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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Multigrid calculation of internal flows in complex geometries

The development, validation, and application of a general purpose multigrid solution algorithm and computer program for the computation of elliptic flows in complex geometries is presented. This computer program combines several desirable features including a curvilinear coordinate system, collocated arrangement of the variables, and Full Multi-Grid/Full Approximation Scheme (FMG/FAS). Provisions are made for the inclusion of embedded obstacles and baffles inside the flow domain. The momentum and continuity equations are solved in a decoupled manner and a pressure corrective equation is used to update the pressures such that the fluxes at the cell faces satisfy local mass continuity. Despite the computational overhead required in the restriction and prolongation phases of the multigrid cycling, the superior convergence results in reduced overall CPU time. The numerical scheme and selected results of several validation flows are presented. Finally, the procedure is applied to study the flowfield in a side-inlet dump combustor and twin jet impingement from a simulated aircraft fuselage.

Smith, K. M.↗
NASA NTRSDate not supplied

Transition prediction in hypersonic regime on complex geometries with RANS-based models

In the near future, RANS computations will continue to play a significant role in the design of hypersonic vehicles with complex geometries. Therefore, it is imperative to continue testing, benchmarking, and refining the RANS models. In the present study, we evaluate RANS-like, transport equations-based models for predicting laminar-turbulent transition over a full-scale scale model of the BOLT flight configuration that was tested in the CUBRC LENS-II wind tunnel test facility. Based on the availability of the experimental results, comparisons are made between computations from several pre-existing transition models and Computational Fluid Dynamics (CFD) codes, with an emphasis on using the same computational meshes and flow conditions for all computations. The analysis covers the sensitivity of the transition predictions to the input parameters for five different transition models (four mainstream models designed for low-speed flows and a uniquely high-speed model), grid resolution, and the details of model implementation across three different flow solvers. The results show that the phenomenological models can describe significant aspects of the measured transition front. However, a number of additional improvements are required before these models can offer more reliable estimates of transition in high-speed flows.

CFD↗
NASA NTRSDate not supplied

Transition Prediction in Hypersonic Regime on Complex Geometries With Rans-Based Models

In the near future, RANS computations will continue to play a significant role in the design of hypersonic vehicles with complex geometries. Therefore, it is imperative to continue testing, benchmarking, and refining the RANS models. In the present study, we evaluate RANS-like, transport equations-based models for predicting laminar-turbulent transition over a full-scale scale model of the BOLT flight configuration that was tested in the CUBRC LENS-II wind tunnel test facility. Based on the availability of the experimental results, comparisons are made between computations from several pre-existing transition models and Computational Fluid Dynamics (CFD) codes, with an emphasis on using the same computational meshes and flow conditions for all computations. The analysis covers the sensitivity of the transition predictions to the input parameters for five different transition models (four mainstream models designed for low-speed flows and a uniquely high-speed model), grid resolution, and the details of model implementation across three different flow solvers. The results show that the phenomenological models can describe significant aspects of the measured transition front. However, a number of additional improvements are required before these models can offer more reliable estimates of transition in high-speed flows.

CFD↗
NASA NTRS1994

A Method for Flow Simulation About Complex Geometries Using Both Structured and Unstructured Grids

A computational fluid dynamics code which utilizes both structured and unstructured grids was developed. The objective of this study was to develop and demonstrate the ability of such a code to achieve solutions about complex geometries in two dimensions. An unstructured grid generator and flow solver were incorporated into the PARC2D structured flow solver. This new unstructured grid generator capability allows for easier generation and manipulation of complex grids. Several examples of the grid generation capabilities are provided. The coupling of different grid topologies and the manipulation of individual grids is shown. Also, grids for realistic geometries, a NACA 0012 airfoil and a wing/nacelle installation, were created. The flow over a NACA 0012 airfoil was used as a test case for the flow solver. Eight separate cases were run. They were both the inviscid and viscous solutions for two freestream Mach numbers and airfoil angle of attacks of 0 to 3.86 degrees. The Mach numbers chosen were for a subsonic case, Mach 0.6, and a case where supersonic regions and a shock wave exists, Mach 0.8. These test case conditions were selected to match experimentally obtained data for code comparison. The results show that the code accurately predicts the flow field for all cases.

Debonis, James R.↗
NASA NTRS2014

Using SpaceClaimTD Direct for Modeling Components with Complex Geometries for the Thermal Desktop-Based Advanced Stirling Radioisotope Generator Model

SpaceClaim/TD Direct has been used extensively in the development of the Advanced Stirling Radioisotope Generator (ASRG) thermal model. This paper outlines the workflow for that aspect of the task and includes proposed best practices and lessons learned. The ASRG thermal model was developed to predict component temperatures and power output and to provide insight into the prime contractor's thermal modeling efforts. The insulation blocks, heat collectors, and cold side adapter flanges (CSAFs) were modeled with this approach. The model was constructed using mostly TD finite difference (FD) surfaces/solids. However, some complex geometry could not be reproduced with TD primitives while maintaining the desired degree of geometric fidelity. Using SpaceClaim permitted the import of original CAD files and enabled the defeaturing/repair of those geometries. TD Direct (a SpaceClaim add-on from CRTech) adds features that allowed the "mark-up" of that geometry. These so-called "mark-ups" control how finite element (FE) meshes are to be generated through the "tagging" of features (e.g. edges, solids, surfaces). These tags represent parameters that include: submodels, material properties, material orienters, optical properties, and radiation analysis groups. TD aliases were used for most tags to allow analysis to be performed with a variety of parameter values. "Domain-tags" were also attached to individual and groups of surfaces and solids to allow them to be used later within TD to populate objects like, for example, heaters and contactors. These tools allow the user to make changes to the geometry in SpaceClaim and then easily synchronize the mesh in TD without having to redefine the objects each time as one would if using TDMesher. The use of SpaceClaim/TD Direct helps simplify the process for importing existing geometries and in the creation of high fidelity FE meshes to represent complex parts. It also saves time and effort in the subsequent analysis.

Power Systems↗
NASA NTRS2014

Using SpaceClaim/TD Direct for Modeling Components with Complex Geometries for the Thermal Desktop-Based Advanced Stirling Radioisotope Generator Model

SpaceClaim/TD Direct has been used extensively in the development of the Advanced Stirling Radioisotope Generator (ASRG) thermal model. This paper outlines the workflow for that aspect of the task and includes proposed best practices and lessons learned. The ASRG thermal model was developed to predict component temperatures and power output and to provide insight into the prime contractors thermal modeling efforts. The insulation blocks, heat collectors, and cold side adapter flanges (CSAFs) were modeled with this approach. The model was constructed using mostly TD finite difference (FD) surfaces solids. However, some complex geometry could not be reproduced with TD primitives while maintaining the desired degree of geometric fidelity. Using SpaceClaim permitted the import of original CAD files and enabled the defeaturing repair of those geometries. TD Direct (a SpaceClaim add-on from CRTech) adds features that allowed the mark-up of that geometry. These so-called mark-ups control how finite element (FE) meshes were generated and allowed the tagging of features (e.g. edges, solids, surfaces). These tags represent parameters that include: submodels, material properties, material orienters, optical properties, and radiation analysis groups. TD aliases were used for most tags to allow analysis to be performed with a variety of parameter values. Domain-tags were also attached to individual and groups of surfaces and solids to allow them to be used later within TD to populate objects like, for example, heaters and contactors. These tools allow the user to make changes to the geometry in SpaceClaim and then easily synchronize the mesh in TD without having to redefine these objects each time as one would if using TD Mesher.The use of SpaceClaim/TD Direct has helped simplify the process for importing existing geometries and in the creation of high fidelity FE meshes to represent complex parts. It has also saved time and effort in the subsequent analysis.

Power Systems↗
NASA NTRS1989

Spectral element simulations of laminar and turbulent flows in complex geometries

Spectral element methods are high-order weighted residual techniques based on spectral expansions of variables and geometry for the Navier-Stokes (NS) and transport equations. Here, practical aspects of these methods and their efficient implementation are examined, and several examples of flows in truly complex geometries are presented. The spectral element discretization for NS equations is introduced, and the convergence of the method is addressed. An efficient data management scheme is discussed in the context of parallel processing computations. The method is validated by comparing the spectral element solutions with the exact eigensolutions for the Orr-Sommerfeld equations in two and three dimensions. Computer-aided flow visualizations are presented for an impulsive flow past a sharp edge wedge. Three-dimensional states of channel flow disrupted by an array of cylindrical eddy promoters are studied, and the results of a direct simulation of the turbulent flow in a plane channel are presented.

Karniadakis, George EM↗
NASA NTRS1993

Efficient Three-Dimensional Direct Simulation Monte Carlo for Complex Geometry Problems

The simulation of flowfields in the transition flow regime is notoriously difficult with high demands on computer resources (CPU time and storage) and user expertise/labor. This paper describes a new, efficient code which has been developed to simulate high Knudsen number flowfields in three dimensions about bodies of arbitrarily complex geometry. The algorithm has been tested over a wide range of conditions, from free molecular to near-continuum flow regimes, for slender and blunt bodies, for re-entry vehicles and spacecraft. A series of validation tests have been conducted using both wind-tunnel measurements and flight data.

Rault, Didier F. G.↗
DOE OSTI2021

Simulation of Low-Rm physics in complex geometries on GPUs with LGR

Efficient modeling of low magnetic Reynolds number (low-Rm) magnetohydrodynamics is often challenging and requires the implementation of innovative techniques to avoid key barriers experienced with prior approaches. We detail a new paradigm for first-principles simulation of the solution to the low-Rm governing equations in complex geometries. As a result of a number of innovative numerical advances, the next-generation GPU (graphics processing unit) accelerated physics code LGR has been successfully applied to the modeling of exploding wire problems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2012

Progress Toward Affordable High Fidelity Combustion Simulations Using Filtered Density Functions for Hypersonic Flows in Complex Geometries

Significant progress has been made in the development of subgrid scale (SGS) closures based on a filtered density function (FDF) for large eddy simulations (LES) of turbulent reacting flows. The FDF is the counterpart of the probability density function (PDF) method, which has proven effective in Reynolds averaged simulations (RAS). However, while systematic progress is being made advancing the FDF models for relatively simple flows and lab-scale flames, the application of these methods in complex geometries and high speed, wall-bounded flows with shocks remains a challenge. The key difficulties are the significant computational cost associated with solving the FDF transport equation and numerically stiff finite rate chemistry. For LES/FDF methods to make a more significant impact in practical applications a pragmatic approach must be taken that significantly reduces the computational cost while maintaining high modeling fidelity. An example of one such ongoing effort is at the NASA Langley Research Center, where the first generation FDF models, namely the scalar filtered mass density function (SFMDF) are being implemented into VULCAN, a production-quality RAS and LES solver widely used for design of high speed propulsion flowpaths. This effort leverages internal and external collaborations to reduce the overall computational cost of high fidelity simulations in VULCAN by: implementing high order methods that allow reduction in the total number of computational cells without loss in accuracy; implementing first generation of high fidelity scalar PDF/FDF models applicable to high-speed compressible flows; coupling RAS/PDF and LES/FDF into a hybrid framework to efficiently and accurately model the effects of combustion in the vicinity of the walls; developing efficient Lagrangian particle tracking algorithms to support robust solutions of the FDF equations for high speed flows; and utilizing finite rate chemistry parametrization, such as flamelet models, to reduce the number of transported reactive species and remove numerical stiffness. This paper briefly introduces the SFMDF model (highlighting key benefits and challenges), and discusses particle tracking for flows with shocks, the hybrid coupled RAS/PDF and LES/FDF model, flamelet generated manifolds (FGM) model, and the Irregularly Portioned Lagrangian Monte Carlo Finite Difference (IPLMCFD) methodology for scalable simulation of high-speed reacting compressible flows.

Drozda, Tomasz G.↗
NASA NTRS2019

Computational Non-Destructive Evaluation Improving Ultrasonic Interrogation of Complex Geometry Composite Parts

Finite element simulation was employed in modeling the ultrasound (UT) pressure pulse propagation through a coupled liquid-composite medium to reproduce experimental data. From the simulation point of view, the proposed approach is challenging when there is a large simulation domain. For example, it is shown that a sub-micron wavelength of an ultrasonic wave requires a mesh size of several microns and this in turn requires significant computational resources, as well as special care in modeling. Some of the simulation results are presented considering that such modeling should reproduce experimental data for a healthy and faulty composite structure with complex geometry. Many possible experimental setups are simulated to demonstrate the non-destructive testing technique. This setup includes the generation of pressure pulse propagating through the tested composite plate and possible scattering by discontinuities (area of different impedance) that may be present in the panel. This scattered pulse together with the baseline pressure pulse generates a signature on the probe element which can be used to locate the position of defects in the structures.

modeling↗
DOE OSTI2024

Learning Only on Boundaries: A Physics-Informed Neural Operator for Solving Parametric Partial Differential Equations in Complex Geometries

Recently, deep learning surrogates and neural operators have shown promise in solving partial differential equations (PDEs). However, they often require a large amount of training data and are limited to bounded domains. In this work, we present a novel physics-informed neural operator method to solve parameterized boundary value problems without labeled data. By reformulating the PDEs into boundary integral equations (BIEs), we can train the operator network solely on the boundary of the domain. This approach reduces the number of required sample points from $O(N^d)$ to $O(N^{d-1}$), where $d$ is the domain’s dimension, leading to a significant acceleration of the training process. Additionally, our method can handle unbounded problems, which are unattainable for existing physics-informed neural networks (PINNs) and neural operators. Finally, our numerical experiments show the effectiveness of parameterized complex geometries and unbounded problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

On the large eddy simulation of turbulent flows in complex geometry

Application of the method of Large Eddy Simulation (LES) to a turbulent flow consists of three separate steps. First, a filtering operation is performed on the Navier-Stokes equations to remove the small spatial scales. The resulting equations that describe the space time evolution of the 'large eddies' contain the subgrid-scale (sgs) stress tensor that describes the effect of the unresolved small scales on the resolved scales. The second step is the replacement of the sgs stress tensor by some expression involving the large scales - this is the problem of 'subgrid-scale modeling'. The final step is the numerical simulation of the resulting 'closed' equations for the large scale fields on a grid small enough to resolve the smallest of the large eddies, but still much larger than the fine scale structures at the Kolmogorov length. In dividing a turbulent flow field into 'large' and 'small' eddies, one presumes that a cut-off length delta can be sensibly chosen such that all fluctuations on a scale larger than delta are 'large eddies' and the remainder constitute the 'small scale' fluctuations. Typically, delta would be a length scale characterizing the smallest structures of interest in the flow. In an inhomogeneous flow, the 'sensible choice' for delta may vary significantly over the flow domain. For example, in a wall bounded turbulent flow, most statistical averages of interest vary much more rapidly with position near the wall than far away from it. Further, there are dynamically important organized structures near the wall on a scale much smaller than the boundary layer thickness. Therefore, the minimum size of eddies that need to be resolved is smaller near the wall. In general, for the LES of inhomogeneous flows, the width of the filtering kernel delta must be considered to be a function of position. If a filtering operation with a nonuniform filter width is performed on the Navier-Stokes equations, one does not in general get the standard large eddy equations. The complication is caused by the fact that a filtering operation with a nonuniform filter width in general does not commute with the operation of differentiation. This is one of the issues that we have looked at in detail as it is basic to any attempt at applying LES to complex geometry flows. Our principal findings are summarized.

Ghosal, Sandip↗
NASA NTRS2000

An Automated Approach to Very High Order Aeroacoustic Computations in Complex Geometries

Computational aeroacoustics requires efficient, high-resolution simulation tools. And for smooth problems, this is best accomplished with very high order in space and time methods on small stencils. But the complexity of highly accurate numerical methods can inhibit their practical application, especially in irregular geometries. This complexity is reduced by using a special form of Hermite divided-difference spatial interpolation on Cartesian grids, and a Cauchy-Kowalewslci recursion procedure for time advancement. In addition, a stencil constraint tree reduces the complexity of interpolating grid points that are located near wall boundaries. These procedures are used to automatically develop and implement very high order methods (>15) for solving the linearized Euler equations that can achieve less than one grid point per wavelength resolution away from boundaries by including spatial derivatives of the primitive variables at each grid point. The accuracy of stable surface treatments is currently limited to 11th order for grid aligned boundaries and to 2nd order for irregular boundaries.

Dyson, Rodger W.↗
DOE OSTI2024

Enabling the broader adoption of fusion simulation on complex geometry

This project addressed a key barrier to advanced fusion and nuclear simulation: the difficulty of performing high-fidelity Monte Carlo neutronics directly on complex, real-world CAD geometry. Traditional workflows require engineers to rebuild CAD models as simplified constructive solid geometry, a time-consuming and error-prone process that limits design iteration and broader adoption of simulation tools. The goal of this Phase I SBIR was to make CAD-based neutronics practical, accessible, and robust for industrial and research users. During the project, Coreform significantly enhanced the Direct Accelerated Geometry Monte Carlo (DAGMC) workflow and fully integrated it into Coreform Cubit as a first-class capability. Major achievements include optimized material assignment and surface meshing workflows, substantial performance improvements to geometry imprinting and preparation, native export of DAGMC models, and new visualization tools to support OpenMC source definition and lost-particle debugging. Coreform also expanded Cubit’s capabilities as a full OpenMC preprocessor, including the ability to convert OpenMC constructive solid geometry models back into CAD for visualization, multiphysics coupling, and debugging. In collaboration with Argonne National Laboratory, the project delivered comprehensive new DAGMC documentation and training materials, transforming DAGMC from a research-oriented tool into a production-ready workflow. Results were disseminated through tutorials, conference training, and multiple well-attended webinars demonstrating integrated CAD-based neutronics and multiphysics workflows. Overall, this project demonstrated that high-fidelity Monte Carlo simulations can be performed directly on complex CAD geometry, reducing setup time, improving usability, and enabling faster, more informed design decisions for fusion and nuclear energy systems.

42 ENGINEERING↗
NASA NTRS1991

Algebraic grid generation for complex geometries

An efficient computer program called GRID2D/3D has been developed to generate single and composite grid systems within geometrically complex two- and three-dimensional (2D and 3D) spatial domains that can deform with time. GRID2D/3D generates single grid systems by using algebraic grid generation methods based on transfinite interpolation. The distribution of grid points within the spatial domain is controlled by stretching functions and grid lines can intersect boundaries of the spatial domain orthogonally. GRID2D/3D generates composite grid systems by patching together two or more single grid systems. The patching can be discontinuous or continuous. For 2D spatial domains the boundary curves are constructed by using either cubic or tension spline interpolation. For 3D spatial domains the boundary surfaces are constructed by using a new technique, developed in this study, referred to as 3D bidirectional Hermite interpolation.

Shih, T. I.-P.↗
NASA NTRS1990

Calculation of turbulent flow in complex geometries with a second-moment closure model

A full Reynolds stress turbulence model is applied to calculate the flow in various channels with complex cross-section. The model is shown to be more robust and to produce more consistent results than algebraic stress models. The relationship between various versions of the latter is provided. It is shown that differential or algebraic stress models derived from a direct application of a popular linear approximation for the pressure-strain terms in the Reynolds stress equations will always underpredict the secondary motion, and hence the accompanying distortion of other flow properties. A simple approximation which leads to better predictions is presented and related to previous practice.

Demuren, A. O.↗
NASA NTRS1997

Solution adaptive Cartesian grid methods for aerodynamic flows with complex geometries

Cartesian methods for computational fluid dynamics are considered to offer an accurate and robust approach for the simulation of aerodynamic flows around geometrically complex bodies. A part of the ongoing research in this domain is reviewed with the aim of providing insight into the fundamental challenges faced by the practitioners of this approach, and a guide to further research. The integration schemes used in Cartesian solvers are similar to those used in other approaches. The emphasis is on the geometric algorithms, surface modeling and boundary conditions required to design a successful Cartesian mesh scheme.

Aftosmis, Michael J.↗