Search NASA⌕ Search

SEARCH · Search NASA

Results for “nonlinear dynamics in fluids”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

A Moving Discontinuous Galerkin Method with Interface Condition Enforcement for Reacting Hypersonic Flows

The necessity of enforcing conservation in computational elements or cells (element conservation) for discontinuous solutions is well understood and respected for solving conservation laws in computational fluid dynamics (CFD). In contrast, interface conservation, where the conservation across cell interfaces is enforced, is long ignored, and yet is also ruled and required by the underlying physics just like element conservation. Violation of the interface conservation across discontinuities is the root cause why an exact discontinuous solution can never be achieved in shock capturing methods. The interface conservation is examined and explored in this talk. Moving discontinuous Galerkin (MDG) finite element method with interface conservation enforcement (MDG-ICE) [1],[2] are then presented for solving compressible flow problems with discontinuities based on the observation that the interface conservation can only be satisfied, only when mesh interfaces are aligned with discontinuities. In the MDG-ICE formulation, both conservative quantities and grid geometry are considered as independent variables. A space-time DG formulation is used to solve the multi-material compressible Euler equations in the standard discontinuous solution space and the discrete grid geometry is solved using a variational formulation in a continuous space. A self-adaptive Levenberg-Marquardt method is utilized to solve the resulting over-determined system of nonlinear equations arising from the MDG-ICE formulation. A number of numerical experiments for a variety of flow problems are conducted to assess the accuracy and performance of the MDG-ICE method. Numerical results obtained indicate that the MDG-ICE method is able to deliver the designed order of both h- and p-convergence even for discontinuous solutions, and detect all types of interfaces, via interface condition enforcement and satisfy, via grid movement, the compressible Euler equations and the associated interface condition.

Discontinuous Galekin↗
NASA NTRS1995

Explicit and implicit compact high-resolution shock-capturing methods for multidimensional Euler equations 1: Formulation

Two classes of explicit compact high-resolution shock-capturing methods for the multidimensional compressible Euler equations for fluid dynamics are constructed. Some of these schemes can be fourth-order accurate away from discontinuities. For the semi-discrete case their shock-capturing properties are of the total variation diminishing (TVD), total variation bounded (TVB), total variation diminishing in the mean (TVDM), essentially nonoscillatory (ENO), or positive type of scheme for 1-D scalar hyperbolic conservation laws and are positive schemes in more than one dimension. These fourth-order schemes require the same grid stencil as their second-order non-compact cousins. One class does not require the standard matrix inversion or a special numerical boundary condition treatment associated with typical compact schemes. Due to the construction, these schemes can be viewed as approximations to genuinely multidimensional schemes in the sense that they might produce less distortion in spherical type shocks and are more accurate in vortex type flows than schemes based purely on one-dimensional extensions. However, one class has a more desirable high-resolution shock-capturing property and a smaller operation count in 3-D than the other class. The extension of these schemes to coupled nonlinear systems can be accomplished using the Roe approximate Riemann solver, the generalized Steger and Warming flux-vector splitting or the van Leer type flux-vector splitting. Modification to existing high-resolution second- or third-order non-compact shock-capturing computer codes is minimal. High-resolution shock-capturing properties can also be achieved via a variant of the second-order Lax-Friedrichs numerical flux without the use of Riemann solvers for coupled nonlinear systems with comparable operations count to their classical shock-capturing counterparts. The simplest extension to viscous flows can be achieved by using the standard fourth-order compact or non-compact formula for the viscous terms.

Yee, H. C.↗
DOE OSTI2024

Self-organization in collisionless, high- β turbulence

The magnetohydrodynamic (MHD) equations, as a collisional fluid model that remains in local thermodynamic equilibrium (LTE), have long been used to describe turbulence in myriad space and astrophysical plasmas. Yet, the vast majority of these plasmas, from the solar wind to the intracluster medium (ICM) of galaxy clusters, are only weakly collisional at best, meaning that significant deviations from LTE are not only possible but common. Recent studies have demonstrated that the kinetic physics inherent to this weakly collisional regime can fundamentally transform the evolution of such plasmas across a wide range of scales. Here, we explore the consequences of pressure anisotropy and Larmor-scale instabilities for collisionless, β $\gg$ 1, turbulence, focusing on the role of a self-organizational effect known as ‘magneto-immutability’. We describe this self-organization analytically through a high-β, reduced ordering of the Chew–Goldberger–Low-MHD (CGL-MHD) equations, finding that it is a robust inertial-range effect that dynamically suppresses magnetic-field-strength fluctuations, anisotropic-pressure stresses and dissipation due to heat fluxes. As a result, the turbulent cascade of Alfvénic fluctuations continues below the putative viscous scale to form a robust, nearly conservative, MHD-like inertial range. These findings are confirmed numerically via Landau-fluid CGL-MHD turbulence simulations that employ a collisional closure to mimic the effects of microinstabilities. We find that microinstabilities occupy a small (~5%) volume-filling fraction of the plasma, even when the pressure anisotropy is driven strongly towards its instability thresholds. We discuss these results in the context of recent predictions for ion-vs-electron heating in low-luminosity accretion flows and observations implying suppressed viscosity in ICM turbulence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

A Comparison of Interface Growth Models Applied to Rayleigh–Taylor and Richtmyer–Meshkov Instabilities

Sophisticated numerical models that contain fluid interfaces rely upon interface evolution models to approximate the transition to turbulence near interfaces, in the presence of Rayleigh–Taylor (RTI) or Richtmyer–Meshkov (RMI) instability. Semi-analytical models have been developed in recent decades to predict the interface growth from an initial state into the nonlinear regime. Two of these models are considered in this study. They are the Goncharov and the z-models. Both of these interface models have strengths and weaknesses, which are examined here. Both of them have been implemented in the xRAGE compressible flow solver, which models fluid interfaces. The flow solver provides the fluids acceleration as a body force to the interface model. The purpose of such interface model is to evolve the early times of interface position as a subgrid model within a compressible flow simulation in order to then initialize a turbulence model. In this work, the interface models are assessed and compared for their evolution of RTI and RMI. The z-model performed better than the Goncharov model for all cases that were explored.

42 ENGINEERING↗
DOE OSTI2022

Droplet formation simulation using mixed finite elements

Droplet formation happens in finite time due to the surface tension force. The linear stability analysis is useful to estimate the size of a droplet but fails to approximate the shape of the droplet. This is due to a highly nonlinear flow description near the point where the first pinch-off happens. A one-dimensional axisymmetric mathematical model was first developed by Eggers and Dupont [“Drop formation in a one-dimensional approximation of the Navier–Stokes equation,” J. Fluid Mech. 262, 205–221 (1994)] using asymptotic analysis. This asymptotic approach to the Navier–Stokes equations leads to a universal scaling explaining the self-similar nature of the solution. Numerical models for the one-dimensional model were developed using the finite difference [Eggers and Dupont, “Drop formation in a one-dimensional approximation of the Navier–Stokes equation,” J. Fluid Mech. 262, 205–221 (1994)] and finite element method [Ambravaneswaran et al., “Drop formation from a capillary tube: Comparison of one-dimensional and two-dimensional analyses and occurrence of satellite drops,” Phys. Fluids 14, 2606–2621 (2002)]. The focus of this study is to provide a robust computational model for one-dimensional axisymmetric droplet formation using the Portable, Extensible Toolkit for Scientific Computation. The code is verified using the Method of Manufactured Solutions and validated using previous experimental studies done by Zhang and Basaran [“An experimental study of dynamics of drop formation,” Phys. Fluids 7, 1184–1203 (1995)]. The present model is used for simulating pendant drops of water, glycerol, and paraffin wax, with an aspiration of extending the application to simulate more complex pinch-off phenomena.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Two-fluid and kinetic transport physics of Kelvin–Helmholtz instabilities in nonuniform low-beta plasmas

Hall-magnetohydrodynamic (Hall-MHD) theory, two-fluid simulations, and kinetic simulations are used in this work to investigate the cross-field transport properties of Kelvin–Helmholtz instabilities in nonuniform low-beta collisionless plasmas. Hall-MHD analysis shows how the linear properties of the instability are modified by density gradients and magnetization. High-order accurate two-fluid and kinetic simulations, with complete dynamics of finite-mass electrons and ions, are applied to a suite of parameter cases to systematically assess the effects of diamagnetic drift, magnetization, charge separation, and finite Larmor motion. Initialization of exact two-species kinetic equilibria facilitates the study of isolated physical effects and enables detailed cross-comparisons between two-fluid and kinetic simulations, including for cases where ion gyroradii are comparable to gradient scale lengths. For nonuniform plasmas with significant space charge, the results of two-fluid and kinetic simulations are found to disagree with Hall-MHD predictions. Kelvin–Helmholtz instability growth rates, per unit shear, are shown to be smaller when ion diamagnetic drift and $E \times B$ drift are parallel and larger when the two drifts are antiparallel. The effect is attributed to polarization drift in the shear layer, which leads to redistribution of charge, alters the electric field that drives plasma advection, and consequently modifies growth rates. Instability-induced mass transport for different parameters is characterized in terms of the flux across the shear layer and a simplified diffusion model. Distribution functions from kinetic simulations are shown to deviate substantially from Maxwellian reconstructions, indicating the importance of kinetic physics during the nonlinear phase of the instability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Modelling and simulation of brinicle formation

Below the Arctic sea ice, under the right conditions, a flux of icy brine flows down into the sea. The icy brine has a much lower fusion point and is denser than normal seawater. As a result, it sinks while freezing everything around it, forming an ice channel called a brinicle (also known as ice stalactite). In this paper, we develop a mathematical model for this phenomenon, assuming cylindrical symmetry. The fluid is considered to be viscous and quasi-stationary. The heat and salt transport are weakly coupled to the fluid motion and are modelled with the corresponding conservation equations, accounting for diffusive and convective effects. Finite-element discretization is employed to solve the coupled system of partial differential equations. We find that the model can capture the general behaviour of the physical system and generate brinicle-like structures while also recovering dendrite composition, which is a physically expected feature aligned with previous experimental results. This represents, to our knowledge, the first complete model proposed that captures the global structure of the physical phenomenon even though it has some discrepancies, such as brine accumulation.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2000

Viscoelastic flow modeling in the extrusion of a dough-like fluid

This work attempts to investigate the effect of viscoelasticity and three-dimensional geometry in screw channels. The Phan-Thien Tanner (PTT) constitutive equation with simplified model parameters was solved in conjunction with the flow equations. Polyflow, a commercially available finite element code was used to solve the resulting nonlinear partial differential equations. The PTT model predicted one log scale lower pressure buildup compared to the equivalent Newtonian results. However, the velocity profile did not show significant changes for the chosen PTT model parameters. Past Researchers neglected viscoelastic effects and also the three dimensional nature of the flow in extruder channels. The results of this paper provide a starting point for further simulations using more realistic model parameters, which may enable the food engineer to more accurately scale-up and design extrusion processes.

NASA Discipline Life Support Systems↗
DOE OSTI2024

Decomposing causality into its synergistic, unique, and redundant components

Causality lies at the heart of scientific inquiry, serving as the fundamental basis for understanding interactions among variables in physical systems. Despite its central role, current methods for causal inference face significant challenges due to nonlinear dependencies, stochastic interactions, self-causation, collider effects, and influences from exogenous factors, among others. While existing methods can effectively address some of these challenges, no single approach has successfully integrated all these aspects. Here, we address these challenges with SURD: Synergistic-Unique-Redundant Decomposition of causality. SURD quantifies causality as the increments of redundant, unique, and synergistic information gained about future events from past observations. The formulation is non-intrusive and applicable to both computational and experimental investigations, even when samples are scarce. We benchmark SURD in scenarios that pose significant challenges for causal inference and demonstrate that it offers a more reliable quantification of causality compared to previous methods.

applied mathematics↗
DOE OSTI2025

Flow-Driven Stretch Fluctuations Govern the Nonlinear Viscoelasticity of Elongating Associative Polymer Networks

We use nonequilibrium molecular dynamics simulations to verify recent tube-model predictions that associative polymer networks exhibit broad stretch fluctuations during elongational flow. Simulations further show that these fluctuating dynamics give rise to the rate-dependent extensional viscosity 𝜂 𝐸 measured in filament stretching experiments on H-bonding networks. Simulations model bivalent associative networks with a reactive bead-spring model for varying association strength and extensional strain rate. We observe that stretch fluctuations are driven by a new form of chain tumbling, where chains continually collapse and elongate as their associations break and reform within the advecting network. This produces a broad, nearly uniform distribution of chain stretch over a wide range of strain rates, manifesting as a rate-independent plateau in the extensional stress. Our results show that the nonlinear viscoelasticity of associative networks is dominated by large fluctuations in molecular response, which cannot be captured by current mean-field models.

biomimetic & bio-inspired materials↗
DOE OSTI2023

Measurement of needle and armature dynamics in a gasoline direct injector by high-speed neutron imaging

In modern spark ignition engines, precise delivery of fuel with gasoline direct injection has become increasingly important in the effort to meet ever stricter efficiency and emissions regulations. Use of multiple small close-coupled injections has become more common in attempt to precisely control fuel distribution in the cylinder, but these strategies are hindered by nonlinear injection effects due to operation in the ballistic region of the solenoid-operated valve and due to armature bounce at the end of injection. Understanding the internal dynamics of the injector is crucial to minimizing and controlling non-linearity and shot-to-shot variation, but the experimental techniques available to date are capable only of tracking the position of either the top of the needle (via laser sensors or by monitoring current and voltage in the solenoid coil) or the bottom of the needle (via transparent nozzles or high-speed x-ray imaging). Furthermore, a complete picture of the axial and radial motion of valve needle has until now remained elusive. In this work, we present high-speed ensemble neutron transmission imaging of an entire 8-hole gasoline direct injector operating at 200 bar, allowing for both visualization and quantification of the actuation dynamics including lift and wobble of the valve ball, oscillation and bending of the valve needle, lift, rocking, and bounce of the armature, compression of the springs, and radial swelling of the solenoid during energization. Because neutrons offer high penetration through the metal injector while also being sensitive to the 1 H nuclei in fuel molecules, it is also possible to simultaneously see the fluid dynamics of the injection process, including filling of the sac volume, emanation of the spray through the nozzle holes and into the downstream gas, and the formation and evolution of fuel films on the tip of the injector and the walls of the spray container.

33 ADVANCED PROPULSION SYSTEMS↗
NASA NTRS1990

Heat Pipe Vapor Dynamics

The dynamic behavior of the vapor flow in heat pipes is investigated at startup and during operational transients. The vapor is modeled as two-dimensional, compressible viscous flow in an enclosure with inflow and outflow boundary conditions. For steady-state and operating transients, the SIMPLER method is used. In this method a control volume approach is employed on a staggered grid which makes the scheme very stable. It is shown that for relatively low input heat fluxes the compressibility of the vapor flow is low and the SIMPLER scheme is suitable for the study of transient vapor dynamics. When the input heat flux is high or the process under a startup operation starts at very low pressures and temperatures, the vapor is highly compressible and a shock wave is created in the evaporator. It is shown that for a wide range of input heat fluxes, the standard methods, including the SIMPLER scheme, are not suitable. A nonlinear filtering technique, along with the centered difference scheme, are then used for shock capturing as well as for the solution of the cell Reynolds-number problem. For high heat flux, the startup transient phase involves multiple shock reflections in the evaporator region. Each shock reflection causes a significant increase in the local pressure and a large pressure drop along the heat pipe. Furthermore, shock reflections cause flow reversal in the evaporation region and flow circulations in the adiabatic region. The maximum and maximum-averaged pressure drops in different sections of the heat pipe oscillate periodically with time because of multiple shock reflections. The pressure drop converges to a constant value at steady state. However, it is significantly higher than its steady-state value at the initiation of the startup transient. The time for the vapor core to reach steady-state condition depends on the input heat flux, the heat pipe geometry, the working fluid, and the condenser conditions. However, the vapor transient time, for an Na-filled heat pipe is on the order of seconds. Depending on the time constant for the overall system, the vapor transient time may be very short. Therefore, the vapor core may be assumed to be quasi-steady in the transient analysis of a heat pipe operation.

Issacci, Farrokh↗
NASA NTRS2015

Use of Generalized Fluid System Simulation Program (GFSSP) for Teaching and Performing Senior Design Projects at the Educational Institutions

This paper describes the experience of the authors in using the Generalized Fluid System Simulation Program (GFSSP) in teaching Design of Thermal Systems class at University of Alabama in Huntsville. GFSSP is a finite volume based thermo-fluid system network analysis code, developed at NASA/Marshall Space Flight Center, and is extensively used in NASA, Department of Defense, and aerospace industries for propulsion system design, analysis, and performance evaluation. The educational version of GFSSP is freely available to all US higher education institutions. The main purpose of the paper is to illustrate the utilization of this user-friendly code for the thermal systems design and fluid engineering courses and to encourage the instructors to utilize the code for the class assignments as well as senior design projects. The need for a generalized computer program for thermofluid analysis in a flow network has been felt for a long time in aerospace industries. Designers of thermofluid systems often need to know pressures, temperatures, flow rates, concentrations, and heat transfer rates at different parts of a flow circuit for steady state or transient conditions. Such applications occur in propulsion systems for tank pressurization, internal flow analysis of rocket engine turbopumps, chilldown of cryogenic tanks and transfer lines, and many other applications of gas-liquid systems involving fluid transients and conjugate heat and mass transfer. Computer resource requirements to perform time-dependent, three-dimensional Navier-Stokes computational fluid dynamic (CFD) analysis of such systems are prohibitive and therefore are not practical. Available commercial codes are generally suitable for steady state, single-phase incompressible flow. Because of the proprietary nature of such codes, it is not possible to extend their capability to satisfy the above-mentioned needs. Therefore, the Generalized Fluid System Simulation Program (GFSSP1) has been developed at NASA Marshall Space Flight Center (MSFC) as a general fluid flow system solver capable of handling phase changes, compressibility, mixture thermodynamics and transient operations. It also includes the capability to model external body forces such as gravity and centrifugal effects in a complex flow network. The objectives of GFSSP development are: a) to develop a robust and efficient numerical algorithm to solve a system of equations describing a flow network containing phase changes, mixing, and rotation; and b) to implement the algorithm in a structured, easy-to-use computer program. The analysis of thermofluid dynamics in a complex network requires resolution of the system into fluid nodes and branches, and solid nodes and conductors as shown in Figure 1. Figure 1 shows a schematic and GFSSP flow circuit of a counter-flow heat exchanger. Hot nitrogen gas is flowing through a pipe, colder nitrogen is flowing counter to the hot stream in the annulus pipe and heat transfer occurs through metal tubes. The problem considered is to calculate flowrates and temperature distributions in both streams. GFSSP has a unique data structure, as shown in Figure 2, that allows constructing all possible arrangements of a flow network with no limit on the number of elements. The elements of a flow network are boundary nodes where pressure and temperature are specified, internal nodes where pressure and temperature are calculated, and branches where flowrates are calculated. For conjugate heat transfer problems, there are three additional elements: solid node, ambient node, and conductor. The solid and fluid nodes are connected with solid-fluid conductors. GFSSP solves the conservation equations of mass and energy, and equation of state in internal nodes to calculate pressure, temperature and resident mass. The momentum conservation equation is solved in branches to calculate flowrate. It also solves for energy conservation equations to calculate temperatures of solid nodes. The equations are coupled and nonlinear; therefore, they are solved by an iterative numerical scheme. GFSSP employs a unique numerical scheme known as simultaneous adjustment with successive substitution (SASS), which is a combination of Newton-Raphson and successive substitution methods. The mass and momentum conservation equations and the equation of state are solved by the Newton-Raphson method while the conservation of energy and species are solved by the successive substitution method. GFSSP is linked with two thermodynamic property programs, GASP2 and WASP3 and GASPAK4, that provide thermodynamic and thermophysical properties of selected fluids. Both programs cover a range of pressure and temperature that allows fluid properties to be evaluated for liquid, liquid-vapor (saturation), and vapor region. GASP and WASP provide properties of 12 fluids. GASPAK includes a library of 36 fluids. GFSSP has three major parts. The first part is the graphical user interface (GUI), visual thermofluid analyzer of systems and components (VTASC). VTASC allows users to create a flow circuit by a 'point and click' paradigm. It creates the GFSSP input file after the completion of the model building process. GFSSP's GUI provides the users a platform to build and run their models. It also allows post-processing of results. The network flow circuit is first built using three basic elements: boundary node, internal node, and branch.

Majumdar, A. K.↗
DOE OSTI2024

Validation of a Hybrid Domain Overlapping Coupling Between SAM and CFD Against the TALL-3D Transients

The System Thermal Hydraulics (STH) code SAM has been coupled to the Computational Fluid Dynamics (CFD) code Simcenter STAR-CCM+ utilizing a hybrid domain overlapping method with an explicit coupling in time. The coupling aims to extend the STH code’s applicability to scenarios where local momentum and energy transfers are important yet difficult for STH codes to capture, such as three-dimensional (3D) mixing. The coupling method’s numerical stability was verified in the past against two closed-loop configurations, and it was validated against a double T-junction experiment with 3D scalar mixing. In the present work, the coupling method is validated against the TALL-3D STH/CFD coupling benchmark facility. TALL-3D is a three-legged, liquid-metal facility with a large, pool-type enclosure (test section) that exhibits 3D flow effects to be modeled by a CFD code. The rest of the system exhibits approximately 1D behavior well-predicted by an STH code. First, the present STAR-CCM+ CFD model of the 3D test section is validated against experimental data. Then, the SAM-STARCCM+ coupled model is validated against six different TALL-3D steady states, including SAM standalone model results for comparison. Lastly, the SAM-STARCCM+ coupled model is validated against two TALL-3D transients, one exhibiting flow reversal in the test section and one exhibiting nonlinear, Limit Cycle Oscillations (LCO). For the first transient, the SAM-STARCCM+ coupled model properly predicts an increase in the test section’s inlet temperature during flow reversal, and this is not predicted by the SAM standalone model. Following flow reversal, the SAM-STARCCM+ coupled model better-predicts the initial flow recovery and following oscillations as the system approaches a final natural circulation state. For the second transient, no true final steady state is observed due to LCO. Neither the SAM-STARCCM+ coupled model nor the SAM standalone model can perfectly capture the experiment’s changing oscillation frequency during the transient. However, the SAM-STARCCM+ coupled model does reproduce the oscillatory feedback observed in the system. This is a significant achievement as the SAM-STARCCM+ coupled model only uses an explicit coupling in time, as opposed to a semi-implicit coupling. In comparison, previous STH/CFD coupling efforts of the TALL-3D facility required semi-implicit coupling to obtain similar results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Assessing physics of ion temperature gradient turbulence via hierarchical reduced-model representations

In this work, the saturation physics of ion temperature gradient (ITG) turbulence is probed by studying how amplitudes and scalings with key parameters vary across a hierarchy of reduced models. The models derive from nonlinear fluid equations for toroidal ITG turbulence under approximations to the mode coupling interactions in wavenumber space and the representation of turbulent decorrelation. Mode coupling approximations include local-in-wavenumber treatments like the spectral density of flux in quasilinear theory, a truncation to three nonlinearly interacting waves, and the interactions in a cascade to high radial wavenumber mediated by a single zonal flow. Turbulent decorrelation treatments are based on the triplet correlation time with and without eddy damping. Model fidelity is assessed by the scalings and magnitudes of the squared amplitudes of unstable mode, stable mode, and zonal flow with respect to the flow-damping rate and temperature gradient. It is shown that all models reproduce fundamental scalings, provided they incorporate the coupling of unstable mode, stable mode, and zonal flow. Accurate amplitude prediction requires eddy damping in the triplet correlation time and proper representation of the zonal-flow drive by interactions associated with the radial wavenumber cascade.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Understanding latent timescales in neural ordinary differential equation models of advection-dominated dynamical systems

The neural ordinary differential equation (ODE) framework has shown considerable promise in recent years in developing highly accelerated surrogate models for complex physical systems characterized by partial differential equations (PDEs). For PDE-based systems, state-of-the-art neural ODE strategies leverage a two-step procedure to achieve this acceleration: a nonlinear dimensionality reduction step provided by an autoencoder, and a time integration step provided by a neural-network based model for the resultant latent space dynamics (the neural ODE). This work explores the applicability of such autoencoder-based neural ODE strategies for PDEs in which advection terms play a critical role. More specifically, alongside predictive demonstrations, physical insight into the sources of model acceleration (i.e., how the neural ODE achieves its acceleration) is the scope of the current study. Such investigations are performed by quantifying the effects of both autoencoder and neural ODE components on latent system time-scales using eigenvalue analysis of dynamical system Jacobians. To this end, the sensitivity of various critical training parameters – de-coupled versus end-to-end training, latent space dimensionality, and the role of training trajectory length, for example – to both model accuracy and the discovered latent system timescales is quantified. Furthermore, this work specifically uncovers the key role played by the training trajectory length (the number of rollout steps in the loss function during training) on the latent system timescales: larger trajectory lengths correlate with an increase in limiting neural ODE time-scales, and optimal neural ODEs are found to recover the largest time-scales of the full-order (ground-truth) system. Demonstrations are performed across fundamentally different unsteady fluid dynamics configurations influenced by advection: (1) the Kuramoto–Sivashinsky equations (2) Hydrogen-Air channel detonations (the compressible reacting Navier–Stokes equations with detailed chemistry), and (3) 2D Atmospheric flow.

Advection-dominated dynamical systems↗
DOE OSTI2023

Stability and Control of Burning Tokamak Plasmas with Resistive Walls (Final Report)

Work supported by the grant, "Stability and Control of Burning Tokamak Plasmas with Resistive Walls" in the period Aug 2017 to 2023 can be cast in three general categories: (1) linear tearing regimes and the effects on the response to error fields and resistive walls: (2) nonlinear tearing modes in the presence of error fields, with locking; and (3) energetic particle effects. In the first category, we have completed a study of tearing mode regimes with extended MHD effects, including parallel dynamics and toroidal effects, notably favorable average curvature. This work has been presented at the 2018 Sherwood Conference. This work has been published in the ArXiv and is being prepared for publication in Physics of Plasmas. A systematic study of shaping in a tokamak plasma with resistive tearing layers and a resistive wall has been presented in the PhD dissertation by Dov Rhodes, a student of Andrew Cole at Columbia University. John Finn was on Rhodes's PhD committee, and was a co-author of a paper published in Physics of Plasmas on that work. A detailed study of nonlinear tearing modes in the presence of finite beta, favorable average curvature, and an error field has been nearly completed. In this study it was found that the response to an error field with real frequency a tearing layer agreed with analytic results, and that tearing mode saturation by flattening of the current profile as well as destabilization due to flattening of the pressure profile were important factors in the locking process. This work was presented at the 2017 APS/DPP Conference and at the 2018 Sherwood Conference. The effects of energetic ions on tearing modes was presented at the 2017 APS/DPP Conference and in the PhD dissertation of Michael Halfmoon. John Finn served as a committee member on Halfmoon's PhD committee. Extensions to this work including two fluid effects were performed and presented at the APS/DPP Conference in 2017.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1999

A fluid--structure interaction finite element analysis of pulsatile blood flow through a compliant stenotic artery

A new model is used to analyze the fully coupled problem of pulsatile blood flow through a compliant, axisymmetric stenotic artery using the finite element method. The model uses large displacement and large strain theory for the solid, and the full Navier-Stokes equations for the fluid. The effect of increasing area reduction on fluid dynamic and structural stresses is presented. Results show that pressure drop, peak wall shear stress, and maximum principal stress in the lesion all increase dramatically as the area reduction in the stenosis is increased from 51 to 89 percent. Further reductions in stenosis cross-sectional area, however, produce relatively little additional change in these parameters due to a concomitant reduction in flow rate caused by the losses in the constriction. Inner wall hoop stretch amplitude just distal to the stenosis also increases with increasing stenosis severity, as downstream pressures are reduced to a physiological minimum. The contraction of the artery distal to the stenosis generates a significant compressive stress on the downstream shoulder of the lesion. Dynamic narrowing of the stenosis is also seen, further augmenting area constriction at times of peak flow. Pressure drop results are found to compare well to an experimentally based theoretical curve, despite the assumption of laminar flow.

Non-NASA Center↗