closely, but perhaps most impressively, is fairly agnostic to increasing grid resolution. The findings in this paper are expected to be generally applicable and will be used to guide the prediction of aeroacoustics environments of other NASA launch vehicles.

CFD↗

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↗