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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.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Iterative subspace algorithms for finite-temperature solution of Dyson equation

One-particle Green’s functions obtained from the self-consistent solution of the Dyson equation can be employed in the evaluation of spectroscopic and thermodynamic properties for both molecules and solids. However, typical acceleration techniques used in the traditional quantum chemistry self-consistent algorithms cannot be easily deployed for the Green’s function methods because of a non-convex grand potential functional and a non-idempotent density matrix. Moreover, the optimization problem can become more challenging due to the inclusion of correlation effects, changing chemical potential, and fluctuations of the number of particles. In this paper, we study acceleration techniques to target the self-consistent solution of the Dyson equation directly. We use the direct inversion in the iterative subspace (DIIS), the least-squared commutator in the iterative subspace (LCIIS), and the Krylov space accelerated inexact Newton method (KAIN). We observe that the definition of the residual has a significant impact on the convergence of the iterative procedure. Based on the Dyson equation, we generalize the concept of the commutator residual used in DIIS and LCIIS and compare it with the difference residual used in DIIS and KAIN. The commutator residuals outperform the difference residuals for all considered molecular and solid systems within both GW and GF2. For a number of bond-breaking problems, we found that an easily obtained high-temperature solution with effectively suppressed correlations is a very effective starting point for reaching convergence of the problematic low-temperature solutions through a sequential reduction of temperature during calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Bipartite mutual information in classical many-body dynamics

Information theoretic measures have helped to sharpen our understanding of many-body quantum states. As perhaps the most well-known example, the entanglement entropy (or more generally, the bipartite mutual information) has become a powerful tool for characterizing the dynamical growth of quantum correlations. By contrast, although computable, the bipartite mutual information (MI) is almost never explored in classical many particle systems; this owes in part to the fact that computing the MI requires keeping track of the evolution of the full probability distribution, a feat which is rarely done (or thought to be needed) in classical many-body simulations. Here, we utilize the MI to analyze the spreading of information in 1D elementary cellular automata (CA). Broadly speaking, we find that the behavior of the MI in these dynamical systems exhibits a few different types of scaling that roughly correspond to known CA universality classes. Of particular note is that we observe a set of automata for which the MI converges parametrically slowly to its thermodynamic value. We develop a microscopic understanding of this behavior by analyzing a two-species model of annihilating particles moving in opposite directions. Furthermore, our work suggests the possibility that information theoretic tools such as the MI might enable a more fine-grained characterization of classical many-body states and dynamics.

Cellular automata↗
DOE OSTI2014

Note: High-speed Z tip scanner with screw cantilever holding mechanism for atomic-resolution atomic force microscopy in liquid

High-speed atomic force microscopy has attracted much attention due to its unique capability of visualizing nanoscale dynamic processes at a solid/liquid interface. However, its usability and resolution have yet to be improved. As one of the solutions for this issue, here we present a design of a high-speed Z-tip scanner with screw holding mechanism. We perform detailed comparison between designs with different actuator size and screw arrangement by finite element analysis. Based on the design giving the best performance, we have developed a Z tip scanner and measured its performance. The measured frequency response of the scanner shows a flat response up to ∼10 kHz. This high frequency response allows us to achieve wideband tip-sample distance regulation. We demonstrate the applicability of the scanner to high-speed atomic-resolution imaging by visualizing atomic-scale calcite crystal dissolution process in water at 2 s/frame.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2015

Reliability of emerging bonded interface materials for large-area attachments

In this study, conventional thermal interface materials (TIMs), such as greases, gels, and phase change materials, pose bottlenecks to heat removal and have long caused reliability issues in automotive power electronics packages. Bonded interface materials (BIMs) with superior thermal performance have the potential to be a replacement to the conventional TIMs. However, due to coefficient of thermal expansion mismatches between different components in a package and resultant thermomechanical stresses, fractures or delamination could occur, causing serious reliability concerns. These defects manifest themselves in increased thermal resistance in the package. In this paper, the results of reliability evaluation of emerging BIMs for large-area attachments in power electronics packaging are reported. Thermoplastic (polyamide) adhesive with embedded near-vertical-aligned carbon fibers, sintered silver, and conventional lead solder (Sn 63 Pb 37 ) materials were bonded between 50.8 mm x 50.8 mm cross-sectional footprint silicon nitride substrates and copper base plate samples, and were subjected to accelerated thermal cycling until failure or 2500 cycles. Damage in the BIMs was monitored every 100 cycles by scanning acoustic microscopy. Thermoplastic with embedded carbon fibers performed the best with no defects, whereas sintered silver and lead solder failed at 2300 and 1400 thermal cycles, respectively. Besides thermal cycling, additional lead solder samples were subjected to thermal shock and thermal cycling with extended dwell periods. A finite element method (FEM)-based model was developed to simulate the behavior of lead solder under thermomechanical loading. Strain energy density per cycle results were calculated from the FEM simulations. A predictive lifetime model was formulated for lead solder by correlating strain energy density results extracted from modeling with cycles-to-failure obtained from experimental accelerated tests. A power-law-based approach was used to formulate the - redictive lifetime model.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2023

Peri-Net-Pro: the neural processes with quantified uncertainty for crack patterns

Abstract This paper develops a deep learning tool based on neural processes (NPs) called the Peri-Net-Pro, to predict the crack patterns in a moving disk and classifies them according to the classification modes with quantified uncertainties. In particular, image classification and regression studies are conducted by means of convolutional neural networks (CNNs) and NPs. First, the amount and quality of the data are enhanced by using peridynamics to theoretically compensate for the problems of the finite element method (FEM) in generating crack pattern images. Second, case studies are conducted with the prototype microelastic brittle (PMB), linear peridynamic solid (LPS), and viscoelastic solid (VES) models obtained by using the peridynamic theory. The case studies are performed to classify the images by using CNNs and determine the suitability of the PMB, LBS, and VES models. Finally, a regression analysis is performed on the crack pattern images with NPs to predict the crack patterns. The regression analysis results confirm that the variance decreases when the number of epochs increases by using the NPs. The training results gradually improve, and the variance ranges decrease to less than 0.035. The main finding of this study is that the NPs enable accurate predictions, even with missing or insufficient training data. The results demonstrate that if the context points are set to the 10th, 100th, 300th, and 784th, the training information is deliberately omitted for the context points of the 10th, 100th, and 300th, and the predictions are different when the context points are significantly lower. However, the comparison of the results of the 100th and 784th context points shows that the predicted results are similar because of the Gaussian processes in the NPs. Therefore, if the NPs are employed for training, the missing information of the training data can be supplemented to predict the results.

Mathematics↗
DOE OSTI2018

Statistical Analysis of the First Passage Path Ensemble of Jump Processes

The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study the first passage path ensemble of both discrete-time and continuous-time jump processes on a finite state space. The main approach is to divide each first passage path into nonreactive and reactive segments and to study them separately. The analysis can be applied to jump processes which are non-ergodic, as well as continuous-time jump processes where the waiting time distributions are non-exponential. In the particular case that the jump processes are both Markovian and ergodic, our analysis elucidates the relations between the study of the first passage paths and the study of the transition paths in transition path theory. We provide algorithms to numerically compute statistics of the first passage path ensemble. The computational complexity of these algorithms scales with the complexity of solving a linear system, for which efficient methods are available. Several examples demonstrate the wide applicability of the derived results across research areas.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

The effect of stochastic re-acceleration on the energy spectrum of shock-accelerated protons

The energy spectra of particles in gradual solar energetic particle (SEP) events do not always have a power-law form attributed to the diffusive shock acceleration mechanism. In particular, the observed spectra in major SEP events can take the form of a broken (double) power law. In this paper, we study the effect of a process that can modify the power-law spectral form produced by the diffusive shock acceleration: the stochastic re-acceleration of energetic protons by enhanced Alfvénic turbulence in the downstream region of a shock wave. There are arguments suggesting that this process can be important when the shock propagates in the corona. We consider a coronal magnetic loop traversed by a shock and perform Monte Carlo simulations of interactions of shock-accelerated protons with Alfvén waves in the loop. The wave-particle interactions are treated self-consistently, so the finiteness of the available turbulent energy is taken into account. The initial energy spectrum of particles is taken to be a power law. The simulations reveal that the stochastic re-acceleration leads either to the formation of a spectrum that is described in a wide energy range by a power law (although the resulting power-law index is different from the initial one) or to a broken power-law spectrum. The resulting spectral form is determined by the ratio of the energy density of shock-accelerated protons to the wave energy density in the shock's downstream region.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Dynamic mechanical behavior of lithium-ion pouch cells subjected to high-velocity impact

With broad-scale deployment of lithium-ion batteries, mechanical-abuse induced failure events such as short circuits and thermal runaway have made safety a focus of attention in battery design. Most previous studies have focused on quasi-static and low-velocity impact analyses, which could not represent the mechanical behavior of lithium-ion batteries in realistic situations. Here we report a combined experimental and computational study on the dynamic response of lithium-ion pouch cells subjected to high-velocity (200 m/s~1000 m/s) impact. Dynamic finite element simulations were performed to study the effects of internal interfacial behavior and external loading and boundary conditions on the dynamic mechanical behavior of pouch cells. Specifically, mechanical resistance across interfaces between different cell components have a pronounced impact on energy distribution and absorption, thereby determining the evolution of subsequent failure events. These results have practical implications for designing cells with liquid versus gel-type electrolytes, for example. Furthermore, finite element simulations on different external loading and boundary conditions indicate that a direct interaction between the impactor and the cell boundaries lead to a significant change in residual velocity, while the response of the pouch cell is independent of the prescribed far-field boundary conditions. In other words, there is not a significant difference in the response of pouch-format cells that have stacked electrodes versus wound electrodes at such high strain rates. These results are significantly different from quasi-static simulations wherein the evolution of failure events follows a very different pathway. In addition, the impact velocity profiles under different initial impact velocities offer the ballistic limit for the pouch cell and inform subsequent propagation analyses at the battery module level. Collectively, the findings presented here not only offer new perspectives on the role of the interfacial resistances and external boundary conditions on the mechanical safety of lithium-ion pouch cells, but also have implications for further investigations on cell design, modeling approaches, and test method development to study safety of lithium-ion batteries under extreme loading conditions.

25 ENERGY STORAGE↗
DOE OSTI2023

Modeling of the Advanced Test Reactor Using OpenMC, Cubit and Griffin

In the pursuit of the ability to perform multiphysics simulations of the Advanced Test Reactor, it is crucial to have a fast and highly accurate deterministic model. To achieve this, a contemporary two-step method is employed. The first step involves generating homogenized cross sections using OpenMC, a cutting-edge Monte Carlo neutron transport code. OpenMC offers excellent modular capabilities, allowing for easy component integration and flexibility in incorporating new designs into the model. The second step involves deterministic transport calculations, which are performed using Griffin, a reactor multiphysics application based on the Multiphysics Object-Oriented Simulation Environment. To ensure the accurate spatial resolution and assignment of material cross sections, a Cubit-generated mesh for the Advanced Test Reactor is utilized as an intermediate step between the OpenMC and Griffin models; Griffin utilizes the mesh for its finite element solution, while OpenMC material IDs are written to the mesh file to be used in Griffin material assignments. Additionally, a Python-based script converts the cross sections generated by OpenMC into the ISOXML format required by Griffin. Preliminary comparisons indicate good agreement between the neutron multiplication factors obtained from the standalone OpenMC model and the Griffin model, with differences of less than 50 pcm in the two-dimensional geometry configuration. However, in three-dimensional calculations, an unacceptably large error is found in the Griffin solution. Future work is planned to resolve this discrepancy.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2015

A static analysis of three-dimensional functionally graded beams through hierarchical one-dimensional finite elements

In this paper, the static response of three-dimensional beams made of functionally graded materials is investigated through a family of hierarchical one-dimensional finite elements. A wide variety of elements is proposed differing by the kinematic formulation and the number of nodes per elements along the beam axis. Elements’ stiffness matrix and load vector are derived in a unified nuclear form that does not depend upon the a priori expansion order over the cross-section nor the finite element approximation along the beam axis. Results are validated towards three-dimensional finite element models as well as equivalent Navier-type analytical solutions. The numerical investigations show that accurate and efficient solutions (when compared with full three-dimensional FEM solutions) can be obtained by the proposed family of hierarchical one-dimensional elements’ family.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Uncertainty quantification for the impact of injection rate fluctuation on the geomechanical response of geological carbon sequestration

We present an analysis of the geomechanical effects of injection rate fluctuations for geological sequestration of carbon dioxide (CO2). Initially, we present analytical solutions for the effects of injection rate fluctuations on CO2 fluid pressure spatial distribution and temporal evolution for a typical injection scenario. Numerical calculations are performed using a finite element method to investigate the effects of injection rate fluctuations on geomechanical deformation, stresses, and potential failure of the aquifer and caprock layers. The numerical method was first validated by the fluid pressure distribution’s good agreement with the analytical solution. It was shown that for any Gaussian fluctuations of injection rate Q with given mean Q and variance ε_Q, the coefficients of variance for fluid pressure (ϵ_p=ε_p ), deformation (ϵ_u=ε_u ), and stresses (ϵ_σ=ε_σ ) increase linearly with the coefficient of variance for injection rate (ϵ_Q=ε_Q ). The proportional constants are identified, and the fluctuations have the most pronounced effect on the geomechanical stresses, and, therefore, on the potential failure of the aquifer and caprock layers. Instead of expensive computational simulation, this study provides an efficient tool to estimate the geomechanical response variance to injection rate fluctuation. A failure analysis was presented based on the numerical results, where probability of failure was estimated for fluctuating injection rates with different mean and variance during the entire injection period. It was found that with increasing injection rate fluctuation, the failure probability increases significantly. Therefore, the risk associated with injection rate fluctuations should be carefully evaluated.

58 GEOSCIENCES↗
DOE OSTI2022

A combined experimental and numerical approach that eliminates the non-uniqueness associated with the Johnson-Cook parameters obtained using inverse methods

Abstract Johnson-Cook constitutive model is a commonly used material model for machining simulations. The model includes five parameters that capture the initial yield stress, strain-hardening, strain-rate hardening, and thermal softening behavior of the material. These parameters are difficult to determine using experiments since the conditions observed during machining (such as high strain-rates of the order of $$10^5$$ 10 5 /sec - $$10^6$$ 10 6 /sec) are challenging to recreate in the laboratory. To address this problem, several researchers have recently proposed inverse approaches where a combination of experiments and analytical models are used to predict the Johnson-Cook parameters. The errors between the measured cutting forces, chip thicknesses and temperatures and those predicted by analytical models are minimized and the parameters are determined. In this work, it is shown that only two of the five Johnson-Cook parameters can be determined uniquely using inverse approaches. Two different algorithms, namely, Adaptive Memory Programming for Global Optimization (AMPGO) and Particle Swarm Optimization (PSO), are used for this purpose. The extended Oxley’s model is used as the analytical tool for optimization. For determining a parameter’s value, a large range for each parameter is provided as an input to the algorithms. The algorithms converge to several different sets of values for the five Johnson-Cook parameters when all the five parameters are considered as unknown in the optimization algorithm. All of these sets, however, yield the same chip shape and cutting forces in FEM simulations. Further analyses show that only the strain-rate and thermal softening parameters can be determined uniquely and the three parameters present in the strain-hardening term of the Johnson-Cook model cannot be determined uniquely using the inverse method. A combined experimental and numerical approach is proposed to eliminate this determine all parameters uniquely.

42 ENGINEERING↗
DOE OSTI2016

Communication: Near-locality of exchange and correlation density functionals for 1- and 2-electron systems

The uniform electron gas and the hydrogen atom play fundamental roles in condensed matter physics and quantum chemistry. The former has an infinite number of electrons uniformly distributed over the neutralizing positively charged background, and the latter only one electron bound to the proton. The uniform electron gas was used to derive the local spin density approximation to the exchange-correlation functional that undergirds the development of the Kohn-Sham density functional theory. We show here that the ground-state exchange-correlation energies of the hydrogen atom and many other 1- and 2-electron systems are modeled surprisingly well by a different local spin density approximation (LSDA0). LSDA0 is constructed to satisfy exact constraints but agrees surprisingly well with the exact results for a uniform two-electron density in a finite, curved three-dimensional space. We also apply LSDA0 to excited or noded 1-electron densities, where it works less well. Furthermore, we show that the localization of the exact exchange hole for a 1- or 2-electron ground state can be measured by the ratio of the exact exchange energy to its optimal lower bound.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

A Novel Design of Guiding Stress Wave Propagation

Impact loads can induce a series of undesirable physical phenomena including vibration, acoustical shock, perforation, fracture and fragmentation, etc. The energy associated with the impact loads can lead to severe structure damage and human injuries. A design approach which effectively reduces these negative impacts through shock/stress wave diversion is highly needed. In this paper, a computational model which predicts stress wave propagation by considering different beam geometries and configurations is developed. Additionally, a novel concept of wave guide design which modifies the stress wave propagation path without disturbance is also presented. Furthermore, this design approach is not only useful for material property characterization particularly at intermediate or high strain rates, but also allows stress wave propagation in a desired direction as the shock/impact energy can be redistributed in controllable paths. The numerical results are experimentally verified through a Drop-Hopkinson bar apparatus at Sandia National Laboratories.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Development of a Griffin model of the advanced test reactor

In the pursuit of a higher fidelity deterministic simulation capability of the Advanced Test Reactor, it is important to have a fast yet accurate deterministic neutronics model. Here, to achieve this, we employed an advanced two-step method. The first step involves generating homogenized cross sections using OpenMC, a cutting-edge Monte Carlo neutron transport code. OpenMC offers excellent modular capabilities, allowing for easy component integration and flexibility in incorporating new designs into the model. The second step involves deterministic transport calculations, which are performed using Griffin, a reactor physics application based on the Multiphysics Object-Oriented Simulation Environment (MOOSE). To ensure the accurate spatial resolution and assignment of material cross sections, a Cubit-generated mesh for the Advanced Test Reactor is utilized as an intermediate step between the OpenMC and Griffin models; Griffin utilizes the mesh for its finite element solution, while OpenMC material identifications are written to the mesh file to be used in Griffin material assignments. Additionally, a Python-based script converts the cross sections generated by OpenMC into the ISOXML format required by Griffin. Initial comparisons using the Griffin diffusion solver indicated good agreement between the neutron multiplication factors obtained from the standalone OpenMC model and the Griffin model, with differences of less than 10 pcm in the 2D geometry configuration; it was later determined that this agreement was likely due to compensating effect and was more likely on the order of –700 pcm relative to the OpenMC solution. However, in three-dimensional calculations, an unacceptably large error (almost 8,000 pcm) was found in the Griffin solution with the diffusion solver. Subsequent calculations using Griffin’s discrete ordinates solver demonstrated substantially improved agreement, within 116 pcm of the OpenMC solution used to generate the cross sections for Griffin. Building on this capability, future work will seek to perform more detailed validation calculations. The ultimate goal is to evaluate both transient and multiphysics simulations of the reactor.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

Theoretical study of intrinsic defects in cubic silicon carbide 3C-SiC

Using the local moment counter charge (LMCC) method to accurately represent the asymptotic electrostatic boundary conditions within density functional theory supercell calculations, we present a comprehensive analysis of the atomic structure and energy levels of point defects in cubic silicon carbide (3C-SiC). Finding that the classical long-range dielectric screening outside the supercell induced by a charged defect is a significant contributor to the total energy. we describe and validate a modified Jost screening model to evaluate this polarization energy. This leads to bulk-converged defect levels in finite size supercells. With the LMCC boundary conditions and a standard Perdew-Burke-Ernzerhof (PBE) exchange correlation functional, the computed defect level spectrum exhibits no band gap problem: the range of defect levels spans ~2.4 eV, an effective defect band gap that agrees with the experimental band gap. Comparing with previous literature, our LMCC-PBE defect results are in consistent agreement with the hybrid-exchange functional results of Oda et al. [J. Chem. Phys. 139, 124707 (2013)] rather than their PBE results. The difference with their PBE results is attributed to their use of a conventional jellium approximation rather than the more rigorous LMCC approach for handling charged supercell boundary conditions. The difference between standard dft and hybrid functional results for defect levels lies not in a band gap problem but rather in solving a boundary condition problem. The LMCC-PBE entirely mitigates the effect of the band gap problem on defect levels. The more computationally economical PBE enables a systematic exploration of 3C-SiC defects, where, most notably, we find that the silicon vacancy undergoes Jahn-Teller-induced distortions from the previously assumed T d symmetry, and that the divacancy, like the silicon vacancy, exhibits a site-shift bistability in p -type conditions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

CFD/FEA Co-Simulation Framework for Analysis of the Thermal Barrier Coating Design and Its Impact on the HD Diesel Engine Performance

Thermal barrier coatings (TBCs) have been investigated both experimentally and through simulation for mixing controlled combustion (MCC) concepts as a method for reducing heat transfer losses and increasing cycle efficiency, but it is still a very active research area. Early studies were inconclusive, with different groups discovering obstacles to realizing the theoretical potential. Nuanced papers have shown that coating material properties, thickness, microstructure, and surface morphology/roughness all can impact the efficacy of the thermal barrier coating and must be accounted for. Adding to the complexities, a strong spatial and temporal heat flux inhomogeneity exists for mixing controlled combustion (diesel) imposed onto the surfaces from the impinging flame jets. In support of the United States Department of Energy SuperTruck II program goal to achieve 55% brake thermal efficiency on a heavy-duty diesel engines, this study sought to develop a deeper insight into the inhomogeneous heat flux from mixing controlled combustion on thermal barrier coatings and to infer concrete guidance for designing coatings. To that end, a co-simulation approach was developed that couples high-fidelity computational fluid dynamics (CFD) modeling of in-cylinder processes and combustion, and finite element analysis (FEA) modeling of the thermal barrier-coated and metal engine components to resolve spatial and temporal thermal boundary conditions. The models interface at the surface of the combustion chamber; FEA modeling predicts the spatially resolved surface temperature profile, while CFD develops insights into the effect of the thermal barrier coating on the combustion process and the boundary conditions on the gas side. The paper demonstrates the capability of the framework to estimate cycle impacts of the temperature swing at the surface, as well as identify critical locations on the piston/thermal barrier coating that exhibit the highest charge temperature and highest heat fluxes. In addition, the FEA results include predictions of thermal stresses, thus enabling insight into factors affecting coating durability. An example of the capability of the framework is provided to illustrate its use for investigating novel coatings and provide deeper insights to guide future coating design.

42 ENGINEERING↗
DOE OSTI2017

Convergence of the Critical Cooling Rate for Protoplanetary Disk Fragmentation Achieved: The Key Role of Numerical Dissipation of Angular Momentum

We carry out simulations of gravitationally unstable disks using smoothed particle hydrodynamics (SPH) and the novel Lagrangian meshless finite mass (MFM) scheme in the GIZMO code. Our aim is to understand the cause of the nonconvergence of the cooling boundary for fragmentation reported in the literature. We run SPH simulations with two different artificial viscosity implementations and compare them with MFM, which does not employ any artificial viscosity. With MFM we demonstrate convergence of the critical cooling timescale for fragmentation at β{sub crit}≈3. Nonconvergence persists in SPH codes. We show how the nonconvergence problem is caused by artificial fragmentation triggered by excessive dissipation of angular momentum in domains with large velocity derivatives. With increased resolution, such domains become more prominent. Vorticity lags behind density, due to numerical viscous dissipation in these regions, promoting collapse with longer cooling times. Such effect is shown to be dominant over the competing tendency of artificial viscosity to diminish with increasing resolution. When the initial conditions are first relaxed for several orbits, the flow is more regular, with lower shear and vorticity in nonaxisymmetric regions, aiding convergence. Yet MFM is the only method that converges exactly. Our findings are of general interest, as numerical dissipation via artificial viscosity or advection errors can also occur in grid-based codes. Indeed, for the FARGO code values of β{sub crit} significantly higher than our converged estimate have been reported in the literature. Finally, we discuss implications for giant planet formation via disk instability.

79 ASTRONOMY AND ASTROPHYSICS↗