Results for “Mesh refinement” — Page 8

NASA NTRS2004

Developing parallel GeoFEST(P) using the PYRAMID AMR library

The PYRAMID parallel unstructured adaptive mesh refinement (AMR) library has been coupled with the GeoFEST geophysical finite element simulation tool to support parallel active tectonics simulations. Specifically, we have demonstrated modeling of coseismic and postseismic surface displacement due to a simulated Earthquake for the Landers system of interacting faults in Southern California. The new software demonstrated a 25-times resolution improvement and a 4-times reduction in time to solution over the sequential baseline milestone case. Simulations on workstations using a few tens of thousands of stress displacement finite elements can now be expanded to multiple millions of elements with greater than 98% scaled efficiency on various parallel platforms over many hundreds of processors. Our most recent work has demonstrated that we can dynamically adapt the computational grid as stress grows on a fault. In this paper, we will describe the major issues and challenges associated with coupling these two programs to create GeoFEST(P). Performance and visualization results will also be described.

adaptive mesh refinement (AMR)↗

DOE OSTI2025

Asynchronous-many-task systems: Challenges and opportunities - Scaling an AMR astrophysics code on exascale machines using Kokkos and HPX

Dynamic and adaptive mesh refinement is pivotal in high-resolution, multi-physics, multi-model simulations, necessitating precise physics resolution in localized areas across expansive domains. Today’s supercomputers’ extreme heterogeneity presents a significant challenge for dynamically adaptive codes, highlighting the importance of achieving performance portability at scale. Our research focuses on astrophysical simulations, particularly stellar mergers, to elucidate early universe dynamics. Here, we present Octo-Tiger, leveraging Kokkos, HPX, and SIMD for portable performance at scale in complex, massively parallel adaptive multi-physics simulations. Octo-Tiger supports diverse processors, accelerators, and network backends. Experiments demonstrate exceptional scalability across several heterogeneous supercomputers including Perlmutter, Frontier, and Fugaku, encompassing major GPU architectures and x86, ARM, and RISC-V CPUs. Parallel efficiency of 47.59% (110,080 cores and 6880 hybrid A100 GPUs) on a full-system run on Perlmutter (26% HPCG peak performance) and 51.37% (using 32,768 cores and 2048 MI250X) on Frontier are achieved.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Chemical timescale effects on detonation convergence

Numerical simulations of detonation-containing flows have emerged as crucial tools for designing next- generation power and propulsion devices. As these tools mature, it is important for the combustion community to properly understand and isolate grid resolution effects when simulating detonations. To this end, the objective of this work is to provide a comprehensive analysis of the numerical convergence of unsteady detonation simulations, with focus on isolating the impacts of chemical timescale modifications on convergence characteristics in the context of operator splitting. With the aid of an AMReX-based adaptive mesh refinement flow solver-which enables resolutions up to ($\mathcal{O}$ (1000) cells-per-induction length-the convergence analysis is conducted using two kinetics configurations: (1) the simplified three-step Arrhenius-based model mechanism of Short and Quirk (1997), where chemical timescales in the detonation are modified by adjusting activation energies in the initiation and branching reactions, and (2) a detailed hydrogen- air mechanism, where the chemical timescales are adjusted by varying the ambient pressure. The convergence of unsteady self-sustained detonations in one-dimensional channels is then analyzed with reference to steady-state theoretical baseline solutions using these mechanisms. The goal of the analysis is to provide a detailed comparison of the effects of grid resolution on both macroscopic (peak pressures and wave speeds) and microscopic (wave structure) quantities of interest, drawing connections between the deviations from steady-state baselines and minimum chemical timescales. In particular, chemical timescale reductions were found to have minimal impact on the convergence of macroscopic properties. Furthermore, analyses of microscopic convergence trends, particularly in the reaction front location, revealed a key insight: maintaining the induction time while eliminating prohibitive chemical timescales through mechanism simplifications and combustion modeling can significantly enhance detonation convergence properties. Ultimately, this work uncovers resolution-dependent unsteady detonation convergence regimes and highlights the important role played by not only the chemical timescales, but also the ratio between the chemical timescale and induction time on the numerical convergence of the detonation wave structure.

Adaptive mesh refinement↗

DOE OSTI2025

E3SM‐Arctic: Regionally Refined Coupled Model for Advanced Understanding of Arctic Systems Interactions

Earth system models are essential tools for climate projections, but coarse resolutions limit regional accuracy, especially in the Arctic. Regionally refined meshes (RRMs) enhance resolution in key areas while maintaining computational efficiency. This paper provides an overview of the United States (U.S.) Department of Energy's (DOE's) Energy Exascale Earth System Model version 2.1 with an Arctic RRM, hereafter referred to as E3SMv2.1-Arctic, for the atmosphere (25 km), land (25 km), and ocean/ice (10 km) components. We evaluate the atmospheric component and its interactions with land, ocean, and cryosphere by comparing the RRM (E3SM2.1-Arctic) historical simulations (1950–2014) with the uniform low-resolution (LR) counterpart, reanalysis products, and observational data sets. The RRM generally reduces biases in the LR model, improving simulations of Arctic large-scale mean fields, such as precipitation, atmospheric circulation, clouds, atmospheric river frequency, and sea ice thickness. However, it introduces a seasonally dependent surface air temperature bias, reducing the LR cold bias in summer but enhancing the LR warm bias in winter, which contributes to the underestimated winter sea ice area and volume. Radiative feedback analysis shows similar climate feedback strengths in both model configurations, with the RRM exhibiting a more positive surface albedo feedback and contributing to a stronger surface warming than LR. These findings underscore the importance of high-resolution modeling for advancing our understanding of Arctic climate changes and their broader global impacts, although some persistent biases appear to be independent of model resolution at 10–100 km scales.

Energy Exascale Earth System Model (E3SM)↗

NASA NTRS1997

Large-Eddy Simulation of a High Reynolds Number Flow Around a Cylinder Including Aeroacoustic Predictions

The dynamic subgrid-scale model is employed in large-eddy simulations of flow over a cylinder at a Reynolds number, based on the diameter of the cylinder, of 90,000. The Centric SPECTRUM(trademark) finite element solver is used for the analysis. The far field sound pressure is calculated from Lighthill-Curle's equation using the computed fluctuating pressure at the surface of the cylinder. The sound pressure level at a location 35 diameters away from the cylinder and at an angle of 90 deg with respect to the wake's downstream axis was found to have a peak value of approximately 110 db. Slightly smaller peak values were predicted at the 60 deg and 120 deg locations. A grid refinement study suggests that the dynamic model demands mesh refinement beyond that used here.

Spyropoulos, Evangelos T.↗

NASA NTRSDate not supplied

Cartesian Mesh Simulations for the Third AIAA Sonic Boom Prediction Workshop

Simulation results are presented for all cases from the Third AIAA Sonic Boom Prediction Workshop. An inviscid, embedded-boundary Cartesian-mesh flow solver is used in conjunction with adjoint-based mesh adaptation to compute nearfield pressure signatures. Specialized techniques are applied to maximize accuracy and minimize cost on Cartesian meshes. The Richardson-based error estimate highlights regions of the signatures most sensitive to mesh refinement. Timing results and coarse, medium, and fine mesh sizes for nearfield cases demonstrate that the parallel decomposition approach is efficient in both computational time and wall-clock. Pressure signals are propagated to the ground using an augmented Burgers’ equation solver to predict boom carpets. Ground signatures and loudness metrics are presented for a standard atmosphere as well as more realistic atmospheric profiles, which affect overall noise levels and can significantly widen the boom carpet. Mesh convergence studies show that high sampling frequencies, around 500 kHz, are required for propagation, and the sampling frequency increases at large off-track angles with longer acoustic ray paths and propagation times. The numerical methods yield accurate results for predicting low sonic boom signatures while being among the least computationally expensive of the workshop.

ARMD↗

NASA NTRS2009

Computations of Aerodynamic Performance Databases Using Output-Based Refinement

Objectives: Handle complex geometry problems; Control discretization errors via solution-adaptive mesh refinement; Focus on aerodynamic databases of parametric and optimization studies: 1. Accuracy: satisfy prescribed error bounds 2. Robustness and speed: may require over 105 mesh generations 3. Automation: avoid user supervision Obtain "expert meshes" independent of user skill; and Run every case adaptively in production settings.

Nemec, Marian↗

NASA NTRS1995

Adaptively-refined overlapping grids for the numerical solution of systems of hyperbolic conservation laws

Adaptive mesh refinement (AMR) in conjunction with higher-order upwind finite-difference methods have been used effectively on a variety of problems in two and three dimensions. In this paper we introduce an approach for resolving problems that involve complex geometries in which resolution of boundary geometry is important. The complex geometry is represented by using the method of overlapping grids, while local resolution is obtained by refining each component grid with the AMR algorithm, appropriately generalized for this situation. The CMPGRD algorithm introduced by Chesshire and Henshaw is used to automatically generate the overlapping grid structure for the underlying mesh.

Brislawn, Kristi D.↗

DOE OSTI2026

Hydrogeological assessment of CO2 containment assurance and wellbore integrity at a Gulf Coast storage site

Abstract A large-scale carbon capture and storage (CCS) initiative on the Texas Gulf Coast serves as a premier demonstration of the U.S. Department of Energy’s CarbonSAFE program. Targeting deep saline formations, specifically Oligo-Miocene deltaic sequences, the project aims to establish technical and commercial viability for geologic CO2 storage within a major industrial corridor. This study provides a rigorous hydrogeological assessment to support Class VI permitting by quantifying the high degree of containment security. Utilizing a compositional reservoir simulator, we developed a suite of 27 distinct simulation cases to evaluate vertical plume dynamics near both planned injection wells and proximal legacy infrastructure. To ensure numerical accuracy near wellbores, we implemented a refined mesh strategy, determining that a 5.6 ft × 5.6 ft grid refinement offered the optimal balance between computational efficiency and descriptive precision. The modeling framework utilized a systematic sensitivity-based approach to evaluate the mechanical redundancy of the subsurface system by performing a bounding analysis of wellbore interfaces against hypothetical high-permeability microannuli. By systematically isolating competing physical drivers, including permeability, porosity, gas hysteresis, thermal gradients, salinity, and solubility trapping (quantified via Henry’s law with dynamically adjusted coefficients), this work moves beyond binary assessments to establish a nuanced hierarchy of containment factors. The results confirm that primary trapping mechanisms (e.g., gas hysteresis and solubility), combined with the site's unique geomechanical stratigraphy, significantly restrict vertical mobility and reinforce the robust containment security of the reservoir. Baseline results demonstrate substantial vertical separation between the CO2 plume and the upper confining system, ensuring robust containment. Sensitivity analysis reveals that even under highly conservative bounding scenarios—assuming theoretical 10-Darcy pathways at specific wellbore locations—the 2,900-ft thick multi-layered confining zone remains a reliable barrier. In these hypothetical upper-bound cases, peak upward fluxes of CO2 and saltwater after 15 years of injection remain localized and dissipate rapidly within the lower sections of the confining interval, leaving the integrity of the seal uncompromised. Furthermore, the study identifies that while localized wellbore pathways define theoretical upper bounds of vertical migration, the Area of Review (AoR) is primarily sensitive to regional thermal gradients and hysteresis, which can influence the AoR by over 3,000 acres in pessimistic configurations. Also, primary trapping mechanisms, specifically gas hysteresis and solubility, work in tandem with the Gulf Coast’s unique geomechanical stratigraphy to significantly restrict vertical mobility. Ductile, smectite-rich mudstones facilitate natural borehole convergence and the self-healing of potential conduits, creating a natural geomechanical bridge that effectively mitigates migration potential at both current injection points and legacy-well locations. This comprehensive modeling effort demonstrates that the integration of high-resolution wellbore simulations and regional geomechanical observations confirms the long-term storage security of the studied site, providing a physics-based foundation for industrial-scale CCS deployments. This modeling framework establishes a baseline for future research into coupled geomechanical effects, such as time-dependent borehole convergence, to further refine long-term containment projections. Acknowledgements We thank the Gulf Coast Carbon Center (GCCC) at the Bureau of Economic Geology for foundational research support. We appreciate Alex Bump for technical guidance and David Hoffman for model mesh generation. This work used TACC’s Frontera cluster for simulations and CMG Ltd. software licenses provided to UT-Austin. This material is based upon work supported by the Department of Energy under Award Number DE-FE0032338. Disclaimer This material is based upon work supported by the U.S. Department of Energy’s Fossil Energy and Carbon Management Office under the CarbonSAFE program, award Number DE-FE0032338. The views expressed herein do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

58 GEOSCIENCES↗

DOE OSTI2026

Hydrogeological assessment of CO2 containment assurance and wellbore integrity at a Gulf Coast storage site

Abstract A large-scale carbon capture and storage (CCS) initiative on the Texas Gulf Coast serves as a premier demonstration of the U.S. Department of Energy’s CarbonSAFE program. Targeting deep saline formations, specifically Oligo-Miocene deltaic sequences, the project aims to establish technical and commercial viability for geologic CO2 storage within a major industrial corridor. This study provides a rigorous hydrogeological assessment to support Class VI permitting by quantifying the high degree of containment security. Utilizing a compositional reservoir simulator, we developed a suite of 27 distinct simulation cases to evaluate vertical plume dynamics near both planned injection wells and proximal legacy infrastructure. To ensure numerical accuracy near wellbores, we implemented a refined mesh strategy, determining that a 5.6 ft × 5.6 ft grid refinement offered the optimal balance between computational efficiency and descriptive precision. The modeling framework utilized a systematic sensitivity-based approach to evaluate the mechanical redundancy of the subsurface system by performing a bounding analysis of wellbore interfaces against hypothetical high-permeability microannuli. By systematically isolating competing physical drivers, including permeability, porosity, gas hysteresis, thermal gradients, salinity, and solubility trapping (quantified via Henry’s law with dynamically adjusted coefficients), this work moves beyond binary assessments to establish a nuanced hierarchy of containment factors. The results confirm that primary trapping mechanisms (e.g., gas hysteresis and solubility), combined with the site's unique geomechanical stratigraphy, significantly restrict vertical mobility and reinforce the robust containment security of the reservoir. Baseline results demonstrate substantial vertical separation between the CO2 plume and the upper confining system, ensuring robust containment. Sensitivity analysis reveals that even under highly conservative bounding scenarios—assuming theoretical 10-Darcy pathways at specific wellbore locations—the 2,900-ft thick multi-layered confining zone remains a reliable barrier. In these hypothetical upper-bound cases, peak upward fluxes of CO2 and saltwater after 15 years of injection remain localized and dissipate rapidly within the lower sections of the confining interval, leaving the integrity of the seal uncompromised. Furthermore, the study identifies that while localized wellbore pathways define theoretical upper bounds of vertical migration, the Area of Review (AoR) is primarily sensitive to regional thermal gradients and hysteresis, which can influence the AoR by over 3,000 acres in pessimistic configurations. Also, primary trapping mechanisms, specifically gas hysteresis and solubility, work in tandem with the Gulf Coast’s unique geomechanical stratigraphy to significantly restrict vertical mobility. Ductile, smectite-rich mudstones facilitate natural borehole convergence and the self-healing of potential conduits, creating a natural geomechanical bridge that effectively mitigates migration potential at both current injection points and legacy-well locations. This comprehensive modeling effort demonstrates that the integration of high-resolution wellbore simulations and regional geomechanical observations confirms the long-term storage security of the studied site, providing a physics-based foundation for industrial-scale CCS deployments. This modeling framework establishes a baseline for future research into coupled geomechanical effects, such as time-dependent borehole convergence, to further refine long-term containment projections. Acknowledgements We thank the Gulf Coast Carbon Center (GCCC) at the Bureau of Economic Geology for foundational research support. We appreciate Alex Bump for technical guidance and David Hoffman for model mesh generation. This work used TACC’s Frontera cluster for simulations and CMG Ltd. software licenses provided to UT-Austin. This material is based upon work supported by the Department of Energy under Award Number DE-FE0032338. Disclaimer This material is based upon work supported by the U.S. Department of Energy’s Fossil Energy and Carbon Management Office under the CarbonSAFE program, award Number DE-FE0032338. The views expressed herein do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

58 GEOSCIENCES↗

NASA NTRS2014

Toward Automatic Verification of Goal-Oriented Flow Simulations

We demonstrate the power of adaptive mesh refinement with adjoint-based error estimates in verification of simulations governed by the steady Euler equations. The flow equations are discretized using a finite volume scheme on a Cartesian mesh with cut cells at the wall boundaries. The discretization error in selected simulation outputs is estimated using the method of adjoint-weighted residuals. Practical aspects of the implementation are emphasized, particularly in the formulation of the refinement criterion and the mesh adaptation strategy. Following a thorough code verification example, we demonstrate simulation verification of two- and three-dimensional problems. These involve an airfoil performance database, a pressure signature of a body in supersonic flow and a launch abort with strong jet interactions. The results show reliable estimates and automatic control of discretization error in all simulations at an affordable computational cost. Moreover, the approach remains effective even when theoretical assumptions, e.g., steady-state and solution smoothness, are relaxed.

Simulations↗

NASA NTRS2014

Numerical Simulations For the F-16XL Aircraft Configuration

Numerical simulations of flow around the F-16XL are presented as a contribution to the Cranked Arrow Wing Aerodynamic Project International II (CAWAPI-II). The NASA Tetrahedral Unstructured Software System (TetrUSS) is used to perform numerical simulations. This CFD suite, developed and maintained by NASA Langley Research Center, includes an unstructured grid generation program called VGRID, a postprocessor named POSTGRID, and the flow solver USM3D. The CRISP CFD package is utilized to provide error estimates and grid adaption for verification of USM3D results. A subsonic high angle-of-attack case flight condition (FC) 25 is computed and analyzed. Three turbulence models are used in the calculations: the one-equation Spalart-Allmaras (SA), the two-equation shear stress transport (SST) and the kε turbulence models. Computational results, and surface static pressure profiles are presented and compared with flight data. Solution verification is performed using formal grid refinement studies, the solution of Error Transport Equations, and adaptive mesh refinement. The current study shows that the USM3D solver coupled with CRISP CFD can be used in an engineering environment in predicting vortex-flow physics on a complex configuration at flight Reynolds numbers.

Elmiligui, Alaa A.↗

NASA NTRS2004

Evaluating Performance of Components

Parallel Component Performance Benchmarks is a computer program developed to aid the evaluation of the Common Component Architecture (CCA) - a software architecture, based on a component model, that was conceived to foster high-performance computing, including parallel computing. More specifically, this program compares the performances (principally by measuring computing times) of componentized versus conventional versions of the Parallel Pyramid 2D Adaptive Mesh Refinement library - a software library that is used to generate computational meshes for solving physical problems and that is typical of software libraries in use at NASA s Jet Propulsion Laboratory.

Katz, Daniel↗

NASA NTRS2014

Cart3D Simulations for the First AIAA Sonic Boom Prediction Workshop

Simulation results for the First AIAA Sonic Boom Prediction Workshop (LBW1) are presented using an inviscid, embedded-boundary Cartesian mesh method. The method employs adjoint-based error estimation and adaptive meshing to automatically determine resolution requirements of the computational domain. Results are presented for both mandatory and optional test cases. These include an axisymmetric body of revolution, a 69deg delta wing model and a complete model of the Lockheed N+2 supersonic tri-jet with V-tail and flow through nacelles. In addition to formal mesh refinement studies and examination of the adjoint-based error estimates, mesh convergence is assessed by presenting simulation results for meshes at several resolutions which are comparable in size to the unstructured grids distributed by the workshop organizers. Data provided includes both the pressure signals required by the workshop and information on code performance in both memory and processing time. Various enhanced techniques offering improved simulation efficiency will be demonstrated and discussed.

Predictions↗

NASA NTRS1985

Flow structure capturing on overset patched meshes

The present paper describes the application of a simple, robust stable implicit approach to solutions of the conservative equations of gasdynamics on either composite or overset meshes to capture flow structures such as shocks with high resolution in complex geometric domains. Without requiring special flux conservative operators, but rather, interpolating conservative variable data at mesh boundaries, the well posed upwind method provides accurate and oscillation free solutions, even when shocks cross the interior patch boundaries. In three problems with flow complexities that require grid refinement, the paper demonstrates the capability to conveniently carry out for gasdynamics the adaptive refined meshing strategy in overset patches proposed by Berger and Oliger (1984), and it extends this technique to rapidly convergent implicit methods for the Euler and Navier-Stokes equations. The numerical experiments show concretely, in a realistic aerodynamic problem, the savings in mesh points (about an order of magnitude here in two dimensions) for similar accuracy that flow structure aligned adaptive patched meshing affords compared to uniform grid refinement.

Venkatapathy, E.↗

DOE OSTI2024

A block-spectral adaptive H-/$p$-refinement strategy for shock-dominated problems

An adaptive H-/p-refinement strategy using a novel sensor is devised and tested in a block-spectral compressible Euler code equipped with adaptive-mesh refinement (AMR) and high-order flux-reconstruction numerics. At each Gauss quadrature point (or solution point) within each spectral block (or mesh element) the discrete velocity jump ΔU = ∂U/∂y 1 Δy 1 + ∂V/∂y 2 Δy 2 + ∂W/∂y 3 Δy 3 is calculated and normalized by the local speed of sound, a. Here, the grid spacing, Δx i , is calculated in each direction as the distance between auxiliary Gauss-Lobatto points, staggered relative to the solution points. The polynomial order is increased from p = 0 to p = p max in regions of weak compression, (ΔU/a) crit < ΔU/a < 0 and kept at p = p max in regions of flow expansion ΔU/a ≥ 0, while staying at the H = 0 base mesh level. Regions experiencing strong compressions, i.e. ΔU/a < (ΔU/a) crit , are H-refined up to H = H max where H max is applied at the location of maximum compression, ΔU/a = min(ΔU/a) in the domain, while keeping p = 0 to guarantee robustness and monotonicity of the solution in the H refined region. The critical value of (ΔU/a) crit = -0.06 is found to effectively separate smooth and non-smooth solution regions, supported by a 1D detonation initiation test case in ideal gas and a shock-to-detonation transition in high explosives. Using this value, the Sod shock tube, Shu-Osher problem, double Mach reflection and a 2D detonation in a high-explosive are simulated with the proposed adaptive H-/p-refinement. In the Sod shock tube case, p-refinement resolves the (weak) contact discontinuity while H-refinement enhances the grid resolution in the shock exploiting the monotonicity of the p = 0 reconstruction. For the Shu-Osher problem, p-refinement captures the small-scale oscillations trailing the shock that would be otherwise attenuated, while H-refinement triggered by the ΔU-sensor appropriately tracks the shock. In the double Mach reflection problem, H-refinement confines the numerical diffusion around the reflected shock while p-refinement recaptures many physical features trailing the shock. Finally, in the 2D high-explosive detonation case, H-refinement follows the leading shock and resolves the curvature of the detonation wave, while p-refinement adds resolution to the trailing reaction zone. Finally, the proposed methodology is tested in a detonation-wave propagation test case in high-explosives with numerical predictions comparing favorably against experiments.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1980

Numerical calculation of steady inviscid full potential compressible flow about wind turbine blades

An exact nonlinear mathematical model that accounts for three-dimensional cascade effects about the inner portions of the rotor blades and compressibility effects about the tip regions of the blades was derived. An artificially time dependent version was iteratively solved by a finite volume technique involving an artificial viscosity and a three-level consecutive mesh refinement. The exact boundary conditions were applied by generating a boundary conforming periodic computation mesh.

Dulikravich, D. S.↗

NASA NTRS1980

Numerical calculation of steady inviscid full potential compressible flow about wind turbine blades

The air flow through a propeller-type wind turbine rotor is characterized by three-dimensional rotating cascade effects about the inner portions of the rotor blades and compressibility effects about the tip regions of the blades. In the case of large rotor diameter and/or increased rotor angular speed, the existence of small supersonic zones terminated by weak shocks is possible. An exact nonlinear mathematical model (called a steady Full Potential Equation - FPE) that accounts for the above phenomena has been rederived. An artificially time dependent version of FPE was iteratively solved by a finite volume technique involving an artificial viscosity and a three-level consecutive mesh refinement. The exact boundary conditions were applied by generating a boundary conforming periodic computation mesh.

Dulikravich, D. S.↗