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NASA NTRS1987

A fixed grid numerical methodology for phase change problems involving a moving heat source

A numerical method for solving phase change problems involving a moving heat source is presented and illustrated by a two-dimensional example. The method uses a fixed grid and does not require the implementation of the Stefan condition at the solid-liquid interface; the procedure can thus be easily implemented using existing fixed grid codes. The problem considered as an example involves natural convection flow in the molten metal during tungsten inert gas welding.

Prakash, C.↗

NASA NTRS1988

Unsteady transonic airfoil computation using implicit Euler scheme on body-fixed grid

The unsteady Euler equations have been derived for the flow relative motion with respect to a frame of reference that is rigidly attached to the moving airfoil. The grid is generated once by an elliptic solver without a need for dynamic grid computation. An implicit factored finite-volume scheme has been developed and implemented through a fully vectorized computer program. Implicit second-order and explicit second and fourth-order dissipations are added to the scheme. The boundary conditions are explicitly satisfied. The scheme is applied to steady and unsteady transonic airfoil flows and the results are in good agreement with the experimental data. For forced harmonic airfoil motions, periodic solutions are achieved within the third cycle of oscillation.

Kandil, Osama A.↗

NASA NTRS1989

Unsteady transonic airfoil computation using implicit Euler scheme on body-fixed grid

Explore the source record for details and available documents.

Kandil, Osama A.↗

NASA NTRSDate not supplied

USM3D-ME Contributions to the 5th AIAA High Lift Prediction Workshop

This paper presents the results of Reynolds-averaged Navier-Stokes (RANS) simulations conducted by NASA’s flow solver, mixed-element USM3D (USM3D-ME), for the 5th AIAA High-Lift Prediction Workshop. As part of the Fixed-Grid RANS Technology Focus Group (TFG), these simulations were performed to assess the accuracy and efficiency of the USM3D-ME solutions in predicting high-lift flows. The High-Lift Common Research Model (CRM-HL) served as the primary geometry. Several CRM-HL configurations were used for three case studies: a verification study (Case 1), a configuration buildup study (Case 2), and a Reynolds-number variation study (Case 3). Overall, USM3D-ME RANS results aligned with the solutions selected by the Fixed-Grid RANS TFG and available wind tunnel data Simulations for Cases 1 and Configuration 2.1 achieved machine-zero residual convergence, with aerodynamic coefficients converging to steady-state values. However, Configurations 2.2-2.4 and Case 3 encountered iterative- and grid-convergence challenges, particularly at high angles of attack. Compared with the experimental data available for Configurations 2.2-2.4, close agreement was demonstrated at low angles of attack. However, for angles of attack approaching the maximum lift conditions, the predicted lift coefficient and pitching moment deviated from experimental values. The drag-coefficient predictions were in a relatively good agreement, however, slight overpredictions were observed at the highest angle of attack corresponding to the maximum-lift condition. Although iterative convergence for Configurations 2.2-2.4 at high angles of attack remains a persistent challenge, averaging aerodynamic coefficients over the last 5000 iterations yielded satisfactory agreement with the available wind tunnel experimental data. During the workshop, the lack of iterative convergence was attributed to the vortex structures emanating from the slat brackets. To investigate this issue further, post-workshop simulations were conducted on Configuration 2.2. In one study, RANS simulations were performed on a simplified geometry with the slat brackets removed. The second study focused on performing URANS simulations on the original Configuration 2.2 geometry. Preliminary results from both studies are presented and compared with wind tunnel data for Configuration 2.2. Consistent with the findings of other participants in the Fixed-Grid RANS TFG, this study emphasizes the necessity for further exploration and advancement in RANS technology for predicting high-lift flows.

CFD↗

NASA NTRSDate not supplied

USM3D-ME Contributions to the 5th AIAA High Lift Prediction Workshop

This paper presents the results of Reynolds-averaged Navier-Stokes (RANS) simulations conducted by the NASA flow solver, mixed-element USM3D (USM3D-ME), for the 5th AIAA High-Lift Prediction Workshop. As part of the Fixed-Grid RANS Technology Focus Group (TFG), these simulations were performed to assess the accuracy and efficiency of the USM3D-ME solutions in predicting high-lift flows. The High-Lift Common Research Model (CRM-HL) served as the primary geometry. Several CRM-HL configurations were used for three case studies: a verification study (Case 1), a configuration buildup study (Case 2), and a Reynolds-number variation study (Case 3). Overall, USM3D-ME RANS results aligned with the solutions selected by the Fixed-Grid RANS TFG and available wind tunnel data. Simulations for Case 1 and Configuration 2.1 achieved machine-zero residual convergence, with aerodynamic coefficients converging to steady-state values. However, Configurations 2.2-2.4 and Case 3 encountered iterative- and grid-convergence challenges, particularly at high angles of attack. Compared with the experimental data available for Configurations 2.2-2.4, close agreement was demonstrated at low angles of attack. However, for angles of attack approaching the maximum lift conditions, the predicted lift coefficient and pitching moment deviated from experimental values. The drag-coefficient predictions were in relatively good agreement, however, slight overpredictions were observed at the highest angle of attack corresponding to the maximum-lift condition. Although iterative convergence for Configurations 2.2-2.4 at high angles of attack remains a persistent challenge, averaging aerodynamic coefficients over the last 5000 iterations yielded satisfactory agreement with the available wind tunnel experimental data. During the workshop, the lack of iterative convergence was attributed to the vortex structures emanating from the slat brackets. To investigate this issue further, post-workshop simulations were conducted on Configuration 2.2. In one study, RANS simulations were performed on a simplified geometry with the slat brackets removed. The second study focused on performing unsteady RANS (URANS) simulations on the original Configuration 2.2 geometry. Preliminary results from both studies are presented and compared with wind tunnel data for Configuration 2.2. Consistent with the findings of other participants in the Fixed-Grid RANS TFG, this study emphasizes the necessity for further exploration and advancement in RANS technology for predicting high-lift flows.

Aerodynamics↗

NASA NTRSDate not supplied

Mixed-element USM3D Contributions to the 4th AIAA High-Lift Prediction Workshop

This paper discusses results of the mixed-element USM3D (USM3D-ME) simulations performed for the 4th AIAA High-Lift Prediction Workshop. The workshop was separated into six Technical Focus Groups to investigate the impact of geometry modeling, grid, and computational methods for predicting high lift flows. This work was performed under the Fixed Grid RANS Technical Focus Group. The primary geometry selected for the workshop was the High-Lift Common Research Model. The performed simulations included a flap deflection study and both a grid refinement study and pitch sweep for the nominal flap deflection configuration. The results show that USM3D-ME RANS solutions, generally, tends to underpredict the lift coefficient and to predict a less negative pitching moment relative to the experimental data. The predicted drag coefficient values agree better with experiment for smaller angles of attack but were observed to be larger than experiment for the largest angle of attack simulated. The results of the grid refinement study demonstrated a lack of grid convergence for the provided grid family. The results of the grid refinement study are consistent with the submissions to the Fixed Grid and Mesh Adaptation Technical Focus Groups. Grid convergence for the provided grid family remains elusive for the international community. A 2D Multielement Airfoil configuration was included to enable a turbulence model verification study, which illustrated favorable agreement between USM3D-ME and the solutions provided by other flow solvers.

CFD↗

NASA NTRSDate not supplied

Mixed-Element USM3D Contributions to the 4th AIAA High-Lift Prediction Workshop

CFD↗

NASA NTRS2018

Unstructured Grid Adaptation and Solver Technology for Turbulent Flows

Unstructured grid adaptation is a tool to control Computational Fluid Dynamics (CFD) discretization error. However, adaptive grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Issues that prevent the use of adaptive grid methods are identified by applying unstructured grid adaptation methods to a series of benchmark cases. Once identified, these challenges to existing adaptive workflows can be addressed. Unstructured grid adaptation is evaluated for test cases described on the Turbulence Modeling Resource (TMR) web site, which documents uniform grid refinement of multiple schemes. The cases are turbulent flow over a Hemisphere Cylinder and an ONERA M6Wing. Adaptive grid force and moment trajectories are shown for three integrated grid adaptation processes with Mach interpolation control and output error based metrics. The integrated grid adaptation process with a finite element (FE) discretization produced results consistent with uniform grid refinement of fixed grids. The integrated grid adaptation processes with finite volume schemes were slower to converge to the reference solution than the FE method. Metric conformity is documented on grid/metric snapshots for five grid adaptation mechanics implementations. These tools produce anisotropic boundary conforming grids requested by the adaptation process.

Park, Michael A.↗

NASA NTRS1993

Space marching calculations about hypersonic configurations using a solution-adaptive mesh algorithm

A solution-adaptive marching algorithm is developed and applied to a three-dimensional parabolized Navier-Stokes equation solver. The resulting algorithm obtains accurate solutions by using a spatial-marching/adaptive grid procedure. The adaptation step redistributes grid points line by line in both crossflow directions, with grid point motion controlled by forces analogous to tensional and torsional spring forces with the tensional force proportional to the error measure or weighting functions. The solution-adaptive marching procedure is applied to the hypersonic flow about two generic aircraft configurations. The first of these is an all-body-type geometry with elliptical cross sections and is studied at angles of attack of 0.5, and 15 deg. The second geometry is a generic blended-wing-body design. Results are presented that demonstrate the improvements in flowfield resolution obtainable with the solution-adaptive marching procedure over conventional fixed grid techniques. Computed pitot pressure profiles obtained using the solution-adaptive algorithm show improved agreement with experimental data compared to predictions obtained using a fixed grid.

Harvey, Albert D.↗

NASA NTRSDate not supplied

Using XR for Improving Scientific Discovery With Numerical Weather Models

Earth science (ES) digital twins will help us understand the complex interactions and interrelationships that make up our Earth system and the impacts of earth science phenomena on it. Our work addresses two underdeveloped areas in current ES digital twin work: improving the understanding and interaction with ES model outputs by using Virtual and Mixed Reality (XR) tools and improving the non-intuitive mapping of continuous ES natural phenomena to gridded reference frames in current numerical models. Traditionally, scientists working on ES view and analyze the results of calculated or measured observables with static 1-dimensional (1D), 2D or 3D plots displayed on flat computer screens or paper. Using such limited mediums, it can be very difficult to identify, track and understand the evolution of key features due to poor viewing angles and the nature of flat computer screens. In addition, numerical models, such as the NASA Goddard Earth Observing System (GEOS) ES model, are almost exclusively formulated, visualized and analyzed in an Eulerian reference frame with fixed grid points in space and time. However, ES phenomena such as convective clouds, hurricanes and wildfire smoke plumes are visualized and analyzed in a Lagrangian reference frame: therefore it is often difficult and unnatural to understand these phenomena in relation to each other, visualized either in an Eulerian or Lagrangian context. In 3D visualizations, data generally takes one of three forms: gridded (e.g., voxelized) data, where space is divided into regions; point clouds, where data is represented as a set of points; and meshes, where objects are rendered as surfaces composed of small polygons (usually triangles). A gridded, Eulerian reference frame has been the default representation for the 2D visual analysis of atmospheric data in part because the numerical methods used to generate atmospheric model data in the first place use a gridded approach, with equations defining the relationships between the physical variables in each of a grid's cells across successive timesteps. In our work, we are particularly interested in data from GEOS. Another reason why gridded representations tend to be used for visualizing data from such models is because trajectories are difficult to interpret from representations on 2D surfaces, due to line-of-sight ambiguity. Instead of a fixed grid from GEOS, we embed a trajectory model to simulate particles' movement throughout a GEOS run. We then ingest these particle trajectories as animated point clouds with a NASA open source XR toolkit, the Mixed Reality Exploration Toolkit (MRET), and merge GEOS data with ES phenomena data onto one combined visualization that the user can intuitively interact with. Efficient rendering of arbitrarily large point clouds is an ongoing challenge being addressed by the computer science community, with the GPU-based optimizations and efficient GPU memory utilization a common theme of recent advances, especially for XR, where sustained high frame rate is mandatory to save the user from suffering due to simulation sickness. In this work, we describe and evaluate our progress in choosing and implementing appropriate methods for rendering arbitrarily large point clouds within MRET for XR. While tracking the XR headset enables the immersion of a user within a 3D scene of a data visualization, tracking of XR handheld controllers or user’s hands enables us to implement intuitive user interactions with the visualized datasets. Conventional tools require a user working with an ES visualization to conduct many interactions to commit their intended selections or manipulations with a visualized dataset; for example to specify a set of points in 3D space. Doing so in a 2D flat screen interface has traditionally required specifying a set of points in three distinct 2D coordinate systems (XY, XZ, and YZ), which is cumbersome. In other scientific domains, it has been shown that specifying or selecting a location or volume in XR using handheld controllers or tracked hands allows for greater speed and accuracy. We anticipate the same will hold true for atmospheric data, and we will share initial results of measuring the utility of such an interface. Notably, as the data being visualized is generated by GEOS as a prediction based on initial conditions, an intended application of our tool is to serve as part of an iterative feedback loop. Through XR, a scientist will review and manipulate a GEOS model run, modifying the conditions as needed to do subsequent runs of GEOS. Thereby, XR-based improvements to speed and accuracy of 3D tagging of points minimizes the effort required by both the scientist and the computer cluster conducting the necessary calculations.

Thomas Grubb↗

NASA NTRS2017

Generating Land Surface Reflectance for the New Generation of Geostationary Satellite Sensors with the MAIAC Algorithm

The latest generation of geostationary satellite sensors, including the GOES-16/ABI and the Himawari 8/AHI, provide exciting capability to monitor land surface at very high temporal resolutions (5-15 minute intervals) and with spatial and spectral characteristics that mimic the Earth Observing System flagship MODIS. However, geostationary data feature changing sun angles at constant view geometry, which is almost reciprocal to sun-synchronous observations. Such a challenge needs to be carefully addressed before one can exploit the full potential of the new sources of data. Here we take on this challenge with Multi-Angle Implementation of Atmospheric Correction (MAIAC) algorithm, recently developed for accurate and globally robust applications like the MODIS Collection 6 re-processing. MAIAC first grids the top-of- atmosphere measurements to a fixed grid so that the spectral and physical signatures of each grid cell are stacked (“remembered”) over time and used to dramatically improve cloud/shadow/snow detection, which is by far the dominant error source in the remote sensing. It also exploits the changing sun-view geometry of the geostationary sensor to characterize surface BRDF with augmented angular resolution for accurate aerosol retrievals and atmospheric correction. The high temporal resolutions of the geostationary data indeed make the BRDF retrieval much simpler and more robust as compared with sun-synchronous sensors such as MODIS. As a prototype test for the geostationary-data processing pipeline on NASA Earth Exchange (GEONEX), we apply MAIAC to process 18 months of data from Himawari 8/AHI over Australia. We generate a suite of test results, including the input TOA reflectance and the output cloud mask, aerosol optical depth (AOD), and the atmospherically-corrected surface reflectance for a variety of geographic locations, terrain, and land cover types. Comparison with MODIS data indicates a general agreement between the retrieved surface reflectance products. Furthermore, the geostationary results satisfactorily capture the movement of clouds and variations in atmospheric dust/aerosol concentrations, suggesting that high quality land surface and vegetation datasets from the advanced geostationary sensors can help complement and improve the corresponding EOS products.

geostationary satellite sensors↗

DOE OSTI2022

Energy Exascale Earth System Model v2.0.1

First patch release of v2.0.0 Changes since v2.0.0 [Important change] Fix ocean threading bug seen in debug cases on Chrysalis with Intel 20.0.4. Was introduced around time of v2.0.0 tag. Does not change v2.0.0 answers on Chrysalis because those didn't use threading or debugging. [EAM] Add semi-lagrangian tracer transport for theta-l (F90 and C++), add new algorithm for finding tropopause, add DSCREAM to allow v2 and SCREAM settings in same code such as adjust_ps [EAM-MMF] 60L default, allow C++ back end of RRTMGP (EAM too). [EAMxx] add nu-top functionality, fix forcing functor, add ttype9 and dcmip2012 tests 2.1, 2.2, and 3 HOMME: remove obsolete remap algs, option to specify dynamics alg indep of tracer, new sponge layer, add imex tests [ELM] Add topography-based subgrid (topounits), add FATES-ELM Nitro., Phos. and CH4 coupling, add land-use ts for NARRM, add lulc for SSP3 RCP7, Fix nutrient fertilization exp test and carbon isotope flux, Fix xactive lnd dry deposition, add lake water storage option, fix plant hydraulics 2d params, fix carbon budget calc, fix soil nutrient conc. bug, fix mosart dam bug, add test for new ELM, MOSART features, fix bug in O3 dry dep stomatal resistances, fix plant hydraulics restart BFB error, update mkmapdata. [MOSART] fix bug for reading the latitude from an unstructured input file, fix oversat in bubble test. [MPAS-ocean] Add CFC11, CFC12 tracers, add 2D spherical transport tests, fix del4 tracer mixing, add MARBL ocean tracer mixing, modify harmonic analysis options, add GPU port of vmix routines, fix calc of ML-averaged BV freq. [MPAS-seaice] Change extents of initial polar disks for oRRS18to6v3 grid, fix ice BGC with MARBL, update spherical test cases, fix DON coupling, Remove Cf from sea ice constants. [MPAS-landice] add CRYO1850-4xCO2 compset [CIME] add GCP, ANL GCE, Spock, Perlmutter, deprecate config_compilers.xml, fix and clean-up cmake macros, fix slurm bindings, refactor CIME internal testing, cleanup SCORPIO perf data, allow position independent compset naming, [also] update v2 benchmarking suite, extend e3sm_prod with throughput and memory checks

E3SM Project, DOE↗

DOE OSTI2022

Numerical and experimental investigation of the flame kernel growth in a methane/air mixture near the lean flammability limit

Lean combustion has the potential to improve the thermal efficiency of spark-ignition engines, but it faces the significant challenge of increased cycle-to-cycle variation due to low mixture reactivity and unstable flame dynamics. Computational fluid dynamics (CFD) employing predictive models can guide engine design and optimize operating strategies for lean combustion. However, ignition and combustion models have rarely been validated at fuel-lean conditions, and a fundamental understanding of the early flame kernel growth process is also lacking for a successful sub-model development. Here, the present study develops a numerical simulation framework used to investigate early flame kernel growth in methane/air mixtures. A nanosecond-pulsed discharge (NPD) approach is employed to effectively decouple the flame kernel growth from the electrical discharge due to their difference in timescales, and equivalence ratios near the experimentally measured lean flammability limit (LFL) are selected to focus on challenging mixture conditions. Three numerical investigations, such as the choice of turbulence modeling, grid size, and grid control strategies, are examined to match both LFL and flame kernel structure measured from experiments. It is demonstrated that a quasi-direct numerical simulation (QDNS) with a fixed grid embedding of 10 μm can predict the LFL as φ CFD =0.61 and match the displacement speed of the kernel’s boundary marked in schlieren images. To predict the LFL and flame kernel shape, a fine grid (Δ≤12.5 μm) is needed to capture the consumption of formaldehyde (CH 2 O) in kernel’s reaction branches attached to the anode, and adaptive mesh refinement is replaced with the fixed embedding due to loss of simulation accuracy. Also, it is found that a large-eddy simulation (LES) using the Dynamic Structure model is not suitable for the NPD-induced flame kernel simulation because artificial sub-grid turbulent kinetic energy induced by shock dynamics alters the flow velocity calculation, resulting in divergence of LES from QDNS. Lastly, the simulation well matches the experimental data for the flame kernel evolution in three mixture conditions (φ = 0.7, 0.61, 0.55), showing toroidal flame kernel expansion and flame kernel growth/extinction.

33 ADVANCED PROPULSION SYSTEMS↗

NASA NTRSDate not supplied

High-Fidelity CFD Verification Workshop 2024 Summary: Spalart-Allmaras QCR2000-R Turbulence Model

This paper summarizes solutions submitted for the Reynolds-averaged Navier-Stokes (RANS) test suite of the High-Fidelity CFD Verification Workshop. The goal of the workshop is to establish standards for verification of computational fluid dynamics (CFD) approaches to simulations of steady and unsteady turbulent flows. The RANS verification studies focus on a one-equation Spalart-Allmaras model with quadratic constitutive relation and rotation correction, SA-neg-QCR2000-R. The verification test cases are a two-dimensional subsonic flow around a Joukowski airfoil, a three-dimensional subsonic flow around an extruded NACA 0012 wing in a tunnel, and a subsonic flow around a wing-body configuration developed for verification of solvers participating in the 5 𝑡 ℎ High-Lift Prediction Workshop. The turbulencemodel formulation, geometry, flow conditions, grids, and reference solutions are described in detail. Solutions for the test cases are computed by seven established CFD solvers on adaptedand fixed-grid families using different discretization approaches. While some noticeable differences between solutions remain, the results achieved by contributing solvers show that different solutions computed for the same RANS model on different grid families can converge to a common limit with grid refinement. The apparent requirements for grid convergence are a well designed family of grids that provide sufficient resolution in important areas and a strong solver capable of deep iterative convergence on each grid. For each test case in the study, the variation between aerodynamic forces computed by different solvers on the finest grids of different families is less than 2%.

Boris Diskin↗

DOE OSTI2024

Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows

High-order Godunov methods for gas dynamics have become a standard tool for simulating different classes of astrophysical flows. Their accuracy is mostly determined by the spatial interpolant used to reconstruct the pair of Riemann states at cell interfaces and by the Riemann solver that computes the interface fluxes. In most Godunov-type methods, these two steps can be treated independently, so that many different schemes can in principle be built from the same numerical framework. Because astrophysical simulations often test out the limits of what is feasible with the computational resources available, it is essential to find the scheme that produces the numerical solution with the desired accuracy at the lowest computational cost. However, establishing the best combination of numerical options in a Godunov-type method to be used for simulating a complex hydrodynamic problem is a nontrivial task. In fact, formally more accurate schemes do not always outperform simpler and more diffusive methods, especially if sharp gradients are present in the flow. For this work, we used our fully compressible Seven-League Hydro (SLH) code to test the accuracy of six reconstruction methods and three approximate Riemann solvers on two- and three-dimensional (2D and 3D) problems involving subsonic flows only. We considered Mach numbers in the range from 10 −3 to 10 −1 , which are characteristic of many stellar and geophysical flows. In particular, we considered a well-posed, 2D, Kelvin–Helmholtz instability problem and a 3D turbulent convection zone that excites internal gravity waves in an overlying stable layer. Although the different combinations of numerical methods converge to the same solution with increasing grid resolution for most of the quantities analyzed here, we find that (i) there is a spread of almost four orders of magnitude in computational cost per fixed accuracy between the methods tested in this study, with the most performant method being a combination of a low-dissipation Riemann solver and a sextic reconstruction scheme; (ii) the low-dissipation solver always outperforms conventional Riemann solvers on a fixed grid when the reconstruction scheme is kept the same; (iii) in simulations of turbulent flows, increasing the order of spatial reconstruction reduces the characteristic dissipation length scale achieved on a given grid even if the overall scheme is only second order accurate; (iv) reconstruction methods based on slope-limiting techniques tend to generate artificial, high-frequency acoustic waves during the evolution of the flow; and (v) unlimited reconstruction methods introduce oscillations in the thermal stratification near the convective boundary, where the entropy gradient is steep.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Compiling Quantum Circuits for Dynamically Field-Programmable Neutral Atoms Array Processors

Dynamically field-programmable qubit arrays (DPQA) have recently emerged as a promising platform for quantum information processing. In DPQA, atomic qubits are selectively loaded into arrays of optical traps that can be reconfigured during the computation itself. Leveraging qubit transport and parallel, entangling quantum operations, different pairs of qubits, even those initially far away, can be entangled at different stages of the quantum program execution. Such reconfigurability and non-local connectivity present new challenges for compilation, especially in the layout synthesis step which places and routes the qubits and schedules the gates. In this paper, we consider a DPQA architecture that contains multiple arrays and supports 2D array movements, representing cutting-edge experimental platforms. Within this architecture, we discretize the state space and formulate layout synthesis as a satisfiability modulo theories problem, which can be solved by existing solvers optimally in terms of circuit depth. For a set of benchmark circuits generated by random graphs with complex connectivities, our compiler OLSQ-DPQA reduces the number of two-qubit entangling gates on small problem instances by 1.7x compared to optimal compilation results on a fixed planar architecture. To further improve scalability and practicality of the method, we introduce a greedy heuristic inspired by the iterative peeling approach in classical integrated circuit routing. Using a hybrid approach that combined the greedy and optimal methods, we demonstrate that our DPQA-based compiled circuits feature reduced scaling overhead compared to a grid fixed architecture, resulting in 5.1X less two-qubit gates for 90 qubit quantum circuits. These methods enable programmable, complex quantum circuits with neutral atom quantum computers, as well as informing both future compilers and future hardware choices.

Physics↗

NASA NTRS1996

A Cell-Centered Multigrid Algorithm for All Grid Sizes

Multigrid methods are optimal; that is, their rate of convergence is independent of the number of grid points, because they use a nested sequence of coarse grids to represent different scales of the solution. This nesting does, however, usually lead to certain restrictions of the permissible size of the discretised problem. In cases where the modeler is free to specify the whole problem, such constraints are of little importance because they can be taken into consideration from the outset. We consider the situation in which there are other competing constraints on the resolution. These restrictions may stem from the physical problem (e.g., if the discretised operator contains experimental data measured on a fixed grid) or from the need to avoid limitations set by the hardware. In this paper we discuss a modification to the cell-centered multigrid algorithm, so that it can be used br problems with any resolution. We discuss in particular a coarsening strategy and choice of intergrid transfer operators that can handle grids with both an even or odd number of cells. The method is described and applied to linear equations obtained by discretization of two- and three-dimensional second-order elliptic PDEs.

Gjesdal, Thor↗

DOE OSTI2021

Effect of topology changes on the breakup of a periodic liquid jet

Here, the breakup of a periodic jet is examined computationally, using a front-tracking/finite-volume method, where the interface is represented by connected marker points moving with the fluid, while the governing equations are solved on a fixed grid. Tracking the interface allows control of whether topology changes take place or not. The Reynolds and Capillary numbers are kept relatively low ($Re = 150$ and $Ca = 2$) so most of the flow is well resolved. The effect of topology changes is examined by following the jet until it has mostly disintegrated, for different “coalescence criterion,” based on the thickness of thin films and threads. The evolution of both two-dimensional and fully three-dimensional flows is examined. It is found that although there is a significant difference between the evolution when no breakup takes place and when it does, once breakup takes place the evolution is relatively insensitive to exactly how it is triggered for a range of coalescence criterion, and any differences are mostly confined to the smallest scales.

97 MATHEMATICS AND COMPUTING↗