Results for “mesh refinement” — Page 26

NASA NTRSDate not supplied

Near-Body Mesh Adaption for Transitional Flows Using OVERFLOW

Accurate modeling of boundary-layer transition is an important aspect of developing greener air transport technologies. In that regard, transition models based on auxiliary transport equations offer a robust approach that is easily integrated into the Reynolds-averaged Navier-Stokes (RANS) solvers. Recent workshops under NATO and AIAA have identified the verification of transport-equations-based transition modeling as a critical aspect of reducing the scatter between the predictions of different CFD codes. Follow-on work has highlighted the need for highly dense grids to achieve an asymptotic convergence of transition related flow metrics. The present work examines the role of automatic near-body mesh adaptation capability in the NASA OVERFLOW CFD solver to enable verification studies in an efficient manner, and for establishing best practices for designing grids for the RANS-based transition models. A sensor function relevant to the Langtry-Menter \gamma-Re_{\theta t}\ transition model has been identified and used for error-based mesh adaptation for canonical configurations comprising a flat plate, and the S809 and NLR-7301 airfoils. The efficacy of the mesh adaptation approach is assessed for flow conditions involving multiple transition scenarios such as natural transition, separation-induced transition, and shock-induced transition. The results from this exploratory study indicate that the meshes adapted using the proposed sensor provide solutions that approach the references solutions obtained with uniformly refined hand-crafted meshes, in terms of the chosen metrics, and yield modest yet significant savings in grid count. We also highlight areas for improvement in the grid adaptation methodology within OVERFLOW.

CFD↗

NASA NTRSDate not supplied

Near-Body Mesh Adaption for Transitional Flows Using OVERFLOW

Accurate modeling of boundary-layer transition is an important aspect of developing greener air transport technologies. In that regard, transition models based on auxiliary transport equations offer a robust approach that is easily integrated into the Reynolds-averaged Navier-Stokes (RANS) solvers. Recent workshops under NATO and AIAA have identified the verification of transport-equations-based transition modeling as a critical aspect of reducing the scatter between the predictions of different CFD codes. Follow-on work has highlighted the need for highly dense grids to achieve an asymptotic convergence of transition related flow metrics. The present work examines the role of automatic near-body mesh adaptation capability in the NASA OVERFLOW CFD solver to enable verification studies in an efficient manner, and for establishing best practices for designing grids for the RANS-based transition models. A sensor function relevant to the Langtry-Menter \gamma-Re_{\theta t}\ transition model has been identified and used for error-based mesh adaptation for canonical configurations comprising a flat plate, and the S809 and NLR-7301 airfoils. The efficacy of the mesh adaptation approach is assessed for flow conditions involving multiple transition scenarios such as natural transition, separation-induced transition, and shock-induced transition. The results from this exploratory study indicate that the meshes adapted using the proposed sensor provide solutions that approach the references solutions obtained with uniformly refined hand-crafted meshes, in terms of the chosen metrics, and yield modest yet significant savings in grid count. We also highlight areas for improvement in the grid adaptation methodology within OVERFLOW.

CFD↗

NASA NTRS2003

Toward Immersed Boundary Simulation of High Reynolds Number Flows

In the immersed boundary (IB) method, the surface of an object is reconstructed with forcing terms in the underlying flow field equations. The surface may split a computational cell removing the constraint of the near wall gridlines to be aligned with the surface. This feature greatly simplifies the grid generation process which is cumbersome and expensive in particular for structured grids and complex geometries. The IB method is ideally suited for Cartesian flow solvers. The flow equations written in Cartesian coordinates appear in a very simple form and several numerical algorithms can be used for an efficient solution of the equations. In addition, the accuracy of numerical algorithms is dependent on the underlying grid and it usually deteriorates when the grid deviates from a Cartesian mesh. The challenge for the IB method lies in the representation of the wall boundaries and in providing an adequate near wall flow field resolution. The issue of enforcing no-slip boundary conditions at the immersed surface has been addressed by several authors by imposing a local reconstruction of the solution. Initial work by Verzicco et al. was based on a simple linear, one-dimensional operator and this approach proved to be accurate for boundaries largely aligned with the grid lines. Majumdar et al. used various multidimensional and high order polynomial interpolations schemes. These high order schemes, however, are keen to introduce wiggles and spurious extrema. Iaccarino & Verzicco and Kalitzin & Iaccarino proposed a tri-linear reconstruction for the velocity components and the turbulent scalars. A modified implementation that has proven to be more robust is reported in this paper. The issue of adequate near wall resolution in a Cartesian framework can initially be addressed by using a non-uniform mesh which is stretched near the surface. In this paper, we investigate an unstructured approach for local grid refinement that utilizes Cartesian mesh features. The computation of high Reynolds number wall bounded flows is particularly challenging as it requires the consideration of thin turbulent boundary layers, i.e. near wall regions with large gradients of the flow field variables. For such flows, the representation of the wall boundary has a large impact on the accuracy of the computation. It is also critical for the robustness and convergence of the flow solver.

Kalitzin, Georgi↗

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 NTRS1998

PLUM: Parallel Load Balancing for Unstructured Adaptive Meshes

Dynamic mesh adaption on unstructured grids is a powerful tool for computing large-scale problems that require grid modifications to efficiently resolve solution features. By locally refining and coarsening the mesh to capture physical phenomena of interest, such procedures make standard computational methods more cost effective. Unfortunately, an efficient parallel implementation of these adaptive methods is rather difficult to achieve, primarily due to the load imbalance created by the dynamically-changing nonuniform grid. This requires significant communication at runtime, leading to idle processors and adversely affecting the total execution time. Nonetheless, it is generally thought that unstructured adaptive- grid techniques will constitute a significant fraction of future high-performance supercomputing. Various dynamic load balancing methods have been reported to date; however, most of them either lack a global view of loads across processors or do not apply their techniques to realistic large-scale applications.

Oliker, Leonid↗

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↗

NASA NTRS1999

High Order Approximations for Compressible Fluid Dynamics on Unstructured and Cartesian Meshes

The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining challenges facing the field of computational fluid dynamics. In structural mechanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the computation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order accuracy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence suggests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Center. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18, 1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25, 1998 at the NASA Ames Research Center in the United States. During this special course, lecturers from Europe and the United States gave a series of comprehensive lectures on advanced topics related to the high-order numerical discretization of partial differential equations with primary emphasis given to computational fluid dynamics (CFD). Additional consideration was given to topics in computational physics such as the high-order discretization of the Hamilton-Jacobi, Helmholtz, and elasticity equations. This volume consists of five articles prepared by the special course lecturers. These articles should be of particular relevance to those readers with an interest in numerical discretization techniques which generalize to very high-order accuracy. The articles of Professors Abgrall and Shu consider the mathematical formulation of high-order accurate finite volume schemes utilizing essentially non-oscillatory (ENO) and weighted essentially non-oscillatory (WENO) reconstruction together with upwind flux evaluation. These formulations are particularly effective in computing numerical solutions of conservation laws containing solution discontinuities. Careful attention is given by the authors to implementational issues and techniques for improving the overall efficiency of these methods. The article of Professor Cockburn discusses the discontinuous Galerkin finite element method. This method naturally extends to high-order accuracy and has an interpretation as a finite volume method. Cockburn addresses two important issues associated with the discontinuous Galerkin method: controlling spurious extrema near solution discontinuities via "limiting" and the extension to second order advective-diffusive equations (joint work with Shu). The articles of Dr. Henderson and Professor Schwab consider the mathematical formulation and implementation of the h-p finite element methods using hierarchical basis functions and adaptive mesh refinement. These methods are particularly useful in computing high-order accurate solutions containing perturbative layers and corner singularities. Additional flexibility is obtained using a mortar FEM technique whereby nonconforming elements are interfaced together. Numerous examples are given by Henderson applying the h-p FEM method to the simulation of turbulence and turbulence transition.

Barth, Timothy↗

DOE OSTI2024

Leveraging a Neural Network-Enhanced Reproducing Kernel Particle Method for Multiphysics Degradation Modeling of Energy Storage Materials

Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and resulting in reduced performance and service life. A coupled electro-chemo-mechanical reproducing kernel particle method (RKPM) formulation has been developed to analyze this system. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), pixel-based model construction by RKPM is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. Here, a neural network-enhanced reproducing kernel particle method (NN-RKPM) [1, 2] is introduced to effectively model damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RKPM is additionally used to inform how crack opening and closure in turn affect the coupled chemical equations and material microstructure. Reference: [1] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, pp 4422-4454, https://doi.org/10.1002/nme.7040, 2022. [2] Baek, J., Chen, J. S., "A Neural Network-Based Enrichment of Reproducing Kernel Approximation for Modeling Brittle Fracture", Computer Methods in Applied Mechanics and Engineering Vol. 410, 116590, 2024.

degradation↗

NASA NTRS2011

Numerical Implementation of a Multiple-ISV Thermodynamically-Based Work Potential Theory for Modeling Progressive Damage and Failure in Fiber-Reinforced Laminates

A thermodynamically-based work potential theory for modeling progressive damage and failure in fiber-reinforced laminates is presented. The current, multiple-internal state variable (ISV) formulation, enhanced Schapery theory (EST), utilizes separate ISVs for modeling the effects of damage and failure. Damage is considered to be the effect of any structural changes in a material that manifest as pre-peak non-linearity in the stress versus strain response. Conversely, failure is taken to be the effect of the evolution of any mechanisms that results in post-peak strain softening. It is assumed that matrix microdamage is the dominant damage mechanism in continuous fiber-reinforced polymer matrix laminates, and its evolution is controlled with a single ISV. Three additional ISVs are introduced to account for failure due to mode I transverse cracking, mode II transverse cracking, and mode I axial failure. Typically, failure evolution (i.e., post-peak strain softening) results in pathologically mesh dependent solutions within a finite element method (FEM) setting. Therefore, consistent character element lengths are introduced into the formulation of the evolution of the three failure ISVs. Using the stationarity of the total work potential with respect to each ISV, a set of thermodynamically consistent evolution equations for the ISVs is derived. The theory is implemented into commercial FEM software. Objectivity of total energy dissipated during the failure process, with regards to refinements in the FEM mesh, is demonstrated. The model is also verified against experimental results from two laminated, T800/3900-2 panels containing a central notch and different fiber-orientation stacking sequences. Global load versus displacement, global load versus local strain gage data, and macroscopic failure paths obtained from the models are compared to the experiments.

Pineda, Evan J.↗

NASA NTRS2012

A Thermodynamically-Based Mesh Objective Work Potential Theory for Predicting Intralaminar Progressive Damage and Failure in Fiber-Reinforced Laminates

A thermodynamically-based work potential theory for modeling progressive damage and failure in fiber-reinforced laminates is presented. The current, multiple-internal state variable (ISV) formulation, enhanced Schapery theory (EST), utilizes separate ISVs for modeling the effects of damage and failure. Damage is considered to be the effect of any structural changes in a material that manifest as pre-peak non-linearity in the stress versus strain response. Conversely, failure is taken to be the effect of the evolution of any mechanisms that results in post-peak strain softening. It is assumed that matrix microdamage is the dominant damage mechanism in continuous fiber-reinforced polymer matrix laminates, and its evolution is controlled with a single ISV. Three additional ISVs are introduced to account for failure due to mode I transverse cracking, mode II transverse cracking, and mode I axial failure. Typically, failure evolution (i.e., post-peak strain softening) results in pathologically mesh dependent solutions within a finite element method (FEM) setting. Therefore, consistent character element lengths are introduced into the formulation of the evolution of the three failure ISVs. Using the stationarity of the total work potential with respect to each ISV, a set of thermodynamically consistent evolution equations for the ISVs is derived. The theory is implemented into commercial FEM software. Objectivity of total energy dissipated during the failure process, with regards to refinements in the FEM mesh, is demonstrated. The model is also verified against experimental results from two laminated, T800/3900-2 panels containing a central notch and different fiber-orientation stacking sequences. Global load versus displacement, global load versus local strain gage data, and macroscopic failure paths obtained from the models are compared to the experiments.

Pineda, Evan J.↗

DOE OSTI2025

Multiphysics Meshfree Degradation Modeling of Energy Storage Materials with Kernel Enrichment

Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and ultimately diminishing performance and service life. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), pixel-based meshfree model construction by the reproducing kernel particle method (RKPM) is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. The first kernel enrichment discussed will be the interface modified reproducing kernel (IM-RK) [1, 2], constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. The IM-RK is especially useful for areas in which a known discontinuity-type is expected a priori. The second kernel enrichment to be discussed is a neural network-enhanced reproducing kernel (NN-RK) [3, 4], which is introduced to effectively model non-obvious damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RK is additionally used to inform how crack opening and closure in turn affect the electro-chemo-mechanical responses in the material microstructure. Reference: [1] Wang, Y., Baek, J., Tang, Y. et al. "Support vector machine guided reproducing kernel particle method for image-based modeling of microstructures," Comput Mech 73, 907-942 (2024). https://doi.org/10.1007/s00466-023-02394-9. [2] Susuki, K., Allen, J. & Chen, J. S.. "Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method," Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-02016-9. [3] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, 4422-4454 (2022). https://doi.org/10.1002/nme.7040.

25 ENERGY STORAGE↗

DOE OSTI2026

Kernel Enriched Meshfree Multiphysics Degradation Modeling of Energy Storage Materials

Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and ultimately diminishing performance and service life. With microstructural images supplied by the National Laboratory of the Rockies (NLR), pixel-based meshfree model construction by the reproducing kernel particle method (RKPM) is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. The first kernel enrichment discussed will be the interface modified reproducing kernel (IM-RK) [1, 2], constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. The IM-RK is especially useful for areas in which a known discontinuity-type is expected a priori. The second kernel enrichment to be discussed is a neural network-enhanced reproducing kernel (NN-RK) [3, 4], which is introduced to effectively model non-obvious damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RK is additionally used to inform how crack opening and closure in turn affect the electro-chemo-mechanical responses in the material microstructure. References: [1] Wang, Y., Baek, J., Tang, Y. et al. "Support vector machine guided reproducing kernel particle method for image-based modeling of microstructures," Comput Mech 73, 907-942 (2024). https://doi.org/10.1007/s00466-023-02394-9. [2] Susuki, K., Allen, J. & Chen, J. S.. "Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method," Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-02016-9. [3] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, 4422-4454 (2022). https://doi.org/10.1002/nme.7040.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1994

Development of an adaptive hp-version finite element method for computational optimal control

In this research effort, the usefulness of hp-version finite elements and adaptive solution-refinement techniques in generating numerical solutions to optimal control problems has been investigated. Under NAG-939, a general FORTRAN code was developed which approximated solutions to optimal control problems with control constraints and state constraints. Within that methodology, to get high-order accuracy in solutions, the finite element mesh would have to be refined repeatedly through bisection of the entire mesh in a given phase. In the current research effort, the order of the shape functions in each element has been made a variable, giving more flexibility in error reduction and smoothing. Similarly, individual elements can each be subdivided into many pieces, depending on the local error indicator, while other parts of the mesh remain coarsely discretized. The problem remains to reduce and smooth the error while still keeping computational effort reasonable enough to calculate time histories in a short enough time for on-board applications.

Hodges, Dewey H.↗

NASA NTRS1987

Computation of vortex sheet roll-up in the Trefftz plane

Two vortex-sheet evolution problems arising in aerodynamics are studied numerically. The approach is based on desingularizing the Cauchy principal value integral which defines the sheet's velocity. Numerical evidence is presented which indicates that the approach converges with respect to refinement in the mesh-size and the smoothing parameter. For elliptic loading, the computed roll-up is in good agreement with Kaden's asymptoic spiral at early times. Some aspects of the solution's instability to short-wavelength perturbations, for a small value of the smoothing parameter, are inferred by comparing calculations performed with different levels of computer round-off error. The tip vortices' deformation, due to their mutual interaction, is shown in a long-time calculation. Computations for a simulated fuselage-flap configuration show a complicated process of roll-up, deformation and interaction involving the tip vortex and the inboard neighboring vortices.

Krasny, Robert↗

NASA NTRS1993

Parallel-Vector Algorithm For Rapid Structural Anlysis

New algorithm developed to overcome deficiency of skyline storage scheme by use of variable-band storage scheme. Exploits both parallel and vector capabilities of modern high-performance computers. Gives engineers and designers opportunity to include more design variables and constraints during optimization of structures. Enables use of more refined finite-element meshes to obtain improved understanding of complex behaviors of aerospace structures leading to better, safer designs. Not only attractive for current supercomputers but also for next generation of shared-memory supercomputers.

Agarwal, Tarun R.↗

NASA NTRS1993

Advanced adaptive computational methods for Navier-Stokes simulations in rotorcraft aerodynamics

A phase 2 research and development effort was conducted in area transonic, compressible, inviscid flows with an ultimate goal of numerically modeling complex flows inherent in advanced helicopter blade designs. The algorithms and methodologies therefore are classified as adaptive methods, which are error estimation techniques for approximating the local numerical error, and automatically refine or unrefine the mesh so as to deliver a given level of accuracy. The result is a scheme which attempts to produce the best possible results with the least number of grid points, degrees of freedom, and operations. These types of schemes automatically locate and resolve shocks, shear layers, and other flow details to an accuracy level specified by the user of the code. The phase 1 work involved a feasibility study of h-adaptive methods for steady viscous flows, with emphasis on accurate simulation of vortex initiation, migration, and interaction. Phase 2 effort focused on extending these algorithms and methodologies to a three-dimensional topology.

Stowers, S. T.↗

NASA NTRS1993

Three-dimensional unstructured grid refinement and optimization using edge-swapping

This paper presents a three-dimensional (3-D) 'edge-swapping method based on local transformations. This method extends Lawson's edge-swapping algorithm into 3-D. The 3-D edge-swapping algorithm is employed for the purpose of refining and optimizing unstructured meshes according to arbitrary mesh-quality measures. Several criteria including Delaunay triangulations are examined. Extensions from two to three dimensions of several known properties of Delaunay triangulations are also discussed.

Gandhi, Amar↗

NASA NTRS2000

Radiation Heat Transfer Between Diffuse-Gray Surfaces Using Higher Order Finite Elements

This paper presents recent work on developing methods for analyzing radiation heat transfer between diffuse-gray surfaces using p-version finite elements. The work was motivated by a thermal analysis of a High Speed Civil Transport (HSCT) wing structure which showed the importance of radiation heat transfer throughout the structure. The analysis also showed that refining the finite element mesh to accurately capture the temperature distribution on the internal structure led to very large meshes with unacceptably long execution times. Traditional methods for calculating surface-to-surface radiation are based on assumptions that are not appropriate for p-version finite elements. Two methods for determining internal radiation heat transfer are developed for one and two-dimensional p-version finite elements. In the first method, higher-order elements are divided into a number of sub-elements. Traditional methods are used to determine radiation heat flux along each sub-element and then mapped back to the parent element. In the second method, the radiation heat transfer equations are numerically integrated over the higher-order element. Comparisons with analytical solutions show that the integration scheme is generally more accurate than the sub-element method. Comparison to results from traditional finite elements shows that significant reduction in the number of elements in the mesh is possible using higher-order (p-version) finite elements.

Gould, Dana C.↗