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At least 937 records · Page 52

Methods and Results of a Search for Gravitational Waves Associated with Gamma-Ray Bursts Using the GEO 600, LIGO, and Virgo Detectors

In this paper we report on a search for short-duration gravitational wave bursts in the frequency range 64 Hz-1792 Hz associated with gamma-ray bursts (GRBs), using data from GEO600 and one of the LIGO or Virgo detectors. We introduce the method of a linear search grid to analyze GRB events with large sky localization uncertainties such as the localizations provided by the Fermi Gamma-ray Burst Monitor (GBM). Coherent searches for gravitational waves (GWs) can be computationally intensive when the GRB sky position is not well-localized, due to the corrections required for the difference in arrival time between detectors. Using a linear search grid we are able to reduce the computational cost of the analysis by a factor of O(10) for GBM events. Furthermore, we demonstrate that our analysis pipeline can improve upon the sky localization of GRBs detected by the GBM, if a high-frequency GW signal is observed in coincidence. We use the linear search grid method in a search for GWs associated with 129 GRBs observed satellite-based gamma-ray experiments between 2006 and 2011. The GRBs in our sample had not been previously analyzed for GW counterparts. A fraction of our GRB events are analyzed using data from GEO600 while the detector was using squeezed-light states to improve its sensitivity; this is the first search for GWs using data from a squeezed-light interferometric observatory. We find no evidence for GW signals, either with any individual GRB in this sample or with the population as a whole. For each GRB we place lower bounds on the distance to the progenitor, assuming a fixed GW emission energy of 10(exp -2)Stellar Mass sq c, with a median exclusion distance of 0.8 Mpc for emission at 500 Hz and 0.3 Mpc at 1 kHz. The reduced computational cost associated with a linear search grid will enable rapid searches for GWs associated with Fermi GBM events in the Advanced detector era.

methods↗

The Role of Fuels in Transforming Energy End-Use in Buildings and Industrial Processes

This book examines what role fuels have in the transformation of end-use in buildings and industrial processes. Energy efficient technologies are necessary to lower the carbon footprint for a transition towards clean energy in a sustainable manner. Efficient utilization of primary energy resources including renewables to support the current and future energy needs while targeting grid resiliency, energy and environmental security, at an affordable cost is of significant value. Analysis of configurations consisting of heat pumps, fuel driven thermal providers and power systems is presented. Sensitivity of electrical grid's carbon intensity towards carbon footprint in comparison with fuel driven technologies is necessary to recognize the true value proposition of currently available energy solutions for different end consumers. Similarly, the role of low carbon, zero carbon, and carbon negative fuels such as power to gas, power to liquid, hydrogen, biogas, etc. in conjunction with polygeneration technologies are discussed. Transformation of the primary energy resources from conventional fossil fuels to renewable fuels or electricity will have a significant impact on the overall carbon footprint of various end use sectors, including buildings. Hence, this book also examines two different scenarios focused on sensitivity of the pace of decarbonization of electrical grid and fuel supply on operational energy related carbon emissions.

Cheekatamarla, Praveen↗

A Geometry Based Infra-structure for Computational Analysis and Design

The computational steps traditionally taken for most engineering analysis (CFD, structural analysis, and etc.) are: Surface Generation - usually by employing a CAD system; Grid Generation - preparing the volume for the simulation; Flow Solver - producing the results at the specified operational point; and Post-processing Visualization - interactively attempting to understand the results For structural analysis, integrated systems can be obtained from a number of commercial vendors. For CFD, these steps have worked well in the past for simple steady-state simulations at the expense of much user interaction. The data was transmitted between phases via files. Specifically the problems with this procedure are: (1) File based. Information flows from one step to the next via data files with formats specified for that procedure. (2) 'Good' Geometry. A bottleneck in getting results from a solver is the construction of proper geometry to be fed to the grid generator. With 'good' geometry a grid can be constructed in tens of minutes (even with a complex configuration) using unstructured techniques. (3) One-Way communication. All information travels on from one phase to the next. Until this process can be automated, more complex problems such as multi-disciplinary analysis or using the above procedure for design becomes prohibitive.

Haimes, Robert↗

Transmission and Distribution Real-Time Analysis Software for Monitoring and Control: Design and Simulation Testing

The US electric grid is facing operational, stability, and security challenges. Transmission system operators need some measure of visibility into distribution system renewable generation. Distribution system generation needs to support transmission system voltage. The grid is experiencing an expansion in measurement systems. How to take full advantage of this expansion and defend against attacks, both cyber and physical, poses additional challenges. This paper introduces software designed to meet these challenges. At the center of the software is an Integrated System Model (ISM) that spans from transmission to secondary distribution. The ISM is employed in real-time abnormality detection, voltage stability forecasting, and multi-mode control. The software architecture along with selected analysis modules is presented. Testing results are presented for: 1—attacks on utility infrastructure; 2—energy savings from optimal control; 3—distribution system control response during a low voltage transmission system event; 4—cyber-attacks on PV inverters, where physical inverters are used in hardware-in-the-simulation-loop studies. Contributions of this work include real-time analysis that spans from three-phase transmission through secondary distribution; an approach for detecting abnormalities that employs measurements from three independent measurement systems; and a multi-mode distribution system control that responds to cyber-attacks, physical attacks, equipment failures, and transmission system needs.

14 SOLAR ENERGY↗

Analysis and design of ion thrusters for large space systems

This study undertakes the analysis and conceptual design of a 0.5 Newton electrostatic ion thruster suitable for use on large space system missions in the next decade. Either argon or xenon gas shall be used as propellant. A 50 cm diameter discharge chamber was selected to meet stipulated performance goals. The discharge plasma is contained at the boundary by a periodic structure of alternating permanent magnets generating a series of line cusps. Anode strips between the magnets collect Maxwellian electrons generated by a central cathode. Ion extraction utilizes either two or three grid optics at the user's choice. An extensive analysis was undertaken to investigate optics behavior in the high power environment of this large thruster. A plasma bridge neutralizer operating on inert gas provides charge neutralizing electrons to complete the design. The resulting conceptual thruster and the necessary power management and control requirements are described.

James, E. L.↗

Using XR for Improving Scientific Discovery With Numerical Weather Models

Earth science (ES) digital twins will help us understand the complex interactions and interrelationships that make up our Earth system and the impacts of earth science phenomena on it. Our work addresses two underdeveloped areas in current ES digital twin work: improving the understanding and interaction with ES model outputs by using Virtual and Mixed Reality (XR) tools and improving the non-intuitive mapping of continuous ES natural phenomena to gridded reference frames in current numerical models. Traditionally, scientists working on ES view and analyze the results of calculated or measured observables with static 1-dimensional (1D), 2D or 3D plots displayed on flat computer screens or paper. Using such limited mediums, it can be very difficult to identify, track and understand the evolution of key features due to poor viewing angles and the nature of flat computer screens. In addition, numerical models, such as the NASA Goddard Earth Observing System (GEOS) ES model, are almost exclusively formulated, visualized and analyzed in an Eulerian reference frame with fixed grid points in space and time. However, ES phenomena such as convective clouds, hurricanes and wildfire smoke plumes are visualized and analyzed in a Lagrangian reference frame: therefore it is often difficult and unnatural to understand these phenomena in relation to each other, visualized either in an Eulerian or Lagrangian context. In 3D visualizations, data generally takes one of three forms: gridded (e.g., voxelized) data, where space is divided into regions; point clouds, where data is represented as a set of points; and meshes, where objects are rendered as surfaces composed of small polygons (usually triangles). A gridded, Eulerian reference frame has been the default representation for the 2D visual analysis of atmospheric data in part because the numerical methods used to generate atmospheric model data in the first place use a gridded approach, with equations defining the relationships between the physical variables in each of a grid's cells across successive timesteps. In our work, we are particularly interested in data from GEOS. Another reason why gridded representations tend to be used for visualizing data from such models is because trajectories are difficult to interpret from representations on 2D surfaces, due to line-of-sight ambiguity. Instead of a fixed grid from GEOS, we embed a trajectory model to simulate particles' movement throughout a GEOS run. We then ingest these particle trajectories as animated point clouds with a NASA open source XR toolkit, the Mixed Reality Exploration Toolkit (MRET), and merge GEOS data with ES phenomena data onto one combined visualization that the user can intuitively interact with. Efficient rendering of arbitrarily large point clouds is an ongoing challenge being addressed by the computer science community, with the GPU-based optimizations and efficient GPU memory utilization a common theme of recent advances, especially for XR, where sustained high frame rate is mandatory to save the user from suffering due to simulation sickness. In this work, we describe and evaluate our progress in choosing and implementing appropriate methods for rendering arbitrarily large point clouds within MRET for XR. While tracking the XR headset enables the immersion of a user within a 3D scene of a data visualization, tracking of XR handheld controllers or user’s hands enables us to implement intuitive user interactions with the visualized datasets. Conventional tools require a user working with an ES visualization to conduct many interactions to commit their intended selections or manipulations with a visualized dataset; for example to specify a set of points in 3D space. Doing so in a 2D flat screen interface has traditionally required specifying a set of points in three distinct 2D coordinate systems (XY, XZ, and YZ), which is cumbersome. In other scientific domains, it has been shown that specifying or selecting a location or volume in XR using handheld controllers or tracked hands allows for greater speed and accuracy. We anticipate the same will hold true for atmospheric data, and we will share initial results of measuring the utility of such an interface. Notably, as the data being visualized is generated by GEOS as a prediction based on initial conditions, an intended application of our tool is to serve as part of an iterative feedback loop. Through XR, a scientist will review and manipulate a GEOS model run, modifying the conditions as needed to do subsequent runs of GEOS. Thereby, XR-based improvements to speed and accuracy of 3D tagging of points minimizes the effort required by both the scientist and the computer cluster conducting the necessary calculations.

Thomas Grubb↗

A statistical evaluation and comparison of VISSR Atmospheric Sounder (VAS) data

In order to account for the temporal and spatial discrepancies between the VAS and rawinsonde soundings, the rawinsonde data were adjusted to a common hour of release where the new observation time corresponded to the satellite scan time. Both the satellite and rawinsonde observations of the basic atmospheric parameters (T Td, and Z) were objectively analyzed to a uniform grid maintaining the same mesoscale structure in each data set. The performance of each retrieval algorithm in producing accurate and representative soundings was evaluated using statistical parameters such as the mean, standard deviation, and root mean square of the difference fields for each parameter and grid level. Horizontal structure was also qualitatively evaluated by examining atmospheric features on constant pressure surfaces. An analysis of the vertical structure of the atmosphere were also performed by looking at colocated and grid mean vertical profiles of both the satellite and rawinsonde data sets. Highlights of these results are presented.

Jedlovec, G. J.↗

Aerodynamic shape optimization using sensitivity analysis on third-order Euler equations

Two major advancements of an aerodynamic optimization method with two design variables are described. The first is represnted by an improved flow prediction method that uses the third-order accurate discretization of the Euler equations. This method makes it possible to predict the flowfield of a perturbed shape which generates shocks and other large gradients without intermediate CFD analysis. The second advancement is the use of every surface grid point as a design variable in the aerodynamic shape optimization problem. The improved algorithm is demonstrated by optimizing the ramp shape of a scramjet-afterbody configuration for maximum axial thrust. It is concluded that the improved flow-field prediction method eliminates most of the flow analysis and a priori guessing of all possible shapes from which the optimum is to be selected.

Baysal, Oktay↗

Multi-Timescale Integrated Dynamic and Scheduling Model (MIDAS-Solar)

Solar photovoltaic (PV) installations have experienced unprecedented growth in the United States. PV will become not only an energy producer but also a necessary provider of ancillary services at multiple timescales. Conventional methods to simulate power system operations - such as long-term production simulation (which typically considers schedules from hours to minutes by using an optimization framework) and short-term transient studies (which simulate dynamics from seconds to sub-seconds using state variables and differential equations) are not sufficient for studying the multiple-timescale variation of solar generation and its impact on system reliability. Long-term system economics and short-term system dynamics are highly coupled, particularly when the penetration level of renewable generation is extremely high, because the uncertainty and variability of solar generation will impact both power systems steady-state and dynamic performance. This project helps meet and exceed the Solar Energy Technologies Office goal of systems integration by directly addressing this stability and reliability challenge for electric grid planning and operation. This will be accomplished by developing temporally comprehensive, closed-loop simulation models that seamlessly simulate power systems operations from economic scheduling (day-ahead to hours) to dynamic response analysis (seconds to sub-seconds). Both a multi-timescale grid model and an integrated PV model will be developed in this project to accurately study the impacts of PV variability and uncertainty on system reliability at multiple timescales. Using quasi-dynamic simulation methods and data-driven security assessment (DSA) criteria will allow the dynamic characteristics of PV to be fed forward into longer-timescale scheduling models for a complete understanding of the effect of short-term PV dynamics on bulk systems operations (e.g., reserve scheduling and deployment). Upon completion of the proposed model, this project will help operators accurately assess system reliability by deploying energy and reserve scheduling under critical contingency conditions and studying interactions among all types of essential reliability services provided by modern PV power plants.

14 SOLAR ENERGY↗

Batch mode grid generation: An endangered species

Non-interactive grid generation schemes should thrive as emphasis shifts from development of numerical analysis and design methods to application of these tools to real engineering problems. A strong case is presented for the continued development and application of non-interactive geometry modeling methods. Guidelines, strategies, and techniques for developing and implementing these tools are presented using current non-interactive grid generation methods as examples. These schemes play an important role in the development of multidisciplinary analysis methods and some of these applications are also discussed.

Schuster, David M.↗

Survey and Gap Prioritization of U.S. Electric Vehicle Charge Management Deployments

The goal of this study was to survey and characterize the scope of current technical and programmatic knowledge pertaining to EV charge management technologies and practices in the US and relevant international jurisdictions. This characterization of existing field demonstrations and knowledge derived were used to determine gaps in the SCM demonstration landscape. Addressing these gaps through research and demonstration could increase confidence in the U.S. that load management and EV charge control could achieve overarching societal benefits. A survey of charge management deployments and input from stakeholders was completed to determine the state-of-the-art of smart charge management (SCM) where SCM is defined as controlling the amount of power exchanged between chargers and EVs to meet customers' charging needs while also responding to external power demand or pricing signals to provide load management, resilience, or other benefits to the customer and electric grid. The survey was the basis of the gap analysis in this report and determines which areas are well understood, with high confidence, and which areas need further investigation. Existing examples of EV charge management are characterized here to determine aspects that are ready for widespread deployment and have been demonstrated in the field. These include demonstration studies, pilots, programs, and EV-specific tariffs. In all, 110 examples of charge management were characterized. The data sources were public literature and utility filings as well as targeted interviews. In addition, 43 interviews with stakeholders were conducted with a consistent set of questions used in each interview. This study prioritized gaps in demonstrated SCM capabilities based on 1) Urgency of the particular use-case to offset traditional grid assets, 2) Impact, extensibility, and scaling of results across the entire spectrum of 3000+ utility service territories including projected technical and market potential for a given grid service, and 3) Value of federal funding in addressing the gap, including potential to leverage and/or add scope to existing field demonstrations funded by other non-federal funding mechanisms.

33 ADVANCED PROPULSION SYSTEMS↗

Engineering Overview of a Multidisciplinary HSCT Design Framework Using Medium-Fidelity Analysis Codes

An objective of the HPCC Program at NASA Langley has been to promote the use of advanced computing techniques to more rapidly solve the problem of multidisciplinary optimization of a supersonic transport configuration. As a result, a software system has been designed and is being implemented to integrate a set of existing discipline analysis codes, some of them CPU-intensive, into a distributed computational framework for the design of a High Speed Civil Transport (HSCT) configuration. The proposed paper will describe the engineering aspects of integrating these analysis codes and additional interface codes into an automated design system. The objective of the design problem is to optimize the aircraft weight for given mission conditions, range, and payload requirements, subject to aerodynamic, structural, and performance constraints. The design variables include both thicknesses of structural elements and geometric parameters that define the external aircraft shape. An optimization model has been adopted that uses the multidisciplinary analysis results and the derivatives of the solution with respect to the design variables to formulate a linearized model that provides input to the CONMIN optimization code, which outputs new values for the design variables. The analysis process begins by deriving the updated geometries and grids from the baseline geometries and grids using the new values for the design variables. This free-form deformation approach provides internal FEM (finite element method) grids that are consistent with aerodynamic surface grids. The next step involves using the derived FEM and section properties in a weights process to calculate detailed weights and the center of gravity location for specified flight conditions. The weights process computes the as-built weight, weight distribution, and weight sensitivities for given aircraft configurations at various mass cases. Currently, two mass cases are considered: cruise and gross take-off weight (GTOW). Weights information is obtained from correlations of data from three sources: 1) as-built initial structural and non-structural weights from an existing database, 2) theoretical FEM structural weights and sensitivities from Genesis, and 3) empirical as-built weight increments, non-structural weights, and weight sensitivities from FLOPS. For the aeroelastic analysis, a variable-fidelity aerodynamic analysis has been adopted. This approach uses infrequent CPU-intensive non-linear CFD to calculate a non-linear correction relative to a linear aero calculation for the same aerodynamic surface at an angle of attack that results in the same configuration lift. For efficiency, this nonlinear correction is applied after each subsequent linear aero solution during the iterations between the aerodynamic and structural analyses. Convergence is achieved when the vehicle shape being used for the aerodynamic calculations is consistent with the structural deformations caused by the aerodynamic loads. To make the structural analyses more efficient, a linearized structural deformation model has been adopted, in which a single stiffness matrix can be used to solve for the deformations under all the load conditions. Using the converged aerodynamic loads, a final set of structural analyses are performed to determine the stress distributions and the buckling conditions for constraint calculation. Performance constraints are obtained by running FLOPS using drag polars that are computed using results from non-linear corrections to the linear aero code plus several codes to provide drag increments due to skin friction, wave drag, and other miscellaneous drag contributions. The status of the integration effort will be presented in the proposed paper, and results will be provided that illustrate the degree of accuracy in the linearizations that have been employed.

Weston, R. P.↗

CFD Parametric Study of Consortium Impeller

Current design of high performance turbopumps for rocket engines requires effective and robust analytical tools to provide design impact in a productive manner. The main goal of this study is to develop a robust and effective computational fluid dynamics (CFD) pump model for general turbopump design and analysis applications. A Finite Difference Navier-Stokes flow solver, FDNS, which includes the extended k-epsilon turbulence model and appropriate moving interface boundary conditions, was developed to analyze turbulent flows in turbomachinery devices. A second-order central difference scheme plus adaptive dissipation terms was employed in the FDNS code, along with a predictor plus multi-corrector pressure-based solution procedure. The multi-zone, multi-block capability allows the FDNS code to efficiently solve flow fields with complicated geometry. The FDNS code has been benchmarked by analyzing the pump consortium inducer, and it provided satisfactory results. In the present study, a CFD parametric study of the pump consortium impeller was conducted using the FDNS code. The pump consortium impeller, with partial blades, is a new design concept of the advanced rocket engines. The parametric study was to analyze the baseline design of the consortium impeller and its modification which utilizes TANDEM blades. In the present study, the TANDEM blade configuration of the consortium impeller considers cut full blades for about one quarter chord length from the leading edge and clocks the leading edge portion with an angle of 7.5 or 22.5 degrees. The purpose of the present study is to investigate the effect and trend of the TANDEM blade modification and provide the result as a design guideline. A 3-D flow analysis, with a 103 x 23 x 30 mesh grid system and with the inlet flow conditions measured by Rocketdyne, was performed for the baseline consortium impeller. The numerical result shows that the mass flow rate splits through various blade passages are relatively uniform. Due to the complexity of blade geometries, the TANDEM blade configurations were analyzed with the multi-zone grid structure. Both the 7.5 deg- and the 22.5 deg-clocking TANDEM blade cases utilized a 80K mesh system. The numerical result of two TANDEM blade modifications indicates the efficiency and the head are worse than those of the baseline case due to larger flow distortion. The gap between the TANDEM blade and the full blade allows the flow passes through and heavily loads the pressure side of the partial blade such that flow reversal occurs near the suction side of the splitter. The flow split at the exit of impeller blades is very non-uniform for TANDEM blade cases, and this will greatly induce the side load on the diffuser. Therefore, the TANDEM blade modification in the present CFD analysis does not improve the performance of the consortium impeller.

Cheng, Gary C.↗

Sustainable Port Operations: Powered by NREL

Seaports are vital economic hubs that allow the United States to compete on a global scale. But the heavy vehicles and cargo equipment that enable their operations also emit harmful air pollutants and greenhouse gas emissions. For nearly two decades, National Renewable Energy Laboratory (NREL) researchers have worked toward comprehensive seaport decarbonization. They fuse world-class analysis with deep vehicle and transportation systems knowledge to guide strategic deployment of low- and zero-emissions vehicles, charging and refueling infrastructure, and grid improvements. Together, these capabilities can enable sustainable port operations. This fact sheet outlines major seaport and airport decarbonization capabilities across the laboratory, including: fleet research, energy data, and insights for decarbonization; comprehensive hydrogen infrastructure deployment; optimized charging through grid integration; strategic blueprinting for clean, optimized technology deployment; and integrating diversity, equity, inclusion, and accessibility considerations into decarbonization efforts.

ADVANCED PROPULSION SYSTEMS,ENERGY CONSERVATION, C↗

Bridging the Gap on Data and Analysis for Distribution System Planning: Information That Utilities Can Provide Regulators, State Energy Offices and Other Stakeholders

Electric utilities conduct planning annually to ensure their distribution system meets technical standards, policies, and regulations; addresses forecasted grid conditions; satisfies customer needs; and advances utility priorities. The plan identifies grid deficiencies, analyzes potential solutions, and prioritizes capital investments and other expenditures. About 20 U.S. states and jurisdictions require regulated utilities to file some type of distribution system plan with the public utility commission for review. Requirements for sharing distribution system data and analyses vary widely, from few specific requirements to a detailed list of information that must be provided. While utilities conduct extensive analysis to develop distribution system plans, in most jurisdictions regulators and stakeholders do not know what data are available and how the utility uses the data in planning and investing. This report aims to bridge the gap by increasing understanding of the types of data and analyses utilities employ to develop distribution system plans and how the information affects their decision-making. The report describes information that states and stakeholders can ask for related to 11 data categories: -Forecasting loads and distributed energy resources (DERs) -Scenario analysis -Worst-performing circuits -Asset management strategy -Hosting capacity analysis -Value of DERs -Grid needs assessment -Cost-effectiveness framework for investments -Distribution system investment strategy and implementation -Geotargeted programs -Non-wires alternatives procurements.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Inter-IBR Oscillation Modes

This research addresses the following question: For a weak grid with multiple-IBRs, what is the nature of oscillation modes? The analysis of a system consisting of two identical IBRs offers a glimpse of the picture. It shows that the system has a weak-grid mode and an inter-IBR mode. For the weak-grid mode, two IBRs work as an aggregated one to interact with the grid. Furthermore, this mode is sensitive to IBR exporting power level and grid strength. For the inter-IBR mode, two IBRs oscillate against each other. This mode is less sensitive to grid strength and power level.

14 SOLAR ENERGY↗

A Machine Learning Framework to Deconstruct the Primary Drivers for Electricity Market Price Events

As the electricity grid is moving towards a 100% Renewable Energy Source Bulk Power Grid, the overall operations of the power system operations and electricity markets are changing. The electricity markets are not only dispatching resources economically but also taking into account various controllable actions like renewable curtailment, transmission congestion mitigation, and energy storage optimization to make sure the grid is operating reliably. As a result, price formations in electricity markets have become quite complex. Traditional root cause analysis and statistical approaches are rendered inapplicable to analyze and infer the main drivers behind price formation in the modern grid and markets with variable renewable energy (VRE). In this paper, we propose a machine learning analysis framework to deconstruct some primary drivers for price formation in modern electricity markets with high renewable energy and the outcomes can be utilized for various critical aspects of market design, renewable dispatch and curtailment, operations, and cyber-security applications. The framework can be applied to any ISO or market data and in this paper it is applied to open-source publicly available datasets from California Independent System Operator (CAISO) and ISO New England.

machine learning (ML), electricity markets, Renewa↗

Numerical Analysis of Regular Material Point Method and its Application to Multiphase Flows

The material point method (MPM) is gaining wide popularity in engineering research to model and simulate complex multiphase flow dynamics. The method relies on solving the governing equations of motion and transport in a Lagrangian framework using particles also known as material points. The fluid and kinematic properties are stored on the material points while the spatial gradient calculation and temporal integration are performed on a background grid. This Lagrangian framework allows for large deformations, easy integration of constitutive models, and direct import of complex geometries as particles. However, despite their increasing popularity, very few studies have addressed the issues of numerical resolution and stability of MPM techniques. The presence of additional factors such as the number of material points-per-cell, the location of the material points, the CFL-like condition used in time update, and the grid shape functions also increase the complexity of the error analysis when compared to other finite element methods. In this presentation, we analyze the various forms of error incurred in the application of MPM to continuum mechanics and multiphase flows. The effect of the previously mentioned factors on the error dynamics is studied. The application of these principles to canonical and industrial problems is also presented.

high pressure reverse osmosis↗