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NASA NTRS1985

The numerical viscosity of entropy stable schemes for systems of conservation laws

Discrete approximations to hyperbolic systems of conservation laws are studied. The amount of numerical viscosity present in such schemes, is quantified and related to their entropy stability by means of comparison. To this end, conservative schemes which are also entropy conservative are constructed. These entropy conservative schemes enjoy second-order accuracy; moreover, they admit a particular interpretation within the finite-element frameworks, and hence can be formulated on various mesh configurations. It is then shown that conservative schemes are entropy stable if and only if they contain more viscosity than the mentioned above entropy conservative ones.

Tadmor, E.↗

DOE OSTI2016

Draco,Version 6.x.x

Draco is an object-oriented component library geared towards numerically intensive, radiation (particle) transport applications built for parallel computing hardware. It consists of semi-independent packages and a robust build system. The packages in Draco provide a set of components that can be used by multiple clients to build transport codes. The build system can also be extracted for use in clients. Software includes smart pointers, Design-by-Contract assertions, unit test framework, wrapped MPI functions, a file parser, unstructured mesh data structures, a random number generator, root finders and an angular quadrature component.

Thompson, Kelly↗

NASA NTRS1995

Automation of three-dimensional structured mesh generation for turbomachinery blade passages

Hybrid tools have been developed which greatly reduce the time required to generate three-dimensional structured CFD meshes for turbomachinery blade passages. RAGGS, an existing Rockwell proprietary, general purpose mesh generation and visualization system, provides the starting point and framework for tool development. Utilities which manipulate and interface with RAGGS tools have been developed to (1) facilitate blade geometry inputs from point or CAD representations, (2) automate auxiliary surface creation, and (3) streamline and automate edge, surface, and subsequent volume mesh generation from minimal inputs. The emphasis of this approach has been to maintain all the functionality of the general purpose mesh generator while simultaneously eliminating the bulk of the repetitive and tediuos manual steps in the mesh generation process. Using this approach, mesh generation cycle times have been reduced from the order of days down to the order of hours.

Ascoli, Edward P.↗

DOE OSTI2024

Simulation of Compound Flooding Using River‐Ocean Two‐Way Coupled E3SM Ensemble on Variable‐Resolution Meshes

Abstract Coastal zone compound flooding (CF) can be caused by the interactive fluvial and oceanic processes, particularly when coastal backwater propagates upstream and interacts with high river discharge. The modeling of CF is limited in existing Earth System Models (ESMs) due to coarse mesh resolutions and one‐way coupled river‐ocean components. In this study, we present a novel multi‐scale coupling framework within the Energy Exascale Earth System Model (E3SM), integrating global atmosphere and land with interactively coupled river and ocean models using different meshes with refined resolutions near the coastline. To evaluate this framework, we conducted ensemble simulations of a CF event (Hurricane Irene in 2011) in a Mid‐Atlantic estuary. The results demonstrate that the novel E3SM configuration can reasonably reproduce river discharge and sea surface height variations. The two‐way river‐ocean coupling improves the representation of coastal backwater effects at the terrestrial‐aquatic interface that are caused by the combined actions of tide and storm surge during the CF event, thus providing a valuable modeling tool for better understanding the river‐estuary‐ocean dynamics in extreme events under climate change. Notably, our results show that the most significant CF impacts occur when the highest storm surge generated by a tropical cyclone meets with a moderate river discharge. This study highlights the state‐of‐the‐art advancements developed within E3SM for simulating multi‐scale coastal processes.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2019

Adaptive inverse ray-tracing for accurate and efficient modeling of cross beam energy transfer in hydrodynamics simulations

Integrated hydrodynamics simulations of inertial confinement fusion rely on reduced physics models. To reproduce experimental trends, these models often feature tuning parameters, but this comes with a risk: the over-tuning of one model can hide physics inadequacies in another. The ray-based models of cross-beam-energy transfer (CBET) represent this risk. In this paper, we present an accurate and efficient model of CBET suitable for inline implementation in 3D hydrodynamics simulations. Inverse Ray Tracing (IRT) is used to compute the ray field in a 3D permittivity profile described on an unstructured tetrahedral mesh using the Inline Field Reconstruction and Interaction using Inverse Tracing framework. CBET is accounted for through perturbations to the permittivity associated with ion acoustic waves driven by the overlapped fields. Large gradients in the permittivity are resolved by coupling the IRT to a recursive Adaptive Mesh Refinement (AMR) algorithm. The use of AMR also allows for the resolution of caustics, with accurate field reconstruction performed using the Etalon integral method. Comparisons of the model with wave-based solutions from the Laser Plasma Simulation Environment demonstrate its ability to control energy conservation and gain convergence through the AMR depth only, without the use of ad hoc physical models or artificial tuning parameters.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2003

Analysis and Improvement of Upwind and Centered Schemes on Quadrilateral and Triangular Meshes

Second-order accurate upwind and centered schemes are presented in a framework that facilitates their analysis and comparison. The upwind scheme employed consists of a reconstruction step (MUSCL approach) followed by an upwind step (Roe's flux-difference splitting). The two centered schemes are of Lax-Friedrichs (L-F) type. They are the nonstaggered versions of the Nessyahu-Tadmor (N-T) scheme and the CE/SE method with epilson = 1/2. The upwind scheme is extended to the case of two spatial dimensions (2D) in a straightforward manner. The N-T and CE/SE schemes are extended in a manner similar to the 2D extensions of the CE/SE scheme by Wang and Chang for a triangular mesh and by Zhang, Yu, and Chang for a quadrilateral mesh. The slope estimates, however, are simplified. Fourier stability and accuracy analyses are carried out for these schemes for the standard 1D and the 2D quadrilateral mesh cases. In the nonstandard case of a triangular mesh, the triangles must be paired up when analyzing the upwind and N-T schemes. An observation resulting in an extended N-T scheme which is faster and uses only one-third of the storage for flow data compared with the CE/SE method is presented. Numerical results are shown. Other improvements to the schemes are discussed.

Huynh, H. T.↗

NASA NTRSDate not supplied

Enabling Metric-Based Mesh Adaptation for Advanced Compressible Flow Simulations Using US3D

This work presents a metric-based mesh adaptation capability added to the flow solver US3D that is used to improve the accuracy of atmospheric entry simulations. Flow past an entry vehicle in free-flight is usually unsteady and characterized by anisotropic flow features like a strong bow shock and small-scale isotropic flow features like turbulent eddies in the wake. The results presented in this paper demonstrate that we are currently able to iteratively apply metric-based mesh adaptation to improve the solution accuracy by simultaneously targeting isotropic and anisotropic flow features. A simplified workflow of running CFD simulations for entry vehicles is presented where we start off with a coarse initial mesh to compute a first approximation of the flow. This coarse mesh is then iteratively refined using the newly developed metric to improve the resolution of the CFD computation. Furthermore, we demonstrate that we are able to adapt large mesh sizes in a timely fashion which allows us to start thinking about applying this adaptive framework to unsteady atmospheric entry CFD simulations.

Mesh adaptation↗

NASA NTRS2015

Tetrahedral-Mesh Simulation of Turbulent Flows with the Space-Time Conservative Schemes

Direct numerical simulations of turbulent flows are predominantly carried out using structured, hexahedral meshes despite decades of development in unstructured mesh methods. Tetrahedral meshes offer ease of mesh generation around complex geometries and the potential of an orientation free grid that would provide un-biased small-scale dissipation and more accurate intermediate scale solutions. However, due to the lack of consistent multi-dimensional numerical formulations in conventional schemes for triangular and tetrahedral meshes at the cell interfaces, numerical issues exist when flow discontinuities or stagnation regions are present. The space-time conservative conservation element solution element (CESE) method - due to its Riemann-solver-free shock capturing capabilities, non-dissipative baseline schemes, and flux conservation in time as well as space - has the potential to more accurately simulate turbulent flows using unstructured tetrahedral meshes. To pave the way towards accurate simulation of shock/turbulent boundary-layer interaction, a series of wave and shock interaction benchmark problems that increase in complexity, are computed in this paper with triangular/tetrahedral meshes. Preliminary computations for the normal shock/turbulence interactions are carried out with a relatively coarse mesh, by direct numerical simulations standards, in order to assess other effects such as boundary conditions and the necessity of a buffer domain. The results indicate that qualitative agreement with previous studies can be obtained for flows where, strong shocks co-exist along with unsteady waves that display a broad range of scales, with a relatively compact computational domain and less stringent requirements for grid clustering near the shock. With the space-time conservation properties, stable solutions without any spurious wave reflections can be obtained without a need for buffer domains near the outflow/farfield boundaries. Computational results for the isotropic turbulent flow decay, at a relatively high turbulent Mach number, show a nicely behaved spectral decay rate for medium to high wave numbers. The high-order CESE schemes offer very robust solutions even with the presence of strong shocks or widespread shocklets. The explicit formulation in conjunction with a close to unity theoretical upper Courant number bound has the potential to offer an efficient numerical framework for general compressible turbulent flow simulations with unstructured meshes.

Chang, Chau-Lyan↗

NASA NTRS2010

Exploring Discretization Error in Simulation-Based Aerodynamic Databases

This work examines the level of discretization error in simulation-based aerodynamic databases and introduces strategies for error control. Simulations are performed using a parallel, multi-level Euler solver on embedded-boundary Cartesian meshes. Discretization errors in user-selected outputs are estimated using the method of adjoint-weighted residuals and we use adaptive mesh refinement to reduce these errors to specified tolerances. Using this framework, we examine the behavior of discretization error throughout a token database computed for a NACA 0012 airfoil consisting of 120 cases. We compare the cost and accuracy of two approaches for aerodynamic database generation. In the first approach, mesh adaptation is used to compute all cases in the database to a prescribed level of accuracy. The second approach conducts all simulations using the same computational mesh without adaptation. We quantitatively assess the error landscape and computational costs in both databases. This investigation highlights sensitivities of the database under a variety of conditions. The presence of transonic shocks or the stiffness in the governing equations near the incompressible limit are shown to dramatically increase discretization error requiring additional mesh resolution to control. Results show that such pathologies lead to error levels that vary by over factor of 40 when using a fixed mesh throughout the database. Alternatively, controlling this sensitivity through mesh adaptation leads to mesh sizes which span two orders of magnitude. We propose strategies to minimize simulation cost in sensitive regions and discuss the role of error-estimation in database quality.

Aftosmis, Michael J.↗

DOE OSTI2019

Target Formulation and Construction in Mesh Quality Improvement

In the Target-matrix Optimization Paradigm (TMOP), it’s long been understood that one must create a set of target matrices before the mesh can be optimized. But there is still no general method to create correct, effective targets in response to a specific mesh quality improvement goal. The TMOP literature describes how certain sets of target matrices can be used to control the shape or size of mesh elements, but those examples address only a fraction of the problems that can occur in mesh quality improvement and were not derived from a general framework for target matrix construction. In this work, a general method of target construction is introduced based on an independent set of geometric parameters which are intrinsic to the Jacobian matrices upon which TMOP is based. The parameters enable a systematic approach to target definition and construction. The approach entails two parts. The first part defines correspondences between available raw data (stuff about the mesh and/or the physical solution) and intermediate data (e.g., a field of error estimates). Once the correspondences are established, the raw data is processed into intermediate field data existing on mesh sample points. The second part is to create a model that represents the values of the geometric target parameters as functions of the intermediate data. The model is then tested numerically to establish model constants and effectiveness. This systematic approach to target construction is illustrated in a set of examples to show how it can be applied to common problems in mesh optimization such as equidistribution of geometric properties, preservation of existing good quality, and adaptation of the mesh to the solution. The result is a systematic method of target construction for TMOP which can be applied to a wide variety of planar and volume mesh quality improvement tasks.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Numerical Modeling of Atmospheric Rime Ice Accretion on an Airfoil Using an Eulerian Approach

This paper presents an approach to numerically simulate the inherently unsteady rime ice accretion problem on a two-dimensional airfoil and elucidate the associated variations under different icing conditions. The airflow field and the water impingement on the airfoil are obtained based on an Eulerian two-phase model. A dynamic mesh strategy is employed to unsteadily account for the changes in the ice profile and its impact on the air and droplet flow by continuously reconstructing the computational grid at each time-step through smoothing and layering mechanisms. All main icing modules including the airflow field, droplet trajectory, icing thickness profile, and mesh management are fully coupled within the same computational framework without resorting to any external tools. Classical icing theory is employed to model the rime ice roughness, and it is assumed that the ice accretes in a direction normal to the airfoil surface. The governing Reynolds-averaged Navier–Stokes (RANS) conservation equations along with the energy and continuity equations are solved to produce the velocity and temperature fields. A convective film heat transfer coefficient is computed based on the surface heat flux and a recovery temperature which takes into account the dissipative heat release in the boundary layer in the vicinity of the airfoil surface. With the implemented strategy and calculating the convective heat transfer coefficient, the water film thickness is also calculated along with the ice shape. Furthermore, the model is validated by comparing the local collection efficiency distribution and ice shape with experimental data, and the results show that the implemented approach provides acceptable predictions of ice accretion profiles and rates.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2024

MOOSE-Workbench integration and MOOSE meshing capability enhancements to facilitate inputs and outputs for multiphysics modeling

The Multiphysics Object-Oriented Simulation Environment (MOOSE) is an open-source framework that supports many of the US Department of Energy’s (DOE’s) Nuclear Energy Advanced Modeling and Simulation (NEAMS) technical areas (TA). These TAs develop and use NEAMS physics and coupling modules in multiple ways to enable the research and development of complex physics models. In addition to the MOOSE framework, the NEAMS Workbench user interface provides a common analysis environment with user-interaction accelerators that streamline the tasks of model creation, review, execution, and out put inspection. In FY 2024, objectives were realized in the MOOSE framework application development support and user-oriented improvements. Application development improvements support both developers and users with an expanded Reactor Module and Mesh System, stateful material property support for mortar contact, and customizable convergence criteria. Additionally, new user-oriented features were implemented in the MOOSE framework language server, including autocompletion snippets, definition from source and find reference navigations, and syntax overrides. Lastly, improvements were made to the input interpreter necessary to support the MOOSE language server and the NEAMS Workbench so that they can interact with syntactically incomplete user inputs. These improvements and more were intended to address stakeholder feedback and improve developer and user ability to conduct advanced nuclear energy modeling and simulation in support of DOE and industry needs.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

MOOSE–Workbench Integration and MOOSE Meshing Capability Enhancements to Facilitate Inputs and Outputs for Multiphysics Modeling

The Multiphysics Object-Oriented Simulation Environment (MOOSE) is an open-source framework that supports many of the US Department of Energy’s (DOE’s) Nuclear Energy Advanced Modeling and Simulation (NEAMS) technical areas (TA). These TAs develop and use NEAMS physics and coupling modules in multiple ways to enable the research and development of complex physics models. In addition to the MOOSE framework, the NEAMS Workbench user interface provides a common analysis environment with user-interaction accelerators that streamline the tasks of model creation, review, execution, and output inspection. In FY 2024, objectives were realized in the MOOSE framework application development support and user-oriented improvements. Application development improvements support both developers and users with an expanded Reactor Module and Mesh System, stateful material property support for mortar contact, and customizable convergence criteria. Additionally, new user-oriented features were implemented in the MOOSE framework language server, including autocompletion snippets, definition from source and find reference navigations, and syntax overrides. Lastly, improvements were made to the input interpreter necessary to support the MOOSE language server and the NEAMS Workbench so that they can interact with syntactically incomplete user inputs. These improvements and more were intended to address stakeholder feedback and improve developer and user ability to conduct advanced nuclear energy modeling and simulation in support of DOE and industry needs.

97 - MATHEMATICS AND COMPUTING↗

NASA NTRS2023

Fan Noise Predictions of the NASA Source Diagnostic Test Using Unsteady Simulations with LAVA Part I: Near-Field Aerodynamics and Turbulence

A sliding mesh technique within the Launch, Ascent, and Vehicle Aerodynamics (LAVA) computational framework is validated using the experimental dataset collected as part of the NASA Source Diagnostic Test (SDT) campaign. Two modeling approaches are explored: the unsteady Reynolds-Averaged Navier Stokes (URANS) with Spalart-Allmaras (SA) turbulence model closure, and a hybrid Reynolds-Averaged Navier Stokes/Large Eddy Simulation (RANS/LES) paradigm employing a Zonal Detached Eddy Simulation (ZDES) closure with enhanced shielding protection. Fan stage performance metrics, aerodynamic quantities and turbulent flow structures are analyzed in this work. Initial studies focusing on grid and time-step sensitivity are presented. Sensitivity to different variants of the SA turbulence model is analyzed, supporting the use of the baseline SA model in the production runs. Two conditions are analyzed in detail using URANS and hybrid RANS/LES (HRLES). Mean flow quantities are well-captured by both methods in the low-speed (approach) regime. While URANS misses all the upstream-propagating noise in the inlet due to the rotor-locked tones being evanescent in nature at subsonic fan tip speeds, HRLES captures this broadband component in its pressure field. At the high-speed (sideline) condition, URANS shows better agreement with the SDT data than HRLES in the interstage flow-field. In this regime, URANS captures the tonal content propagating through the inlet, since the tones are now cut-on. Both methods are suitable to capture fan stage performance metrics and mean flow quantities, but only HRLES is able to resolve the fine turbulent structures responsible for broadband noise. The results support the use of the sliding mesh technique implemented in this work for future turbomachinery applications within the LAVA solver framework.

AATT↗

NASA NTRS2023

Fan Noise Predictions of the NASA Source Diagnostic Test Using Unsteady Simulations with LAVA Part I: Near-Field Aerodynamics and Turbulence

AATT↗

NASA NTRS2018

Design of a Modular Monolithic Implicit Solver for Multi-Physics Applications

The design of a modular multi-physics high-order space-time finite-element framework is presented together with its extension to allow monolithic coupling of different physics. One of the main objectives of the framework is to perform efficient high- fidelity simulations of capsule/parachute systems. This problem requires simulating multiple physics including, but not limited to, the compressible Navier-Stokes equations, the dynamics of a moving body with mesh deformations and adaptation, the linear shell equations, non-re effective boundary conditions and wall modeling. The solver is based on high-order space-time - finite element methods. Continuous, discontinuous and C1-discontinuous Galerkin methods are implemented, allowing one to discretize various physical models. Tangent and adjoint sensitivity analysis are also targeted in order to conduct gradient-based optimization, error estimation, mesh adaptation, and flow control, adding another layer of complexity to the framework. The decisions made to tackle these challenges are presented. The discussion focuses first on the "single-physics" solver and later on its extension to the monolithic coupling of different physics. The implementation of different physics modules, relevant to the capsule/parachute system, are also presented. Finally, examples of coupled computations are presented, paving the way to the simulation of the full capsule/parachute system.

Carton De Wiart, Corentin↗

DOE OSTI2024

AMReX v2024

The software framework, AMReX, supports the development of block-structured adaptive mesh refinement (AMR) algorithms for solving systems of partial differential equations. AMR reduces the computational cost and memory footprint compared to a uniform mesh while preserving the essential local descriptions of different physical processes in complex multiphysics algorithms. AMR uses a hierarchical representation of the solution at multiple levels of resolution where the solution on each level is defined on the union of data containers at that resolution. These data containers, which represent the solution over a logically rectangular subregion of the domain, can contain field data defined on a mesh, Lagrangian particles or combinations of both. In addition to these basic data types, AMReX supports a multilevel embedded boundary representation of complex geometry; linear solvers for cell-centered and nodal data; asynchronous I/O in a native format readable by ParaView, VisIt and yt; and interfaces to hypre and PETSc solvers. AMReX enables applications to run on distributed memory architectures with multicore CPUs and with GPU accelerators. AMReX uses a lightweight abstraction layer that effectively hides the details of the architecture from the application. The framework currently supports CUDA, HIP and SYCL for GPU acceleration and OpenMP for multi-core CPU architectures.

Almgren, Ann↗

DOE OSTI2024

Large-Eddy Simulation Study of Flow and Combustion Dynamics in a Full-Scale Hydrogen–Air Rotating Detonation Combustor-Stator Integrated System

In the present work, a first-of-its-kind three-dimensional (3D) large-eddy simulation (LES) study is conducted to numerically investigate the combustion dynamics as well as aero-thermal phenomena in a full-scale nonpremixed hydrogen–air rotating detonation engine (RDE) (with a diverging-shaped lower-end wall), when integrated with nozzle guide vanes (NGV) acting as the turbine stator. The wall-modeled LES framework incorporates hydrogen–air detailed chemical kinetics and adaptive mesh refinement (AMR). A comparative analysis is carried out for two operating conditions with different fuel/air mass flow rates but global equivalence ratio of unity, and considering RDE configurations without and with stator. The LES model is validated against available experimental data for the low mass flux condition with respect to detonation wave speed/height, wave dynamics, and axial static pressure distribution. Numerical results indicate significant deflagrative combustion occurring in the fill region near the inner wall due to formation of recirculation zones in the injection near-field driven by the backward facing step. The leading detonation wave is found to be trailed by an azimuthal reflected-shock combustion (ARSC) wave, consistent with experimental observations, which consumes unburned vitiated reactants that leak through the main detonation wave. The main detonation wave characteristics, such as detonation wave speed/height and combustion efficiency, do not change appreciably with the presence of NGV. A novel combustion diagnostic technique based on chemical explosive mode analysis (CEMA) is employed to quantify the fraction of heat release occurring in the detonative mode versus deflagrative mode for the simulated conditions. The exit flow is found to be nearly fully subsonic and supersonic for the low and high mass flux conditions, respectively. Further analysis of the exit flow profiles shows that the presence of NGV renders the flow more axial and significantly impacts the exit Mach number and total pressure, while the total temperature shows negligible change. In addition, the low mass flux operating point, despite exhibiting more deflagrative losses within the combustor, yields overall lower pressure drop from plenum to exhaust, which is mainly attributed to lower pressure drop across the injectors. Lastly, the rotating detonation engine-nozzle guide vanes (RDE-NGV) configuration exhibits higher total pressure loss compared to rotating detonation engine (RDE) without stator across both the mass flux conditions. In conclusion, this study extends the state-of-the-art in numerical modeling of pressure gain combustion (PGC) systems by demonstrating high-fidelity 3D reacting LES of full-scale RDE-NGV systems relevant to RDE-turbine integration for stationary power generation.

Combustion↗