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DOE OSTI2020

Solving gyrokinetic systems with higher-order time dependence

We discuss theoretical and numerical aspects of gyrokinetics as a Lagrangian field theory when the field perturbation is introduced into the symplectic part. A consequence is that the field equations and particle equations of motion in general depend on the time derivatives of the field. The most well-known example is when the parallel vector potential is introduced as a perturbation, where a time derivative of the field arises only in the equations of motion, so an explicit equation for the fields may still be written. We will consider the conceptually more problematic case where the time-dependent fields appear in both the field equations and equations of motion, but where the additional term in the field equations is formally small. The conceptual issues were described by Burby (J. Plasma Phys., vol. 82 (3), 2016, 905820304): these terms lead to apparent additional degrees of freedom to the problem, so that the electric field now requires an initial condition, which is not required in low-frequency (Darwin) Vlasov–Maxwell equations. Also, the small terms in the Euler–Lagrange equations are a singular perturbation, and these two issues are interlinked. For well-behaved problems the apparent additional degrees of freedom are spurious, and the physically relevant solution may be directly identified. Because we needed to assume that the system is well behaved for small perturbations when deriving gyrokinetic theory, we must continue to assume that when solving it, and the physical solutions are thus the regular ones. The spurious nature of the singular degrees of freedom may also be seen by changing coordinate systems so the varying field appears only in the Hamiltonian. We then describe how methods appropriate for singular perturbation theory may be used to solve these asymptotic equations numerically. We then describe a proof-of-principle implementation of these methods for an electrostatic strong-flow gyrokinetic system; two basic test cases are presented to illustrate code functionality.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2008

Space Science and the International Traffic in Arms Regulations: Summary of a Workshop

The United States seeks to protect its security and foreign-policy interests, in part, by actively controlling the export of goods, technologies, and services that are or may be useful for military development in other nations. "Export" is defined not simply as the sending abroad of hardware but also as the communication of related technology and know-how to foreigners in the United States and overseas. The U.S. government mechanism for controlling dual-use items--items in commerce that have potential military use is the Export Administration Regulations (EAR) administered by the Department of Commerce; items defined in law as defense articles fall under the jurisdiction of the Department of State and the International Traffic in Arms Regulations (ITAR). Because of the potential military implications of the export of defense articles, the ITAR regime imposes much greater burdens (on both the applicant and the government) than does the EAR regime during the process of applying for, and implementing the provisions of, licenses and technical-assistance agreements. Until the early 1990s export control activity related to all space satellites (commercial and scientific) was handled under ITAR. Between 1992 and 1996 the George H.W. Bush and the Clinton administrations transferred jurisdiction over the licensing of civilian communications satellites to the Commerce Department under EAR. In 1999, however, in response to broad concerns about Chinese attempts to acquire U.S. high technology, the U.S. House of Representatives convened the Select Committee on U.S. National Security and Military/Commercial Concerns with the People s Republic of China, also known as the Cox Committee. One of the many consequences of the Cox Committee's report was Congress's mandate that jurisdiction over export and licensing of satellites and related equipment and services, irrespective of military utility, be transferred from the Department of Commerce to the State Department and that such equipment and services be covered as defense articles under ITAR. Scientific satellites were explicitly included despite their use for decades in peaceful internationally conducted cooperative scientific research. It is widely recognized that the shift in regulatory regime from EAR to ITAR has had major deleterious effects on international scientific research activities that depend on satellites, spaceflight hardware, and other items that are now controlled by ITAR. Furthermore, contravening U.S. interests in attracting foreign students to U.S. universities, the capture of space technology by ITAR has caused serious problems in the teaching of university space science and engineering classes, virtually all of which include non-U.S. students. This report is a summary of a September 2007 workshop in which participants from the space research communities and the export-control administration and policy communities came together to discuss problems, effects, and potential solutions regarding the application of ITAR to space science. The principal themes and ideas that emerged from the discussions are summarized.

Finarelli, Margaret G.↗

NASA NTRS1992

Finite element Euler calculations of unsteady transonic cascade flows

A Galerkin finite element procedure incorporating an explicit Runge-Kutta time-stepping scheme has been developed in this work to solve unsteady transonic flow in cascades. The computational domain is discretized by a globally unstructured but locally structured blade-fitted deformable mesh. The Galerkin approximation is applied to the unsteady Euler equations based on a mixed Eulerian-Lagrangian description. The semi-discretized equations are integrated forward in time using a multistage Runge-Kutta scheme. An artificial dissipation operator of the type proposed by Jameson is adapted in the current scheme to capture shocks and suppress nonphysical oscillations. Phase-shifted boundary conditions are used to reduce the computational domain to a single reference passage. Results for both steady and unsteady transonic flows through cascades are presented and compared to existing finite volume solutions.

Hsiao, Chingteng↗

NASA NTRS1993

Computational techniques for high-speed flows with viscous and chemical effects

Algorithms for solving the Euler and the Navier-Stokes equations in conjunction with chemical kinetic equations are presented. The convective flux is estimated from a quasi one dimensional interpolation procedure. Shock, contact, and expansion waves and thermochemical nonequilibrium phenomena are captured by the Lax-Friedrichs technique. Relaxation techniques were developed to enhance their effectiveness in dealing with spatial and temporal stiffness associated with the physical problems. Both explicit and implicit smoothers were implemented into the standard multigrid time stepping method. Unsteady and steady scalar problems are discussed. A perfect gas and equilibrium air shock tube problem is investigated. Numerical schemes and techniques are compared for the problems of shock and boundary layer interaction and three dimensional viscous, nonequilibrium flow encompassing an aerobrake. The results are comparable in accuracy against other high order non-oscillatory techniques. The multigrid methods are assessed using a Mach 8 flow over a complete planar body, a sphere, and a blunt delta wing at 20 deg incidence. Applying an implicit multigrid method on a nested grid of 128 by 64 nodes the reduction factor is 0.25. The central processing unit reduction factor is 2.2 after both the single and multigrid Runge-Kutta solutions converged to machine zero on a grid of 37 by 41 by 73 nodes.

Li, C. P.↗

NASA NTRS2004

Parallel 3D Mortar Element Method for Adaptive Nonconforming Meshes

High order methods are frequently used in computational simulation for their high accuracy. An efficient way to avoid unnecessary computation in smooth regions of the solution is to use adaptive meshes which employ fine grids only in areas where they are needed. Nonconforming spectral elements allow the grid to be flexibly adjusted to satisfy the computational accuracy requirements. The method is suitable for computational simulations of unsteady problems with very disparate length scales or unsteady moving features, such as heat transfer, fluid dynamics or flame combustion. In this work, we select the Mark Element Method (MEM) to handle the non-conforming interfaces between elements. A new technique is introduced to efficiently implement MEM in 3-D nonconforming meshes. By introducing an "intermediate mortar", the proposed method decomposes the projection between 3-D elements and mortars into two steps. In each step, projection matrices derived in 2-D are used. The two-step method avoids explicitly forming/deriving large projection matrices for 3-D meshes, and also helps to simplify the implementation. This new technique can be used for both h- and p-type adaptation. This method is applied to an unsteady 3-D moving heat source problem. With our new MEM implementation, mesh adaptation is able to efficiently refine the grid near the heat source and coarsen the grid once the heat source passes. The savings in computational work resulting from the dynamic mesh adaptation is demonstrated by the reduction of the the number of elements used and CPU time spent. MEM and mesh adaptation, respectively, bring irregularity and dynamics to the computer memory access pattern. Hence, they provide a good way to gauge the performance of computer systems when running scientific applications whose memory access patterns are irregular and unpredictable. We select a 3-D moving heat source problem as the Unstructured Adaptive (UA) grid benchmark, a new component of the NAS Parallel Benchmarks (NPB). In this paper, we present some interesting performance results of ow OpenMP parallel implementation on different architectures such as the SGI Origin2000, SGI Altix, and Cray MTA-2.

Feng, Huiyu↗

NASA NTRSDate not supplied

Cyber Resiliency and the Implementation of a Host-Based Intrusion Detection System in an Urban Air Mobility Environment

With the growth in urban air mobility systems and the increasing reliance on interconnected technologies, ensuring the security of these complex infrastructures has become critical. As cities evolve into smart urban centers, the vulnerability to cyber threats escalates, possibly endangering citizens’ safety and the efficiency of transportation networks. In response to these challenges, this paper presents a study on implementing a Host-Based Intrusion Detection System (HIDS) tailored explicitly to urban mobility environments’ unique demands. This study explores the design, development, and deployment of the proposed HIDS, focusing on its adaptability to monitor the hybrid nature of the urban mobility environment. Leveraging machine learning algorithms and anomaly detection techniques, the HIDS is equipped to continuously monitor and analyze the behavior of individual host systems, vehicles, and devices, thereby providing a proactive approach to threat detection. Implementing a HIDS is a pivotal strategy for enhancing cyber resiliency, as it gives an organization granular visibility into internal system activities, enables rapid detection and response to anomalous behavior and cyber threats, and fortifies the organization’s overall cybersecurity posture. In conclusion, this paper highlights the significance of host-based intrusion detection in urban mobility environments and underscores the necessity of tailored security solutions to safeguard against emerging cyber threats.

UAM↗

NASA NTRS2017

GEOS Atmospheric Model: Challenges at Exascale

The Goddard Earth Observing System (GEOS) model at NASA's Global Modeling and Assimilation Office (GMAO) is used to simulate the multi-scale variability of the Earth's weather and climate, and is used primarily to assimilate conventional and satellite-based observations for weather forecasting and reanalysis. In addition, assimilations coupled to an ocean model are used for longer-term forecasting (e.g., El Nino) on seasonal to interannual times-scales. The GMAO's research activities, including system development, focus on numerous time and space scales, as detailed on the GMAO website, where they are tabbed under five major themes: Weather Analysis and Prediction; Seasonal-Decadal Analysis and Prediction; Reanalysis; Global Mesoscale Modeling, and Observing System Science. A brief description of the GEOS systems can also be found at the GMAO website. GEOS executes as a collection of earth system components connected through the Earth System Modeling Framework (ESMF). The ESMF layer is supplemented with the MAPL (Modeling, Analysis, and Prediction Layer) software toolkit developed at the GMAO, which facilitates the organization of the computational components into a hierarchical architecture. GEOS systems run in parallel using a horizontal decomposition of the Earth's sphere into processing elements (PEs). Communication between PEs is primarily through a message passing framework, using the message passing interface (MPI), and through explicit use of node-level shared memory access via the SHMEM (Symmetric Hierarchical Memory access) protocol. Production GEOS weather prediction systems currently run at 12.5-kilometer horizontal resolution with 72 vertical levels decomposed into PEs associated with 5,400 MPI processes. Research GEOS systems run at resolutions as fine as 1.5 kilometers globally using as many as 30,000 MPI processes. Looking forward, these systems can be expected to see a 2 times increase in horizontal resolution every two to three years, as well as less frequent increases in vertical resolution. Coupling these resolution changes with increases in complexity, the computational demands on the GEOS production and research systems should easily increase 100-fold over the next five years. Currently, our 12.5 kilometer weather prediction system narrowly meets the time-to-solution demands of a near-real-time production system. Work is now in progress to take advantage of a hybrid MPI-OpenMP parallelism strategy, in an attempt to achieve a modest two-fold speed-up to accommodate an immediate demand due to increased scientific complexity and an increase in vertical resolution. Pursuing demands that require a 10- to 100-fold increases or more, however, would require a detailed exploration of the computational profile of GEOS, as well as targeted solutions using more advanced high-performance computing technologies. Increased computing demands of 100-fold will be required within five years based on anticipated changes in the GEOS production systems, increases of 1000-fold can be anticipated over the next ten years.

ESMF↗

NASA NTRS2000

Supercomputing Aspects for Simulating Incompressible Flow

The primary objective of this research is to support the design of liquid rocket systems for the Advanced Space Transportation System. Since the space launch systems in the near future are likely to rely on liquid rocket engines, increasing the efficiency and reliability of the engine components is an important task. One of the major problems in the liquid rocket engine is to understand fluid dynamics of fuel and oxidizer flows from the fuel tank to plume. Understanding the flow through the entire turbo-pump geometry through numerical simulation will be of significant value toward design. One of the milestones of this effort is to develop, apply and demonstrate the capability and accuracy of 3D CFD methods as efficient design analysis tools on high performance computer platforms. The development of the Message Passage Interface (MPI) and Multi Level Parallel (MLP) versions of the INS3D code is currently underway. The serial version of INS3D code is a multidimensional incompressible Navier-Stokes solver based on overset grid technology, INS3D-MPI is based on the explicit massage-passing interface across processors and is primarily suited for distributed memory systems. INS3D-MLP is based on multi-level parallel method and is suitable for distributed-shared memory systems. For the entire turbo-pump simulations, moving boundary capability and efficient time-accurate integration methods are built in the flow solver, To handle the geometric complexity and moving boundary problems, an overset grid scheme is incorporated with the solver so that new connectivity data will be obtained at each time step. The Chimera overlapped grid scheme allows subdomains move relative to each other, and provides a great flexibility when the boundary movement creates large displacements. Two numerical procedures, one based on artificial compressibility method and the other pressure projection method, are outlined for obtaining time-accurate solutions of the incompressible Navier-Stokes equations. The performance of the two methods is compared by obtaining unsteady solutions for the evolution of twin vortices behind a flat plate. Calculated results are compared with experimental and other numerical results. For an unsteady flow, which requires small physical time step, the pressure projection method was found to be computationally efficient since it does not require any subiteration procedure. It was observed that the artificial compressibility method requires a fast convergence scheme at each physical time step in order to satisfy the incompressibility condition. This was obtained by using a GMRES-ILU(0) solver in present computations. When a line-relaxation scheme was used, the time accuracy was degraded and time-accurate computations became very expensive.

Kwak, Dochan↗

DOE OSTI2018

Experimental Determination of Power Losses and Heat Generation in Solar Cells for Photovoltaic-Thermal Applications

Solar cell thermal recovery has recently attracted more and more attention as a viable solution to increase photovoltaic efficiency. However, the convenience of the implementation of such a strategy is bound to the precise evaluation of the recoverable thermal power and to a proper definition of the losses occurring within the solar device. In this work, we establish a framework in which all solar cell losses are defined and described. The aim is to determine the components of the thermal fraction. We therefore describe an experimental method to precisely compute these components from the measurement of the external quantum efficiency, the current–voltage characteristics, and the reflectivity of the solar cell. Applying this method to three different types of devices (bulk, thin film, and multi-junction), we could exploit the relationships among losses for the main three generations of PV cells available nowadays. In addition, since the model is explicitly wavelength dependent, we could show how thermal losses in all cells occur over the whole solar spectrum, and not only in the infrared region. This demonstrates that profitable thermal harvesting technologies should enable heat recovery over the whole solar spectral range.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Upscaling Reactive Transport and Clogging in Shale Microcracks by Deep Learning

Fracture networks in shales exhibit multiscale features. A rock system may contain a few main fractures and thousands of microcracks, whose length and aperture are orders of magnitude smaller than the former. It is computationally prohibitive to resolve all the fractures explicitly for such multiscale fracture networks. One traditional approach is to model the small-scale features (e.g., microcracks in shales) as an effective medium. Although this fracture-matrix conceptualization significantly reduces the problem complexity, there are classes of physical processes that cannot be accurately upscaled by effective medium approximations, e.g., microcrack clogging during mineral reactions. Here, we employ deep learning in place of effective medium theory to upscale physical processes in small-scale features. Specifically, we consider reactive transport in a fracture-microcrack network where microcracks can be clogged by precipitation. A deep learning multiscale algorithm is developed, in which the microcracks are upscaled as a wall boundary condition of the main fractures. The wall boundary condition is constructed by recurrent neural networks, which take concentration histories as input and predict the solute transport from main fractures to microcracks. The deep learning multiscale algorithm is firstly employed in specific scenarios, then a general model is developed which can work under various conditions. The new approach is validated against fully resolved simulations and an analytical solution, providing a reliable and efficient solution for problems that cannot be upscaled by effective medium models.

58 GEOSCIENCES↗

DOE OSTI2019

Online Primal-Dual Methods With Measurement Feedback for Time-Varying Convex Optimization

This paper addresses the design and analysis of feedback-based online algorithms to control systems or networked systems based on performance objectives and engineering constraints that may evolve over time. The emerging timevarying convex optimization formalism is leveraged to model optimal operational trajectories of the systems, as well as explicit local and network-level operational constraints. Departing from existing batch and feed-forward optimization approaches, the design of the algorithms capitalizes on an online implementation of primal-dual projected-gradient methods; the gradient steps are, however, suitably modified to accommodate feedback from the system in the form of measurements - hence, the term 'online optimization with feedback.' By virtue of this approach, the resultant algorithms can cope with model mismatches in the algebraic representation of the system states and outputs, they avoid pervasive measurements of exogenous inputs, and they naturally lend themselves to a distributed implementation. Under suitable assumptions, analytical convergence claims are established in terms of dynamic regret. Furthermore, when the synthesis of the feedback-based online algorithms is based on a regularized Lagrangian function, Q-linear convergence to solutions of the time-varying optimization problem is shown.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1992

A transient FETI methodology for large-scale parallel implicit computations in structural mechanics

Explicit codes are often used to simulate the nonlinear dynamics of large-scale structural systems, even for low frequency response, because the storage and CPU requirements entailed by the repeated factorizations traditionally found in implicit codes rapidly overwhelm the available computing resources. With the advent of parallel processing, this trend is accelerating because explicit schemes are also easier to parallelize than implicit ones. However, the time step restriction imposed by the Courant stability condition on all explicit schemes cannot yet -- and perhaps will never -- be offset by the speed of parallel hardware. Therefore, it is essential to develop efficient and robust alternatives to direct methods that are also amenable to massively parallel processing because implicit codes using unconditionally stable time-integration algorithms are computationally more efficient when simulating low-frequency dynamics. Here we present a domain decomposition method for implicit schemes that requires significantly less storage than factorization algorithms, that is several times faster than other popular direct and iterative methods, that can be easily implemented on both shared and local memory parallel processors, and that is both computationally and communication-wise efficient. The proposed transient domain decomposition method is an extension of the method of Finite Element Tearing and Interconnecting (FETI) developed by Farhat and Roux for the solution of static problems. Serial and parallel performance results on the CRAY Y-MP/8 and the iPSC-860/128 systems are reported and analyzed for realistic structural dynamics problems. These results establish the superiority of the FETI method over both the serial/parallel conjugate gradient algorithm with diagonal scaling and the serial/parallel direct method, and contrast the computational power of the iPSC-860/128 parallel processor with that of the CRAY Y-MP/8 system.

Farhat, Charbel↗

NASA NTRSDate not supplied

Natural Fiber Simulations and Analysis for Composites

As the U.S. government and the aviation industry strive to achieve net-zero carbon emissions by 2050, the Sustainable Manufacturing of Aircraft (SUMAC) project, supported by the Convergent Aeronautics Solutions (CAS) program of the National Aeronautics and Space Administration (NASA), aims to develop sustainably derived thermoplastic composites and manufacturing technologies for future aviation. A multidisciplinary team of experts drives this initiative through a collective effort. The team’s key focus areas are sustainably derived thermoplastic resins, natural fiber reinforcement, composite manufacturing, structural health monitoring, computational materials modeling, and systems analysis. This presentation will give an overview of the SUMAC project. Fiber-scale microscopy analysis characterized fiber cross sections finding that hemp and flax fibers are very deformable and non-circular (circularities of 0.2 were observed), and diameters range from submicron to 20 μm. Fiber shapes range from flattened, with aspect ratios Rlong/Rshort up to 5, to round, Rlong/Rshort =1. And Fiber core perimeters, which likely drives deformability, were calculated Pcore=7 μm. Explicit-fiber yarn simulations, parameterized from single-fiber measurements, resolved and identified slack as a cause for yarn strain-hardening tensile behavior. The bonded network model of PLA, PHA and PA11 resins captures tensile behavior, and can model an infused weave. Computational models of the weave unit cells matched the pattern (including plain, twill and triaxial braid), yarn ply (1to 2), and yarn twist from optical microscopy.

thermoplastic↗

NASA NTRSDate not supplied

Natural Fiber Simulations and Analysis for Composites

thermoplastic↗

DOE OSTI2020

GrAMME: Semisupervised Learning Using Multilayered Graph Attention Models

Modern data analysis pipelines are becoming increasingly complex due to the presence of multiview information sources. While graphs are effective in modeling complex relationships, in many scenarios, a single graph is rarely sufficient to succinctly represent all interactions, and hence, multilayered graphs have become popular. Though this leads to richer representations, extending solutions from the single-graph case is not straightforward. Consequently, there is a strong need for novel solutions to solve classical problems, such as node classification, in the multilayered case. In this article, we consider the problem of semisupervised learning with multilayered graphs. Though deep network embeddings, e.g., DeepWalk, are widely adopted for community discovery, we argue that feature learning with random node attributes, using graph neural networks, can be more effective. To this end, we propose to use attention models for effective feature learning and develop two novel architectures, GrAMME-SG and GrAMME-Fusion, that exploit the interlayer dependences for building multilayered graph embeddings. Using empirical studies on several benchmark data sets, we evaluate the proposed approaches and demonstrate significant performance improvements in comparison with the state-of-the-art network embedding strategies. The results also show that using simple random features is an effective choice, even in cases where explicit node attributes are not available.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1999

Implicit Space-Time Conservation Element and Solution Element Schemes

Artificial numerical dissipation is in important issue in large Reynolds number computations. In such computations, the artificial dissipation inherent in traditional numerical schemes can overwhelm the physical dissipation and yield inaccurate results on meshes of practical size. In the present work, the space-time conservation element and solution element method is used to construct new and accurate implicit numerical schemes such that artificial numerical dissipation will not overwhelm physical dissipation. Specifically, these schemes have the property that numerical dissipation vanishes when the physical viscosity goes to zero. These new schemes therefore accurately model the physical dissipation even when it is extremely small. The new schemes presented are two highly accurate implicit solvers for a convection-diffusion equation. The two schemes become identical in the pure convection case, and in the pure diffusion case. The implicit schemes are applicable over the whole Reynolds number range, from purely diffusive equations to convection-dominated equations with very small viscosity. The stability and consistency of the schemes are analysed, and some numerical results are presented. It is shown that, in the inviscid case, the new schemes become explicit and their amplification factors are identical to those of the Leapfrog scheme. On the other hand, in the pure diffusion case, their principal amplification factor becomes the amplification factor of the Crank-Nicolson scheme.

Chang, Sin-Chung↗

DOE OSTI2018

Closures for Two-fluid Five-moment Equations for Magnetized Plasmas (Final Scientific Report)

In the proposed work, we will develop a complete set of closures for two-fluid five-moment equations for magnetized plasmas. Specifically, we propose to obtain explicit formulas for electrons and ions to express heat flow, viscosity, frictional force, and collisional heating in terms of density, and temperature, flow velocity. For this purpose, we solve a set of general moment equations for the relevant closure moments. An infinite hierarchy of general moment equations is completely equivalent to the original Landau-Fokker-Planck kinetic equation. In the small gyro-period expansion, the parallel components of the general moment equations agree with the moments of the drift-kinetic equation (DKE). The advantages of solving the moment equations include (i) an exact treatment of the collision operator, (ii) closure and transport relations with no flux-surface average, and (iii) a unified form of closures for general collisionality. Practically we solve a truncated set of moment equations and hence must verify the convergence of the solutions by increasing number of moments. The parallel integral (nonlocal) closures obtained by solving a set of linearized parallel moment equations are useful only when the nonlinear coupling of moments to the temperature and magnetic field gradient terms is negligible. When the nonlinear coupling terms are substantial, we propose a Fourier transform method to solve the parallel moment equations. By Fourier-expanding the magnetic field, we can convert the differential equations of parallel moments to linear algebraic equations for Fourier components of the moments. The convergence of the solutions can be confirmed by increasing the number of Fourier modes. Our preliminary study in axisymmetric circular magnetic geometry with a large aspect ratio shows that (i) the solutions for Fourier modes n=0 and n=1 converge when modes up to n=2 are included in the expansion, and (ii) lower collisionality requires more moments for convergent closures, as in the case of the integral closures. The proposed work will start from this simple magnetic geometry to find general parallel closures and then be generalized to explore a non-circular magnetic field with finite aspect-ratio. With parallel moments known, the perpendicular component of moment closures can be obtained by inverting the generalized cross product operator in the general moment equations. These efforts will be performed in conjunction with several multi-institutional projects, NIMROD, the Center for Extended MHD Modeling (CEMM), and the Plasma Science and Innovation (PSI) Center.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Investigating Inherent Numerical Stabilization for the Moist, Compressible, Non‐Hydrostatic Euler Equations on Collocated Grids

This study investigates inherent numerical dissipation due to upwind fluxes and reconstruction strategies for collocated Finite-Volume integration of the Euler equations. Idealized supercell simulations are used without any explicit dissipation. Flux terms are split into: mass flux, pressure, and advected quantities. They are computed with the following upwind strategies: central, advectively upwind, and acoustically upwind. This is performed for third and ninth-order-accurate reconstructions with and without Weighted Essentially Non-Oscillatory limiting. Acoustic-only upwinding for pressure and mass flux terms and advective-only upwinding for advected quantities is the most flexible simplification found. It reduces data movement and computations. Assuming a constant speed of sound in acoustic upwinding gives similar results to using the true speed of sound. Dissipation from upwind adapts automatically to grid spacing, time step, reconstruction accuracy, and flow smoothness. While stability is maintained even at 21st-order spatial accuracy, there is a limit to the spatial order of accuracy for which upwinding alone can create a realizable solution in the conditions of this study. Convex combinations of upwind and central solutions for flux terms also reduced dissipation, but as the central proportion grows, solutions become physically unrealizable. The range of length scales of the kinetic energy spectra can be extended along k −5/3 to smaller spatial scales by reducing dissipation either with higher-order reconstructions or using convex combinations of upwind and central fluxes. However, not all extensions of the length scale range along k −5/3 exhibit physically realizable solutions, even though the spectra appear to be physical.

54 ENVIRONMENTAL SCIENCES↗