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Building Blocks for Reliable Complex Nonlinear Numerical Simulations

This chapter describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

Yee, H. C.↗

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

This talk describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

Yee, H. C.↗

Reliability of Complex Nonlinear Numerical Simulations

This work describes some of the procedure to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

Yee, H. C.↗

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

This chapter describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations.

Yee, H. C.↗

Work Practice Simulation of Complex Human-Automation Systems in Safety Critical Situations: The Brahms Generalized berlingen Model

The transition from the current air traffic system to the next generation air traffic system will require the introduction of new automated systems, including transferring some functions from air traffic controllers to on­-board automation. This report describes a new design verification and validation (V&V) methodology for assessing aviation safety. The approach involves a detailed computer simulation of work practices that includes people interacting with flight-critical systems. The research is part of an effort to develop new modeling and verification methodologies that can assess the safety of flight-critical systems, system configurations, and operational concepts. The 2002 Ueberlingen mid-air collision was chosen for analysis and modeling because one of the main causes of the accident was one crew's response to a conflict between the instructions of the air traffic controller and the instructions of TCAS, an automated Traffic Alert and Collision Avoidance System on-board warning system. It thus furnishes an example of the problem of authority versus autonomy. It provides a starting point for exploring authority/autonomy conflict in the larger system of organization, tools, and practices in which the participants' moment-by-moment actions take place. We have developed a general air traffic system model (not a specific simulation of Überlingen events), called the Brahms Generalized Ueberlingen Model (Brahms-GUeM). Brahms is a multi-agent simulation system that models people, tools, facilities/vehicles, and geography to simulate the current air transportation system as a collection of distributed, interactive subsystems (e.g., airports, air-traffic control towers and personnel, aircraft, automated flight systems and air-traffic tools, instruments, crew). Brahms-GUeM can be configured in different ways, called scenarios, such that anomalous events that contributed to the Überlingen accident can be modeled as functioning according to requirements or in an anomalous condition, as occurred during the accident. Brahms-GUeM thus implicitly defines a class of scenarios, which include as an instance what occurred at Überlingen. Brahms-GUeM is a modeling framework enabling "what if" analysis of alternative work system configurations and thus facilitating design of alternative operations concepts. It enables subsequent adaption (reusing simulation components) for modeling and simulating NextGen scenarios. This project demonstrates that BRAHMS provides the capacity to model the complexity of air transportation systems, going beyond idealized and simple flights to include for example the interaction of pilots and ATCOs. The research shows clearly that verification and validation must include the entire work system, on the one hand to check that mechanisms exist to handle failures of communication and alerting subsystems and/or failures of people to notice, comprehend, or communicate problematic (unsafe) situations; but also to understand how people must use their own judgment in relating fallible systems like TCAS to other sources of information and thus to evaluate how the unreliability of automation affects system safety. The simulation shows in particular that distributed agents (people and automated systems) acting without knowledge of each others' actions can create a complex, dynamic system whose interactive behavior is unexpected and is changing too quickly to comprehend and control.

complex systems↗

Eulerian simulation of complex suspensions and biolocomotion in three dimensions

Significance Fluid–structure interactions are ubiquitous in many natural and man-made environments. They are difficult to study analytically, and therefore accurate and flexible computational methods are an indispensable tool in the field. Typically, fluids are simulated with a fixed background computational mesh, whereas a solid is simulated with a mesh that moves with it, making it challenging to couple the two. Here we develop a three-dimensional computational method where both fluid and solid can be represented on a fixed computational grid, which simplifies the coupling between the two phases considerably. Our method can simulate scenarios that are difficult to do with other methods, such as complex suspensions containing soft particles that are both heavier and lighter than the fluid.

3D fluid-structure interaction↗

Comparison of human driver dynamics in simulators with complex and simple visual displays and in an automobile on the road

As part of a comprehensive program exploring driver/vehicle system response in lateral steering tasks, driver/vehicle system describing functions and other dynamic data have been gathered in several milieu. These include a simple fixed base simulator with an elementary roadway delineation only display; a fixed base statically operating automobile with a terrain model based, wide angle projection system display; and a full scale moving base automobile operating on the road. Dynamic data with the two fixed base simulators compared favorably, implying that the impoverished visual scene, lack of engine noise, and simplified steering wheel feel characteristics in the simple simulator did not induce significant driver dynamic behavior variations. The fixed base vs. moving base comparisons showed substantially greater crossover frequencies and phase margins on the road course.

Mcruer, D. T.↗

Simulation of Complex Cracking in Plain Weave C/SiC Composite under Biaxial Loading

Finite element analysis is performed on a mesh, based on computed geometry of a plain weave C/SiC composite with assumed internal stacking, to reveal the pattern of internal damage due to biaxial normal cyclic loading. The simulation encompasses intertow matrix cracking, matrix cracking inside the tows, and separation at the tow-intertow matrix and tow-tow interfaces. All these dissipative behaviors are represented by traction-separation cohesive laws. Not aimed at quantitatively predicting the overall stress-strain relation, the simulation, however, does not take the actual process of fiber debonding into account. The fiber tows are represented by a simple rule-of-mixture model where the reinforcing phase is a hypothetical one-dimensional material. Numerical results indicate that for the plain weave C/SiC composite, 1) matrix-crack initiation sites are primarily determined by large intertow matrix voids and interlayer tow-tow contacts, 2) the pattern of internal damage strongly depends on the loading path and initial stress, 3) compressive loading inflicts virtually no damage evolution. KEY WORDS: ceramic matrix composite, plain weave, cohesive model, brittle failure, smeared crack model, progressive damage, meso-mechanical analysis, finite element.

Cheng, Ron-Bin↗

Numerical Simulation of Complex Turbomachinery Flows

An unsteady, multiblock, Reynolds Averaged Navier Stokes solver based on Runge-Kutta scheme and Pseudo-time step for turbo-machinery applications was developed. The code was validated and assessed against analytical and experimental data. It was used to study a variety of physical mechanisms of unsteady, three-dimensional, turbulent, transitional, and cooling flows in compressors and turbines. Flow over a cylinder has been used to study effects of numerical aspects on accuracy of prediction of wake decay and transition, and to modify K-epsilon models. The following simulations have been performed: (a) Unsteady flow in a compressor cascade: Three low Reynolds number turbulence models have been assessed and data compared with Euler/boundary layer predictions. Major flow features associated with wake induced transition were predicted and studied; (b) Nozzle wake-rotor interaction in a turbine: Results compared to LDV data in design and off-design conditions, and cause and effect of unsteady flow in turbine rotors were analyzed; (c) Flow in the low-pressure turbine: Assessed capability of the code to predict transitional, attached and separated flows at a wide range of low Reynolds numbers and inlet freestream turbulence intensity. Several turbulence and transition models have been employed and comparisons made to experiments; (d) leading edge film cooling at compound angle: Comparisons were made with experiments, and the flow physics of the associated vortical structures were studied; and (e) Tip leakage flow in a turbine. The physics of the secondary flow in a rotor was studied and sources of loss identified.

Chernobrovkin, A. A.↗

Performance modeling & simulation of complex systems (A systems engineering design & analysis approach)

Modeling of the Multi-mission Image Processing System (MIPS) will be described as an example of the use of a modeling tool to design a distributed system that supports multiple application scenarios. This paper examines: (a) modeling tool selection, capabilities, and operation (namely NETWORK 2.5 by CACl), (b) pointers for building or constructing a model and how the MIPS model was developed, (c) the importance of benchmarking or testing the performance of equipment/subsystems being considered for incorporation the design/architecture, (d) the essential step of model validation and/or calibration using the benchmark results, (e) sample simulation results from the MIPS model, and (f) how modeling and simulation analysis affected the MIPS design process by having a supportive and informative impact.

Hall, Laverne↗

Roadmap on methods and software for electronic structure based simulations in chemistry and materials

This Roadmap article provides a succinct, comprehensive overview of the state of electronic structure methods and software for molecular and materials simulations. Seventeen distinct sections collect insights by 51 leading scientists in the field. Each contribution addresses the status of a particular area, as well as current challenges and anticipated future advances, with a particular eye towards software related aspects and providing key references for further reading. Foundational sections cover density functional theory and its implementation in real-world simulation frameworks, Green's function based many-body perturbation theory, wave-function based and stochastic electronic structure approaches, relativistic effects and semiempirical electronic structure theory approaches. Subsequent sections cover nuclear quantum effects, real-time propagation of the electronic structure, challenges for computational spectroscopy simulations, and exploration of complex potential energy surfaces. The final sections summarize practical aspects, including computational workflows for complex simulation tasks, the impact of current and future high-performance computing architectures, software engineering practices, education and training to maintain and broaden the community, as well as the status of and needs for electronic structure based modeling from the vantage point of industry environments. Overall, the field of electronic structure software and method development continues to unlock immense opportunities for future scientific discovery, based on the growing ability of computations to reveal complex phenomena, processes and properties that are determined by the make-up of matter at the atomic scale, with high precision.

36 MATERIALS SCIENCE↗

Efficient learning of accurate surrogates for simulations of complex systems

Machine learning methods are increasingly deployed to construct surrogate models for complex physical systems at a reduced computational cost. However, the predictive capability of these surrogates degrades in the presence of noisy, sparse or dynamic data. Here, we introduce an online learning method empowered by optimizer-driven sampling that has two advantages over current approaches: it ensures that all local extrema (including endpoints) of the model response surface are included in the training data, and it employs a continuous validation and update process in which surrogates undergo retraining when their performance falls below a validity threshold. We find, using benchmark functions, that optimizer-directed sampling generally outperforms traditional sampling methods in terms of accuracy around local extrema even when the scoring metric is biased towards assessing overall accuracy. Finally, the application to dense nuclear matter demonstrates that highly accurate surrogates for a nuclear equation-of-state model can be reliably autogenerated from expensive calculations using few model evaluations.

79 ASTRONOMY AND ASTROPHYSICS↗

Computer Simulation of Complex Systems at the Extremes of pH (Final Report)

During the final funding period of the above-mentioned grant, a number of key milestones were achieved as they relate to the Separation Science program. Below are the descriptions of those efforts and the papers published in support of them (see also submitted publication list). There was a strong focus during the final funding period was on hydrated protons and the unique properties of acidic solutions, which as pertinent to many separations processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Efficient Learning of Accurate Surrogates for Simulations of Complex Systems

Machine learning methods are increasingly deployed to construct surrogate models for complex physical systems at a reduced computational cost. However, the predictive capability of these surrogates degrades in the presence of noisy, sparse, or dynamic data. We introduce an online learning method empowered by optimizer-driven sampling that has two advantages over current approaches: it ensures that all local extrema (including endpoints) of the model response surface are included in the training data and it employs a continuous validation and update process in which surrogates undergo retraining when their performance falls below a validity threshold. We find, using benchmark functions, that optimizer-directed sampling generally outperforms traditional sampling methods in terms of accuracy around local extrema even when the scoring metric is biased towards assessing overall accuracy. Finally, the application to dense nuclear matter demonstrates that highly accurate surrogates for a nuclear equation of state model can be reliably auto-generated from expensive calculations using few model evaluations.

97 MATHEMATICS AND COMPUTING↗

A Method for Flow Simulation About Complex Geometries Using Both Structured and Unstructured Grids

A computational fluid dynamics code which utilizes both structured and unstructured grids was developed. The objective of this study was to develop and demonstrate the ability of such a code to achieve solutions about complex geometries in two dimensions. An unstructured grid generator and flow solver were incorporated into the PARC2D structured flow solver. This new unstructured grid generator capability allows for easier generation and manipulation of complex grids. Several examples of the grid generation capabilities are provided. The coupling of different grid topologies and the manipulation of individual grids is shown. Also, grids for realistic geometries, a NACA 0012 airfoil and a wing/nacelle installation, were created. The flow over a NACA 0012 airfoil was used as a test case for the flow solver. Eight separate cases were run. They were both the inviscid and viscous solutions for two freestream Mach numbers and airfoil angle of attacks of 0 to 3.86 degrees. The Mach numbers chosen were for a subsonic case, Mach 0.6, and a case where supersonic regions and a shock wave exists, Mach 0.8. These test case conditions were selected to match experimentally obtained data for code comparison. The results show that the code accurately predicts the flow field for all cases.

Debonis, James R.↗