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Annual IC Progress Report

The goal of this project is to computationally investigate the progenitors of astrophysical gamma-ray bursts (GRB), the most extreme explosions in the universe across length and time scales. We have developed a cutting-edge, code-bridging approach to exploring the physics behind these luminous events to test the hypothesis that GRBs with electromagnetic radio emission originate from massive star (MS) and black hole (BH) binary systems. Our multi-scale, multi-physics theoretical framework for GRBs is based on solving well-defined and testable hydrodynamics problems associated with the dynamical evolution of the system. We solve stages of the evolution in a tractable way with a suite of well-developed state-of-the-art computational tools that include the stellar evolution code MESA, the general relativistic magnetohydrodynamics (GRMHD) code Athena++, and the binary black hole (BBH) population synthesis code COSMIC, as well as a number of self-written python post-processing tools.

79 ASTRONOMY AND ASTROPHYSICS↗

Two-dimensional coherent spectrum of high-spin models via a quantum computing approach

Here in this work we present and benchmark a quantum computing approach to calculate the two-dimensional coherent spectrum (2DCS) of high-spin models. Our approach is based on simulating their real-time dynamics in the presence of several magnetic field pulses, which are spaced in time. We utilize the adaptive variational quantum dynamics simulation algorithm for the study due to its compact circuits, which enables simulations over sufficiently long times to achieve the required resolution in frequency space. Specifically, we consider an antiferromagnetic quantum spin model that incorporates Dzyaloshinskii-Moriya interactions and single-ion anisotropy. The obtained 2DCS spectra exhibit distinct peaks at multiples of the magnon frequency, arising from transitions between different eigenstates of the unperturbed Hamiltonian. By comparing the one-dimensional coherent spectrum with 2DCS, we demonstrate that 2DCS provides a higher resolution of the energy spectrum. We further investigate how the quantum resources scale with the magnitude of the spin using two different binary encodings of the high-spin operators: the standard binary encoding and the Gray code. At low magnetic fields both encodings require comparable quantum resources, but at larger field strengths the Gray code is advantageous. Numerical simulations for spin models with increasing number of sites indicate a polynomial system-size scaling for quantum resources. Lastly, we compare the numerical 2DCS with experimental results on a rare-earth orthoferrite system. The observed strength of the magnonic high-harmonic generation signals in the 2DCS of the quantum high-spin model aligns well with the experimental data, showing significant improvement over the corresponding mean-field results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DECOVALEX-2023: Task D Final Report

Task D of DECOVALEX-2023 is focused on the simulation of the coupled thermal hydraulic-mechanical (THM) behaviour in the full-scale engineered barrier system (EBS). The Horonobe EBS experiment is the demonstration of the full-scale EBS in the underground research laboratory (URL) (performed by JAEA in the Horonobe URL in Japan). Task D consisted of the three steps, a preliminary step (Step 0), simulation of the laboratory tests (Step 1) and simulation of the in-situ full-scale EBS experiment (Step 2). Since the Horonobe EBS experiment demonstrates the vertical emplacement option of the EBS, the experiment gallery is also backfilled with the backfill material. Therefore, interaction between the EBS and the backfill material can also be demonstrated, such as deformation (change of density) of the buffer material. The underground water in the Horonobe URL is saline. This fact adds chemical processes to THM behaviour. For example, mechanical properties (such as swelling pressure of the buffer material and backfill material) and hydraulic properties (such as permeability of the buffer material and backfill material) change depending on the water chemistry. Task D was therefore a challenging Task focused on not only the relatively simple THM behaviour but also complex THM behaviour including chemical processes. Six research teams (BGR, CAS, JAEA, KAERI, SNL and Taipower) participated the Task D. BGR, CAS, JAEA, KAERI and Taipower research teams selected a THM approach, while the SNL research team selected a TH approach. Step 1 involved the simulation of laboratory test results and was important to check the numerical codes developed by the research teams. Step 1 was divided into four sub steps. The simulation results through the Step 1 identified the parameters for simulation of the Step 2. Basic parameters of the materials (buffer material, backfill material, rock mass, concrete, sand) were provided by JAEA. Special parameters which research team needed were identified by back analysis of Step 1. Most notably the mechanical behaviour of swelling and displacement depended on the applied model (elastic model or elastoplastic model). Parameters such as Young’s modulus were found to need smaller values than characterised in the fundamental laboratory test results (Step 1-1, 1-2) for the elastic model. Although laboratory experiments are usually simple, test results contained some error. For example, if the saturation level is 100 % or higher, it should be considered an error. This situation was presented in the Step 1-3. A possible reason is that the buffer material is a mixture of bentonite and silica sand. When a specimen is cut to measure volume or weight, sand grains will affect the measurement data. In Step 2, boundary conditions such as temperature on the surface of the simulated overpack, heater power of the electrical heaters installed in the simulated overpack, injection pressure and inflow rate of the test water, were applied. The outer boundary conditions can be selected using measured data (injection pressure and inflow rate of the test water that is controlled by the injection systems installed in the sand layer around the buffer material and in the boundary between backfill material and concrete support). Since such measured data has some noise, research teams developed their own simplified boundary conditions. Inner boundary conditions can be selected using measured data as heater power and temperature on the surface of the simulated overpack. These data also contain some noise, so research teams developed their own simplified developed boundary conditions. Task D validated various approaches thorough the simulation of the in-situ full scale EBS system including backfill of the gallery: variations in the coupling processes (THM or THC), analysis codes, and boundary conditions. Temperature distribution in the buffer material was simulated well by all research teams. This means thermal behaviour is not sensitive to the simulation approaches. Although the water content distribution on the outside of the buffer material was well simulated by all research teams, the simulation results differ from the measured values inside the buffer material (at the centre and inside, near the simulated overpack). The buffer material is made from tap water, but in the in-situ experiment, saline groundwater infiltrates the buffer material. Therefore, the selection of the hydraulic parameters of the buffer material greatly affects the simulation results of the re saturation behaviour of the buffer material. In the Horonobe EBS experiment, measured values suitable for validating the simulation results were not obtained near the simulated overpack. When simulating the pressure and deformation of the buffer material, the measurement data is easily affected by the installation conditions of the measurement sensors, so verifying the measurement data itself remains an issue. Mechanical simulation results differ depending on whether they are considered as elastic or elastoplastic phenomena. The accuracy of measured in-situ data can be assessed by detailed analysis comparing sampling specimen analysis and measured data. The Horonobe EBS experiment is scheduled to be dismantled in the future (FY2026 and 2027). This detailed dismantling investigation will finally confirm the measured data.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Final Review of FY23 ASC ATDM L2 Milestone, MRT #8541, ATDM Multiphysics Scaling on EAS-3

As displayed in the FY23 ASC Implementation Plan (IP) and the Milestone Reporting Tool (MRT), the milestone description and completion criteria state: Demonstrate the capability to execute mission-relevant calculations with a multiphysics code from the Ristra project at scale on the pre-El Capitan Early Access System 3 (EAS-3). These calculations must use the GPU hardware available on EAS-3, the AMD MI-250s, to achieve any reasonable performance.

97 MATHEMATICS AND COMPUTING↗

A VLSI single chip (255,223) Reed-Solomon encoder

A description of a working single chip implementation of a Reed-Solomon encoder. The code used is the Consultative Committee on Space Data Systems (CCSDS) standard (255,223) code. The architecture that leads to this single very large scale integration chip design makes use of a bit-serial finite field multiplication algorithm of E. R. Berlekamp.

Deutsch, L. J.↗

Olympus propagation and communication experiments in the US

The participation of the United States in Olympus experiments is outlined. These include, basic propagation measurement, the Cooperative Data Exchange Experiment (CODE), a rain scatter interference measurement, a small scale diversity experiment, the Personal Access Satellite System (PASS), and all systems that use adaptive fade compensation techniques similar to the Advanced Communications Technology Satellite (ACTS) of NASA.

Davarian, F.↗

Short Duration Base Heating Test Improvements

Significant improvements have been made to a short duration space launch vehicle base heating test technique. This technique was first developed during the 1960's to investigate launch vehicle plume induced convective environments. Recent improvements include the use of coiled nitrogen buffer gas lines upstream of the hydrogen / oxygen propellant charge tubes, fast acting solenoid valves, stand alone gas delivery and data acquisition systems, and an integrated model design code. Technique improvements were successfully demonstrated during a 2.25% scale X-33 base heating test conducted in the NASA/MSFC Nozzle Test Facility in early 1999. Cost savings of approximately an order of magnitude over previous tests were realized due in large part to these improvements.

Bender, Robert L.↗

An overview of aeroelasticity studies for the National Aerospace Plane

The National Aero-Space Plane (NASP), or X-30, is a single-stage-to-orbit vehicle that is designed to takeoff and land on conventional runways. Research in aeroelasticity was conducted by NASA and the Wright Laboratory to support the design of a flight vehicle by the national contractor team. This research includes the development of new computational codes for predicting unsteady aerodynamic pressures. In addition, studies were conducted to determine the aerodynamic heating effects on vehicle aeroelasticity and to determine the effects of fuselage flexibility on the stability of the control systems. It also includes the testing of scale models to better understand the aeroelastic behavior of the X-30 and to obtain data for code validation and correlation. This paper presents an overview of the aeroelastic research which has been conducted to support the airframe design.

Ricketts, Rodney H.↗

An overview of aeroelasticity studies for the National Aero-Space Plane

The National Aero-Space Plane (NASP), or X-30, is a single-stage-to-orbit vehicle that is designed to takeoff and land on conventional runways. Research in aeroelasticity was conducted by the NASA and the Wright Laboratory to support the design of a flight vehicle by the national contractor team. This research includes the development of new computational codes for predicting unsteady aerodynamic pressures. In addition, studies were conducted to determine the aerodynamic heating effects on vehicle aeroelasticity and to determine the effects of fuselage flexibility on the stability of the control systems. It also includes the testing of scale models to better understand the aeroelastic behavior of the X-30 and to obtain data for code validation and correlation. This paper presents an overview of the aeroelastic research which has been conducted to support the airframe design.

Ricketts, Rodney H.↗

Design and Modeling of a Coded-Interleaving System in the Presence of Fading

Future deep space links are migrating towards higher frequency bands such as Ka band and optical. These links are susceptible to non linear effects (e.g. cloud coverage, atmospheric turbulence, scintillation, antenna mis-pointing, jitter, relative motion, etc.) that cause various degrees of fading loss over various time scales. We consider a channel experiencing block fading where the channel coherence time is a lot longer than the length of a codeword. As long as the fading duration is not excessive, an interleaver can be used in a coded-communication system that randomizes the fades among symbols of multiple codewords. This achieves an “averaging” effect that spreads the signal energy more evenly among the codewords, and improves the likelihood that each of them can be decoded correctly. For simplicity, we consider a block interleaver where adjacent symbols of a codeword have a fixed delay (or separation) with each other, and investigate the error-rate performance of a coded-interleaving system (with fixed and finite interleaving depth) in the presence of block fading. Unlike prior research which assumes theoretical channel coherence models, we aim to build upon our analysis using empirical spacecraft signal measurements obtained with the Deep Space Network, and to use the fundamental theories of probability and statistics (e.g. variations of Law of Large Numbers) to quantify the error-rate performance of the coded-interleaving system. We propose to utilize these results in the design of a two-dimensional coded-interleaving system for fading channels.

Sanchez-Net, Marc↗

Control Activity in Support of NASA Turbine Based Combined Cycle (TBCC) Research

Control research for a Turbine Based Combined Cycle (TBCC) propulsion system is the current focus of the Hypersonic Guidance, Navigation, and Control (GN&C) discipline team. The ongoing work at the NASA Glenn Research Center (GRC) supports the Hypersonic GN&C effort in developing tools to aid the design of control algorithms to manage a TBCC airbreathing propulsion system during a critical operating period. The critical operating period being addressed in this paper is the span when the propulsion system transitions from one cycle to another, referred to as mode transition. One such tool, that is a basic need for control system design activities, is computational models (hereto forth referred to as models) of the propulsion system. The models of interest for designing and testing controllers are Control Development Models (CDMs) and Control Validation Models (CVMs). CDMs and CVMs are needed for each of the following propulsion system elements: inlet, turbine engine, ram/scram dual-mode combustor, and nozzle. This paper presents an overall architecture for a TBCC propulsion system model that includes all of the propulsion system elements. Efforts are under way, focusing on one of the propulsion system elements, to develop CDMs and CVMs for a TBCC propulsion system inlet. The TBCC inlet aerodynamic design being modeled is that of the Combined-Cycle Engine (CCE) Testbed. The CCE Testbed is a large-scale model of an aerodynamic design that was verified in a small-scale screening experiment. The modeling approach includes employing existing state-of-the-art simulation codes, developing new dynamic simulations, and performing system identification experiments on the hardware in the NASA GRC 10 by10-Foot Supersonic Wind Tunnel. The developed CDMs and CVMs will be available for control studies prior to hardware buildup. The system identification experiments on the CCE Testbed will characterize the necessary dynamics to be represented in CDMs for control design. These system identification models will also be the reference models to validate the CDM and CVM models. Validated models will give value to the tools used to develop the models.

Stueber, Thomas J.↗

Overview of the Turbine Based Combined Cycle Discipline

The NASA Fundamental Aeronautics Hypersonics project is focused on technologies for combined cycle, airbreathing propulsions systems to enable reusable launch systems for access to space. Turbine Based Combined Cycle (TBCC) propulsion systems offer specific impulse (Isp) improvements over rocket-based propulsion systems in the subsonic takeoff and return mission segments and offer improved safety. The potential to realize more aircraft-like operations with expanded launch site capability and reduced system maintenance are additional benefits. The most critical TBCC enabling technologies as identified in the National Aeronautics Institute (NAI) study were: 1) mode transition from the low speed propulsion system to the high speed propulsion system, 2) high Mach turbine engine development, 3) transonic aero-propulsion performance, 4) low-Mach-number dual-mode scramjet operation, 5) innovative 3-D flowpath concepts and 6) innovative turbine based combined cycle integration. To address several of these key TBCC challenges, NASA s Hypersonics project (TBCC Discipline) initiated an experimental mode transition task that includes an analytic research endeavor to assess the state-of-the-art of propulsion system performance and design codes. This initiative includes inlet fluid and turbine performance codes and engineering-level algorithms. This effort has been focused on the Combined Cycle Engine Large-Scale Inlet Mode Transition Experiment (CCE LIMX) which is a fully integrated TBCC propulsion system with flow path sizing consistent with previous NASA and DoD proposed Hypersonic experimental flight test plans. This experiment is being tested in the NASA-GRC 10 x 10 Supersonic Wind Tunnel (SWT) Facility. The goal of this activity is to address key hypersonic combined-cycle-engine issues: (1) dual integrated inlet operability and performance issues unstart constraints, distortion constraints, bleed requirements, controls, and operability margins, (2) mode-transition constraints imposed by the turbine and the ramjet/scramjet flow paths (imposed variable geometry requirements), (3) turbine engine transients (and associated time scales) during transition, (4) high-altitude turbine engine re-light, and (5) the operating constraints of a Mach 3-7 combustor (specific to the TBCC). The model will be tested in several test phases to develop a unique TBCC database to assess and validate design and analysis tools and address operability, integration, and interaction issues for this class of advanced propulsion systems. The test article and all support equipment is complete and available at the facility. The test article installation and facility build-up in preparation for the inlet performance and operability characterization is near completion and testing is planned to commence in FY11.

Thomas, Scott R.↗

EVs-at-RISC: A Secure and Resilient Interoperable SCM Control System Architecture for Electric Vehicle’s-at-Scale (Final Technical Report)

The EVs-at-RISC project was a five-year research, development, and demonstration initiative to create foundational tools for utility-scale fleet aggregation and Smart Charge Management (SCM) of Electric Vehicles (EV), Electric Vehicle Charging Infrastructure (EVCI), and related Distributed Energy Resources (DER). Rather than seeking to develop and demonstrate highly perfected SCM algorithms and control strategies, this project instead focused on creating foundational software solutions that enable unprecedented digital interoperability across the communications technologies and vendor platforms used to manage EV , EVCI, and DER, as well as existing energy management infrastructure operated by utilities, grid operators, and aggregators. This project then extends these novel interoperability capabilities to develop and deploy powerful middleware abstractions across grid edge networks and EVCI/DER fleet aggregations incorporating modern software tools and best practices, such as CI/CD, to bring the immense capabilities of infrastructure-as-code and policy-as-code to modern grid edge network environments. This addresses the foremost systemic issues preventing realization of any net operational benefits from scaled deployment of behind-the-meter EV, EVCI, and DER assets in electric power grids and markets today. The results of this approach and project unlock massive potential for new SCM capabilities to be easily prototyped, evaluated, and deployed at-scale within the existing grid edge network infrastructure and EVCI/DER technology ecosystem. The EVs-at-RISC project achieves this by extending Open Field Message Bus (OpenFMB), a conceptual model for digital interoperability and distributed intelligence in traditional front-of-meter utility SCADA networks, validating our hypothesis that OpenFMB could be similarly used to solve systemic digital interoperability issues in behind-the-meter environments and unlock real-world utility-scale SCM capabilities without requiring any new proprietary vendor solutions or significant infrastructure reconfiguration.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Updated solid-core nuclear thermal propulsion engine trades

This study examined the application of state-of-the-art propulsion and reactor technologies to a near-term solid-core NERVA-based nuclear thermal propulsion system. Updated reactor performance and weight scaling laws were initially derived and input into a nuclear rocket engine system cycle design analysis code. Nuclear Thermal Propulsion (NTP) engine system weight, size, and performance are presented here for a large range of chamber pressures, nozzle area ratios, and thrust levels for three reactor fuel types operating at their corresponding temperatures. Operational characteristics and design features of representative NTP engine concepts are also presented.

Pelaccio, Dennis G.↗

NASA Tech Briefs, September 2003

Topics include: Oxygen-Partial-Pressure Sensor for Aircraft Oxygen Mask; Three-Dimensional Venturi Sensor for Measuring Extreme Winds; Swarms of Micron-Sized Sensors; Monitoring Volcanoes by Use of Air-Dropped Sensor Packages; Capacitive Sensors for Measuring Masses of Cryogenic Fluids; UHF Microstrip Antenna Array for Synthetic- Aperture Radar; Multimode Broad-Band Patch Antennas; 164-GHz MMIC HEMT Frequency Doubler; GPS Position and Heading Circuitry for Ships; Software for Managing Parametric Studies; Software Aids Visualization of Computed Unsteady Flow; Software for Testing Electroactive Structural Components; Advanced Software for Analysis of High-Speed Rolling-Element Bearings; Web Program for Development of GUIs for Cluster Computers; XML-Based Generator of C++ Code for Integration With GUIs; Oxide Protective Coats for Ir/Re Rocket Combustion Chambers; Simplified Waterproofing of Aerogels; Improved Thermal-Insulation Systems for Low Temperatures; Device for Automated Cutting and Transfer of Plant Shoots; Extension of Liouville Formalism to Postinstability Dynamics; Advances in Thrust-Based Emergency Control of an Airplane; Ultrasonic/Sonic Mechanisms for Drilling and Coring; Exercise Device Would Exert Selectable Constant Resistance; Improved Apparatus for Measuring Distance Between Axles; Six Classes of Diffraction-Based Optoelectronic Instruments; Modernizing Fortran 77 Legacy Codes; Active State Model for Autonomous Systems; Shields for Enhanced Protection Against High-Speed Debris; Scaling of Two-Phase Flows to Partial-Earth Gravity; Neutral-Axis Springs for Thin-Wall Integral Boom Hinges.

Source record↗

Impact of Thermal Scattering Law on Similarity Assessment in Light-Water or Polyethylene-Moderated Systems

A collaborative effort between Pacific Northwest National Laboratory (PNNL) and Oak Ridge National Laboratory (ORNL) is underway to provide a technical basis and methodology for the criticality safety community to use the sum of fractions (SoF) method for generating limits for mixtures of “selected actinide nuclides” included in the ANSI/ANS 8.15 standard. The PNNL scope in this project is to define a range of mixtures of 233 U, 235 U, and 239 Pu moderated with either light water or polyethylene and to examine the critical masses for these mixtures. The ORNL scope is primarily to provide validation support for these studies. More complete discussion of the project and its validation aspects will be presented at the upcoming International Conference on Nuclear Criticality Safety (ICNC) this Fall in Sendai, Japan. Clear differences in benchmark similarity to application systems as assessed by the integral parameter ck are noted in the validation studies performed as part of this project as a function of moderator. The c k value is a correlation coefficient that represents that amount of shared uncertainty in k eff due to cross sections between two systems. Individual nuclide-reaction contributions between the two systems can be simply summed to arrive at the total c k value. Specifically, the c k values for light-water–moderated solution experiments are higher for a water-moderated application than for a polyethylene-moderated application. This result is neither totally unexpected nor surprising, but the magnitude of the difference was difficult to anticipate. The TSUNAMI sequence, in the SCALE 6.2.4 code package developed by ORNL, was used to generate eigenvalues and reactivity effects with perturbation-theory based approach through sensitivity coefficients for all nuclides in the system with all reactions and energy groups. The TSUNAMI-Indices and Parameters (IP) sequence then uses the sensitivity data generated through TSUNAMI to generate relational parameters (i.e., c k ) to determine the degree of similarity between systems. One detail of the SCALE material and data implementation must be discussed at this point. Several thermal scattering laws (TSLs) are available for 1 H. SCALE uses a different nuclide ID number for each TSL; essentially, each version of 1 H is treated as a unique nuclide. For example, 1 H bound in water ( 1 H-H2O) is assigned the nuclide ID 1001, whereas 1 H bound in polyethylene (h-poly) is assigned the nuclide ID 9001001. The same cross section data are used for all reactions in 1 H, regardless of TSL, except for scattering below the TSL cutoff energy. TSUNAMI-IP treats different nuclide IDs as different nuclides; thus, no uncertainty is shared between 1 H-H2O and h-poly, despite much of the same data, including covariance data, being used for both nuclides. This presents a question: how much of the difference in assessed similarity between water- and polyethylene-moderated systems is due to the moderators, and how much is caused by the treatment of 1 H-H2O and h poly with cross section and covariance data. The extended edits generated by TSUANMI-IP allow for an investigation of this issue specifically, as well as a demonstration of the general techniques available within TSUNAMI to understand the results of the similarity assessment. This paper presents and analyzes the similarity assessment of both water- and polyethylene-moderated systems for a single benchmark: PST-002-001.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Coupling of CTF and RELAP5-3D Within an Enhanced Fidelity Nuclear Power Plant Simulator

A robust and accurate multiphysics engineering simulator is being developed to model the core behavior and system response of pressurized water reactors. This simulator relies on the NESTLE and CTF computer codes to model the neutronics and thermal hydraulics (TH), respectively, inside the core on a nodal scale and on the Reactor Excursion and Leak Analysis Program—Three Dimensional (RELAP5-3D) to model the entire nuclear steam supply system. The RELAP5-3D model includes highly detailed nodalization and multidimensional flow modeling throughout the vessel. Previously, pin-resolved data generated via the Virtual Environment for Reactor Analysis core simulator were used to improve the accuracy of the NESTLE core predictions. The engineering simulator being developed as part of this work uses the 3KEYMASTER platform to couple the enhanced NESTLE model to a nodal-fidelity CTF model to balance run time with accuracy; NESTLE provides node-dependent powers to CTF, and CTF provides node-dependent coolant densities and fuel temperatures to NESTLE.An overlapping domain approach is used for the core TH in which RELAP5-3D provides core boundary conditions based on the system response and CTF provides a node-dependent coolant heating rate to the RELAP5-3D core solution. In the preliminary TH demonstration discussed in this paper, CTF and RELAP5-3D provided similar steady-state core predictions, indicating the hydraulic compatibility between the codes, as well as reasonable and expected behavior under hypothetical transient conditions. This provides an initial step in ongoing efforts toward a robust, multiscale TH/neutronics engineering simulator capability.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Subgrid Scale Modeling in Solar Convection Simulations using the ASH Code

The turbulent solar convection zone has remained one of the most challenging and important subjects in physics. Understanding the complex dynamics in the solar con- vection zone is crucial for gaining insight into the solar dynamo problem. Many solar observatories have generated revealing data with great details of large scale motions in the solar convection zone. For example, a strong di erential rotation is observed: the angular rotation is observed to be faster at the equator than near the poles not only near the solar surface, but also deep in the convection zone. On the other hand, due to the wide range of dynamical scales of turbulence in the solar convection zone, both theory and simulation have limited success. Thus, cutting edge solar models and numerical simulations of the solar convection zone have focused more narrowly on a few key features of the solar convection zone, such as the time-averaged di erential rotation. For example, Brun & Toomre (2002) report computational finding of differential rotation in an anelastic model for solar convection. A critical shortcoming in this model is that the viscous dissipation is based on application of mixing length theory to stellar dynamics with some ad hoc parameter tuning. The goal of our work is to implement the subgrid scale model developed at CTR into the solar simulation code and examine how the differential rotation will be a affected as a result. Specifically, we implement a Smagorinsky-Lilly subgrid scale model into the ASH (anelastic spherical harmonic) code developed over the years by various authors. This paper is organized as follows. In x2 we briefly formulate the anelastic system that describes the solar convection. In x3 we formulate the Smagorinsky-Lilly subgrid scale model for unstably stratifed convection. We then present some preliminary results in x4, where we also provide some conclusions and future directions.

Young, Y.-N.↗