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All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Survey of Volumetric Grid Generators

This document is the result of an Internet Survey of Volumetric grid generators. As such we have included information from only the responses which were sent to us. After the initial publication and posting of this survey, we would encourage authors and users of grid generators to send further information. Here is the initial query posted to SIGGRID@nas and the USENET group sci.physics.computational.fluid-dynamics. Date: Sun, 30 Jan 94 11:37:52 -0800 From: woo (Alex Woo x6010 227-6 rm 315) Subject: Info Sought for Survey of Grid Generators I am collecting information and reviews of both government sponsored and commercial mesh generators for large scientific calculations, both block structured and unstructured. If you send me a review of a mesh generator, please indicate its availability and cost. If you are a commercial concern with information on a product, please also include references for possible reviewers. Please email to woo@ra-next.arc.nasa.gov. I will post a summary and probably write a short note for the IEEE Antennas and Propagation Magazine. Alex Woo, MS 227-6 woo@ames.arc.nasa.gov NASA Ames Research Center NASAMAIL ACWOO Moffett Field, CA 94035-1000 SPANET 24582::W00 (415) 604-6010 (FAX) 604-4357 fhplabs,decwrl,uunet)!ames!woo Disclaimer: These are not official statements of NASA or EMCC. We did not include all the submitted text here. Instead we have created a database entry in the freely available and widely used BIBTeX format which has an Uniform Resource Locator (URL) field pointing to more details. The BIBTeX database is modeled after those available from the BIBNET project at University of Utah.

Woo, Alex↗
NASA NTRS1991

Generation and use of unstructured grids for turbomachinery calculations

A wavefront mesh generator for two dimensional triangular meshes as well as a brief description of the solution method used with these meshes are presented. The interest is in creating meshes for solving the equations of fluid mechanics in complex turbomachinery problems, although the mesh generator and flow solver may be used for a larger variety of applications. The focus is on the flexibility and power of the mesh generation method for triangulating extremely complex geometries and in changing the geometry to create a new mesh. Two turbomachinery applications are presented which take advantage of this method: the analysis of pylon/strut and pylon/OGV interaction in the bypass of a turbofan.

Lindquist, Dana R.↗
NASA NTRSDate not supplied

Recent Progress on Rans-Based Transition Model Verification

The current efforts to assess and improve the Reynolds-averaged Navier-Stokes (RANS)-coupled transition models in the NASA FUN3D and OVERFLOW codes are summarized in this study. The first AIAA Transition Modeling Workshop and the NATO AVT-313 Transition Workshop both emphasized the need for code verification for transport equations based transition models as a top priority. We discuss the methods used for the model verification, the resulting grid families, the flow solutions, and other supporting information collected with at least two established NASA flow solvers, namely, FUN3D and OVERFLOW. These results, which will be uploaded onto the NASA Turbulence Modeling Resource, should assist other members of the computational fluid dynamics (CFD) community in verifying their own implementations of various transition models, such as the Langtry-Menter (LM2009) model, the one-equation γ model, and Coder’s amplification factor transport (AFT) model. Grid convergence is assessed using both global and local flow metrics of interest such as lift and drag as well as local skin-friction coefficients. We also explore the anisotropic unstructured metric-based adaptive mesh refinement library known as refine with the NASA FUN3D solver to determine if this capability can achieve the same accuracy as handcrafted structured grids with a significantly smaller node count and to learn the characteristics of the resulting grid distribution, especially in the vicinity of the transition zone.

Transition↗
NASA NTRSDate not supplied

Recent Progress on RANS-Based Transition Model Verification

The current efforts to assess and improve the Reynolds-averaged Navier-Stokes (RANS)-coupled transition models in the NASA FUN3D and OVERFLOW codes are summarized in this study. The first AIAA Transition Modeling Workshop and the NATO AVT-313 Transition Workshop both emphasized the need for code verification for transport equations based transition models as a top priority. We discuss the methods used for the model verification, the resulting grid families, the flow solutions, and other supporting information collected with at least two established NASA flow solvers, namely, FUN3D and OVERFLOW. These results, which will be uploaded onto the NASA Turbulence Modeling Resource, should assist other members of the computational fluid dynamics (CFD) community in verifying their own implementations of various transition models, such as the Langtry-Menter (LM2009) model, the one-equation γ model, and Coder’s amplification factor transport (AFT) model. Grid convergence is assessed using both global and local flow metrics of interest such as lift and drag as well as local skin-friction coefficients. We also explore the anisotropic unstructured metric-based adaptive mesh refinement library known as refine with the NASA FUN3D solver to determine if this capability can achieve the same accuracy as handcrafted structured grids with a significantly smaller node count and to learn the characteristics of the resulting grid distribution, especially in the vicinity of the transition zone.

RANS↗
NASA NTRS1993

Dynamic mesh adaption for triangular and tetrahedral grids

The following topics are discussed: requirements for dynamic mesh adaption; linked-list data structure; edge-based data structure; adaptive-grid data structure; three types of element subdivision; mesh refinement; mesh coarsening; additional constraints for coarsening; anisotropic error indicator for edges; unstructured-grid Euler solver; inviscid 3-D wing; and mesh quality for solution-adaptive grids. The discussion is presented in viewgraph form.

Rupak Biswas↗
DOE OSTI2021

An unstructured C-grid type variational formulation for the sea ice dynamics

Historically, B-grid formulations of sea ice dynamics have been dominant because they have matched the grid type used by ocean models. The reason for the grid match is simple – it facilitates penetration of the curl of ice-ocean stress into the deep ocean with minimal numerical diffusivity because sea ice and ocean velocity are co-located. In recent years, as ocean models have increasingly progressed to C-grids, sea ice models have followed suit on quadrilateral meshes, but the implementation of an unstructured C-grid sea ice models is new. We present an unstructured C-grid discretization of the Elastic Viscous Plastic (EVP) rheology, where the velocity unknowns are discretized at the edges of the mesh cells with n-sides, where typically n is greater than or equal to four, rather than at the vertices, as in the B-grid. Our framework of choice is the Model for Prediction Across Scales (MPAS) within E3SM, the climate model of the U.S. Department of Energy, although our approach is general and could be applied to other models as well. While MPAS-Seaice is currently defined on a B-grid, MPAS-Ocean runs on a C-grid, hence interpolation operators are heavily used when coupled simulations are performed. In this work, we describe a mathematical formulation to transition the dynamics of MPAS-Seaice to a C-grid, in order to ultimately facilitate the coupling with MPAS-Ocean and reduce numerical errors associated with this communication. Numerical results are reported to highlight the features of the method.

58 GEOSCIENCES↗
NASA NTRS2007

Summary of the Third AIAA CFD Drag Prediction Workshop

The workshop focused on the prediction of both absolute and differential drag levels for wing-body and wing-al;one configurations of that are representative of transonic transport aircraft. The baseline DLR-F6 wing-body geometry, previously utilized in DPW-II, is also augmented with a side-body fairing to help reduce the complexity of the flow physics in the wing-body juncture region. In addition, two new wing-alone geometries have been developed for the DPW-II. Numerical calculations are performed using industry-relevant test cases that include lift-specific and fixed-alpha flight conditions, as well as full drag polars. Drag, lift, and pitching moment predictions from previous Reynolds-Averaged Navier-Stokes computational fluid Dynamics Methods are presented, focused on fully-turbulent flows. Solutions are performed on structured, unstructured, and hybrid grid systems. The structured grid sets include point-matched multi-block meshes and over-set grid systems. The unstructured and hybrid grid sets are comprised of tetrahedral, pyramid, and prismatic elements. Effort was made to provide a high-quality and parametrically consistent family of grids for each grid type about each configuration under study. The wing-body families are comprised of a coarse, medium, and fine grid, while the wing-alone families also include an extra-fine mesh. These mesh sequences are utilized to help determine how the provided flow solutions fair with respect to asymptotic grid convergence, and are used to estimate an absolute drag of each configuration.

Vassberg, John C.↗
NASA NTRS2010

Summary of the Fourth AIAA CFD Drag Prediction Workshop

Results from the Fourth AIAA Drag Prediction Workshop (DPW-IV) are summarized. The workshop focused on the prediction of both absolute and differential drag levels for wing-body and wing-body-horizontal-tail configurations that are representative of transonic transport air- craft. Numerical calculations are performed using industry-relevant test cases that include lift- specific flight conditions, trimmed drag polars, downwash variations, dragrises and Reynolds- number effects. Drag, lift and pitching moment predictions from numerous Reynolds-Averaged Navier-Stokes computational fluid dynamics methods are presented. Solutions are performed on structured, unstructured and hybrid grid systems. The structured-grid sets include point- matched multi-block meshes and over-set grid systems. The unstructured and hybrid grid sets are comprised of tetrahedral, pyramid, prismatic, and hexahedral elements. Effort is made to provide a high-quality and parametrically consistent family of grids for each grid type about each configuration under study. The wing-body-horizontal families are comprised of a coarse, medium and fine grid; an optional extra-fine grid augments several of the grid families. These mesh sequences are utilized to determine asymptotic grid-convergence characteristics of the solution sets, and to estimate grid-converged absolute drag levels of the wing-body-horizontal configuration using Richardson extrapolation.

Vassberg, John C.↗
DOE OSTI2020

Compare linear-system solver and preconditioner stacks with emphasis on GPU performance and propose phase-2 NGP solver development pathway

The goal of the ExaWind project is to enable predictive simulations of wind farms comprised of many megawatt-scale turbines situated in complex terrain. Predictive simulations will require computational fluid dynamics (CFD) simulations for which the mesh resolves the geometry of the turbines and captures the rotation and large deflections of blades. Whereas such simulations for a single turbine are arguably petascale class, multi-turbine wind farm simulations will require exascale-class resources. The primary physics codes in the ExaWind project are Nalu-Wind, which is an unstructured-grid solver for the acoustically incompressible Navier-Stokes equations, and OpenFAST, which is a whole-turbine simulation code. The Nalu-Wind model consists of the mass-continuity Poisson-type equation for pressure and a momentum equation for the velocity. For such modeling approaches, simulation times are dominated by linear-system setup and solution for the continuity and momentum systems. For the ExaWind challenge problem, the moving meshes greatly affect overall solver costs as reinitialization of matrices and recomputation of preconditioners is required at every time step. In this report we evaluated GPU-performance baselines for the linear solvers in the Trilinos and hypre solver stacks using two representative Nalu-Wind simulations: an atmospheric boundary layer precursor simulation on a structured mesh, and a fixed-wing simulation using unstructured overset meshes. Both strong-scaling and weak-scaling experiments were conducted on the OLCF supercomputer Summit and similar proxy clusters. We focused on the performance of multi-threaded Gauss-Seidel and two-stage Gauss-Seidel that are extensions of classical Gauss-Seidel; of one-reduce GMRES, a communication-reducing variant of the Krylov GMRES; and algebraic multigrid methods that incorporate the afore-mentioned methods. The team has established that AMG methods are capable of solving linear systems arising from the fixed-wing overset meshes on CPU, a critical intermediate result for ExaWind FY20 Q3 and Q4 milestones. For the fixed-wing strong-scaling study (model with 3M grid-points), the team identified that Nalu-Wind simulations with the new Trilinos and hypre solvers scale to modest GPU counts, maintaining above 70% efficiency up to 6 GPUs. However, there still remain significant bottlenecks to performance: matrix assembly (hypre), AMG setup (hypre and Trilinos) In the weak-scaling experiments (going from 0.4M to 211M gridpoints), it's shown that the solver apply phases are faster on GPUs, but that Nalu-Wind simulation times grow, primarily due to the multigrid-setup process. Finally, based on the report outcomes, we propose a linear solver path-forward for the remainder of the ExaWind project. Near term, the NREL team will continue their work on GPU-based linear-system assembly. They will also investigate how the use of alternatives to the NVIDIA UVM (unified virtual memory) paradigm affects performance. Longer term, the NREL team will evaluate algorithmic performance on other types of accelerators and merge their improvements back to the main hypre repository branch. Near term, the Trilinos team will address performance bottlenecks identified in this milestone, such as implementing a GPU-based segregated momentum solve and reusing matrix graphs across linear-system assembly phases. Longer term, the Trilinos team will do detailed analysis and optimization of multigrid setup.

17 WIND ENERGY↗
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 NTRS1995

Grid generation and surface modeling for CFD

When computing the flow around complex three dimensional configurations, the generation of the mesh is the most time consuming part of any calculation. With some meshing technologies this can take of the order of a man month or more. The requirement for a number of design iterations coupled with ever decreasing time allocated for design leads to the need for a significant acceleration of this process. Of the two competing approaches, block-structured and unstructured, only the unstructured approach will allow fully automatic mesh generation directly from a CAD model. Using this approach coupled with the techniques described in this paper, it is possible to reduce the mesh generation time from man months to a few hours on a workstation. The desire to closely couple a CFD code with a design or optimization algorithm requires that the changes to the geometry be performed quickly and in a smooth manner. This need for smoothness necessitates the use of Bezier polynomials in place of the more usual NURBS or cubic splines. A two dimensional Bezier polynomial based design system is described.

Connell, Stuart D.↗
NASA NTRS2006

Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry

Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach. Thereafter, we focus on a shape optimization problem for an Apollo-like reentry capsule. The optimization seeks to enhance the lift-to-drag ratio of the capsule by modifyjing the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design. This abstract presents only a brief outline of the numerical method and results; full details will be given in the final paper.

Nemec, Marian↗
NASA NTRS1995

Coarsening strategies for unstructured multigrid techniques with application to anisotropic problems

Over the years, multigrid has been demonstrated as an efficient technique for solving inviscid flow problems. However, for viscous flows, convergence rates often degrade. This is generally due to the required use of stretched meshes (i.e., the aspect-ratio AR = delta y/delta x is much less than 1) in order to capture the boundary layer near the body. Usual techniques for generating a sequence of grids that produce proper convergence rates on isotopic meshes are not adequate for stretched meshes. This work focuses on the solution of Laplace's equation, discretized through a Galerkin finite-element formulation on unstructured stretched triangular meshes. A coarsening strategy is proposed and results are discussed.

Morano, E.↗
NASA NTRS1996

Coarsening Strategies for Unstructured Multigrid Techniques with Application to Anisotropic Problems

Over the years, multigrid has been demonstrated as an efficient technique for solving inviscid flow problems. However, for viscous flows, convergence rates often degrade. This is generally due to the required use of stretched meshes (i.e. the aspect-ratio AR = (delta)y/(delta)x much less than 1) in order to capture the boundary layer near the body. Usual techniques for generating a sequence of grids that produce proper convergence rates on isotropic meshes are not adequate for stretched meshes. This work focuses on the solution of Laplace's equation, discretized through a Galerkin finite-element formulation on unstructured stretched triangular meshes. A coarsening strategy is proposed and results are discussed.

Morano, E.↗
NASA NTRS2009

Discrete Adjoint-Based Design Optimization of Unsteady Turbulent Flows on Dynamic Unstructured Grids

An adjoint-based methodology for design optimization of unsteady turbulent flows on dynamic unstructured grids is described. The implementation relies on an existing unsteady three-dimensional unstructured grid solver capable of dynamic mesh simulations and discrete adjoint capabilities previously developed for steady flows. The discrete equations for the primal and adjoint systems are presented for the backward-difference family of time-integration schemes on both static and dynamic grids. The consistency of sensitivity derivatives is established via comparisons with complex-variable computations. The current work is believed to be the first verified implementation of an adjoint-based optimization methodology for the true time-dependent formulation of the Navier-Stokes equations in a practical computational code. Large-scale shape optimizations are demonstrated for turbulent flows over a tiltrotor geometry and a simulated aeroelastic motion of a fighter jet.

Nielsen, Eric J.↗
NASA NTRS1992

Cartesian based grid generation/adaptive mesh refinement

Grid adaptation has recently received attention in the computational fluid dynamics (CFD) community as a means to capture the salient features of a flowfield by either moving grid points of a structured or by adding cells in an unstructured manner. An approach based on a background cartesian mesh is investigated from which the geometry is 'cut' out of the mesh. Once the mesh is obtained, a solution on this coarse grid is found, that indicates which cells need to be refined. This process of refining/solving continues until the flow is grid refined in terms of a user specified global parameter (such as drag coefficient etc.). The advantages of this approach are twofold: the generation of the base grid is independent of the topology of the bodies or surfaces around/through which the flow is to be computed, and the resulting grid (in uncut regions) is highly isotropic, so that the truncation error is low. The flow solver (which, along with the grid generation is still under development) uses a completely unstructured data base, and is a finite volume, upwinding scheme. Current and future work will address generating Navier-Stokes suitable grids by using locally aligned and normal face/cell refining. The attached plot shows a simple grid about two turbine blades.

Coirier, William J.↗
NASA NTRS1991

Parallel unstructured grid generation

A parallel unstructured grid generation algorithm is presented and implemented on the Hypercube. Different processor hierarchies are discussed, and the appropraite hierarchies for mesh generation and mesh smoothing are selected. A domain-splitting algorithm for unstructured grids which tries to minimize the surface-to-volume ratio of each subdomain is described. This splitting algorithm is employed both for grid generation and grid smoothing. Results obtained on the Hypercube demonstrate the effectiveness of the algorithms developed.

Loehner, Rainald↗
DOE OSTI2021

An efficient reconstruction algorithm for diffusion on triangular grids using the nodal discontinuous Galerkin method

High-energy-density (HED) hydrodynamics studies such as those relevant to inertial confinement fusion and astrophysics require highly disparate densities, temperatures, viscosities, and other diffusion parameters over relatively short spatial scales. This presents a challenge for high-order accurate methods to effectively resolve the hydrodynamics at these scales, particularly in the presence of highly disparate diffusion. A significant volume of engineering and physics applications use an unstructured discontinuous Galerkin (DG) method developed based on the finite element mesh generation and algorithmic framework. This work discusses the application of an affine reconstructed nodal DG method for unstructured grids of triangles. Solving the diffusion terms in the DG method is non-trivial due to the solution representations being piecewise continuous. Hence, the diffusive flux is not defined on the interface of elements. The proposed numerical approach reconstructs a smooth solution in a parallelogram that is enclosed by the quadrilateral formed by two adjacent triangle elements. The interface between these two triangles is the diagonal of the enclosed parallelogram. Similar to triangles, the mapping of parallelograms from a physical domain to a reference domain is an affine mapping, which is necessary for an accurate and efficient implementation of the numerical algorithm. Thus, all computations can still be performed on the reference domain, which promotes efficiency in computation and storage. This reconstruction does not make assumptions on choice of polynomial basis. Reconstructed DG algorithms have previously been developed for modal implementations of the convection–diffusion equations. However, to the best of the authors’ knowledge, this is the first practical guideline that has been proposed for applying the reconstructed algorithm on a nodal discontinuous Galerkin method with a focus on accuracy and efficiency. As a result, the algorithm is demonstrated on a number of benchmark cases as well as a challenging substantive problem in HED hydrodynamics with highly disparate diffusion parameters.

Computational efficiency↗