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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Multigrid solution of the Navier-Stokes equations on triangular meshes

A Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite element Galerkin approximation, which can be shown to be equivalent to a finite volume approximation for regular equilateral triangular meshes. Integration steady-state is performed using a multistage time-stepping scheme, and convergence is accelerated by means of implicit residual smoothing and an unstructured multigrid algorithm. Directional scaling of the artificial dissipation and the implicit residual smoothing operator is achieved for unstructured meshes by considering local mesh stretching vectors at each point. The accuracy of the scheme for highly stretched triangular meshes is validated by comparing computed flat-plate laminar boundary layer results with the well known similarity solution, and by comparing laminar airfoil results with those obtained from various well-established structured quadrilateral-mesh codes. The convergence efficiency of the present method is also shown to be competitive with those demonstrated by structured quadrilateral-mesh algorithms.

Mavriplis, D. J.↗
NASA NTRS2012

Effects of Mesh Irregularities on Accuracy of Finite-Volume Discretization Schemes

The effects of mesh irregularities on accuracy of unstructured node-centered finite-volume discretizations are considered. The focus is on an edge-based approach that uses unweighted least-squares gradient reconstruction with a quadratic fit. For inviscid fluxes, the discretization is nominally third order accurate on general triangular meshes. For viscous fluxes, the scheme is an average-least-squares formulation that is nominally second order accurate and contrasted with a common Green-Gauss discretization scheme. Gradient errors, truncation errors, and discretization errors are separately studied according to a previously introduced comprehensive methodology. The methodology considers three classes of grids: isotropic grids in a rectangular geometry, anisotropic grids typical of adapted grids, and anisotropic grids over a curved surface typical of advancing layer grids. The meshes within the classes range from regular to extremely irregular including meshes with random perturbation of nodes. Recommendations are made concerning the discretization schemes that are expected to be least sensitive to mesh irregularities in applications to turbulent flows in complex geometries.

Diskin, Boris↗
NASA NTRS1989

Multigrid solution of the Navier-Stokes equations on triangular meshes

A new Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite-element Galerkin approximation, which can be shown to be equivalent to a finite-volume approximation for regular equilateral triangular meshes. Integration to steady-state is performed using a multistage time-stepping scheme, and convergence is accelerated by means of implicit residual smoothing and an unstructured multigrid algorithm. The convergence efficiency of the present method is shown to be competitive with those demonstrated by structured quadrilateral-mesh algorithms.

Mavriplis, D. J.↗
NASA NTRS1988

Generation of a crowned pinion tooth surface by a surface of revolution

A method of generating crowned pinion tooth surfaces using a surface of revolution is developed. The crowned pinion meshes with a regular involute gear and has a prescribed parabolic type of transmission errors when the gears operate in the aligned mode. When the gears are misaligned the transmission error remains parabolic with the maximum level still remaining very small (less than 0.34 arc sec for the numerical examples). Tooth contact analysis (TCA) is used to simulate the conditions of meshing, determine the transmission error, and determine the bearing contact.

Litvin, F. L.↗
NASA NTRS1988

Crowned spur gears - Methods for generation and Tooth Contact Analysis. II - Generation of the pinion tooth surface by a surface of revolution

A method for generation of crowned pinion tooth surfaces using a surface of revolution is developed. The crowned pinion meshes with a regular involute gear and has a prescribed parabolic type of transmission errors when the gears operate in the aligned mode. When the gears are misaligned the transmission error remains parabolic with the maximum level still remaining very small (less than 0.34 arc second for the numerical examples). Tooth Contact Analysis (TCA) is used to simulate the conditions of meshing, determine the transmission error, and the bearing contact.

Litvin, F. L.↗
NASA NTRS1992

Three-dimensional boundary layer calculation by a characteristic method

A numerical method for solving the three-dimensional boundary layer equations for bodies of arbitrary shape is presented. In laminar flows, the application domain extends from incompressible to hypersonic flows with the assumption of chemical equilibrium. For turbulent boundary layers, the application domain is limited by the validity of the mixing length model used. In order to respect the hyperbolic nature of the equations reduced to first order partial derivative terms, the momentum equations are discretized along the local streamlines using of the osculator tangent plane at each node of the body fitted coordinate system. With this original approach, it is possible to overcome the use of the generalized coordinates, and therefore, it is not necessary to impose an extra hypothesis about the regularity of the mesh in which the boundary conditions are given. By doing so, it is possible to limit, and sometimes to suppress, the pre-treatment of the data coming from an inviscid calculation. Although the proposed scheme is only semi-implicit, the method remains numerically very efficient.

Houdeville, R.↗
NASA NTRS1991

Design of an essentially non-oscillatory reconstruction procedure on finite-element type meshes

An essentially non-oscillatory reconstruction for functions defined on finite-element type meshes was designed. Two related problems are studied: the interpolation of possibly unsmooth multivariate functions on arbitrary meshes and the reconstruction of a function from its average in the control volumes surrounding the nodes of the mesh. Concerning the first problem, we have studied the behavior of the highest coefficients of the Lagrange interpolation function which may admit discontinuities of locally regular curves. This enables us to choose the best stencil for the interpolation. The choice of the smallest possible number of stencils is addressed. Concerning the reconstruction problem, because of the very nature of the mesh, the only method that may work is the so called reconstruction via deconvolution method. Unfortunately, it is well suited only for regular meshes as we show, but we also show how to overcome this difficulty. The global method has the expected order of accuracy but is conservative up to a high order quadrature formula only. Some numerical examples are given which demonstrate the efficiency of the method.

Abgrall, R.↗
NASA NTRS2019

A Multiscale Nonlocal Progressive Damage Model for Composite Materials

In this paper, the advantages of a nonlocal progressive damage formulation are described and demonstrated. An approximation of the nonlocal formulation was implemented coupled with the MAT162 composite damage model as a User defined material model in the LS DYNA environment. A comparison of the local model and the nonlocal model is simulated for an 8-ply laminate under tension is carried for increasing mesh densities. The results show the regularization achieved by nonlocal models by providing mesh independent results.

Kodagali, Karan↗
DOE OSTI2025

An FFT-based micromechanical model for gradient enhanced brittle fracture

Damage models incorporated within FFT-based micromechanical methods have received much attention recently because of the need to better understand and predict brittle and ductile fracture. An important aspect of a damage model is non-local regularization, which removes the mesh dependence of the predictions that otherwise become physically unacceptable upon grid refinement. In this work, the Helmholtz-type equation for non-local gradient regularization of a damage model on a distorted grid is solved using an FFT-based approach. Further, the resulting system of equations is solved using the Jacobi iterative method. The model is applied to simulate brittle fracture of an intermetallic. The influence of the time and space discretization, the length-scale parameter, and intermetallic crystallographic orientation on crack evolution is studied.

36 MATERIALS SCIENCE↗
NASA NTRS1980

Effect of grid system on finite element calculation

Detailed parametric studies of the effect of grid system on finite element calculation for potential flows were made. These studies led to the formulation of a design criteria for optimum mesh system and the development of two methods to generate the optimum mesh system. The guidelines for optimum mesh system are: (1) the mesh structure should be regular; (2) the element should be as regular and equilateral as possible; (3) the distribution of size of element should be consistent with that of flow variables to insure maximum uniformity in error distribution; (4) for non-Dirichlet boundary conditions, smaller boundary elements or higher order interpolation functions should be used; and (5) the mesh should accommodate the boundary geometry as accurately as possible. The results of the parametric studies are presented.

Lee, K. D.↗
DOE OSTI2026

PyHydroGeophysX: An extensible open-source platform for integrating hydrological models with geophysical measurements

Hydrological models and geophysical measurements are widely used tools for understanding subsurface hydrological processes relevant to water resource management, yet they typically remain disconnected due to technical barriers. We present PyHydroGeophysX, an open-source Python platform bridging this gap by providing standardized interfaces between hydrological modeling software (MODFLOW, ParFlow) and geophysical simulation tools (PyGIMLi, SimPEG). The platform implements bidirectional workflows: translating hydrological outputs into simulated geophysical responses through petrophysical models, and extracting hydrological information from geophysical inversions. Key features include bidirectional workflow modules, configurable petrophysical models, time-lapse inversion with temporal regularization, parallel computing, and mesh utilities for property transfer between geophysical and hydrological grids. The modular architecture of PyHydroGeophysX enables researchers to incorporate additional models and methods, fostering broader adoption of integrated hydrogeophysical approaches. The software is freely available on GitHub and is intended for researchers and practitioners working at the intersection of hydrology and geophysics.

Hydrogeophysics↗
NASA NTRS2003

Solution-Adaptive Program for Computing 2D/Axi Viscous Flow

A computer program solves the Navier- Stokes equations governing the flow of a viscous, compressible fluid in an axisymmetric or two-dimensional (2D) setting. To obtain solutions more accurate than those generated by prior such programs that utilize regular and/or fixed computational meshes, this program utilizes unstructured (that is, irregular triangular) computational meshes that are automatically adapted to solutions. The adaptation can refine to regions of high change in gradient or can be driven by a novel residual minimization technique. Starting from an initial mesh and a corresponding data structure, the adaptation of the mesh is controlled by use of minimization functional. Other improvements over prior such programs include the following: (1) Boundary conditions are imposed weakly; that is, following initial specification of solution values at boundary nodes, these values are relaxed in time by means of the same formulations as those used for interior nodes. (2) Eigenvalues are limited in order to suppress expansion shocks. (3) An upwind fluctuation-splitting distribution scheme applied to inviscid flux requires fewer operations and produces less artificial dissipation than does a finite-volume scheme, leading to greater accuracy of solutions.

Wood, William A.↗
DOE OSTI2026

PDE-constrained high-order mesh optimization

Here, we present a novel framework for PDE-constrained r-adaptivity of high-order meshes. The proposed method formulates mesh movement as an optimization problem, with an objective function defined as a convex combination of a mesh quality metric and a measure of the accuracy of the PDE solution obtained via finite element discretization. The proposed formulation achieves optimized, well-defined high-order meshes by integrating mesh quality control, PDE solution accuracy, and robust gradient regularization. We adopt the Target-Matrix Optimization Paradigm to control geometric properties across the mesh, independent of the PDE of interest. To incorporate the accuracy of the PDE solution, we introduce error measures that control the finite element discretization error. The implicit dependence of these error measures on the mesh nodal positions is accurately captured by adjoint sensitivity analysis. Additionally, a convolution-based gradient regularization strategy is used to ensure stable and effective adaptation of high-order meshes. We demonstrate that the proposed framework can improve mesh quality and reduce the error by up to 10 times for the solution of Poisson and linear elasto-static problems. The approach is general with respect to the dimensionality, the order of the mesh, the types of mesh elements, and can be applied to any PDE that admits well-defined adjoint operators.

Computer science↗
NASA NTRS1974

A finite element solution algorithm for the Navier-Stokes equations

A finite element solution algorithm is established for the two-dimensional Navier-Stokes equations governing the steady-state kinematics and thermodynamics of a variable viscosity, compressible multiple-species fluid. For an incompressible fluid, the motion may be transient as well. The primitive dependent variables are replaced by a vorticity-streamfunction description valid in domains spanned by rectangular, cylindrical and spherical coordinate systems. Use of derived variables provides a uniformly elliptic partial differential equation description for the Navier-Stokes system, and for which the finite element algorithm is established. Explicit non-linearity is accepted by the theory, since no psuedo-variational principles are employed, and there is no requirement for either computational mesh or solution domain closure regularity. Boundary condition constraints on the normal flux and tangential distribution of all computational variables, as well as velocity, are routinely piecewise enforceable on domain closure segments arbitrarily oriented with respect to a global reference frame.

Baker, A. J.↗
NASA NTRS1974

Finite element solution algorithm for incompressible fluid dynamics

A finite element solution algorithm is established for the two-dimensional Navier-Stokes equations governing the transient motion of a viscous incompressible fluid, i.e., hydrodynamics. Dependent variable transformation renders the differential equation description uniformly elliptic. The finite element algorithm is established using the Galerkin criterion on a local basis within the Method of Weighted Residuals. It is unconstrained with respect to system linearity, computational mesh uniformity or solution domain closure regularity. The finite element matrices are established using a linear 'natural coordinate function' description. Computational solutions using the COMOC computer program illustrate the various features of the algorithm including recirculating flows.

Baker, A. J.↗
NASA NTRS1987

Octree based automatic meshing from CSG models

Finite element meshes derived automatically from solid models through recursive spatial subdivision schemes (octrees) can be made to inherit the hierarchical structure and the spatial addressability intrinsic to the underlying grid. These two properties, together with the geometric regularity that can also be built into the mesh, make octree based meshes ideally suited for efficient analysis and self-adaptive remeshing and reanalysis. The element decomposition of the octal cells that intersect the boundary of the domain is emphasized. The problem, central to octree based meshing, is solved by combining template mapping and element extraction into a procedure that utilizes both constructive solid geometry and boundary respresentation techniques. Boundary cells that are not intersected by the edge of the domain boundary are easily mapped to predefined element topology. Cells containing edges (and vertices) are first transformed into a planar polyhedron and then triangulated via element extractors. The modeling environments required for the derivation of planar polyhedra and for element extraction are analyzed.

Perucchio, Renato↗
NASA NTRS1987

Geometrical and topological issues in octree based automatic meshing

Finite element meshes derived automatically from solid models through recursive spatial subdivision schemes (octrees) can be made to inherit the hierarchical structure and the spatial addressability intrinsic to the underlying grid. These two properties, together with the geometric regularity that can also be built into the mesh, make octree based meshes ideally suited for efficient analysis and self-adaptive remeshing and reanalysis. The element decomposition of the octal cells that intersect the boundary of the domain is discussed. The problem, central to octree based meshing, is solved by combining template mapping and element extraction into a procedure that utilizes both constructive solid geometry and boundary representation techniques. Boundary cells that are not intersected by the edge of the domain boundary are easily mapped to predefined element topology. Cells containing edges (and vertices) are first transformed into a planar polyhedron and then triangulated via element extractor. The modeling environments required for the derivation of planar polyhedra and for element extraction are analyzed.

Saxena, Mukul↗
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.↗