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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 NTRS2000

A Technique of Treating Negative Weights in WENO Schemes

High order accurate weighted essentially non-oscillatory (WENO) schemes have recently been developed for finite difference and finite volume methods both in structural and in unstructured meshes. A key idea in WENO scheme is a linear combination of lower order fluxes or reconstructions to obtain a high order approximation. The combination coefficients, also called linear weights, are determined by local geometry of the mesh and order of accuracy and may become negative. WENO procedures cannot be applied directly to obtain a stable scheme if negative linear weights are present. Previous strategy for handling this difficulty is by either regrouping of stencils or reducing the order of accuracy to get rid of the negative linear weights. In this paper we present a simple and effective technique for handling negative linear weights without a need to get rid of them.

Shi, Jing↗
NASA NTRS2008

Numerical Studies of Scattering Properties of Leaves and Leaf Moisture Influences on the Scattering at Microwave Wavelengths

This study uses 3-dimensional finite difference time domain method to accurately calculate single-scattering properties of randomly orientated leaves and evaluate the influences of vegetation water content (VWC) on these properties at 19 and 37 GHz frequencies. The studied leaves are assumed to be thin elliptic disks with two different sizes and have various VWC values. Although the leaf moisture produces considerable absorption during scattering processes, the effective efficiencies of extinction and scattering of leaves still near-linearly increase with VWC. Calculated asymmetry factors and phase functions indicate that there are significant amounts of scattering at large scattering angles in microwave wavelengths, which provides good opportunities for off-nadir microwave remote sensing of forests. This study lays a basic foundation in future quantifications of the relations between satellite measurements and physical properties of vegetation canopies.

Lin, Bing↗
NASA NTRS1994

The Application of the FDTD Method to Millimeter-Wave Filter Circuits Including the Design and Analysis of a Compact Coplanar

The finite difference time domain (FDTD) method is applied to the analysis of microwave, millimeter-wave and submillimeter-wave filter circuits. In each case, the validity of this method is confirmed by comparison with measured data. In addition, the FDTD calculations are used to design a new ultra-thin coplanar-strip filter for feeding a THz planar-antenna mixer.

Millimeter-wave filter Coplanar-Strip filter↗
NASA NTRS1985

Higher order methods for convection-diffusion problems

This paper applies C1 cubic Hermite polynomials embedded in an orthogonal collocation scheme to the spatial discretization of the unsteady nonlinear Burgers equation as a model of the equations of fluid mechanics. The temporal discretization is carried out by means of either a noniterative finite difference or an iterative finite difference procedure. Results of this method are compared with those of a second-order finite difference scheme and a splined-cubic Taylor's series scheme. Stability limits are derived and the matrix structure of the several schemes are compared.

Murphy, J. D.↗
NASA NTRS1987

Progress in the prediction of unsteady heat transfer on turbines blades

Progress toward developing a general method for predicting unsteady heat transfer on turbine blades subject to blade-passing frequencies and Reynolds numbers relevant to the Space Shuttle Main Engine (SSME) is discussed. The method employs an invisid/viscous interactive procedure which has been tested extensively for steady subsonic and transonic external airfoil problems. One such example is shown. The agreement with experimental data and with Navier-Stokes calculations yields confidence in the method. The technique is extended to account for wake generated unsteadiness. The flow reversals around the stagnation point caused by the nonuniform onset velocity are accounted for by using the Characteristic Box scheme developed by Cebeci and Stewartson. The coupling between the inviscid and viscous methods is achieved by using a special procedure, which, with a novel inverse finite-difference boundary-layer method, allows the calculations to be performed for a wide range of flow conditions, including separation. Preliminary results are presented for the stagnation region of turbine blades for both laminar and turbulent flows. A laminar model problem corresponding to a flow on a circular cylinder which experiences the periodic passing of wakes from turbine blades is presented to demonstrate the ability of the method to calculate flow reversals around the stagnation region.

Cebeci, T.↗
NASA NTRS1978

Calculation of supersonic viscous flow over delta wings with sharp subsonic leading edges

Two complementary procedures were developed to calculate the viscous supersonic flow over conical shapes at large angles of attack, with application to cones and delta wings. In the first approach the flow is assumed to be conical and the governing equations are solved at a given Reynolds number with a time-marching explicit finite-difference algorithm. In the second method the parabolized Navier-Stokes equations are solved with a space-marching implicit noniterative finite-difference algorithm. This latter approach is not restricted to conical shapes and provides a large improvement in computational efficiency over published methods. Results from the two procedures agree very well with each other and with available experimental data.

Vigneron, Y. C.↗
NASA NTRS1978

Calculation of supersonic viscous flow over delta wings with sharp subsonic leading edges

Two complementary procedures have been developed to calculate the viscous supersonic flow over conical shapes at large angles of attack, with application to cones and delta wings. In the first approach the flow is assumed to be conical and the governing equations are solved at a given Reynolds number with a time-marching explicit finite-difference algorithm. In the second method the parabolized Navier-Stokes equations are solved with a space-marching implicit noniterative finite-difference algorithm. This latter approach is not restricted to conical shapes and provides a large improvement in computational efficiency over published methods. Results from the two procedures agree very well with each other and with available experimental data.

Vigneron, Y. C.↗
NASA NTRS1992

Analysis of iced wings

A method for computing ice shapes along the leading edge of a wing and a method for predicting its aerodynamic performance degradation due to icing is described. Ice shapes are computed using an extension of the LEWICE code which was developed for airfoils. The aerodynamic properties of the iced wing are determined with an interactive scheme in which the solutions of the inviscid flow equations are obtained from a panel method and the solutions of the viscous flow equations are obtained from an inverse three-dimensional finite-difference boundary-layer method. A new interaction law is used to couple the inviscid and viscous flow solutions. The application of the LEWICE wing code to the calculation of ice shapes on a MS-317 swept wing shows good agreement with measurements. The interactive boundary-layer method is applied to a tapered ice wing in order to study the effect of icing on the aerodynamic properties of the wing at several angles of attack.

Cebeci, T.↗
NASA NTRS1992

Analysis of iced wings

A method for computing ice shapes along the leading edge of a wing and a method for predicting its aerodynamic performance degradation due to icing is described. Ice shapes are computed using an extension of the LEWICE code which was developed for airfoils. The aerodynamic properties of the iced wing are determined with an interactive scheme in which the solutions of the inviscid flow equations are obtained from a panel method and the solutions of the viscous flow equations are obtained from an inverse three-dimensional finite-difference boundary-layer method. A new interaction law is used to couple the inviscid and viscous flow solutions. The application of the LEWICE wing code to the calculation of ice shapes on a MS-317 swept wing show good agreement with measurements. The interactive boundary layer method is applied to a tapered iced wing in order to study the effect of icing on the aerodynamic properties of the wing at several angles of attack.

Cebeci, Tuncer↗
NASA NTRS1992

Recent progress in the analysis of iced airfoils and wings

Recent work on the analysis of iced airfoils and wings is described. Ice shapes for multielement airfoils and wings are computed using an extension of the LEWICE code that was developed for single airfoils. The aerodynamic properties of the iced wing are determined with an interactive scheme in which the solutions of the inviscid flow equations are obtained from a panel method and the solutions of the viscous flow equations are obtained from an inverse three-dimensional finite-difference boundary-layer method. A new interaction law is used to couple the inviscid and viscous flow solutions. The newly developed LEWICE multielement code is amplified to a high-lift configuration to calculate the ice shapes on the slat and on the main airfoil and on a four-element airfoil. The application of the LEWICE wing code to the calculation of ice shapes on a MS-317 swept wing shows good agreement with measurements. The interactive boundary-layer method is applied to a tapered iced wing in order to study the effect of icing on the aerodynamic properties of the wing at several angles of attack.

Cebeci, Tuncer↗
NASA NTRS2002

Three-Dimensional High-Order Spectral Finite Volume Method for Unstructured Grids

Many areas require a very high-order accurate numerical solution of conservation laws for complex shapes. This paper deals with the extension to three dimensions of the Spectral Finite Volume (SV) method for unstructured grids, which was developed to solve such problems. We first summarize the limitations of traditional methods such as finite-difference, and finite-volume for both structured and unstructured grids. We then describe the basic formulation of the spectral finite volume method. What distinguishes the SV method from conventional high-order finite-volume methods for unstructured triangular or tetrahedral grids is the data reconstruction. Instead of using a large stencil of neighboring cells to perform a high-order reconstruction, the stencil is constructed by partitioning each grid cell, called a spectral volume (SV), into 'structured' sub-cells, called control volumes (CVs). One can show that if all the SV cells are partitioned into polygonal or polyhedral CV sub-cells in a geometrically similar manner, the reconstructions for all the SVs become universal, irrespective of their shapes, sizes, orientations, or locations. It follows that the reconstruction is reduced to a weighted sum of unknowns involving just a few simple adds and multiplies, and those weights are universal and can be pre-determined once for all. The method is thus very efficient, accurate, and yet geometrically flexible. The most critical part of the SV method is the partitioning of the SV into CVs. In this paper we present the partitioning of a tetrahedral SV into polyhedral CVs with one free parameter for polynomial reconstructions up to degree of precision five. (Note that the order of accuracy of the method is one order higher than the reconstruction degree of precision.) The free parameter will be determined by minimizing the Lebesgue constant of the reconstruction matrix or similar criteria to obtain optimized partitions. The details of an efficient, parallelizable code to solve three-dimensional problems for any order of accuracy are then presented. Important aspects of the data structure are discussed. Comparisons with the Discontinuous Galerkin (DG) method are made. Numerical examples for wave propagation problems are presented.

Liu, Yen↗
DOE OSTI2025

Application of mesh refinement to relativistic magnetic reconnection

During relativistic magnetic reconnection, antiparallel magnetic fields undergo a rapid change in topology, releasing a large amount of energy in the form of non-thermal particle acceleration. This work explores the application of mesh refinement to 2D reconnection simulations to efficiently model the inherent disparity in length-scales. We have systematically investigated the effects of mesh refinement and determined necessary modifications to the algorithm required to mitigate non-physical artifacts at the coarse–fine interface. We have used the ultrahigh-order pseudo-spectral analytical time-domain Maxwell solver to analyze how its use can mitigate the numerical dispersion that occurs with the finite-difference time-domain (or “Yee”) method. Absorbing layers are introduced at the coarse–fine interface to eliminate spurious effects that occur with mesh refinement. We also study how damping the electromagnetic fields and current density in the absorbing layer can help prevent the non-physical accumulation of charge and current density at the coarse–fine interface. Using a mesh refinement ratio of 8 for two-dimensional magnetic reconnection simulations, we obtained good agreement with the high-resolution baseline simulation, using only 36% of the macroparticles and 71% of the node-hours needed for the baseline. The methods presented here are especially applicable to 3D systems where higher memory savings are expected than in 2D, enabling comprehensive, computationally efficient 3D reconnection studies in the future.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1979

Application of the method of integral relations to unsteady fluid flow problems with shocks

A mixed method using both the method of integral relations and the finite difference technique is developed for the solution of unsteady flow problems. The integral relations method is based upon a chosen interpolating function dependent only on the time domain. The resulting local semidiscrete finite element equations obtained are assembled into a global form. The spatial derivatives at the nodes are replaced by finite difference operators and the discretized nonlinear algebraic system is solved by an iterative scheme. Solutions are obtained for the one-dimensional gasdynamics equation, the one-dimensional wave equation and Burger's model of turbulence. Agreement with other numerical and analytical solutions is excellent for the gasdynamics problem and satisfactory for the Burger equation in cases of small viscous effects.

Wadia, A. R.↗
NASA NTRS1989

Domain decomposition methods for systems of conservation laws: Spectral collocation approximations

Hyperbolic systems of conversation laws are considered which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level a domain deposition method based on an iteration by subdomain procedure was introduced yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The method is set for a general nonlinear problem in several space variables. The convergence analysis, however, is carried out only for a linear one-dimensional system with continuous solutions. A precise form of the error reduction factor at each iteration is derived. Although the method is applied here to the case of spectral collocation approximation only, the idea is fairly general and can be used in a different context as well. For instance, its application to space discretization by finite differences is straight forward.

Quarteroni, Alfio↗
DOE OSTI2021

Gradient-based optimization of 3D MHD equilibria

Using recently developed adjoint methods for computing the shape derivatives of functions that depend on magnetohydrodynamic (MHD) equilibria (Antonsen et al. , J. Plasma Phys. , vol. 85, issue 2, 2019; Paul et al. , J. Plasma Phys. , vol. 86, issue 1, 2020), we present the first example of analytic gradient-based optimization of fixed-boundary stellarator equilibria. We take advantage of gradient information to optimize figures of merit of relevance for stellarator design, including the rotational transform, magnetic well and quasi-symmetry near the axis. With the application of the adjoint method, we reduce the number of equilibrium evaluations by the dimension of the optimization space ( ${\sim }50\text {--}500$ ) in comparison with a finite-difference gradient-based method. We discuss regularization objectives of relevance for fixed-boundary optimization, including a novel method that prevents self-intersection of the plasma boundary. We present several optimized equilibria, including a vacuum field with very low magnetic shear throughout the volume.

Physics↗
NASA NTRS1979

Spectral methods for problems in complex geometries

Techniques that permit the efficient application of spectral methods to solve problems in nearly arbitrary geometries are presented. These methods were found to be viable alternatives to finite difference and finite element processes. The spectral methods applied are extensions of the standard techniques of separation of variables to the solution of arbitrarily complicated problems.

Orszag, S. A.↗
NASA NTRS1993

Hybrid techniques for complex aerospace electromagnetics problems

Important aerospace electromagnetics problems include the evaluation of antenna performance on aircraft and the prediction and control of the aircraft's electromagnetic signature. Due to the ever increasing complexity and expense of aircraft design, aerospace engineers have become increasingly dependent on computer solutions. Traditionally, computational electromagnetics (CEM) has relied primarily on four disparate techniques: the method of moments (MoM), the finite-difference time-domain (FDTD) technique, the finite element method (FEM), and high frequency asymptotic techniques (HFAT) such as ray tracing. Each of these techniques has distinct advantages and disadvantages, and no single technique is capable of accurately solving all problems of interest on computers that are available now or will be available in the foreseeable future. As a result, new approaches that overcome the deficiencies of traditional techniques are beginning to attract a great deal of interest in the CEM community. Among these new approaches are hybrid methods which combine two or more of these techniques into a coherent model. During the ASEE Summer Faculty Fellowship Program a hybrid FEM/MoM computer code was developed and applied to a geometry containing features found on many modern aircraft.

Aberle, Jim↗