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DOE OSTI2019

Compensation of Dispersion in Sinuous Antennas for Polarimetric Ground Penetrating Radar Applications

In order to improve the accuracy of subsurface target classification with ground penetrating radar (GPR) systems, it is desired to transmit and receive ultra-wide band pulses with varying combinations of polarization (a technique referred to as polarimetry). The sinuous antenna exhibits such desirable properties as ultra-wide bandwidth, polarization diversity, and low-profile form factor, making it an excellent candidate for the radiating element of such systems. However, sinuous antennas are dispersive since the active region moves with frequency along the structure, resulting in the distortion of radiated pulses. This distortion may be compensated in signal processing with accurately simulated or measured antenna phase information. However, in a practical GPR, the antenna performance may deviate from that simulated, accurate measurements may be impractical, and/or the dielectric loading of the environment may cause deviations. In such cases, it may be desirable to employ a simple dispersion model based on antenna design parameters which may be optimized in situ. This paper explores the dispersive properties of the sinuous antenna and presents a simple, adjustable, model that may be used to correct dispersed pulses. Here, the dispersion model is successfully applied to both simulated and measured scenarios, thereby enabling the use of sinuous antennas in polarimetric GPR applications.

47 OTHER INSTRUMENTATION↗

DOE OSTI2020

Performance Portability Evaluation of OpenCL Benchmarks across Intel and NVIDIA Platforms

We evaluate the capabilities of vendor-provided OpenCL implementations for performance portability across multiple computing platforms. The Rodinia benchmark suite is used for this evaluation. We apply the metric defined by Pennycook et al., and we use roofline efficiency from the Roofline performance model as the "performance efficiency" in the metric's definition. We found that the delivered performance portability is similar for several benchmarks, even if the roofline-based performance efficiencies across platforms are very different among the benchmarks. To help distinguish between these instances, we extend the metric by adding the standard deviation of the performance efficiencies for each benchmark. We argue that the standard deviation gives additional insight into performance portability assessment since it adds the performance variability across platforms. Additionally, we discuss the challenges to measure performance portability associated with algorithms and system software. In terms of algorithms, we need to carefully construct the benchmarks and appropriately use the concurrency available on a platform. In terms of system software, we depend on the vendor performance tools to support the desired programming model and runtime to be able to measure the metrics of interest.

GPU↗

DOE OSTI2016

TH-AB-201-01: A Feasibility Study of Independent Dose Verification for CyberKnife

Purpose: CyberKnife irradiation is composed of tiny-size, multiple and intensity-modulated beams compared to conventional linacs. Few of the publications for Independent dose calculation verification for CyberKnife have been reported. In this study, we evaluated the feasibility of independent dose verification for CyberKnife treatment as Secondary check. Methods: The followings were measured: test plans using some static and single beams, clinical plans in a phantom and using patient’s CT. 75 patient plans were collected from several treatment sites of brain, lung, liver and bone. In the test plans and the phantom plans, a pinpoint ion-chamber measurement was performed to assess dose deviation for a treatment planning system (TPS) and an independent verification program of Simple MU Analysis (SMU). In the clinical plans, dose deviation between the SMU and the TPS was performed. Results: In test plan, the dose deviations were 3.3±4.5%, and 4.1±4.4% for the TPS and the SMU, respectively. In the phantom measurements for the clinical plans, the dose deviations were −0.2±3.6% for the TPS and −2.3±4.8% for the SMU. In the clinical plans using the patient’s CT, the dose deviations were −3.0±2.1% (Mean±1SD). The systematic difference was partially derived from inverse square law and penumbra calculation. Conclusion: The independent dose calculation for CyberKnife shows −3.0±4.2% (Mean±2SD) and our study, the confidence limit was achieved within 5% of the tolerance level from AAPM task group 114 for non-IMRT treatment. Thus, it may be feasible to use independent dose calculation verification for CyberKnife treatment as the secondary check. This research is partially supported by Japan Agency for Medical Research and Development (AMED)

60 APPLIED LIFE SCIENCES↗

DOE OSTI2011

Random errors in interferometry with the least-squares method

This investigation analyzes random errors in interferometric surface profilers using the least-squares method when random noises are present. Two types of random noise are considered here: intensity noise and position noise. Two formulas have been derived for estimating the standard deviations of the surface height measurements: one is for estimating the standard deviation when only intensity noise is present, and the other is for estimating the standard deviation when only position noise is present. Measurements on simulated noisy interferometric data have been performed, and standard deviations of the simulated measurements have been compared with those theoretically derived. The relationships have also been discussed between random error and the wavelength of the light source and between random error and the amplitude of the interference fringe.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2010

Optimal Model-Based Fault Estimation and Correction for Particle Accelerators and Industrial Plants Using Combined Support Vector Machines and First Principles Models

Timely estimation of deviations from optimal performance in complex systems and the ability to identify corrective measures in response to the estimated parameter deviations has been the subject of extensive research over the past four decades. The implications in terms of lost revenue from costly industrial processes, operation of large-scale public works projects and the volume of the published literature on this topic clearly indicates the significance of the problem. Applications range from manufacturing industries (integrated circuits, automotive, etc.), to large-scale chemical plants, pharmaceutical production, power distribution grids, and avionics. In this project we investigated a new framework for building parsimonious models that are suited for diagnosis and fault estimation of complex technical systems. We used Support Vector Machines (SVMs) to model potentially time-varying parameters of a First-Principles (FP) description of the process. The combined SVM & FP model was built (i.e. model parameters were trained) using constrained optimization techniques. We used the trained models to estimate faults affecting simulated beam lifetime. In the case where a large number of process inputs are required for model-based fault estimation, the proposed framework performs an optimal nonlinear principal component analysis of the large-scale input space, and creates a lower dimension feature space in which fault estimation results can be effectively presented to the operation personnel. To fulfill the main technical objectives of the Phase I research, our Phase I efforts have focused on: (1) SVM Training in a Combined Model Structure - We developed the software for the constrained training of the SVMs in a combined model structure, and successfully modeled the parameters of a first-principles model for beam lifetime with support vectors. (2) Higher-order Fidelity of the Combined Model - We used constrained training to ensure that the output of the SVM (i.e. the parameters of the beam lifetime model) are physically meaningful. (3) Numerical Efficiency of the Training - We investigated the numerical efficiency of the SVM training. More specifically, for the primal formulation of the training, we have developed a problem formulation that avoids the linear increase in the number of the constraints as a function of the number of data points. (4) Flexibility of Software Architecture - The software framework for the training of the support vector machines was designed to enable experimentation with different solvers. We experimented with two commonly used nonlinear solvers for our simulations. The primary application of interest for this project has been the sustained optimal operation of particle accelerators at the Stanford Linear Accelerator Center (SLAC). Particle storage rings are used for a variety of applications ranging from 'colliding beam' systems for high-energy physics research to highly collimated x-ray generators for synchrotron radiation science. Linear accelerators are also used for collider research such as International Linear Collider (ILC), as well as for free electron lasers, such as the Linear Coherent Light Source (LCLS) at SLAC. One common theme in the operation of storage rings and linear accelerators is the need to precisely control the particle beams over long periods of time with minimum beam loss and stable, yet challenging, beam parameters. We strongly believe that beyond applications in particle accelerators, the high fidelity and cost benefits of a combined model-based fault estimation/correction system will attract customers from a wide variety of commercial and scientific industries. Even though the acquisition of Pavilion Technologies, Inc. by Rockwell Automation Inc. in 2007 has altered the small business status of the Pavilion and it no longer qualifies for a Phase II funding, our findings in the course of the Phase I research have convinced us that further research will render a workable model-based fault estimation and correction for particle accelerators and industrial plants feasible.

43 PARTICLE ACCELERATORS↗

DOE OSTI2026

Model-based, in-situ, non-destructive qualification and certification of parts made by autonomous additive manufacturing

To address the significant productivity challenges associated with the qualification and certification (Q&C) tasks of additively manufactured (AM) parts, which have traditionally relied on rigorous post‐build inspection and testing, we propose an integrated framework that combines model‐based qualification and certification (MBQ&C) with autonomous additive manufacturing (AAM). MBQ&C employs high‐fidelity predictive models, developed within the Integrated Computational Materials Engineering (ICME) paradigm, to simulate process–structure–property–performance relationships for assessing a part’s fitness for use. Since predictive models are commonly machine learning (ML)-based or reduced-order surrogates of validated physics models, they run efficiently, enabling timely inference. In parallel, the self-driving AAM utilises ML-based adaptive, closed‐loop control strategies to avoid, mitigate, or repair defects and anomalies during fabrication, thereby increasing the likelihood of producing acceptable parts. A key feature of the combined AAM-MBQ&C framework is that predictive models explicitly incorporate defects or anomalies that persist after the build, using instance-specific data captured via in-situ sensing. This customisation enables a build‐specific assessment of fitness for use, rather than relying on nominal or generic parameters. Such individualised evaluation provides a robust basis for Q&C-related acceptance decisions relating to each build. Additionally, the rapid solution capabilities of ML or reduced-order models enable the determination of a part’s suitability for service shortly after build completion. As the framework matures, it has the potential to substantially reduce reliance on conventional point‐design approaches—such as time‐consuming post‐build computed tomography scanning and costly destructive testing. Thus, the AAM-MBQ&C framework represents a transformative, scalable strategy for quality assurance of AM components, as parts produced within a stable, validated, and certified envelope can be certified with reduced testing. Key benefits include: (1) significant gains in Q&C productivity through efficient, model-centric assessment; (2) performance-based classification of defects into critical and non-critical categories; (3) the ability to predict potential deviations in the performance of parts affected by real-time, adaptive process control interventions relative to those produced under a certified process, and (4) the enabling of virtual Q&C for service environments that are difficult, hazardous, or impractical to access or reproduce experimentally. Collectively, these capabilities strengthen the business case for AM, particularly for high‐consequence and mission‐critical applications. Finally, although this work focuses on powder-based AM, the proposed techniques could be extended to AM processes employing alternative feedstock forms.

Gunasegaram, Dayalan↗

DOE OSTI2015

SU-E-J-167: Dosimetric Consequences From Minimal Displacements in APBI with SAVI Applicators

Purpose: To determine the importance of providing proper solid immobilization in every fraction of treatment in APBI with brachytherapy. Methods: 125 patients treated with APBI brachytherapy with SAVI applicators at SFRO Boca Raton, from 2013–2015 were considered for this retrospective study. The CT scans of each patient, which were taken before each treatment, were imported in to the Oncentra treatment planning system. Then they were compared with the initial CT scan which was used for the initial plan. Deviation in displacements in reference to ribs and skin surface was measured and dosimetric evaluations respective to the initial image were performed. Results: Small deviations in displacements were observed from the SAVI applicator to the ribs and the skin surface. Dosimetric evaluations revealed, very small changes in the inter-fractionation position make significant differences in the maximum dose to critical organs. Additionally, the volume of the cavity also changed between fractions. As a Result, the maximum dose manifested variance between 10% and 32% in ribs and skin surface respectively. Conclusion: It appears that taking a CT scan before each treatment is necessary to minimize the risk of delivering undesired high doses to the critical organs. This study indicates, in 30% of the cases re-planning was necessary between treatments. We conclude that, treatment planning teams should evaluate the placement of the device by analyzing the CT images before each treatment and they must be prepared for re-planning if needed. This study also reveals the urgent need of improving the immobilization methods with APBI when treating with the SAVI applicator.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2012

Reliable detection of fluence anomalies in EPID-based IMRT pretreatment quality assurance using pixel intensity deviations

Purpose: This work uses repeat images of intensity modulated radiation therapy (IMRT) fields to quantify fluence anomalies (i.e., delivery errors) that can be reliably detected in electronic portal images used for IMRT pretreatment quality assurance. Methods: Repeat images of 11 clinical IMRT fields are acquired on a Varian Trilogy linear accelerator at energies of 6 MV and 18 MV. Acquired images are corrected for output variations and registered to minimize the impact of linear accelerator and electronic portal imaging device (EPID) positioning deviations. Detection studies are performed in which rectangular anomalies of various sizes are inserted into the images. The performance of detection strategies based on pixel intensity deviations (PIDs) and gamma indices is evaluated using receiver operating characteristic analysis. Results: Residual differences between registered images are due to interfraction positional deviations of jaws and multileaf collimator leaves, plus imager noise. Positional deviations produce large intensity differences that degrade anomaly detection. Gradient effects are suppressed in PIDs using gradient scaling. Background noise is suppressed using median filtering. In the majority of images, PID-based detection strategies can reliably detect fluence anomalies of {>=}5% in {approx}1 mm{sup 2} areas and {>=}2% in {approx}20 mm{sup 2} areas. Conclusions: The ability to detect small dose differences ({<=}2%) depends strongly on the level of background noise. This in turn depends on the accuracy of image registration, the quality of the reference image, and field properties. The longer term aim of this work is to develop accurate and reliable methods of detecting IMRT delivery errors and variations. The ability to resolve small anomalies will allow the accuracy of advanced treatment techniques, such as image guided, adaptive, and arc therapies, to be quantified.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2014

Muon reconstruction efficiency and momentum resolution of the ATLAS experiment in proton–proton collisions at √s = 7 TeV in 2010

This paper presents a study of the performance of the muon reconstruction in the analysis of proton–proton collisions at √s = 7 TeV at the LHC, recorded by the ATLAS detector in 2010. This performance is described in terms of reconstruction and isolation efficiencies and momentum resolutions for different classes of reconstructed muons. The results are obtained from an analysis of J/ψ meson and Z boson decays to dimuons, reconstructed from a data sample corresponding to an integrated luminosity of 40 pb -1 . The measured performance is compared to Monte Carlo predictions and deviations from the predicted performance are discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2017

Community Microgrid Scheduling Considering Network Operational Constraints and Building Thermal Dynamics

Here, this paper proposes a Mixed Integer Conic Programming (MICP) model for community microgrids considering the network operational constraints and building thermal dynamics. The proposed optimization model optimizes not only the operating cost, including fuel cost, purchasing cost, battery degradation cost, voluntary load shedding cost and the cost associated with customer discomfort due to room temperature deviation from the set point, but also several performance indices, including voltage deviation, network power loss and power factor at the Point of Common Coupling (PCC). In particular, the detailed thermal dynamic model of buildings is integrated into the distribution optimal power flow (D-OPF) model for the optimal operation of community microgrids. The heating, ventilation and air-conditioning (HVAC) systems can be scheduled intelligently to reduce the electricity cost while maintaining the indoor temperature in the comfort range set by customers. Numerical simulation results show the effectiveness of the proposed model and significant saving in electricity cost could be achieved with network operational constraints satisfied.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2016

Analysis of a planetary-rotation system for evaporated optical coatings

The impact of planetary-design considerations for optical coating deposition is analyzed, including the ideal number of planets, variations in system performance, and the deviation of planet motion from the ideal. System capacity is maximized for four planets, although substrate size can significantly influence this result. Guidance is provided in the design of high-performance deposition systems based on the relative impact of different error modes. As a result, errors in planet mounting such that the planet surface is not perpendicular to its axis of rotation are particularly problematic, suggesting planetary design modifications would be appropriate.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Performance of Public Film Cooling Geometries Produced Through Additive Manufacturing

Abstract Film cooling is an essential cooling technology to allow modern gas turbines to operate at high temperatures. For years, researchers in this community have worked to improve the effectiveness of film cooling configurations by maximizing the coolant coverage and minimizing the heat flux from the hot gas into the part. Working toward this goal has generated many promising film cooling concepts with unique shapes and configurations. However, until recently, many of these designs were challenging to manufacture in actual turbine hardware due to limitations with legacy manufacturing methods. Now, with the advances in additive manufacturing, it is possible to create turbine parts using high-temperature nickel alloys that feature detailed and unique geometry features. Armed with this new manufacturing power, this study aims to build and test the promising designs from the public literature that were previously difficult or impossible to implement. In this study, different cooling hole designs were manufactured in test coupons using a laser powder bed fusion process. Each nickel alloy coupon featured a single row of engine scale cooling holes, fed by a microchannel. To evaluate performance, the overall cooling effectiveness of each coupon was measured using a matched Biot test at engine relevant conditions. The results showed that certain hole shapes are better suited for additive manufacturing than others and that the manufacturing process can cause significant deviations from the performance reported in the literature.

Engineering↗

DOE OSTI2017

Statistical Framework for Planning a Component Shelf Life Program.

This document outlines a statistical framework for establishing a shelf-life program for components whose performance is measured by the value of a continuous variable such as voltage or function time. The approach applies to both single measurement devices and repeated measurement devices, although additional process control charts may be useful in the case of repeated measurements. The approach is to choose a sample size that protects the margin associated with a particular variable over the life of the component. Deviations from expected performance of the measured variable are detected prior to the complete loss of margin. This ensures the reliability of the component over its lifetime.

47 OTHER INSTRUMENTATION↗

DOE OSTI2024

Impact of mechanical tolerances on partial turn skipping in helical flux compression generator

Maintaining tight mechanical tolerances of the components used in helical flux compression generators is crucial for optimizing device performance. Moving beyond current literature, which provides various approximations for acceptable tolerances, a 3D simulation of the armature stator interaction during generator operation was developed, revealing that existing equations frequently misestimate the tolerance limits. Without restricting the generality of the presented approach, the focus was primarily on the armature’s concentricity and roundness, comparing the acceptable tolerance limits between generators of different sizes. An analytical approach for select geometries was developed, confirming the 3D results. Quantitative results reveal that a steeper Gurney angle and increased winding pitch allow for less restrictive tolerances for eccentricity and ellipticity. Even small deviations from the ideal armature positioning and shape will result in fluctuations of the output current time-derivative, observed experimentally and in simulation. Larger deviations then cause partial turn skipping, associated with loss of magnetic flux. The simulation elucidates the impact of tolerance deviations on generator performance by offering precise tolerance ranges for various generator sizes, thereby facilitating informed design decisions.

42 ENGINEERING↗

DOE OSTI2023

Assessing the Optical Performance Impact of Tracking Error in an Operational Concentrated Solar Power Plant Using Monte Carlo Ray-Tracing Simulation

Concentrating Solar Power (CSP) provides firm and dispatchable electricity due to its thermal storage and hybridization capabilities, which supports the decarbonization of our energy supply. Of the various CSP technologies, parabolic trough collectors are the most mature, with over 500 MW operating worldwide. The optical performance of parabolic trough systems is sensitive to tracking error, which is defined as the angular offset of a collector away from the sun position in the transversal plane. Tracking error commonly occurs due to non-continuous adjustment of the trough angle to point toward the sun, but other factors such as gravity, heating, and wind loading can also contribute to tracking error. Researchers have explored the impact of tracking error on optical performance both numerically and experimentally, but existing studies do not include measurements from operational utility-scale power plants. Tilt angle measurements of parabolic troughs at operational utility-scale power plants illustrate spatial variations in optical performance and include various sources of tracking error such as gravity, heating, and wind loading. To fully characterize wind driven loads on parabolic troughs, we are conducting a long-term field measurement campaign at the Nevada Solar One CSP plant located in Boulder City, NV, which has a nominal capacity of 72 MW and 0.5 hours of full-load storage. We record load measurements on four outer trough rows, collecting support structure bending moments, drive torque moments, dynamic accelerations of the spaceframe, mirror displacement, and tilt angles. Using the tilt measurements acquired at 20 Hz frequency, we calculate the deviation between the nominal sun position and the tracker angle. Using a Monte-Carlo ray-tracing simulation software, we assess the impact of the tracker angle deviation on optical performance throughout the diurnal cycle at various spatial locations within the CSP plant. In our view, this first-of-a-kind study will provide important guidance for future trough designs that reduce the impact of various sources of tracking error on performance.

concentrating solar power↗

DOE OSTI2013

Evaluation of a new six degrees of freedom couch for radiation therapy

Purpose: The aim of this work is to evaluate the geometric accuracy of a prerelease version of a new six degrees of freedom (6DoF) couch. Additionally, a quality assurance method for 6DoF couches is proposed.Methods: The main principle of the performance tests was to request a known shift for the 6DoF couch and to compare this requested shift with the actually applied shift by independently measuring the applied shift using different methods (graph paper, laser, inclinometer, and imaging system). The performance of each of the six axes was tested separately as well as in combination with the other axes. Functional cases as well as realistic clinical cases were analyzed. The tests were performed without a couch load and with a couch load of up to 200 kg and shifts in the range between −4 and +4 cm for the translational axes and between −3° and +3° for the rotational axes were applied. The quality assurance method of the new 6DoF couch was performed using a simple cube phantom and the imaging system.Results: The deviations (mean ± one standard deviation) accumulated over all performance tests between the requested shifts and the measurements of the applied shifts were −0.01 ± 0.02, 0.01 ± 0.02, and 0.01 ± 0.02 cm for the longitudinal, lateral, and vertical axes, respectively. The corresponding values for the three rotational axes couch rotation, pitch, and roll were 0.03°± 0.06°, −0.04°± 0.12°, and −0.01°± 0.08°, respectively. There was no difference found between the tests with and without a couch load of up to 200 kg.Conclusions: The new 6DoF couch is able to apply requested shifts with high accuracy. It has the potential to be used for treatment techniques with the highest demands in patient setup accuracy such as those needed in stereotactic treatments. Shifts can be applied efficiently and automatically. Daily quality assurance of the 6DoF couch can be performed in an easy and efficient way. Long-term stability has to be evaluated in further tests.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2025

Employing MACS/ViBRANT as a Surrogate MARVEL Reactor for Startup Reactivity Tuning and Supervisory Control Processes

Advanced nuclear reactors are a key part of the future of nuclear energy both in the United States and globally. They offer unique benefits for various energy-demanding applications, including use in remote locations, compact size, modular manufacturing, remote monitoring, low and/or variable power rating operation, and reliance on novel technologies to enhance operational safety. To achieve economic feasibility, advanced reactors must significantly reduce their workforces in comparison with the current fleet. Achieving this reduction will occur through reducing staff workloads using technology to achieve autonomous or semi-autonomous operations, demonstrated by comprehensive testing and validation activities. These operations will require both software and hardware platforms during the design and testing phases. While simulations are useful during the design phase, their performance can significantly deviate during actual deployment on hardware. This report presents the outcomes of a collaborative technical initiative between the U.S. Department of Energy (DOE) Microreactor Program (MRP) and Advanced Sensors and Instrumentation (ASI) Program. The collaboration utilized the Microreactor Automated Control System (MACS) hardware platform to bridge the gap between theoretical reactor design and actual startup and control operations. Two key use cases were investigated: facilitating the startup testing period and demonstrating supervisory control. The first use case details the key Microreactor Applications Research Validation and Evaluation (MARVEL) reactor startup physics testing activities conducted using the MACS platform. These activities included drum worth measurements, shutdown margin assessment, temperature feedback analysis, and scram time evaluation, as well as unique testing that would apply to the MARVEL reactor to demonstrate the testing methodologies in a low-risk environment. The MACS platform, serving as a surrogate representation of the MARVEL reactor, proved instrumental in performing these tests. The exercise revealed aspects that led to optimized processes, refined hardware design, and enhanced base software capabilities. By maturing methods and technologies in this manner, the initiative promises to reduce wasted time in the actual on-site reactor deployment effort, thereby saving significant time and resources. The second use case focuses on the development and implementation of supervisory control methods aimed at managing core tilt, which can result from asymmetrical operations or manufacturing imperfections in fuel rods or reactivity control devices. A key objective was to assess and compare the use of artificial intelligence (AI) for supervisory control. The effort aimed to define the role of supervisory control to enhance performance without risking control instability. This effort explored three distinct approaches: rules-based (RB) methods, optimization techniques, and reinforcement learning (RL) algorithms. Each approach was evaluated for its ease of implementation, its usability, and its effectiveness in responding to asymmetries in neutron flux. Comparative analysis of these approaches provided valuable insights into their applicability and effectiveness, offering a robust framework for advanced reactor operations. Together, these two use cases highlight the potential of hardware test beds to help streamline the design, operation, and control of advanced nuclear reactors. This collaborative effort underscores the importance of continued innovation and experimentation in achieving the next generation of safe, reliable, and economically viable nuclear energy solutions.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2011

Comparison of the generalized Riemann solver and the gas-kinetic scheme for inviscid compressible flow simulations

The generalized Riemann problem (GRP) scheme for the Euler equations and gas-kinetic scheme (GKS) for the Boltzmann equation are two high resolution shock capturing schemes for fluid simulations. The difference is that one is based on the characteristics of the inviscid Euler equations and their wave interactions, and the other is based on the particle transport and collisions. The similarity between them is that both methods can use identical MUSCL-type initial reconstructions around a cell interface, and the spatial slopes on both sides of a cell interface involve in the gas evolution process and the construction of a time-dependent flux function. Although both methods have been applied successfully to the inviscid compressible flow computations, their performances have never been compared. Since both methods use the same initial reconstruction, any difference is solely coming from different underlying mechanism in their flux evaluation. Therefore, such a comparison is important to help us to understand the correspondence between physical modeling and numerical performances. Since GRP is so faithfully solving the inviscid Euler equations, the comparison can be also used to show the validity of solving the Euler equations itself. The numerical comparison shows that the GRP exhibits a slightly better computational efficiency, and has comparable accuracy with GKS for the Euler solutions in 1D case, but the GKS is more robust than GRP. For the 2D high Mach number flow simulations, the GKS is absent from the shock instability and converges to the steady state solutions faster than the GRP. The GRP has carbuncle phenomena, likes a cloud hanging over exact Riemann solvers. The GRP and GKS use different physical processes to describe the flow motion starting from a discontinuity. One is based on the assumption of equilibrium state with infinite number of particle collisions, and the other starts from the non-equilibrium free transport process to evolve into an equilibrium one through particle collisions. The different mechanism in the flux evaluation deviates their numerical performance. Through this study, we may conclude scientifically that it may NOT be valid to use the Euler equations as governing equations to construct numerical fluxes in a discretized space with limited cell resolution. To adapt the Navier-Stokes (NS) equations is NOT valid either because the NS equations describe the flow behavior on the hydrodynamic scale and have no any corresponding physics starting from a discontinuity. This fact alludes to the consistency of the Euler and Navier-Stokes equations with the continuum assumption and the necessity of a direct modeling of the physical process in the discretized space in the construction of numerical scheme when modeling very high Mach number flows. The development of numerical algorithm is similar to the modeling process in deriving the governing equations, but the control volume here cannot be shrunk to zero.

97 MATHEMATICS AND COMPUTING↗