Paul Norman

GPU-accelerated Classical Trajectory Calculation Direct Simulation Monte Carlo applied to shock waves

Abstract In this work we outline a Classical Trajectory Calculation Direct Simulation Monte Carlo (CTC-DSMC) implementation that uses the no-time-counter scheme with a cross-section determined by the interatomic potential energy surface (PES). CTC-DSMC solutions for translational and rotational relaxation in one-dimensional shock waves are compared directly to pure Molecular Dynamics simulations employing an identical PES, where exact agreement is demonstrated for all cases. For the flows considered, long-lived collisions occur within the simulations and their implications for multi-body collisions as well as algorithm implications for the CTC-DSMC method are discussed. A parallelization technique for CTC-DSMC simulations using a heterogeneous multicore CPU/GPU system is demonstrated. Our approach shows good scaling as long as a sufficiently large number of collisions are calculated simultaneously per GPU (∼100,000) at each DSMC iteration. We achieve a maximum speedup of 140× on a 4 GPU/CPU system vs. the performance on one CPU core in serial for a diatomic nitrogen shock. The parallelization approach presented here significantly reduces the cost of CTC-DSMC simulations and has the potential to scale to large CPU/GPU clusters, which could enable future application to 3D flows in strong thermochemical nonequilibrium.

Rovibrational coupling in molecular nitrogen at high temperature: An atomic-level study

This article contains an atomic-level numerical investigation of rovibrational relaxation in molecular nitrogen at high temperature (>4000 K), neglecting dissociation. We conduct our study with the use of pure Molecular Dynamics (MD) and Classical Trajectory Calculations (CTC) Direct Simulation Monte Carlo (DSMC), verified to produce statistically identical results at the conditions of interest here. MD and CTC DSMC solely rely on the specification of a potential energy surface: in this work, the site-site Ling-Rigby potential. Additionally, dissociation is prevented by modeling the N–N bond either as a harmonic or an anharmonic spring. The selected molecular model was shown to (i) recover the shear viscosity (obtained from equilibrium pure MD Green-Kubo calculations) of molecular nitrogen over a wide range of temperatures, up to dissociation; (ii) predict well the near-equilibrium rotational relaxation behavior of N2; (iii) reproduce vibrational relaxation times in excellent accordance with the Millikan-...

A Computational Chemistry Methodology for Developing an Oxygen-Silica Finite Rate Catalytic Model for Hypersonic Flows

The goal of this work is to model the heterogeneous recombination of atomic oxygen on silica surfaces, which is of interest for accurately predicting the heating on vehicles traveling at hypersonic velocities. This is accomplished by creating a nite rate catalytic model, which describes recombination from an atomistic perspective with a set of elementary gassurface reactions. Fundamental to surface catalytic reactions are the chemical structures on the surface where recombination can occur. Using molecular dynamics simulations with the ReaxFF potential, we nd that the chemical sites active in oxygen atom recombination on silica surfaces consist of a small number of speci c defects. The individual reactions in our nite rate catalytic model are based on the possible outcomes of oxygen interaction with these defects. The parameters of the functional forms of the rates, including activation energies and pre-exponential factors, are found by carrying out molecular dynamics simulations of individual events. We nd that the recombination coe cients predicted by the nite rate catalytic model display an exponential dependence with temperature, in qualitative agreement with experiment at (T > 1000 K). However, the ReaxFF potential requires reparametrization with new quantum chemical calculations speci c to the defect structures observed.

ClAssical Trajectory Calculation Direct Simulation Monte Carlo: GPU acceleration and three body collisions

In this work we outline a Classical Trajectory Calculation Direct Simulation Monte Carlo (CTC-DSMC) implementation that uses the no-time-counter scheme with a cross-section that is determined by the interatomic potential energy surface. CTC-DSMC solutions for translational and rotational relaxation in one-dimensional shock waves are compared directly to pure Molecular Dynamics simulations employing an identical potential energy surface, where exact agreement is demonstrated for all cases. A preliminary algorithm for determining the three body collision rate in CTC-DSMC simulations is presented. This algorithm is validated for the simple case of molecules with no interatomic potential, and is found to be in excellent agreement with molecular dynamics simulations. A parallelization technique for CTC-DSMC simulations involving only two body collisions using a heterogeneous multicore CPU/GPU system is demonstrated. This scheme shows good scaling as long as a suciently large number of collisions are calculated simultaneously per GPU ( 100,000) at each DSMC iteration. We achieve a maximum speedup of 140 on a 4 GPU/CPU system vs. the performance on one CPU core in serial for a diatomic nitrogen shock. The parallelization approach presented here signicantly

Analysis of rovibrational relaxation in nitrogen via direct atomic simulation

Pure Molecular Dynamics (MD) and Classical Trajectory Calculations (CTC) Direct Simulation Monte Carlo (DSMC) are used to analyze the rovibrational behavior of molecular nitrogen for temperatures greater than 4,000 K. Both techniques are shown to produce statistically identical results at the conditions of interest here. Furthermore, they solely rely on the specification of a potential energy surface (PES). In this work, we used the site-site Ling-Rigby potential, and modeled the N-N bond either as a harmonic spring or an anharmonic spring (for bound states ) or with the Morse potential (to model bond breaking). Selected preliminary results, obtained with a global fit of a quantum-chemistry PES, are also included. We show that the Ling-Rigby molecular model (i) recovers the shear viscosity (obtained from equilibrium pure MD Green-Kubo calculations) of molecular nitrogen over a wide range of temperatures, up to dissociation; (ii) predicts well the near-equilibrium rotational relaxation behavior of N2; (iii) reproduces vibrational relaxation times in excellent accordance with the Millikan-White correlation and previous semiclassical trajectory calculations in the low temperature range, i.e., between 4,000 K and 10,000 K. By simulating isothermal relaxations in a periodic box, we found that the traditional two-temperature model assumptions become invalid at high temperatures (> 10, 000 K), due to a significant coupling between rotational and vibrational modes for bound states. This led us to add a modification to both the Jeans and the Landau-Teller equations to include a coupling term, essentially described by an additional relaxation time for internal energy equilibration. The model thus obtained was parametrized by fitting temperature histories obtained with molecular-level calculations. The degree of anharmonicity of the N-N bond determines the strength of the rovibrational coupling, with possible implication on rovibration/chemistry interaction at the onset of N2 dissociation. Initial results for vibrational relaxation times are also obtained with the quantum-chemistry based PES of Paukku and co-workers in the low temperature range (< 10, 000 K) and were found to agree well with the experimental data. Although the bound assumption is largely unrealistic under equilibrium conditions at temperatures above about 10,000 K, high-temperature extrapolations are nonetheless very important for flows characterized by extreme nonequilibrium. This is demonstrated through the direct MD simulation of a reflected shock wave in dissociating N2.

Modeling Air-SiO2 Surface Catalysis under Hypersonic Conditions with ReaxFF Molecular Dynamics

The goal of this work is to model surface catalysis in partially dissociated Air-SiO2 systems, which is of interest for accurately predicting heating on hypersonic vehicles. This is accomplished through molecular dynamics simulations using the ReaxFF potential, which is able to model chemical reactions. The ReaxFF potential is found to accurately reproduce experimental results for the bulk structure of -quartz SiO2. Potential energy surfaces for oxygen adsorption on -quartz show that the ReaxFF potential may need further training to reproduce results from quantum chemical calculations. A numerical method for measuring recombination coe cients on a silica surface is developed, and tested for gases at 10 atm and 100 atm over the temperature range (500-2000 K). We nd that recombination coe cients for oxygen on quartz are higher than those measured experimentally, however, the trend in recombination coe cients is exponential with temperature as seen in experiment.

Computational modeling of the flow environment in inductively coupled plasma jet facilities

The goals of this work are to evaluate under what conditions the flow in an inductively coupled plasma jet facility is in thermochemical equilibrium and to evaluate the accuracy of mapping subsonic ground based testing conditions to hypersonic flight. To accomplish this we use the US3D code in these different regimes, ensuring that identical thermal and chemical models are consistently applied to each case and accurate comparisons are drawn. Our simulations indicate that at lower operating pressures (2000 Pa), the flow upstream of the test article is in chemical nonequilibrium, while at higher pressures (10,000 Pa) the flow is very close to chemical equilibrium. The chemical nonequilibrium found at the low pressure condition is caused by molecular species diffusing towards the plasma jet core at a rate higher than the dissociation rate. At both high and low pressures, the flow in the jet upstream of the test article remains in thermal equilibrium, however, the flow within the boundary layer is found to be in thermal nonequilibrium. We find that for cases with perfect air, we are able to match the stagnation point heatflux of a subsonic flow over an axisymmetric probe with a hypersonic flow to within 7%. In a case where a spherical geometry is used in both subsonic and hypersonic cases, we are able to match the stagnation point heat flux within 1%. This indicates that the probe geometry may be important when considering which hypersonic conditions the ground based testing results represent.

A finite-rate model for oxygen-silica catalysis through computational chemistry simulation

The goal of this work is to model the heterogeneous recombination of atomic oxygen on silica surfaces, which is of interest for accurately predicting the heating on vehicles traveling at hypersonic velocities. This is accomplished by creating a finite rate catalytic model, which describes recombination from an atomistic perspective with a set of elementary gas-surface reactions. Fundamental to surface catalytic reactions are the chemical structures on the surface where recombination can occur. Using molecular dynamics simulations with the ReaxFF potential, we find that the chemical sites active in oxygen atom recombination on silica surfaces consist of a small number of specific defects. The individual reactions in our finite rate catalytic model are based on the possible outcomes of oxygen interaction with these defects. The parameters of the functional forms of the rates, including activation energies and pre-exponential factors, are found by carrying out molecular dynamics simulations of individual events. We find that the recombination coefficients predicted by the finite rate catalytic model display an exponential dependence with temperature, in qualitative agreement with experiment at between 1000 K - 1500 K. However, the ReaxFF potential requires reparametrization with new quantum chemical calculations specific to the reaction pathways presented in this work.

Molecular Dynamics Modeling of Hypersonic Gas‐Phase and Gas‐Surface Reactions

Efforts to use molecular dynamics (MD) to develop both non‐equilibrium dissociation models required in the shock layer as well as gas‐surface interaction models specifically for surface catalysis will be summarized. First, an accelerated MD algorithm for dilute gases is presented, called the Event‐Driven/Time‐Driven (ED/TD) MD method. The method detects and moves molecules directly to their impending collision while still integrating each collision, including multi‐body collisions, using conventional Time‐Driven (TD) MD with an arbitrary inter‐atomic potential. The simulation thus proceeds at time steps approaching the mean‐collision‐time. Preliminary nonequilibrium relaxation and normal shock wave simulations are in excellent agreement with direct simulation Monte Carlo (DSMC) results with large speedups over conventional TD MD, especially at low densities. Second, an MD simulation technique to study surface catalysis employing the ReaxFF inter‐atomic potential is detailed. SiO2 surfaces are equilibrated...