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At least 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Neural units with time-dependent functionality

We show that the time-resolved dynamics of an underdamped harmonic oscillator can be used to do multifunctional computation, performing distinct computations at distinct times within a single dynamical trajectory. We consider the amplitude of an oscillator whose inputs influence its frequency. The activity of the oscillator at fixed times is a nonmonotonic function of its inputs, so it can solve problems such as XOR that are not linearly separable. The activity of the oscillator at fixed input is a nonmonotonic function of time, so it is multifunctional in a temporal sense, and able to carry out distinct nonlinear computations at distinct times within the same dynamical trajectory. We show that a single oscillator, observed at different times, can act as all of the elementary logic gates and perform binary addition, the latter usually implemented in hardware using five logic gates. We show that a set of n oscillators, observed at different times, can perform an arbitrary number of analog-to-n-bit digital conversions. We also show that oscillators can be trained by gradient descent to perform distinct classification tasks at distinct times. Computing with time-dependent functionality can be done in or out of equilibrium, and suggests a way of reducing the number of parameters or devices required to do nonlinear computations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Biasing topological charge injection in topological matter

Here we explore the interplay between topologies in the momentum and real spaces to formulate a thermodynamic description of nonequilibrium injection of topological charges under external bias. We show that the edge modes engendered by the momentum-space topology can play a functional role of connecting the external reservoirs to the bulk transport of topological charges in the real space. We illustrate our general results with two examples: the spin-torque injection of skyrmions in an electrically biased integer quantum Hall system, and the vortex injection in a topological $p + ip$ superconductor coupled to heat reservoirs. Based on the universal fractional entropy of the Majorana zero modes bound to the vortices, their controllable injection proposed in this work could provide a route for creating and manipulating Majorana fermions.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Viscosity of the magnetized strongly coupled one-component plasma

The viscosity tensor of the magnetized one-component plasma, consisting of five independent shear viscosity coefficients, a bulk viscosity coefficient, and a cross coefficient, is computed using equilibrium molecular dynamics simulations and the Green-Kubo relations. A broad range of Coulomb coupling and magnetization strength conditions are studied. Magnetization is found to strongly influence the shear viscosity coefficients when the gyrofrequency exceeds the Coulomb collision frequency. Three regimes are identified as the Coulomb coupling strength and magnetization strength are varied. Here, the Green-Kubo relations are used to separate kinetic and potential energy contributions to each viscosity coefficient, showing how each contribution depends upon the magnetization strength. The shear viscosity coefficient associated with the component of the pressure tensor parallel to the magnetic field, and the two coefficients associated with the component perpendicular to the magnetic field, are all found to merge to a common value at strong Coulomb coupling.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Floquet Spin Splitting and Spin Generation in Antiferromagnets

In antiferromagnetic spintronics, accessing the spin degrees of freedom is essential for generating spin currents and manipulating magnetic order, which generally requires lifting spin degeneracy. This is typically achieved through relativistic spin-orbit coupling or nonrelativistic spin splitting in altermagnets. Here, we propose an alternative approach: a dynamical spin splitting induced by an optical field in antiferromagnets. By coupling the driven system to a thermal bath, we demonstrate the emergence of steady-state pure spin currents as well as linear-response longitudinal and transverse spin currents. Crucially, thermal bath engineering enables a nonrelativistic Edelstein effect—the generation of a net spin accumulation—without relying on spin-orbit coupling. Furthermore, our results provide a broadly applicable and experimentally tunable route to control spins in antiferromagnets, offering new opportunities for spin generation and manipulation in antiferromagnetic spintronics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Data-Driven Discovery of Active Nematic Hydrodynamics

Active nematics can be modeled using phenomenological continuum theories that account for the dynamics of the nematic director and fluid velocity through partial differential equations (PDEs). While these models provide a statistical description of the experiments, the relevant terms in the PDEs and their parameters are usually identified indirectly. We adapt a recently developed method to automatically identify optimal continuum models for active nematics directly from spatio-temporal data, via sparse regression of the coarse-grained fields onto generic low order PDEs. After extensive benchmarking, we apply the method to experiments with microtubule-based active nematics, finding a surprisingly minimal description of the system. Furthermore, our approach can be generalized to gain insights into active gels, microswimmers, and diverse other experimental active matter systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Structural transitions in the GTP cap visualized by cryo-electron microscopy of catalytically inactive microtubules

Microtubules (MTs) are nonequilibrium polymers that switch between states of growth and shrinkage. This property is critical for their function and is a consequence of GTP hydrolysis in the MT. The structure of the stable GTP part of the MT (the GTP cap) has previously been inferred from MTs polymerized with nonhydrolyzable GTP analogs. Here, we report high-resolution structures of MTs truly containing GTP, polymerized from mutated, hydrolysis-deficient tubulins. We find that GTP-MTs have an “expanded lattice” and a “closed seam,” structural characteristics possibly responsible for stabilizing the GTP cap. These results provide insight into the structural transitions at growing MT ends, furthering our understanding of the bistable nature of MTs.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Thermalization at low temperatures via weakly damped multisite baths

We study the thermalization properties of one-dimensional open quantum systems coupled to baths at their boundary. The baths are driven to their thermal states via Lindblad operators, while the system undergoes Hamiltonian dynamics. We specifically consider multisite baths and investigate the extent to which the late-time steady state resembles a Gibbs state at some controllable temperature set by the baths. We study three models: a noninteracting fermion model accessible via free-fermion technology, and two interacting models, the XZ model and the chiral clock model, which are accessible via tensor network methods. We show that, by tuning towards the weak coupling and slow relaxation limits, one can engineer low temperatures in the bulk of the system provided the bath size is big enough. Here, we use this capability to study energy transport in the XZ model at lower temperatures than previously reported. Our work paves the way for future studies of interacting open quantum systems at low temperatures.

1-dimensional spin chains↗
DOE OSTI2025

Role of effective mass and long-range interactions in the band-gap renormalization of photoexcited semiconductors

Understanding how to control changes in the electronic structure and related dynamical renormalizations by external driving fields is the key for understanding ultrafast spectroscopy and applications in electronics. Here, we focus on the band gap's modulation by external electric fields and uncover the effect of band dispersion on the gap renormalization. We employ the Green's function formalism using the real-time Dyson expansion to account for dynamical correlations induced by photodoping. The many-body formalism captures the dynamics of systems with long-range interactions, carrier mobility, and variable electron and hole effective mass. We also demonstrate that mean-field simulations based on the Hartree-Fock Hamiltonian, which lacks dynamical correlations, yields a qualitatively incorrect picture of band-gap renormalization. We find the trend that increasing effective mass, thus decreasing mobility, leads to as much as a 6% enhancement in band-gap renormalization. Further, the renormalization is strongly dependent on the degree of photodoping. As the screening induced by free electrons and holes effectively reduces any long-range and interband interactions for highly excited systems, we show that there is a specific turnover point with a minimal band gap. Here, we further demonstrate that the optical gap renormalization follows the same trend though its magnitude is altered by the Moss-Burstein effect.

Approximation methods for many-body systems↗
NASA NTRS2019

InSight's Reconstructed Aerothermal Environments

The InSight Mars Lander successfully landed on the surface on November 26, 2018. This poster will describe the methodologies and margins used in developing the aerothermal environments for design of the thermal protection systems (TPS), as well as a prediction of as-flown environments based on the best estimated trajectory. The InSight mission spacecraft design approach included the effects of radiant heat flux to the aft body from the wake for the first time on a US Mars Mission, due to overwhelming evidence in ground testing for the European ExoMars mission (2009/2010) [1] and 2010 tests in the Electric Arc Shock Tube (EAST) facility [2]. The radiant energy on an aftbody was also recently confirmed via measurement on the Schiaparelli mission [3]. In addition, the InSight mission expected to enter the Mars atmosphere during the dust storm season, so the heatshield TPS was designed to accommodate the extra recession due to the potential dust impact. This poster will compare the predicted aerothermal environments using the reconstructed best estimated trajectory to the design environments. Design Approach: The InSight spacecraft was planned to be a near-design-to-print copy of the Phoenix spacecraft. The determination of the heatshield TPS requirements was approached as if it was a new design due to the new requirement of flying through a dust storm. The baseline for aftbody was build-to-print, and all analyses focused on ensuring adequate margin. This proved to be a challenge because the Phoenix aftbody was designed to withstand only convective heating and the InSight aftbody was evaluated for both convective and radiative heating. Aerothermal environments were predicted using the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) and the Data Parallel Line Relaxation (DPLR) CFD codes, and the Nonequilibrium Radiative Transport and Spectra Program (NEQAIR) utilizing bounding design trajectories derived from Monte Carlo analyses from the Program to Optimize Simulated Trajectories II (POST2). In all cases, super-catalytic flowfields were assigned to ensure the most conservative heating results. Two trajectories were evaluated: 1) the trajectory with the maximum heat flux was utilized to determine the flowfield characteristics and the viability of the selection of TPS materials; and 2) the trajectory with the maximum heat load was used to determine the required thicknesses of the TPS materials. Evaluation of the MEDLI data [4], along with ground test data [5] led to the determination of whether or not the flow would transition from laminar to turbulent on the heatshield, which also determined the TPS sizing location for the heatshield. Aerothermal margins were added for the convective heating and developed for the radiative heating. TPS material sizing was determined with the Reaction Kinetic Ablation Program (REKAP) and the Fully Implicit Ablation and Thermal Analysis program (FIAT) using a three-branched approach to account for aerothermal, material response, and material properties uncertainties. In addition, the heatshield recession was augmented by an analysis of the effect of entry through a potential dusty atmosphere using a methodology developed in References [6] and [7]. These analyses resulted in an increase to the Phoenix heatshield TPS thickness. Reconstruction Efforts: Once the best estimated trajectory is reconstructed by the team, the LAURA/HARA (High-Temperature Aerothermo-dynamic Radiation model) and DPLR/NEQAIR code pairs will be used to predict the as-flown aerothermal conditions. In these runs, fully-catalytic flowfields will be assigned because it is a more physically accurate description of the chemistry in the flow. Once again, determination of the onset of turbulence on the heatshield will be evaluated. The as-flown aerothermal environments will then be compared to the design environments.

Beck, R. A.↗
DOE OSTI2025

Strong Hilbert space fragmentation and fractons from subsystem and higher-form symmetries

Here, we introduce a route to Hilbert space fragmentation in high dimensions leveraging the group-word formalism. We show that taking strongly fragmented models in one dimension and “lifting” to higher dimensions using subsystem symmetries can yield strongly fragmented dynamics in higher dimensions, with subdimensional (e.g., lineonic) excitations. This provides a route to higher-dimensional strong fragmentation, and also a route to fractonic behavior. Meanwhile, lifting one-dimensional fragmented models to higher dimensions using higher-form symmetries yields models with topologically robust fragmentation. In three or more spatial dimensions, one can also “mix and match” subsystem and higher-form symmetries, leading to canonical fracton models such as X cube. We speculate that this approach could also yield a route to non-Abelian fractons. These constructions unify a number of phenomena that have been discussed in the literature, as well as furnishing models with unique properties.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Stochastic thermodynamic cycles of a mesoscopic thermoelectric engine

Here, we analyze a steady-state thermoelectric engine, whose working substance consists of two capacitively coupled quantum dots. One dot is tunnel-coupled to a hot reservoir serving as a heat source, the other one to two electrically biased reservoirs at a colder temperature, such that work is extracted under the form of a steady-state current against the bias. In single realizations of the dynamics of this steady-state engine autonomous, four-stroke cycles can be identified. The cycles are purely stochastic, in contrast to mechanical autonomous engines which exhibit self-oscillations. In particular, these cycles fluctuate in direction and duration and occur in competition with other spurious cycles. Using a stochastic thermodynamic approach, we quantify the cycle fluctuations and relate them to the entropy produced during individual cycles. We identify the cycle mainly responsible for the engine performance and quantify its statistics with tools from graph theory. We show that such stochastic cycles are made possible because the work extraction mechanism is itself stochastic instead of the periodic time dependence in the working-substance Hamiltonian which can be found in conventional mechanical engines. Our investigation brings new perspectives about the connection between cyclic and steady-state engines.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Laser Measurements and Modeling of Shock Tunnel Freestream Velocity and Multispecies Thermal Nonequilibrium

Coherent anti-Stokes Raman scattering (CARS) and nitric oxide molecular tagging velocimetry (NO-MTV) were used to characterize the freestream in Sandia’s Hypersonic Shock Tunnel (HST) using a burst-mode laser operated at 100 kHz. Experiments were performed at nominal freestream velocities of 3 and 4 km/s using both air and N 2 test gas. The CARS diagnostic provides nonequilibrium characterization of the flow by measuring vibrational and rotational temperatures of N 2 and O 2 , which are compared to NO temperatures from separate laser absorption experiments. Simultaneous, collinear freestream velocities were measured using NO MTV along with pitot pressure measurements. Furthermore, this extensive freestream dataset is compared to nonequilibrium CFD that is capable of modeling species-specific, vibrational temperatures throughout the nozzle expansion. Significant nonequilibrium between vibrational and rotational temperatures was measured at each flow condition. N 2 exhibits the most nonequilibrium, followed by O 2 and NO. The CFD model captures this trend, although it consistently overpredicts N 2 and O 2 vibrational temperatures. At 3 km/s, the modeled NO nonequilibrium is underpredicted, whereas it is overpredicted at 4 km/s. Good agreement is seen between CFD and the velocity and rotational temperature measurements. Experiments with water added to the test gas yielded no discernable difference in vibrational relaxation.

Aerodynamics↗
NASA NTRS2014

Turbulence Modeling Verification and Validation

Computational fluid dynamics (CFD) software that solves the Reynolds-averaged Navier-Stokes (RANS) equations has been in routine use for more than a quarter of a century. It is currently employed not only for basic research in fluid dynamics, but also for the analysis and design processes in many industries worldwide, including aerospace, automotive, power generation, chemical manufacturing, polymer processing, and petroleum exploration. A key feature of RANS CFD is the turbulence model. Because the RANS equations are unclosed, a model is necessary to describe the effects of the turbulence on the mean flow, through the Reynolds stress terms. The turbulence model is one of the largest sources of uncertainty in RANS CFD, and most models are known to be flawed in one way or another. Alternative methods such as direct numerical simulations (DNS) and large eddy simulations (LES) rely less on modeling and hence include more physics than RANS. In DNS all turbulent scales are resolved, and in LES the large scales are resolved and the effects of the smallest turbulence scales are modeled. However, both DNS and LES are too expensive for most routine industrial usage on today's computers. Hybrid RANS-LES, which blends RANS near walls with LES away from walls, helps to moderate the cost while still retaining some of the scale-resolving capability of LES, but for some applications it can still be too expensive. Even considering its associated uncertainties, RANS turbulence modeling has proved to be very useful for a wide variety of applications. For example, in the aerospace field, many RANS models are considered to be reliable for computing attached flows. However, existing turbulence models are known to be inaccurate for many flows involving separation. Research has been ongoing for decades in an attempt to improve turbulence models for separated and other nonequilibrium flows. When developing or improving turbulence models, both verification and validation are important steps in the process. Verification insures that the CFD code is solving the equations as intended (no errors in the implementation). This is typically done either through the method of manufactured solutions (MMS) or through careful step-by-step comparisons with other verified codes. After the verification step is concluded, validation is performed to document the ability of the turbulence model to represent different types of flow physics. Validation can involve a large number of test case comparisons with experiments, theory, or DNS. Organized workshops have proved to be valuable resources for the turbulence modeling community in its pursuit of turbulence modeling verification and validation. Workshop contributors using different CFD codes run the same cases, often according to strict guidelines, and compare results. Through these comparisons, it is often possible to (1) identify codes that have likely implementation errors, and (2) gain insight into the capabilities and shortcomings of different turbulence models to predict the flow physics associated with particular types of flows. These are valuable lessons because they help bring consistency to CFD codes by encouraging the correction of faulty programming and facilitating the adoption of better models. They also sometimes point to specific areas needed for improvement in the models. In this paper, several recent workshops are summarized primarily from the point of view of turbulence modeling verification and validation. Furthermore, the NASA Langley Turbulence Modeling Resource website is described. The purpose of this site is to provide a central location where RANS turbulence models are documented, and test cases, grids, and data are provided. The goal of this paper is to provide an abbreviated survey of turbulence modeling verification and validation efforts, summarize some of the outcomes, and give some ideas for future endeavors in this area.

Rumsey, Christopher L.↗
DOE OSTI2022

Large Exchange Coupling Between Localized Spins and Topological Bands in MnBi 2 Te 4

Magnetism in topological materials creates phases exhibiting quantized transport phenomena with potential technological applications. The emergence of such phases relies on strong interaction between localized spins and the topological bands, and the consequent formation of an exchange gap. However, this remains experimentally unquantified in intrinsic magnetic topological materials. Here, this interaction is quantified in MnBi 2 Te 4 , a topological insulator with intrinsic antiferromagnetism. This is achieved by optically exciting Bi-Te p states comprising the bulk topological bands and interrogating the consequent Mn 3d spin dynamics, using a multimodal ultrafast approach. Ultrafast electron scattering and magneto-optic measurements show that the p states demagnetize via electron-phonon scattering at picosecond timescales. Despite being energetically decoupled from the optical excitation, the Mn 3d spins, probed by resonant X-ray scattering, are observed to disorder concurrently with the p spins. Together with atomistic simulations, this reveals that the exchange coupling between localized spins and the topological bands is at least 100 times larger than the superexchange interaction, implying an optimal exchange gap of at least 25 meV in the surface states. Here, by quantifying this exchange coupling, this study validates the materials-by-design strategy of utilizing localized magnetic order to manipulate topological phases, spanning static to ultrafast timescales.

36 MATERIALS SCIENCE↗
NASA NTRS2021

Overview of Dragonfly Entry Aerosciences Measurements (DrEAM)

NASA Ames Research Center (ARC) leads the Dragonfly Entry Aerosciences Measurements (DrEAM) project, which is an aeroshell instrumentation suite on the Dragonfly mission that fulfills the Engineering Science Investigation requirement for the New Frontiers mission. NASA ARC is partnering with NASA Langley Research Center (LaRC) and the German Aerospace Center (DLR) to provide a comprehensive sensor suite, including a DLR-provided Data Acquisition System (DAS). DrEAM will provide key aerothermodynamic data and performance analysis for Dragonfly’s forebody and backshell Thermal Protection System (TPS). Titan’s atmosphere predominantly consists of ni-trogen (~98% by mole) with small amounts of me-thane (~2% by mole) and other trace gases. CN is a strong radiator, and is found in nonequilibrium con-centrations for Titan entry. The accurate modeling of nonequilibrium CN radiation has proven to be a diffi-cult task. Prompted by the Huygens mission, many experimental campaigns and analyses were performed to better understand the aerothermal environments experienced by the probe during Titan entry [1]. How-ever, the Huygens probe carried no heatshield instru-mentation. Therefore, the DrEAM sensor suite will sig-nificantly advance the state-of-the-art not only by documenting the environment and performance of Dragonfly’s entry system but also by making key in situ measurements in Titan’s atmosphere for the first time. Aerothermal environments and TPS response will be measured using sensors whose flight heritage is tak-en from the Mars Entry, Descent, and Landing In-strumentation 2 (MEDLI2) thermocouple plugs and the COMbined Aerothermal and Radiometer Sensor (COMARS) suite [2], with the latter supplied by DLR. The MEDLI2 project used embedded thermocouples to directly measure the in-depth TPS temperature-time history at several locations on the heat shield and backshell of the Mars 2020 entry vehicle. These tem-perature measurements, in turn, can be used to infer surface environments via an inverse analysis proce-dure analogous to that used for MEDLI. For DrEAM, the thermocouple plug subsystem will be known as Dragonfly Sensors for Aero-Thermal Reconstruction (DragSTR). On Schiaparelli, the COMARS suite in-cluded three total surface-mounted heat flux sensors, three pressure sensors, and one radiometer. For DrEAM, the COMARS package will be known as the COmbined Sensor System for Titan Atmosphere (COSSTA). Since the methane concentration in the Titan atmos-phere is directly proportional to the radiative heat flux, the COSSTA measurements will be used to reduce the current uncertainty in the methane volume fraction. Atmospheric density measurements and capsule aero-dynamic data will be obtained through the onboard Inertial Measurement Unit (IMU), supplemented by pressure transducers similar to those used by the MEDLI and MEDLI2 projects. The DrEAM pressure sensors will be known as the Dragonfly Atmospheric Flight Transducers. (DrAFT). The pressure measure-ments, when combined with data from the on-board IMU, will allow for reconstruction of such quantities as vehicle Mach number, freestream density, and atmos-pheric winds. DrAFT measurements will enhance Dragonfly trajectory reconstruction and enable a sepa-ration of the aerodynamics from the atmosphere, as was done for MEDLI [3] and is currently in process for the MEDLI2 flight data set.

EDL↗
DOE OSTI2022

Mana and thermalization: Probing the feasibility of near-Clifford Hamiltonian simulation

Quantum hydrodynamics is the emergent classical dynamics governing transport of conserved quantities in generic strongly interacting quantum systems. Here, recent matrix product operator methods [1,2] have made simulations of quantum hydrodynamics in 1+1D tractable, but they do not naturally generalize to 2+1D or higher, and they offer limited guidance as to the difficulty of simulations on quantum computers. Near-Clifford simulation algorithms are not limited to one dimension, and future error-corrected quantum computers will likely be bottlenecked by non-Clifford operations. We therefore investigate the non-Clifford resource requirements for simulation of quantum hydrodynamics using mana, a resource theory of non-Clifford operations. For infinite-temperature starting states, we find that the mana of subsystems quickly approaches zero, while for starting states with energy above some threshold the mana approaches a nonzero value. Surprisingly, in each case the finite-time mana is governed by the subsystem entropy, not the thermal state mana; we argue that this is because mana is a sensitive diagnostic of finite-time deviations from canonical typicality.

1-dimensional spin chains↗
NASA NTRS2013

Comparative Study on High-Order Positivity-preserving WENO Schemes

In gas dynamics and magnetohydrodynamics flows, physically, the density and the pressure p should both be positive. In a standard conservative numerical scheme, however, the computed internal energy is obtained by subtracting the kinetic energy from the total energy, resulting in a computed p that may be negative. Examples are problems in which the dominant energy is kinetic. Negative may often emerge in computing blast waves. In such situations the computed eigenvalues of the Jacobian will become imaginary. Consequently, the initial value problem for the linearized system will be ill posed. This explains why failure of preserving positivity of density or pressure may cause blow-ups of the numerical algorithm. The adhoc methods in numerical strategy which modify the computed negative density and/or the computed negative pressure to be positive are neither a conservative cure nor a stable solution. Conservative positivity-preserving schemes are more appropriate for such flow problems. The ideas of Zhang & Shu (2012) and Hu et al. (2012) precisely address the aforementioned issue. Zhang & Shu constructed a new conservative positivity-preserving procedure to preserve positive density and pressure for high-order WENO schemes by the Lax-Friedrichs flux (WENO/LLF). In general, WENO/LLF is too dissipative for flows such as turbulence with strong shocks computed in direct numerical simulations (DNS) and large eddy simulations (LES). The new conservative positivity-preserving procedure proposed in Hu et al. (2012) can be used with any high-order shock-capturing scheme, including high-order WENO schemes using the Roe's flux (WENO/Roe). The goal of this study is to compare the results obtained by non-positivity-preserving methods with the recently developed positivity-preserving schemes for representative test cases. In particular the more difficult 3D Noh and Sedov problems are considered. These test cases are chosen because of the negative pressure/density most often exhibited by standard high-order shock-capturing schemes. The simulation of a hypersonic nonequilibrium viscous shock tube that is related to the NASA Electric Arc Shock Tube (EAST) is also included. EAST is a high-temperature and high Mach number viscous nonequilibrium flow consisting of 13 species. In addition, as most common shock-capturing schemes have been developed for problems without source terms, when applied to problems with nonlinear and/or sti source terms these methods can result in spurious solutions, even when solving a conservative system of equations with a conservative scheme. This kind of behavior can be observed even for a scalar case (LeVeque & Yee 1990) as well as for the case consisting of two species and one reaction (Wang et al. 2012). For further information concerning this issue see (LeVeque & Yee 1990; Griffiths et al. 1992; Lafon & Yee 1996; Yee et al. 2012). This EAST example indicated that standard high-order shock-capturing methods exhibit instability of density/pressure in addition to grid-dependent discontinuity locations with insufficient grid points. The evaluation of these test cases is based on the stability of the numerical schemes together with the accuracy of the obtained solutions.

WENO↗