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Assessing the Effects of Various Surface Textures and Features on Turbulent Heat Transfer in Hypersonic Flight

Experiments were conducted in the NASA Ames Hypervelocity Free Flight Aerodynamic Facility (ballistic range) to quantify the effects on turbulent convective heat transfer of distributed surface roughness, and of isolated features, representative of thermal protection systems on atmospheric entry vehicles. The surface textures and features were applied on the conic frusta of 45o sphere-cone models having a nose-to-base radius ratio of 0.5, similar to the forebody geometry of the Galileo and Pioneer-Venus entry probes. Test conditions were selected to provide turbulent roughness Reynolds numbers, k+, in the ranges expected for outer planet entry missions. Turbulent flow on the conic frustum was achieved by tripping the flow on the sphere-segment nose cap with distributed surface roughness, created by sand-blasting the nose cap. Surface textures included distributed, acreage, roughness, as well as cavity and groove discrete features. The majority of the data to be presented are results for distributed roughness, which includes both random, sand-grain-like roughness, and regular pattern roughness. The pattern roughness was designed to represent the roughness on woven thermal protection system materials, such as NASA’s 3-D Medium Density Carbon Phenolic (3MDCP), also known as HEEET, developed by the Heatshield for Extreme Entry Environments Technology project. The pattern roughness tested is a 3-D wavy surface, and includes three different roughness element height-to-spacing ratios representative of two configurations of 3MDCP, and spanning ratios measured both before, and after, ablation in an arc jet test facility. The patterns tested in the ballistic range were laser-etched on metal models, and represented an idealized version of the real-world materials in which each roughness element was nearly identical. Additional tests were performed wherein the laser-etched patterns were degraded by sand-blasting with various sized grit media, to produce regular patterns with superimposed irregular roughness, more representative of flight materials. Results of each will be compared. The discrete features tested included cylindrical cavities and rectangular grooves of various width-to-depth ratios. Cavities represent either heatshield damage, such as from micro-meteoroid and orbital debris (MMOD) damage, or from designed penetrations, such as on the Genesis sample return capsule. The grooves were scaled representations of seams between segments of HEEET material in a notional tiled thermal protection system. The tests examined the effects on turbulent heating downstream of the isolated features. The tests were conducted at speeds between 3 km/s and 4 km/s in air between 0.15 atm and 0.25 atm (Mach numbers between 9 and 12). Roughness Reynolds numbers, k+, ranged from 12 to 70 for the sand roughness, and as high as 200 for the pattern roughness. Boundary-layer parameters required for calculating k+ were evaluated using computational fluid dynamics simulations using the DPLR (Data Parallel Line Relaxation) code. Each model included both rough- and smooth-wall segments, and heat transfer augmentation factors were determined as the ratio of the rough-wall to smooth-wall heat flux measured on each test.

hypersonic↗

Recent Advancements in the PATO Material Response Code

Introduction: Predicting the complicated multiphysics phenomena during atmospheric entry requires high-fidelity modeling tools to refine estimates of mission risks during entry. To this end, new capabilities are being added to the Porous-material Analysis Toolbox based on OpenFOAM (PATO). PATO is an open-source software for Computational Material Response (CMR) of reactive porous materials submitted to high-temperature environments. The objective of this work is to highlight current efforts to add to and improve upon the modeling capabilities of PATO. These include efforts to loosely couple PATO with other discipline specialized codes including hypersonic Computational Fluid Dynamics (CFD), to assess the interaction effects between pyrolysis gas blowing and the boundary layer, and Computational Solid Mechanics (CSM), to address modeling of mechanical erosion. Other refinements include surface phenomena modeling capabilities to address the effects of silicone-based coatings applied to the TPS during flight preparation, and a unified multiphase solver for a mixed porous-material and plain-fluid domain. Coupling CMR with CFD (CMR/CFD): A loose coupling between PATO and the Data Parallel Line Relaxation (DPLR) CFD code has been achieved by making use of a blowing boundary condition at the heatshield surface available in DPLR. Starting with heat flux estimates with no pyrolysis gas blowing at the surface, blowing gases are computed by the CMR and passed to the CFD such that aerothermal properties of the environment can be recomputed for a new CMR computation. This leads to an iterative process which is supplemented with an estimate of the radiative heat flux using the Nonequilibrium air radiation (NEQAIR) program. The entire iterative process is illustrated in Figure 1. This coupling strategy has been utilized in computing the MSL material response. The goal is to compare the coupled CMR/CFD results with material response results obtained using traditional blowing corrections. Coupling CMS with CMR: A mechanical erosion model is currently being implemented in PATO to account for the additional mass removal induced by high shear conditions. The modeling process at each timestep consists of updating the mechanical properties as a function of temperature and computing the stress tensor and displacement fields of the material. Then, a failure criteria model determines the regions in which the stress exceeds the ultimate strength values resulting in mesh movement to account for mass removal. This model allows the material response simulation to compute the recession due to both oxidation and shear-induced erosion. The model is demonstrated by computing material response of sphere-cone arc jet samples. Surface Modeling Capabilities: NuSil, a silicone-based coating, was sprayed onto the MSL and Mars 2020 heatshields to mitigate shedding of phenolic dust. To better understand the effects of the NuSil coating on the material response, a novel model has been implemented in PATO. In this model, the equilibrium of the charred NuSil surface is modeled as pure silica, and a constant offset, inspired by the classical spallation model, is added to the the char blowing rate and wall enthalpy to reproduce HyMETS experimental results. The model has also been used to estimate the 3D material response of the MSL heatshield. Unified Solver: In addition to the iterative loose coupling approach mentioned above, a multiphase unified solver is being developed to couple the environment (plain-fluid phase) and the porous-material phase. The solver is based on the volume averaged conservation of mass, momentum, and energy for the macroscale with closure models which include microscale effects through effective physicochemical properties. The unified solver has been used to compute flow through a porous plug and solve the Beavers and Joseph problem. Since the strong coupling between phases is inherent to this solver, modeling assumptions present in other coupling methods of material response are mitigated. This strategy also makes it feasible to capture the competition between surface and volume ablation in the same computational domain, which is usually not possible with other coupling approaches.

Material Response↗

Recent Advancements in the PATO Material Response Code

Introduction: Predicting the complicated multiphysics phenomena during atmospheric entry requires high-fidelity modeling tools to refine estimates of mission risks during entry. To this end, new capabilities are being added to the Porous-material Analysis Toolbox based on OpenFOAM (PATO) [1,2,3]. PATO is an open-source software for Computational Material Response (CMR) of reactive porous materials submitted to high-temperature environments. The objective of this work is to highlight current efforts to add to and improve upon the modeling capabilities of PATO. These include efforts to loosely couple PATO with other discipline specialized codes including hypersonic Computational Fluid Dynamics (CFD), to assess the interaction effects between pyrolysis gas blowing and the boundary layer, and Computational Solid Mechanics (CSM), to address modeling of mechanical erosion. Other refinements include surface phenomena modeling capabilities to address the effects of silicone-based coatings applied to the TPS during flight preparation, and a unified multiphase solver for a mixed porous-material and plain-fluid domain. Coupling CMR with CFD (CMR/CFD): A loose coupling between PATO and the Data Parallel Line Relaxation (DPLR) [4] CFD code has been achieved by making use of a blowing boundary condition at the heatshield surface available in DPLR. Starting with heat flux estimates with no pyrolysis gas blowing at the surface, blowing gases are computed by the CMR and passed to the CFD such that aerothermal properties of the environment can be recomputed for a new CMR computation. This leads to an iterative process which is supplemented with an estimate of the radiative heat flux using the Nonequilibrium air radiation (NEQAIR) [5] program. The entire iterative process is illustrated in Figure 1. This coupling strategy has been utilized in computing the MSL material response. The goal is to compare the coupled CMR/CFD results with material response results obtained using traditional blowing corrections. Coupling CMS with CMR: A mechanical erosion model is currently being implemented in PATO to account for the additional mass removal induced by high shear conditions. The modeling process at each timestep consists of updating the mechanical properties as a function of temperature and computing the stress tensor and displacement fields of the material. Then, a failure criteria model determines the regions in which the stress exceeds the ultimate strength values resulting in mesh movement to account for mass removal. This model allows the material response simulation to compute the recession due to both oxidation and shear-induced erosion. The model is demonstrated by computing material response of sphere-cone arc jet samples. Surface Modeling Capabilities: NuSil, a silicone-based coating, was sprayed onto the MSL and Mars 2020 heatshields to mitigate shedding of phenolic dust. To better understand the effects of the NuSil coating on the material response, a novel model has been implemented in PATO. In this model, the equilibrium of the charred NuSil surface is modeled as pure silica, and a constant offset, inspired by the classical spallation model, is added to the the char blowing rate and wall enthalpy to reproduce HyMETS experimental results. The model has also been used to estimate the 3D material response of the MSL heatshield [6]. Unified Solver: In addition to the iterative loose coupling approach mentioned above, a multiphase unified solver is being developed to couple the environment (plain-fluid phase) and the porous-material phase. The solver is based on the volume averaged conservation of mass, momentum, and energy for the macroscale with closure models which include microscale effects through effective physicochemical properties. The unified solver has been used to compute flow through a porous plug and solve the Beavers and Joseph problem [7]. Since the strong coupling between phases is inherent to this solver, modeling assumptions present in other coupling methods of material response are mitigated. This strategy also makes it feasible to capture the competition between surface and volume ablation in the same computational domain, which is usually not possible with other coupling approaches.

Thermal Protection Systems↗

Identification and Study of Validation Level Test Cases for Computational Modeling of Non-Charring Ablators

Computational modeling of Thermal Protection System (TPS) materials, used for aerospace applications, provides numerous advantages in preliminary selection and design of a heatshield material and shape for atmospheric entry vehicles. However, to serve as a reliable tool for prediction of material thermal and ablative behavior, the modeling approach needs to be validated against real experimental and flight data, preferably at a range of applied conditions. The validation study is typically very complex as it requires reliable measured data not only for the material thermal response and surface recession, but also well characterized environmental conditions. The validation problem becomes even more complex when the material thermal response is dictated by multi-physics effects such as solid conduction, in-depth thermal decomposition, pyrolysis gas flow and chemical reactions. The multi-physics effects complicate not only the modeling effort, but also the experimental measurement for validation of various aspects of the highly coupled problem. In this study, an attempt is made to identify suitable experimental data that could serve as a source for validation of material thermal response modeling tools. To reduce the computational complexity, this study focuses only on non-charring ablators, where the material thermal response could be modeled with a single governing equation for solid conduction and the ablation is limited only to the surface of the material. With a well characterized and publicly available experimental data being sparse, the study is limited in presenting test cases for only three materials: camphor, graphite and FiberForm® in the sequence of increased modeling complexity. Graphite is a commonly used TPS material for aerospace applications, both for leading edges of high-speed vehicles and internal insulation of solid rocket motors. FiberForm® is a porous carbon pre-form used in preparation of the well known PICA material Tran et al. [1996]. Inclusion of camphor into the list is conditioned with the relative simplicity in modeling the material thermal and chemical response and the low-enthalpy flow environment. In addition, camphor has been used as a simple test material for study of flow transition behavior by Stock and Ginoux [1973] and assessment of a heatshield shape change at flight relevant conditions by Rotondi et al. [2022]. In this work, the identified experimental data was extracted from the public literature and test cases that yet have been published. As it was found from the review, not a single test case contains an exhaustive set of data that would validate every aspect of the material physics. However, in the data collected, various aspects of the material behavior can be still validated, such as surface and in-depth temperature, amount of recession and a shape change. The identified experimental data for each case is accompanied with a characterized flow environment and simulated boundary conditions predicted by a Data-Parallel Line Relaxation (DPLR) code Wright et al. [1998]. In addition, material thermal response numerical simulations in each test case are performed with Kentucky Aerothermodynamics and Thermal Response System (KATS-MR) Zibitsker et al. [2022] providing a comparative study and a sanity check for the proposed validation data. Sample results from the performed numerical study are shown below. Figure 1 shows distribution of surface heat flux and pressure values on a hemi-cylinder model made of FiberForm® and tested in HyMETS arc-jet facility. The results are shown for the high pressure condition among the two tests. Flow simulation was performed with DPLR code on a quarter of original geometry. In the figure, the quarter shape was mirrored across zx and xy planes to show the complete distribution. Figure 2 shows the material response results for the high pressure case (7500 Pa), simulated with KATS-MR and a comparison to the experimental data for the surface temperature and shape shape. The simulation was performed on a 2-D slice, extracted in the xy plane at the middle of the sample. Figure 3 shows the material response simulation for the low pressure case (3500 Pa) and a comparison to the experimental data for surface temperature and shape change.

ablation↗

Laser Absorption Spectroscopy Measurements of Post-Shock Non-Equilibrium Species in the NASA Ames Electric Arc Shock Tube

The NASA Ames Electric Arc Shock Tube (EAST) is a unique facility capable of generating high enthalpy, shock-heated impulse gas flows representative of the kinetic and radiative conditions encountered by atmospheric entry vehicles. The facility maintains a successful history with emission spectroscopy, providing measurements of absolute radiance upon which various validation studies are anchored. The central objective of this work is to develop a comprehensive tunable diode laser absorption spectroscopy (TDLAS) sensing capability to provide complementary experimental insights to existing emission techniques. More specifically, a fast-scanning TDLAS-based diagnostic targeting the cyano radical (CN) in the near-infrared(near-IR) near 926.6 nm is employed in mixtures of 2.2% CH4in N2by mole for a sweep of incident shock velocities ranging 3.0-5.5 km/s and fill pressures 0.3-1.15 Torr. Laser scan rates up to 500 kHz probe multiple absorption features to provide quantitative measurements of temperature and species number density profiles behind the incident shock. In all instances, the temperature trend is consistent between emission-inferred and TDLAS-inferred measurements. However, at the lower-velocity conditions, there is an appreciable offset between the Data Parallel Line Relaxation Code (DPLR) simulation and experimental measurements. A similar behavior is observed in number density profiles, with emission measurements providing inferences of the CN(B) and CN(A) state, while TDLAS measurements provide an additional inference of the CN(X) state. In the fast-scanned experiments, measurement inferred number densities suggest a much faster production of CN at early times than captured by the model. This discrepancy motivates ongoing, additional spectroscopic and kinetics CN experiments to resolve the accuracy of modeling assumptions.

Efaine Chang↗

Validating Drag and Heating Coefficients for Hollow Reentry Objects in Continuum Flow Using a Mach 7 Ludwieg Tube

Drag and heating coefficient databases and models are crucial to destructive reentry simulation. The NASA Orbital Debris Program Office (ODPO) develops, maintains, and performs analysis with the Object Reentry Survival Analysis Tool (ORSAT), which comprises drag and heating models for free molecular, transitional, and continuum flow regimes. These models have, in the past, only included solid, convex, blunt shapes (such as boxes, spheres, and cylinders). Previous work led by ODPO includes the extension of these models to hollow cylinders and square boxes in free molecular and transitional flow using the Direct Simulation Monte Carlo (DSMC) method. Since 2019, the ODPO has continued its program of DSMC simulations and extended the project to include analyses with the NASA Data Parallel Line Relaxation (DPLR) program on hollow cylinders and boxes (with varying wall thickness-diameter ratio). In fall 2022, the ODPO began a collaboration with the University of Texas San Antonio (UTSA) to use the Mach 7 Ludwieg Tube facility to validate the model built using numerical simulations. This facility can replicate (at a scale of approximately 100:1) the conditions seen by reentering objects near typical demise altitudes. We present here the drag and heating coefficients derived from the continued DSMC simulations, the new DPLR simulations, and the 26-test series at UTSA.

Chris Ostrom↗

Recent Updates to the Object Reentry Survival Analysis Tool (ORSAT) Version 7.1

The Object Reentry Survival Analysis Tool (ORSAT) code is maintained and used by the NASA Orbital Debris Program Office (ODPO) and has been under continuous development and improvement since the mid-1990s. ORSAT is an object-oriented reentry simulation tool; it models a satellite as a collection of discrete components that follow independent trajectories upon the breakup of the parent object. Version 7.1 of the tool incorporates five years of new thermal and aerodynamic model development, multi-processor parametric study capability, codebase upgrades, and numerous bug-fixes. The thermal demise model was completely rewritten using a forward-time/central-space numerical stencil and incorporating a new pyrolysis model for fiber-reinforced plastic (FRP) materials. New aerodynamic and aeroheating models for hollow cylinders and hollow square prisms were developed using a combination of flow simulations in the direct simulation Monte Carlo (DSMC) Analysis Code (DAC) and Data Parallel Line Relaxation (DPLR) code and free-flight tests in the University of Texas at San Antonio’s Hypersonic Wind Tunnel. The latest version also incorporates a mechanical, strength-based demise model for FRP materials. Minor improvements include an update to the Fortran 2018 codebase; improved integration and speed with the Python-based, multi-core, parametric study tool, AutoORSAT; and fixes for many minor bugs. This new version of ORSAT will enable more accurate reentry risk assessments for modern satellites. This paper presents an overview of these changes and a summary of the verification and validation performed on the final code.

Benton R. Greene↗

Recent Updates to the Object Reentry Survival Analysis Tool (ORSAT) Version 7.1

The Object Reentry Survival Analysis Tool (ORSAT) code is maintained and used by the NASA Orbital Debris Program Office (ODPO) and has been under continuous development and improvement since the mid-1990s. ORSAT is an object-oriented reentry simulation tool; it models a satellite as a collection of discrete components that follow independent trajectories upon the breakup of the parent object. Version 7.1 of the tool incorporates five years of new thermal and aerodynamic model development, multi-processor parametric study capability, codebase upgrades, and numerous bug-fixes. The thermal demise model was completely rewritten using a forward-time/central-space numerical stencil and incorporating a new pyrolysis model for fiber-reinforced plastic (FRP) materials. New aerodynamic and aeroheating models for hollow cylinders and hollow square prisms were developed using a combination of flow simulations in the direct simulation Monte Carlo (DSMC) Analysis Code (DAC) and Data Parallel Line Relaxation (DPLR) code and free-flight tests in the University of Texas at San Antonio’s Hypersonic Wind Tunnel. The latest version also incorporates a mechanical, strength-based demise model for FRP materials. Minor improvements include an update to the Fortran 2018 codebase; improved integration and speed with the Python-based, multi-core, parametric study tool, AutoORSAT; and fixes for many minor bugs. This new version of ORSAT will enable more accurate reentry risk assessments for modern satellites. This paper presents an overview of these changes and a summary of the verification and validation performed on the final code.

Benton R. Greene↗

Validating Drag and Heating Coefficients for Hollow Reentry Objects in Continuum Flow Using a Mach 7 Ludwieg Tube

Drag and heating coefficient databases and models are crucial to destructive reentry simulation. The NASA Orbital Debris Program Office (ODPO) develops, maintains, and performs analysis with the Object Reentry Survival Analysis Tool (ORSAT), which comprises drag and heating models for free molecular, transitional, and continuum flow regimes. These models have, in the past, only included solid, convex, blunt shapes (such as boxes, spheres, and cylinders). Previous work led by ODPO includes the extension of these models to hollow cylinders and square boxes in free molecular and transitional flow using the Direct Simulation Monte Carlo (DSMC) method. Since 2019, the ODPO has continued its program of DSMC simulations and extended the project to include analyses with the NASA Data Parallel Line Relaxation (DPLR) program on hollow cylinders and boxes (with varying wall thickness-diameter ratio). In fall 2022, the ODPO began a collaboration with the University of Texas San Antonio (UTSA) to use the Mach 7 Ludwieg Tube facility to validate the model built using numerical simulations. This facility can replicate (at a scale of approximately 100:1) the conditions seen by reentering objects near typical demise altitudes. We present here the drag and heating coefficients derived from the continued DSMC simulations, the new DPLR simulations, and the 26-test series at UTSA.

Chris Ostrom↗

Magnetohydrodynamic and Aerodynamic Assessment of Ballistic Entry of a 70deg Spherecone at Mars and Venus

An electrical conductivity database for continuum flow in a CO2 atmosphere over a 70 deg spherecone was created using the Data Parallel Line Relaxation Code computational fluid dynamics software to inform development of future magnetohydrodynamic subsystems at Venus and Mars. Sixteen freestream conditions were considered at Mars with atmospheric relative velocities from 5 to 8 km/s and altitudes between 20 and 80 km. Sixteen freestream conditions were considered at Venus with atmospheric relative velocities from 9 to 12 km/s and altitudes between 85 and 115 km. Results indicate that the total electrical conductivity in the flow volume always increases as velocity increases. At low velocities, the electrical conductivity is higher at high altitudes, while at high velocities, the electrical conductivity is higher at low altitudes. Three of the 80 km altitude computational fluid dynamics solutions show good agreement with Direct Simulation Monte Carlo results. In general, computational fluid dynamics predicts thinner shocks, higher electron number density, and similar vibrational temperatures as direct simulation Monte Carlo. The magnetohydrodynamic force was calculated at both Mars and Venus. Results indicate there may not be sufficient control authority to use magnetohydrodynamics as a trajectory control mechanism at Mars without artificially increasing the electrical conductivity of the flow, but there may be appreciable control authority for a drag-modulated aerocapture at Venus.

Destiny M Fawley↗

Scalable line and plane relaxation in a parallel structured multigrid solver

The efficient solution of sparse, linear systems that arise through the discretization of partial differential equations remains a key challenge for a range of high performance scientific simulations. One approach for reducing data movement and improving performance is by exposing and exploiting structure in a problem through the use of robust structured multilevel solvers. By choosing coarsening that preserves the structure of the problem, these methods maintain efficient structured computation and communication throughout the multigrid hierarchy. However, when coarsening is not permitted to be dependent on the operator, anisotropy must be addressed by the smoother — producing error compatible for coarse-grid correction with structured coarsening. Here, the components required in a scalable parallel structured solver are described with a focus on memory and communication efficiency of robust smoothers. While the implementation of communication and memory reduction techniques in smoothers integrated in a complete 3D solver present a significant engineering challenge, a novel approach is proposed that addresses these challenges systematically through a change to the solver’s execution model. Enabled by user-level threading paired with a set of data and communication abstractions, this approach permits seamless aggregation of communication in plane smoothers — directly reusing code for a 2D distributed multilevel cycle. Results show an effective reduction in communication costs for coarse-grid problems, and result in a speedup of 8.7x in smoothing routines shown in Fig. 12 using this approach. This produces a significant improvement to strong scalability while maintaining favorable weak scaling behavior. Finally, a parallel scaling study using a series of refined meshes is included that demonstrates the effectiveness of this approach in an application of interest.

97 MATHEMATICS AND COMPUTING↗

Broadening of the D lines and the relaxation of the resonance levels of sodium due to collisions with helium.

Calculated potentials for the NaHe molecule are used to obtain collision-induced widths and shifts for the sodium D lines together with cross sections for fine-structure transitions and the relaxation of the multipole polarizations of the resonance levels. The atomic collision is treated in an adiabatic approximation in which the colliding atoms form a molecular system which rotates during the collision. We find the resonance lines to be broadened equally and to be approximately 70% wider, and with associated shifts of an order of magnitude smaller, than expected on the basis of van der Waals forces. The dependence of the cross sections for relaxation of the multipole polarizations of the resonance levels on the molecular-coupling conditions and the rotation of the system during collision is discussed and indicates a limitation of the sum rule for these cross sections.

Lewis, E. L.↗

A nonlinear relaxation/quasi-Newton algorithm for the compressible Navier-Stokes equations

A highly efficient implicit method for the computation of steady, two-dimensional compressible Navier-Stokes flowfields is presented. The discretization of the governing equations is hybrid in nature, with flux-vector splitting utilized in the streamwise direction and central differences with flux-limited artificial dissipation used for the transverse fluxes. Line Jacobi relaxation is used to provide a suitable initial guess for a new nonlinear iteration strategy based on line Gauss-Seidel sweeps. The applicability of quasi-Newton methods as convergence accelerators for this and other line relaxation algorithms is discussed, and efficient implementations of such techniques are presented. Convergence histories and comparisons with experimental data are presented for supersonic flow over a flat plate and for several high-speed compression corner interactions. Results indicate a marked improvement in computational efficiency over more conventional upwind relaxation strategies, particularly for flowfields containing large pockets of streamwise subsonic flow.

Edwards, Jack R.↗

Mapping robust parallel multigrid algorithms to scalable memory architectures

The convergence rate of standard multigrid algorithms degenerates on problems with stretched grids or anisotropic operators. The usual cure for this is the use of line or plane relaxation. However, multigrid algorithms based on line and plane relaxation have limited and awkward parallelism and are quite difficult to map effectively to highly parallel architectures. Newer multigrid algorithms that overcome anisotropy through the use of multiple coarse grids rather than line relaxation are better suited to massively parallel architectures because they require only simple point-relaxation smoothers. The parallel implementation of a V-cycle multiple semi-coarsened grid (MSG) algorithm or distributed-memory architectures such as the Intel iPSC/860 and Paragon computers is addressed. The MSG algorithms provide two levels of parallelism: parallelism within the relaxation or interpolation on each grid and across the grids on each multigrid level. Both levels of parallelism must be exploited to map these algorithms effectively to parallel architectures. A mapping of an MSG algorithm to distributed-memory architectures that demonstrate how both levels of parallelism can be exploited is described. The results is a robust and effective multigrid algorithm for distributed-memory machines.

Overman, Andrea↗

The improved robustness of multigrid elliptic solvers based on multiple semicoarsened grids

Multigrid convergence rates degenerate on problems with stretched grids or anisotropic operators, unless one uses line or plane relaxation. For 3-D problems, only plane relaxation suffices, in general. While line and plane relaxation algorithms are efficient on sequential machines, they are quite awkward and inefficient on parallel machines. A new multigrid algorithm is presented based on the use of multiple coarse grids, that eliminates the need for line or plane relaxation in anisotropic problems. This algorithm was developed and the standard multigrid theory was extended to establish rapid convergence for this class of algorithms. The new algorithm uses only point relaxation, allowing easy and efficient parallel implementation, yet achieves robustness and convergence rates comparable to line and plane relaxation multigrid algorithms. The algorithm described is a variant of Mulder's multigrid algorithm for hyperbolic problems. The latter uses multiple coarse grids to achieve robustness, but is unsuitable for elliptic problems, since its V-cycle convergence rate goes to one as the number of levels increases. The new algorithm combines the contributions from the multiple coarse grid via a local switch, based on the strength of the discrete operator in each coordinate direction.

Naik, Naomi H.↗

Energy relaxation dynamics in a nodal-line semimetal

Here we study the temperature relaxation dynamics of nodal-line semimetals after a sudden excitation in the presence of acoustic and optical phonon modes. We find that the nodal line constrains the electron momenta in scattering processes, and as a result, the temperature relaxation due to acoustic phonons is exponential as a function of time. However, depending on initial conditions, other functional forms are possible. In typical pump-probe experiments, the temperature relaxation is linear due to acoustic phonons with rates that vary as ~n 1/2 with density. The temperature relaxation due to optical phonons is also linear with rates ~n -1/2 or ~n .

36 MATERIALS SCIENCE↗

Mapping robust parallel multigrid algorithms to scalable memory architectures

The convergence rate of standard multigrid algorithms degenerates on problems with stretched grids or anisotropic operators. The usual cure for this is the use of line or plane relaxation. However, multigrid algorithms based on line and plane relaxation have limited and awkward parallelism and are quite difficult to map effectively to highly parallel architectures. Newer multigrid algorithms that overcome anisotropy through the use of multiple coarse grids rather than relaxation are better suited to massively parallel architectures because they require only simple point-relaxation smoothers. In this paper, we look at the parallel implementation of a V-cycle multiple semicoarsened grid (MSG) algorithm on distributed-memory architectures such as the Intel iPSC/860 and Paragon computers. The MSG algorithms provide two levels of parallelism: parallelism within the relaxation or interpolation on each grid and across the grids on each multigrid level. Both levels of parallelism must be exploited to map these algorithms effectively to parallel architectures. This paper describes a mapping of an MSG algorithm to distributed-memory architectures that demonstrates how both levels of parallelism can be exploited. The result is a robust and effective multigrid algorithm for distributed-memory machines.

Overman, Andrea↗