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NASA NTRS2006

Unstructured CFD and Noise Prediction Methods for Propulsion Airframe Aeroacoustics

Using unstructured mesh CFD methods for Propulsion Airframe Aeroacoustics (PAA) analysis has the distinct advantage of precise and fast computational mesh generation for complex propulsion and airframe integration arrangements that include engine inlet, exhaust nozzles, pylon, wing, flaps, and flap deployment mechanical parts. However, accurate solution values of shear layer velocity, temperature and turbulence are extremely important for evaluating the usually small noise differentials of potential applications to commercial transport aircraft propulsion integration. This paper describes a set of calibration computations for an isolated separate flow bypass ratio five engine nozzle model and the same nozzle system with a pylon. These configurations have measured data along with prior CFD solutions and noise predictions using a proven structured mesh method, which can be used for comparison to the unstructured mesh solutions obtained in this investigation. This numerical investigation utilized the TetrUSS system that includes a Navier-Stokes solver, the associated unstructured mesh generation tools, post-processing utilities, plus some recently added enhancements to the system. New features necessary for this study include the addition of two equation turbulence models to the USM3D code, an h-refinement utility to enhance mesh density in the shear mixing region, and a flow adaptive mesh redistribution method. In addition, a computational procedure was developed to optimize both solution accuracy and mesh economy. Noise predictions were completed using an unstructured mesh version of the JeT3D code.

Pao, S. Paul↗

DOE OSTI2023

Local Decomposition of Hexahedral Singular Nodes into Singular Curves

Hexahedral (hex) meshing is a long studied topic in geometry processing with many challenging associated problems. Hex meshes vary from structured to unstructured depending on application or domain of interest. Fully structured meshes require that all interior mesh edges be adjacent to four hexes each. Edges failing this criteria are singular and indicate an unstructured hex mesh. Singular edges join together into singular curves that either form closed cycles, end on the mesh boundary, or end at a singular node, a complex junction of more than two singular curves. Hex meshes with more complex singular nodes tend to have more distorted elements and smaller scaled Jacobian values. In this work, we study the topology of singular nodes. We show that all eight of the most common singular nodes are decomposable into just singular curves. We further show that all singular nodes, regardless of edge valence, are locally decomposable. Finally we demonstrate these decompositions on hex meshes, thereby decreasing their distortion and converting all singular nodes into singular curves. In conclusion, with this decomposition, the enigmatic complexity of 3D singular nodes becomes effectively 2D.

97 MATHEMATICS AND COMPUTING↗

NASA NTRSDate not supplied

An Overset Grid Motion Driver for Resolving Entry Vehicle CFD Simulations with Large Changes in Wake Orientation

Time-accurate computational fluid dynamics (CFD) simulations using overset meshes can enable reduced computational cost compared to a rigid, monolithic mesh for blunt-body atmospheric entry vehicles. If the vehicle has a significant change in attitude, the high-density region of the overset mesh designed for resolving the subsonic wake can be kept in position as the wake orientation changes relative to the body. Current simulations generally keep the wake mesh fixed in attitude while the body rotates, assuming the wake orientation remains relatively constant. However, changes in the relative velocity over a long-duration simulation or effects of the body geometry can invalidate this assumption. This work presents a method for calculating the desired mesh orientation to resolve a blunt body wake using the atmosphere-relative velocity of the vehicle. A motion driver using these calculations is implemented in a CFD-in-the-loop flight model bridging the FUN3D flow solver and POST2 trajectory propagator. Overset meshing is performed using the Yoga extension for FUN3D. Results are presented for simulations with both overset and monolithic meshes under large changes in relative velocity (and therefore wake orientation). The results demonstrate that the motion driver successfully orients an overset wake mesh to capture the subsonic wake with sufficient resolution despite variable body rotation and body-relative freestream velocity.

CFD↗

NASA NTRSDate not supplied

An Overset Grid Motion Driver for Resolving Entry Vehicle CFD Simulations with Large Changes in Wake Orientation

Computational Fluid Dynamics↗

DOE OSTI2021

No evidence of top–down effects by ants on litter decomposition in a temperate grassland

Ants play multiple roles in ecosystems, but their ability to affect decomposition processes in temperate grasslands is relatively unknown. We investigated whether the suppression of ant populations influenced litter decomposition in grasslands via predation of some decomposers (e.g., mites and springtails) and/or microbial activity and composition. We performed two successful ant suppression treatments (seven weeks, 37% suppression, year 1, 10 weeks, 70% suppression, year 2) over the course of a 59-week experiment. We then assayed the effects of ant suppression using coarse- and fine-mesh litterbags and evaluated litter chemistry, microbial and arthropod communities, and microbial enzyme activity. Ant suppression efforts reduced ant abundance and altered ant, arthropod decomposer, and non-ant predator community composition. However, ant suppression did not affect decomposer arthropod abundance, litter mass loss, microbial composition, or enzyme activity in litterbags. Litterbag mesh size did not alter microbial composition, perhaps due to a failure to exclude decomposers, as mites and springtails were more or equally abundant in fine-mesh bags. Nevertheless, mesh size did change litter chemistry, suggesting that mesh size-mediated microenvironments affect decomposition environment regardless of invertebrate exclusion. Coarse-mesh litterbags had higher concentrations of microbial sugars, lignin, and N and lower concentrations of litter C and crystalline cellulose than fine-mesh litterbags. Litterbag mesh size may alter decomposition processes irrespective of invertebrate abundance. We found no evidence that ant predation was an important driver of decomposer populations or decomposition in these systems, and we suspect redundancy at the top of the detrital food web dilutes the role of ants.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

A discontinuous piecewise polynomial generalized moving least squares scheme for robust finite element analysis on arbitrary grids

A variational approach is developed with a meshless discretization to enable accurate and robust numerical simulation of partial differential equations for meshes that are of poor quality. Traditional finite element methods use the mesh to both discretize the geometric domain and to define the finite element shape functions. The latter creates a dependence between the quality of the mesh and the properties of the finite element basis that may adversely affect the accuracy of the discretized problem. Here, we propose a new approach for defining finite element shape functions that breaks this dependence and separates mesh quality from the discretization quality, which we call discontinuous piecewise polynomial generalized moving least squares (DPP-GMLS). At the core of the approach is a meshless definition of the shape functions, which limits the purpose of the mesh to representing the geometric domain and integrating the basis functions without having any role in their approximation quality. The resulting non-conforming space can be utilized within a standard discontinuous Galerkin framework, providing a rigorous foundation for solving partial differential equations on low-quality meshes. We present a collection of numerical experiments demonstrating our approach in a wide range of settings: strongly coercive elliptic problems, linear elasticity in the compressible regime, and the stationary Stokes problem. We demonstrate convergence for all problems and stability for element pairs for problems which usually require inf-sup compatibility for conforming methods, also referring to a minor modification possible through the symmetric interior penalty Galerkin framework for stabilizing element pairs that would otherwise be traditionally unstable. Mesh robustness is particularly critical for elasticity, and we provide an example that our approach provides a greater than 5 x improvement in accuracy and allows for taking an 8 x larger stable timestep for a highly deformed mesh, compared to the continuous Galerkin finite element method.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Enriched immersed boundary method (EIBM) for interface-coupled multi-physics and applications to convective conjugate heat transfer

It is challenging to develop numerical methods that simultaneously maintain accuracy of resolving boundary conditions and mesh flexibility to handle the interface in interface-coupled multi-physics problems involving large property discontinuity. On the one hand, boundary-fitted methods possess high accuracy in capturing the interfacial phenomenon but involve complicated volumetric mesh generation, mesh-motion, and even re-meshing procedures. On the other hand, immersed boundary methods (IBM) provide mesh flexibility but sometimes suffer from inferior interface representations, leading to poor enforcement of boundary conditions. This paper presents an enriched immersed boundary method (EIBM) to overcome this challenge and demonstrates its efficacy in conjugate heat transfer, a representative example in interface-coupled multi-physics systems that have implications for many industrial processes. Further, the core technique of the method is to enhance IBM’s accuracy of the fluid–solid interface by enriching the degrees of freedom of the cut elements to enforce temperature and flux compatibilities and resolve all the physical unknowns on the background mesh to simplify the volumetric mesh generation. We implement the EIBM under the framework of a variational multiscale formulation for coupled Navier–Stokes and thermodynamics equations. The enriched DoFs enable better enforcement of temperature and flux compatibilities with large conductivity ratios across the fluid–solid interface. At the same time, the immersed nature of the proposed method still attains mesh flexibility. The EIBM’s accuracy is thoroughly evaluated through a set of examples, ranging from benchmark problems with analytical solutions to real-world cooling processes of a moving metallic structure with complex geometry.

42 ENGINEERING↗

DOE OSTI2015

Bed Agglomeration During the Steam Gasification of a High Lignin Corn Stover Simultaneous Saccharification and Fermentation (SSF) Digester Residue

This research investigates the bed agglomeration phenomena during the steam gasification of a high lignin residue produced from the simultaneous saccharification and fermentation (SSF) of corn stover in a bubbling fluidized bed. The studies were conducted at 895°C using alumina as bed material. Biomass was fed at 1.5 kg/hr, while steam was fed to give a velocity equal to 2.5 times the minimum fluidization velocity, with a steam/carbon ratio of 0.9. The pelletized feedstock was co-fed with a cooling nitrogen stream to mitigate feed line plugging issues. Tar production was high at 50.3 g/Nm3, and the fraction of C10+ compounds was greater than that seen in the gasification of traditional lignocellulosic feedstocks. Carbon closures over 94 % were achieved for all experiments. Bed agglomeration was found to be problematic, indicated by pressure drop increases observed below the bed and upstream of the feed line. Two size categories of solids were recovered from the reactor, +60 mesh and -60 mesh. After a 2.75-hour experiment, 61.7 wt % was recovered as -60 mesh particles and 38.2 wt% of the recovered reactor solids were +60 mesh. A sizeable percentage, 31.8 wt%, was +20 mesh. The -60 mesh particles were mainly formed by the initial bed material (Al2O3). Almost 50 wt. % of the + 20 mesh particles was found to be formed by organics. The unreacted carbon remaining in the reactor resulted in a low conversion rate to product gas. ICP-AES, SEM, SEM-EDS, and XRD confirmed that the large agglomerates (+ 20 mesh) were not encapsulated bed material but rather un-gasified feedstock pellets with sand particles attached to it.

bioenergy↗

DOE OSTI2023

The Legendre Polynomial Axial Expansion Method

This work presents a new formulation of the axial expansion transport method explicitly using Legendre polynomials for arbitrarily high-order expansions. This new formulation also features an alternative method of axial leakage calculation to allow for nonextruded flat source region meshes. This alternative axial leakage is introduced alongside a balance equation requirement to ensure that neutron balance is preserved in the coarse mesh for a given axial leakage formulation, which allows for effective coarse mesh finite difference acceleration. A matrix exponential table method is derived to allow for fast computations of arbitrarily high-order matrix exponentials for this work and precludes the need for further research into matrix exponential calculations for this method. Numerical results are presented that demonstrate the stability of the axial expansion method in systems with voidlike regions, showcase the speedup from matrix exponential tables, and investigate the axial convergence of the method in terms of both expansion order and mesh size.

Herring, Nicholas↗

DOE OSTI2015

SU-E-J-108: Solving the Chinese Postman Problem for Effective Contour Deformation

Purpose: To develop a practical approach for accurate contour deformation when deformable image registration (DIR) is used for atlas-based segmentation or contour propagation in image-guided radiotherapy. Methods: A contour deformation approach was developed on the basis of 3D mesh operations. The 2D contours represented by a series of points in each slice were first converted to a 3D triangular mesh, which was deformed by the deformation vectors resulting from DIR. A set of parallel 2D planes then cut through the deformed 3D mesh, generating unordered points and line segments, which should be reorganized into a set of 2D contour points. It was realized that the reorganization problem was equivalent to solving the Chinese Postman Problem (CPP) by traversing a graph built from the unordered points with the least cost. Alternatively, deformation could be applied to a binary mask converted from the original contours. The deformed binary mask was then converted back into contours at the CT slice locations. We performed a qualitative comparison to validate the mesh-based approach against the image-based approach. Results: The DIR could considerably change the 3D mesh, making complicated 2D contour representations after deformation. CPP was able to effectively reorganize the points in 2D planes no matter how complicated the 2D contours were. The mesh-based approach did not require a post-processing of the contour, thus accurately showing the actual deformation in DIR. The mesh-based approach could keep some fine details and resulted in smoother contours than the image-based approach did, especially for the lung structure. Image-based approach appeared to over-process contours and suffered from image resolution limits. The mesh-based approach was integrated into in-house DIR software for use in routine clinic and research. Conclusion: We developed a practical approach for accurate contour deformation. The efficiency of this approach was demonstrated in both clinic and research applications. This work was partially supported by Cancer Prevention & Research Institute of Texas (CPRIT) RP110562.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2019

A Comparison of Classical and Aggregation-Based Algebraic Multigrid Preconditioners for High-Fidelity Simulation of Wind Turbine Incompressible Flows

This paper presents a comparison of parallel strong scaling performance of classical and aggregation algebraic multigrid (AMG) preconditioners in the context of wind turbine simulations. Fluid motion is governed by the incompressible Navier--Stokes equations, discretized in space with control-volume finite elements and in time with an inexact projection scheme using an implicit integrator. A discontinuous-Galerkin sliding-mesh algorithm captures rotor motion. The momentum equations are solved with iterative Krylov methods, preconditioned by symmetric Gauss--Seidel (SGS) in Trilinos and $\ell_1$ SGS in hypre. The mass-continuity equation is solved with GMRES preconditioned by AMG and can account for the majority of simulation time. Reducing this continuity solve time is crucial. Wind turbine simulations present two unique challenges for AMG preconditioned solvers: the computational meshes include strongly anisotropic elements, and mesh motion requires matrix reinitialization and computation of preconditioners at each time step. Detailed timing profiles are presented and analyzed, and best practices are discussed for both classical and aggregation-based AMG. Results are presented for simulations of two different wind turbines with up to 6 billion grid points on two different computer architectures. For moving mesh problems that require linear-system reinitialization, the well-established strategy of amortizing preconditioner setup costs over a large number of time steps to reduce the solve time is no longer valid. Instead, results show that faster time to solution is achieved by reducing preconditioner setup costs at the expense of linear-system solve costs. Standard smoothed aggregation with Chebyshev relaxation was found to perform poorly when compared with classical AMG in terms of solve time and robustness. However, plain aggregation was comparable to classical AMG.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Regression Based Approach for Robust Finite Element Analysis on Arbitrary Grids. LDRD Final Report

This report summarizes the work performed under a one-year LDRD project aiming to enable accurate and robust numerical simulation of partial differential equations for meshes that are of poor quality. Traditional finite element methods use the mesh to both discretize the geometric domain and to define the finite element shape functions. The latter creates a dependence between the quality of the mesh and the properties of the finite element basis that may adversely affect the accuracy of the discretized problem. In this project, we propose a new approach for defining finite element shape functions that breaks this dependence and separates mesh quality from the discretization quality. At the core of the approach is a meshless definition of the shape functions, which limits the purpose of the mesh to representing the geometric domain and integrating the basis functions without having any role in their approximation quality. The resulting non-conforming space can be utilized within a standard discontinuous Galerkin framework providing a rigorous foundation for solving partial differential equations on low-quality meshes. We present a collection of numerical experiments demonstrating our approach in a wide range of settings: strongly coercive elliptic problems, linear elasticity in the compressible regime, and the stationary Stokes problem. We demonstrate convergence for all problems and stability for element pairs for problems which usually require inf-sup compatibility for conforming methods, also referring to a minor modification possible through the symmetric interior penalty Galerkin framework for stabilizing element pairs that would otherwise be traditionally unstable. Mesh robustness is particularly critical for elasticity, and we provide an example that our approach provides a greater than 5x improvement in accuracy and allows for taking an 8x larger stable timestep for a highly deformed mesh, compared to the continuous Galerkin finite element method. The report concludes with a brief summary of ongoing projects and collaborations that utilize or extend the products of this work.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Non-conformal interface-cohesive modeling with the shifted boundary method

The accurate simulation of boundary- and interface-dominated problems on complex geometries remains challenging when boundary- or interface-fitted meshes are difficult to generate, particularly for curved boundaries, polycrystalline microstructures, and dense interface networks. The Shifted Boundary Method (SBM) alleviates this meshing burden by shifting the enforcement of boundary conditions from the true boundary to a nearby surrogate boundary and recovering the effect of the true boundary through geometric correction terms, thereby enabling standard finite element spaces on non-boundary-fitted meshes. In this report, we develop a general shiftedboundary and shifted-interface framework within the open-source MOOSE framework. We first present a general SBM implementation for complex geometries on non-boundary-fitted meshes. We then adopt the Shifted Interface Method (SIM) for internal interfaces and develop a unified shifted-interface treatment in which the interface law is enforced on a surrogate interface and the effect of the true interface is recovered through shifted jumps, fluxes, and tractions. This perspective brings scalar thermal-contact and vector-valued cohesive-zone mechanics into a single framework, the latter realized as the Shifted Cohesive Zone Method (SCZM) and coupled with history-dependent constitutive models from NEML2. We further extend the MOOSE mesh infrastructure to support cohesive-zone calculations on distributed meshes. The framework is verified and demonstrated through three progressive studies: Poisson’s equation on a smoothed starshaped domain, a manufactured thermal-contact problem on a non-interface-fitted mesh, and a two-dimensional polycrystalline representative volume element combining crystal plasticity with cohesive grain-boundary interfaces. Across these studies, the shifted formulations reproduce boundary- and interface-fitted reference solutions with high fidelity, indicating that the proposed framework provides an accurate and efficient route to boundary- and interface-dominated simulations on arbitrary geometries without requiring fitted meshes.

Yang, Cheng-Hau↗

NASA NTRS1989

Application of unstructured grid methods to steady and unsteady aerodynamic problems

The purpose is to describe the development of unstructured grid methods which have several advantages when compared to methods which make use of structured grids. Unstructured grids, for example, easily allow the treatment of complex geometries, allow for general mesh movement for realistic motions and structural deformations of complete aircraft configurations which is important for aeroelastic analysis, and enable adaptive mesh refinement to more accurately resolve the physics of the flow. Steady Euler calculations for a supersonic fighter configuration to demonstrate the complex geometry capability; unsteady Euler calculations for the supersonic fighter undergoing harmonic oscillations in a complete-vehicle bending mode to demonstrate the general mesh movement capability; and vortex-dominated conical-flow calculations for highly-swept delta wings to demonstrate the adaptive mesh refinement capability are discussed. The basic solution algorithm is a multi-stage Runge-Kutta time-stepping scheme with a finite-volume spatial discretization based on an unstructured grid of triangles in 2D or tetrahedra in 3D. The moving mesh capability is a general procedure which models each edge of each triangle (2D) or tetrahedra (3D) with a spring. The resulting static equilibrium equations which result from a summation of forces are then used to move the mesh to allow it to continuously conform to the instantaneous position or shape of the aircraft. The adaptive mesh refinement procedure enriches the unstructured mesh locally to more accurately resolve the vortical flow features. These capabilities are described in detail along with representative results which demonstrate several advantages of unstructured grid methods. The applicability of the unstructured grid methodology to steady and unsteady aerodynamic problems and directions for future work are discussed.

Batina, John T.↗

NASA NTRS2003

Accelerating Large Data Analysis By Exploiting Regularities

We present techniques for discovering and exploiting regularity in large curvilinear data sets. The data can be based on a single mesh or a mesh composed of multiple submeshes (also known as zones). Multi-zone data are typical to Computational Fluid Dynamics (CFD) simulations. Regularities include axis-aligned rectilinear and cylindrical meshes as well as cases where one zone is equivalent to a rigid-body transformation of another. Our algorithms can also discover rigid-body motion of meshes in time-series data. Next, we describe a data model where we can utilize the results from the discovery process in order to accelerate large data visualizations. Where possible, we replace general curvilinear zones with rectilinear or cylindrical zones. In rigid-body motion cases we replace a time-series of meshes with a transformed mesh object where a reference mesh is dynamically transformed based on a given time value in order to satisfy geometry requests, on demand. The data model enables us to make these substitutions and dynamic transformations transparently with respect to the visualization algorithms. We present results with large data sets where we combine our mesh replacement and transformation techniques with out-of-core paging in order to achieve significant speed-ups in analysis.

Moran, Patrick J.↗

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.↗

NASA NTRS2011

Technique for Calculating Solution Derivatives With Respect to Geometry Parameters in a CFD Code

A solution has been developed to the challenges of computation of derivatives with respect to geometry, which is not straightforward because these are not typically direct inputs to the computational fluid dynamics (CFD) solver. To overcome these issues, a procedure has been devised that can be used without having access to the mesh generator, while still being applicable to all types of meshes. The basic approach is inspired by the mesh motion algorithms used to deform the interior mesh nodes in a smooth manner when the surface nodes, for example, are in a fluid structure interaction problem. The general idea is to model the mesh edges and nodes as constituting a spring-mass system. Changes to boundary node locations are propagated to interior nodes by allowing them to assume their new equilibrium positions, for instance, one where the forces on each node are in balance. The main advantage of the technique is that it is independent of the volumetric mesh generator, and can be applied to structured, unstructured, single- and multi-block meshes. It essentially reduces the problem down to defining the surface mesh node derivatives with respect to the geometry parameters of interest. For analytical geometries, this is quite straightforward. In the more general case, one would need to be able to interrogate the underlying parametric CAD (computer aided design) model and to evaluate the derivatives either analytically, or by a finite difference technique. Because the technique is based on a partial differential equation (PDE), it is applicable not only to forward mode problems (where derivatives of all the output quantities are computed with respect to a single input), but it could also be extended to the adjoint problem, either by using an analytical adjoint of the PDE or a discrete analog.

Mathur, Sanjay↗

DOE OSTI2024

Investigation of CAD-based Geometry Workflows for Multiphysics Fusion Problems Using OpenMC and MOOSE

Fusion system designs are complex and require intricate and accurate meshes to be properly modeled. In this study, we investigate the use of CAD-based geometry workflows in fusion systems multiphysics problems. A simplified tokamak was introduced and modeled in CAD using a multiphysics coupling of OpenMC Monte Carlo transport and MOOSE heat conduction. The meshed geometry was prepared using direct accelerated geometry Monte Carlo (DAGMC) for particle transport, and a volumetric mesh was also prepared to be used in MOOSE and to tally OpenMC results. Cardinal was used to run OpenMC Monte Carlo particle transport within MOOSE framework. The heat source distribution and tritium production were calculated in OpenMC. The data transfer system was used to transfer heat source and temperature distribution between OpenMC and MOOSE. Two computational studies related to mesh refinement were performed: (1) refining the DAGMC and volumetric meshes used for tallying results and solving heat conduction and (2) only refining the DAGMC particle transport mesh. The refinement of the tally mesh has a much larger effect on the runtime compared to the refinement of the DAGMC particle transport surface mesh.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗