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DOE OSTI2022

Data and scripts associated with the manuscript "Using Mutual Information for Global Sensitivity Analysis on Watershed Modeling"

This package contains the data and scripts used in "Using Mutual Information for Global Sensitivity Analysis on Watershed Modeling" (Jiang et al., 2022). The ARW_SWAT.zip file contains the SWAT simulation and the sensitivity analysis result in the American River Watershed. The Portage_SWAT.zip file contains the SWAT simulation and the sensitivity analysis result in the Portage River Watershed. The src folder contains the source code of sensitivity analysis and plotting functions. The notebooks folder contains the Jupyter notebooks for performing sensitivity analysis and other post analyses.Global Sensitivity Analysis (GSA) often is applied to assess the sensitivity of model outputs to their inputs using ensemble simulations. However, increasing model complexity and the associated computational cost have limited the use of most GSA approaches for process-based watershed models. We propose to use Mutual Information (MI) as a computationally efficient GSA method for watershed modeling. Such MI computed from several hundred realizations usually can capture nonlinear relationships between inputs and outputs of interest. We perform MI-based watershed sensitivity analyses in studies of the Portage River Watershed in Ohio and the American River Watershed in Washington. In these studies, MI is used to evaluate the sensitivity of river discharges simulated by the Soil and Water Assessment Tool to no less than 20 parameters for each watershed. Our MI-based sensitivity analyses achieved convergence with about 300~500 realizations, a small fraction of the ensemble size (i.e., several thousand) required by the Sobol method. Nevertheless, MI yields similar sensitivity ranking compared to the Sobol method, especially for sensitive parameters. Our study thus sheds new light on the use of MI as an affordable GSA method for computationally intensive models such as the hyper-resolution, watershed hydrobiogeochemical models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Data and scripts associated with the manuscript "Encoding Diel Hysteresis and the Birch Effect in Dryland Soil Respiration Models through Knowledge-Guided Deep Learning"

This package contains the data and scripts used in "Encoding Diel Hysteresis and the Birch Effect in Dryland Soil Respiration Models through Knowledge-Guided Deep Learning" (Jiang et al., 2022). The data.zip file contains the flux tower and automated chamber observations used for developing the deep learning model for modeling soil respiration. The scripts.zip file contains the Jupyter notebooks and python scripts for preprocessing the data, training the deep learning models, and postprocessing the results. The src.zip contains the source code for training the deep learning model, performing mutual information analysis, and plotting functions. The trained_models.zip contains multiple folders used for hosting the trained deep-learning models and the associated soil respiration predictions. The whole process is performed using python. We include the REAMD.md to document the python package requirements.Soil respiration in dryland ecosystems is challenging to model due to its complex interactions with environmental drivers. Knowledge-guided deep learning provides a much more effective means of accurately representing these complex interactions than traditional Q10-based models. Mutual information analysis revealed that future soil temperature shares more information with soil respiration than past soil temperature, consistent with their clockwise diel hysteresis. We explicitly encoded diel hysteresis, soil drying, and soil rewetting effects on soil respiration dynamics in a newly designed Long Short Term Memory (LSTM) model. The model takes both past and future environmental drivers as inputs to predict soil respiration. The new LSTM model substantially outperformed three Q10-based models and the Community Land Model when reproducing the observed soil respiration dynamics in a semi-arid ecosystem. The new LSTM model clearly demonstrated its superiority for temporally extrapolating soil respiration dynamics, such that the resulting correlation with observational data is up to 0.7 while the correlations of both Q10-based models and the Community Land Model (CLM) are less than 0.4. Our results underscore the high potential for knowledge-guided deep learning to replace Q10-based soil respiration modules in Earth system models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2017

Django Remote Submission

The Django Remote Submission (DRS) is a Django (Django, n.d.) application to manage long running job submission, including starting the job, saving logs, and storing results. It is an independent project available as a standalone pypi package (PyPi, n.d.). It can be easily integrated in any Django project. The source code is freely available as a GitHub repository (django-remote-submission, n.d.). To run the jobs in background, DRS takes advantage of Celery (Celery, n.d.), a powerful asynchronous job queue used for running tasks in the background, and the Redis Server (Redis, n.d.), an in-memory data structure store. Celery uses brokers to pass messages between a Django Project and the Celery workers. Redis is the message broker of DRS. In addition DRS provides real time monitoring of the progress of Jobs and associated logs. Through the Django Channels project (Channels, n.d.), and the usage of Web Sockets, it is possible to asynchronously display the Job Status and the live Job output (standard output and standard error) on a web page.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

easyaccess: Enhanced SQL command line interpreter for astronomical surveys

easyaccess is an enhanced command line interpreter and Python package created to facilitate access to astronomical catalogs stored in SQL Databases. It provides a custom interface with custom commands and was specifically designed to access data from the Dark Energy Survey Oracle database, including autocompletion of tables, columns, users and commands, simple ways to upload and download tables using csv, fits and HDF5 formats, iterators, search and description of tables among others. It can easily be extended to another surveys or SQL databases. The package was completely written in Python and support customized addition of commands and functionalities. Visit https://github.com/mgckind/easyaccess to view installation instructions, tutorials, and the Python source code for easyaccess.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2022

CMinx: A CMake Documentation Generator

This manuscript introduces CMinx, a program for generating application programming interface (API) documentation written in the CMake language, and CMake modules in particular. Since most of CMinx’s intended audience is comprised of C/C++ developers, CMinx is designed to operate similar to Doxygen, the de facto C/C++ API documentation tool. Specifically, developers annotate their CMake source with “documentation” comments, which are traditional CMake block comments starting with an extra “[” character. The documentation comments, written in reST, describe to the reader how the functions, parameters, and variables should be used. Running CMinx on the annotated source code generates reST files containing the API documentation. The reST files can then be converted into static websites with tools such as Sphinx or easily converted to another format via Pandoc.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

pvOps: a Python package for empirical analysis of photovoltaic field data

The purpose of pvOps is to support empirical evaluations of data collected in the field related to the operations and maintenance (O&M) of photovoltaic (PV) power plants. pvOps presently contains modules that address the diversity of field data, including text-based maintenance logs, current-voltage (IV) curves, and timeseries of production information. The package functions leverage machine learning, visualization, and other techniques to enable cleaning, processing, and fusion of these datasets. These capabilities are intended to facilitate easier evaluation of field patterns and extraction of relevant insights to support reliability-related decision-making for PV sites. The open-source code, examples, and instructions for installing the package through PyPI can be accessed through the GitHub repository.

14 SOLAR ENERGY↗

DOE OSTI2011

Parallelizing AT with MatlabMPI

The Accelerator Toolbox (AT) is a high-level collection of tools and scripts specifically oriented toward solving problems dealing with computational accelerator physics. It is integrated into the MATLAB environment, which provides an accessible, intuitive interface for accelerator physicists, allowing researchers to focus the majority of their efforts on simulations and calculations, rather than programming and debugging difficulties. Efforts toward parallelization of AT have been put in place to upgrade its performance to modern standards of computing. We utilized the packages MatlabMPI and pMatlab, which were developed by MIT Lincoln Laboratory, to set up a message-passing environment that could be called within MATLAB, which set up the necessary pre-requisites for multithread processing capabilities. On local quad-core CPUs, we were able to demonstrate processor efficiencies of roughly 95% and speed increases of nearly 380%. By exploiting the efficacy of modern-day parallel computing, we were able to demonstrate incredibly efficient speed increments per processor in AT's beam-tracking functions. Extrapolating from prediction, we can expect to reduce week-long computation runtimes to less than 15 minutes. This is a huge performance improvement and has enormous implications for the future computing power of the accelerator physics group at SSRL. However, one of the downfalls of parringpass is its current lack of transparency; the pMatlab and MatlabMPI packages must first be well-understood by the user before the system can be configured to run the scripts. In addition, the instantiation of argument parameters requires internal modification of the source code. Thus, parringpass, cannot be directly run from the MATLAB command line, which detracts from its flexibility and user-friendliness. Future work in AT's parallelization will focus on development of external functions and scripts that can be called from within MATLAB and configured on multiple nodes, while expending minimal communication overhead with the integrated MATLAB library.

43 PARTICLE ACCELERATORS↗

DOE OSTI2011

Software Construction and Composition Tools for Petascale Computing SCW0837 Progress Report

The majority of scientific software is distributed as source code. As the number of library dependencies and supported platforms increases, so does the complexity of describing the rules for configuring and building software. In this project, we have performed an empirical study of the magnitude of the build problem by examining the development history of two DOE-funded scientific software projects. We have developed MixDown, a meta-build tool, to simplify the task of building applications that depend on multiple third-party libraries. The results of this research indicate that the effort that scientific programmers spend takes a significant fraction of the total development effort and that the use of MixDown can significantly simplify the task of building software with multiple dependencies.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2011

Cyber Friendly Fire

Cyber friendly fire (FF) is a new concept that has been brought to the attention of Department of Defense (DoD) stakeholders through two workshops that were planned and conducted by the Air Force Research Laboratory (AFRL) and research conducted for AFRL by the Pacific Northwest National Laboratory. With this previous work in mind, we offer a definition of cyber FF as intentional offensive or defensive cyber/electronic actions intended to protect cyber systems against enemy forces or to attack enemy cyber systems, which unintentionally harms the mission effectiveness of friendly or neutral forces. Just as with combat friendly fire, a fundamental need in avoiding cyber FF is to maintain situation awareness (SA). We suggest that cyber SA concerns knowledge of a system's topology (connectedness and relationships of the nodes in a system), and critical knowledge elements such as the characteristics and vulnerabilities of the components that comprise the system (and that populate the nodes), the nature of the activities or work performed, and the available defensive (and offensive) countermeasures that may be applied to thwart network attacks. A training implication is to raise awareness and understanding of these critical knowledge units; an approach to decision aids and/or visualizations is to focus on supporting these critical knowledge units. To study cyber FF, we developed an unclassified security test range comprising a combination of virtual and physical devices that present a closed network for testing, simulation, and evaluation. This network offers services found on a production network without the associated costs of a real production network. Containing enough detail to appear realistic, this virtual and physical environment can be customized to represent different configurations. For our purposes, the test range was configured to appear as an Internet-connected Managed Service Provider (MSP) offering specialized web applications to the general public. The network is essentially divided into a production component that hosts the web and network services, and a user component that hosts thirty employee workstations and other end devices. The organization's network is separated from the Internet by a Cisco ASA network security device that both firewalls and detects intrusions. Business sensitive information is stored in various servers. This includes data comprising thousands of internal documents, such as finance and technical designs, email messages for the organization's employees including the CEO, CFO, and CIO, the organization's source code, and Personally Identifiable client data. Release of any of this information to unauthorized parties would have a significant, detrimental impact on the organization's reputation, which would harm earnings. The valuable information stored in these servers pose obvious points of interest for an adversary. We constructed several scenarios around this environment to support studies in cyber SA and cyber FF that may be run in the test range. We describe mitigation strategies to combat cyber FF including both training concepts and suggestions for decision aids and visualization approaches. Finally, we discuss possible future research directions.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2011

SAPHIRE 8 Software Quality Assurance Oversight

The software quality assurance oversight consists of updating and maintaining revision control of the SAPHIRE 8 quality assurance program documentation and of monitoring revision control of the SAPHIRE 8 source code. This report summarizes the oversight efforts through description of the revision control system (RCS) setup, operation and contents. Documents maintained under revision control include the Acceptance Test Plan (ATP), Configuration Management Plan, Quality Assurance Plan, Software Project Plan, Requirements Traceability Matrix (RTM), System Test Plan, SDP Interface Training Manual, and the SAPHIRE 8, "New Features and Capabilities Overview".

42 ENGINEERING↗

DOE OSTI2012

COMPOSE-HPC: A Transformational Approach to Exascale

The goal of the COMPOSE-HPC project is to 'democratize' tools for automatic transformation of program source code so that it becomes tractable for the developers of scientific applications to create and use their own transformations reliably and safely. This paper describes our approach to this challenge, the creation of the KNOT tool chain, which includes tools for the creation of annotation languages to control the transformations (PAUL), to perform the transformations (ROTE), and optimization and code generation (BRAID), which can be used individually and in combination. We also provide examples of current and future uses of the KNOT tools, which include transforming code to use different programming models and environments, providing tests that can be used to detect errors in software or its execution, as well as composition of software written in different programming languages, or with different threading patterns.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2011

Advancement of DOE's EnergyPlus Building Energy Simulation Payment

EnergyPlus{sup TM} is a new generation computer software analysis tool that has been developed, tested, and commercialized to support DOE's Building Technologies (BT) Program in terms of whole-building, component, and systems R&D (http://www.energyplus.gov). It is also being used to support evaluation and decision making of zero energy building (ZEB) energy efficiency and supply technologies during new building design and existing building retrofits. The 5-year project was managed by the National Energy Technology Laboratory and was divided into 5 budget period between 2006 and 2011. During the project period, 11 versions of EnergyPlus were released. This report summarizes work performed by an EnergyPlus development team led by the University of Central Florida's Florida Solar Energy Center (UCF/FSEC). The team members consist of DHL Consulting, C. O. Pedersen Associates, University of Illinois at Urbana-Champaign, Oklahoma State University, GARD Analytics, Inc., and WrightSoft Corporation. The project tasks involved new feature development, testing and validation, user support and training, and general EnergyPlus support. The team developed 146 new features during the 5-year period to advance the EnergyPlus capabilities. Annual contributions of new features are 7 in budget period 1, 19 in period 2, 36 in period 3, 41 in period 4, and 43 in period 5, respectively. The testing and validation task focused on running test suite and publishing report, developing new IEA test suite cases, testing and validating new source code, addressing change requests, and creating and testing installation package. The user support and training task provided support for users and interface developers, and organized and taught workshops. The general support task involved upgrading StarTeam (team sharing) software and updating existing utility software. The project met the DOE objectives and completed all tasks successfully. Although the EnergyPlus software was enhanced significantly under this project, more enhancements are needed for further improvement to ensure that EnergyPlus is able to simulate the latest technologies and perform desired HAVC system operations for the development of next generation HVAC systems. Additional development will be performed under a new 5-year project managed by the National Renewable Energy Laboratory.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2012

NEAMS Static Analysis

Advanced Static Analysis tools can find defects in source code without actually running the code. These tools are capable of finding a large set of defects depending on which checkers are enabled. The tool used on the NEAMS project is developed by a company named “Klocwork.” For C and C++ codes it has more than 150 checkers.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2012

White Paper on Data Repository Reorganization Proposal for the xLPR Project

As the xLPR project moves along, it is important to properly manage the knowledge generated by the different groups. We focus specifically on the knowledge and communications written in files, including general documents, source code and executable files. Data generated through the project are different in nature and, for this reason, need to be treated differently. To that end, ORNL put in place a series of tools that facilitate proper storage and management of project data, document and code changes, group collaboration, knowledge transfer, transparency, accountability and auditability. This paper describes the approaches/tools that we recommend for moving the project forward on knowledge management.

Klasky, Hilda B.↗

DOE OSTI2012

High Performance Computing Productivity Study - Evaluation of Parallel Tools Platform (PTP) Eclipse Plug-In

This report is a DARPA funded Work For Others (WFO) evaluation of the Parallel Tools Platform (PTP) version 5.0.3 (Released October 18, 2011). PTP is currently being developed and supported as an open source product managed by Project Lead Greg Watson and team at IBM plus several other contributors. The tool has been in development since 2005 with a goal of providing an infrastructure for the integration of high performance computing tools. Basic functionality such as source code editing, compiling, launching, and debugging, plus more advanced features including performance monitoring and deployment have been bundled into an Eclipse Integrated Development Environment (IDE) plug-in to give parallel application programmers the features and improved productivity gained from using a common, well established development platform. The evaluation encompasses the basic aspects of using PTP, beginning with the installation and configuration of the plug-in, followed by code development and debugging. Each aspect is evaluated based on the expectations of my experience as an Eclipse user and is presented in the following format: • Feature description • User Experience • Evaluation The feature description is based on the provided documentation for PTP and the ‘generic’ expectations of what the feature should provide. The user experience reveals the actual use and exercise of the feature – specifically in the context and perspective of the evaluation platform provided by Lawrence Livermore National Laboratory. The evaluation of each feature includes the overall outcome of the user experience, along with the expectations that were not met, met, or exceeded along with any issues that were encountered.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

Parallel tools GUI framework-DOE SBIR phase I final technical report

Many parallel performance, profiling, and debugging tools require a graphical way of displaying the very large datasets typically gathered from high performance computing (HPC) applications. Most tool projects create their graphical user interfaces (GUI) from scratch, many times spending their project resources on simply redeveloping commonly used infrastructure. Our goal was to create a multiplatform GUI framework, based on Nokia/Digia’s popular Qt libraries, which will specifically address the needs of these parallel tools. The Parallel Tools GUI Framework (PTGF) uses a plugin architecture facilitating rapid GUI development and reduced development costs for new and existing tool projects by allowing the reuse of many common GUI elements, called “widgets.” Widgets created include, 2D data visualizations, a source code viewer with syntax highlighting, and integrated help and welcome screens. Application programming interface (API) design was focused on minimizing the time to getting a functional tool working. Having a standard, unified, and userfriendly interface which operates on multiple platforms will benefit HPC application developers by reducing training time and allowing users to move between tools rapidly during a single session. However, Argo Navis Technologies LLC will not be submitting a DOE SBIR Phase II proposal and commercialization plan for the PTGF project. Our preliminary estimates for gross income over the next several years was based upon initial customer interest and income generated by similar projects. Unfortunately, as we further assessed the market during Phase I, we grew to realize that there was not enough demand to warrant such a large investment. While we do find that the project is worth our continued investment of time and money, we do not think it worthy of the DOE's investment at this time. We are grateful that the DOE has afforded us the opportunity to make this assessment, and come to this conclusion.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Water Security Toolkit User Manual Version 1.2.

The Water Security Toolkit (WST) is a suite of open source software tools that can be used by water utilities to create response strategies to reduce the impact of contamination in a water distribution network . WST includes hydraulic and water quality modeling software , optimizati on methodologies , and visualization tools to identify: (1) sensor locations to detect contamination, (2) locations in the network in which the contamination was introduced, (3) hydrants to remove contaminated water from the distribution system, (4) locations in the network to inject decontamination agents to inactivate, remove, or destroy contaminants, (5) locations in the network to take grab sample s to help identify the source of contamination and (6) valves to close in order to isolate contaminate d areas of the network. This user manual describes the different components of WST , along w ith examples and case studies. License Notice The Water Security Toolkit (WST) v.1.2 Copyright c 2012 Sandia Corporation. Under the terms of Contract DE-AC04-94AL85000, there is a non-exclusive license for use of this work by or on behalf of the U.S. government. This software is distributed under the Revised BSD License (see below). In addition, WST leverages a variety of third-party software packages, which have separate licensing policies: Acro Revised BSD License argparse Python Software Foundation License Boost Boost Software License Coopr Revised BSD License Coverage BSD License Distribute Python Software Foundation License / Zope Public License EPANET Public Domain EPANET-ERD Revised BSD License EPANET-MSX GNU Lesser General Public License (LGPL) v.3 gcovr Revised BSD License GRASP AT&T Commercial License for noncommercial use; includes randomsample and sideconstraints executable files LZMA SDK Public Domain nose GNU Lesser General Public License (LGPL) v.2.1 ordereddict MIT License pip MIT License PLY BSD License PyEPANET Revised BSD License Pyro MIT License PyUtilib Revised BSD License PyYAML MIT License runpy2 Python Software Foundation License setuptools Python Software Foundation License / Zope Public License six MIT License TinyXML zlib License unittest2 BSD License Utilib Revised BSD License virtualenv MIT License Vol Common Public License vpykit Revised BSD License Additionally, some precompiled WST binary distributions might bundle other third-party executables files: Coliny Revised BSD License (part of Acro project) Dakota GNU Lesser General Public License (LGPL) v.2.1 PICO Revised BSD License (part of Acro project) i Revised BSD License Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. * Neither the name of Sandia National Laboratories nor Sandia Corporation nor the names of its con- tributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IM- PLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL SANDIA CORPORATION BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUD- ING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ii Acknowledgements This work was supported by the U.S. Environmental Protection Agency through its Office of Research and Development (Interagency Agreement # DW8992192801). The material in this document has been subject to technical and policy review by the U.S. EPA, and approved for publication. The views expressed by individual authors, however, are their own, and do not necessarily reflect those of the U.S. Environmental Protection Agency. Mention of trade names, products, or services does not convey official U.S. EPA approval, endorsement, or recommendation. The Water Security Toolkit is an extension of the Threat Ensemble Vulnerability Assessment-Sensor Place- ment Optimization Tool (TEVA-SPOT), which was also developed with funding from the U.S. Environ- mental Protection Agency through its Office of Research and Development (Interagency Agreement # DW8992192801). The authors acknowledge the following individuals for their contributions to the devel- opment of TEVA-SPOT: Jonathan Berry (Sandia National Laboratories), Erik Boman (Sandia National Laboratories), Lee Ann Riesen (Sandia National Laboratories), James Uber (University of Cincinnati), and Jean-Paul Watson (Sandia National Laboratories). iii Acronyms ATUS American Time-Use Survey BLAS Basic linear algebra sub-routines CFU Colony-forming unit CVAR Conditional value at risk CWS Contamination warning system EA Evolutionary algorithm EDS Event detection system EPA U.S. Environmental Protection Agency EC Extent of Contamination ERD EPANET results database file GLPK GNU Linear Programming Kit GRASP Greedy randomized adaptive sampling process HEX Hexadecimal HTML HyperText markup language INP EPANET input file LP Linear program MC Mass consumed MILP Mixed integer linear program MIP Mixed integer program MSX Multi-species extension for EPANET NFD Number of failed detections NS Number of sensors NZD Non-zero demand PD Population dosed PE Population exposed PK Population killed TAI Threat assessment input file TCE Tailed-conditioned expectation TD Time to detection TEC Timed extent of contamination TEVA Threat ensemble vulnerability assessment TSB Tryptic soy broth TSG Threat scenario generation file TSI Threat simulation input file VAR Value at risk VC Volume consumed WST Water Security Toolkit YML YAML configuration file format for WST iv Symbols Notation Definition Example { , } set brackets { 1,2,3 } means a set containing the values 1,2, and 3. [?] is an element of s [?] S means that s is an element of the set S . [?] for all s = 1 [?] s [?] S means that the statement s = 1 is true for all s in set S . P summation P n i =1 s i means s 1 + s 2 + * * * + s n . \ set minus S \ T means the set that contains all those elements of S that are not in set T . %7C given %7C is used to define conditional probability. P ( s %7C t ) means the prob- ability of s occurring given that t occurs. %7C ... %7C cardinality Cardinality of a set is the number of elements of the set. If set S = { 2,4,6 } , then %7C S %7C = 3. v

Klise, Katherine A.↗

DOE OSTI2015

An Exact, Compressible One-Dimensional Riemann Solver for General, Convex Equations of State

This note describes an algorithm with which to compute numerical solutions to the one- dimensional, Cartesian Riemann problem for compressible flow with general, convex equations of state. While high-level descriptions of this approach are to be found in the literature, this note contains most of the necessary details required to write software for this problem. This explanation corresponds to the approach used in the source code that evaluates solutions for the 1D, Cartesian Riemann problem with a JWL equation of state in the ExactPack package [16, 29]. Numerical examples are given with the proposed computational approach for a polytropic equation of state and for the JWL equation of state.

97 MATHEMATICS AND COMPUTING↗