SEARCH · Engineering Papers
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
The LANL fork of the AthenaPK project, which contains curvlinear coordinates The Code is a set of modifications to AthenaPK, an existing open source 3D hydrodynamics and magnetohydrodynamics simulation software for astrophysics, which enable simulation with uniform curvilinear geometries. Specifically it extends the existing Cartesian coordinates to uniform spherical coordinate and uniform cylindrical coordinate systems
Two-dimensional inlet flow fields in a supersonic free stream are calculated by an implicit, shock-capturing, finite-difference method. The Euler equations are subjected to a general curvilinear transformation and a body-fitted coordinate system is employed. The method is used to solve supercritical, critical, and subcritical flow fields which are simulated by prescribing appropriate conditions at the inlet outflow boundary. Results are presented for a drooped-cowl inlet.
Aerodynamic loads on a multi-bladed helicopter rotor in forward flight at transonic tip conditions are calculated. The unsteady, three-dimensional, time-accurate compressible Reynolds-averaged thin layer Navier-Stokes equations are solved in a rotating coordinate system on a body-conformed, curvilinear grid of C-H topology. Detailed boundary layer and global numerical comparisons of NACA-0012 symmetrical and CAST7-158 supercritical airfoils are made under identical forward flight conditions. The rotor wake effects are modeled by applying a correction to the geometric angle of attack of the blade. This correction is obtained by computing the local induced downwash velocity with a free wake analysis program. The calculations are performed on the Numerical Aerodynamic Simulation Cray 2 and the VPS32 (a derivative of a Cyber 205 at the Langley Research Center) for a model helicopter rotor in forward flight.
It has been claimed that either oculomotor or static depth cues provide the signals about self-rotation necessary approx.-1 deg/s. We tested this hypothesis by simulating self-motion along a curved path with the eyes fixed in the head (plus or minus 16 deg/s of rotation). Curvilinear motion offers two advantages: 1) heading remains constant in retinotopic coordinates, and 2) there is no visual-oculomotor conflict (both actual and simulated eye position remain stationary). We simulated 400 ms of rotation combined with 16 m/s of translation at fixed angles with respect to gaze towards two vertical planes of random dots initially 12 and 24 m away, with a field of view of 45 degrees. Four subjects were asked to fixate a central cross and to respond whether they were translating to the left or right of straight-ahead gaze. From the psychometric curves, heading bias (mean) and precision (semi-interquartile) were derived. The mean bias over 2-5 runs was 3.0, 4.0, -2.0, -0.4 deg for the first author and three naive subjects, respectively (positive indicating towards the rotation direction). The mean precision was 2.0, 1.9, 3.1, 1.6 deg. respectively. The ability of observers to make relatively accurate and precise heading judgments, despite the large rotational flow component, refutes the view that extra-flow-field information is necessary for human visual heading estimation at high rotation rates. Our results support models that process combined translational/rotational flow to estimate heading, but should not be construed to suggest that other cues do not play an important role when they are available to the observer.
Collision avoidance relies on representative Cartesian uncertainty volumes in order to calculate probabilities of collision. Among the potential shortcomings of a covariance matrix representation of state errors, the most worrisome is the coordinate mismatch between the Cartesian framework in which these matrices are distributed and the curvilinear path that satellite orbits actually follow. The present study compares curvilinear-based and Cartesian covariance representations for ~50,000 conjunctions to determine the frequency in which significant deviations from Gaussianity are observed, then compares the 2-D Pc result from the Cartesian covariance to a Monte Carlo Pc conducted in element space to assess operational significance.
Collision avoidance relies on representative Cartesian uncertainty volumes in order to calculate probabilities of collision. Among the potential shortcomings of a covariance matrix representation of state errors, the most worrisome is the coordinate mismatch between the Cartesian framework in which these matrices are distributed and the curvilinear path that satellite orbits actually follow. The present study compares curvilinear-based and Cartesian covariance representations for ~50,000 conjunctions to determine the frequency in which significant deviations from Gaussianity are observed, then compares the 2-D Pc result from the Cartesian covariance to a Monte Carlo Pc conducted in element space to assess operational significance.
In modelling the noise propagation in a duct of a ducted fan engine, the authors needed the boundary condition satisfied by the acoustic pressure on a lined duct wall in the presence of flow. The result in the form used by the authors was derived by M. K. Myers who presented a formal derivation of a related result by K. Taylor. A good review of the subject can be found in reference. Here, a brief and simple derivation of the acoustic boundary condition of Myers is given. The main difference in the derivation from that in reference is that the Gaussian co-ordinate system (q(sup 1), q(sup 2), q(sup 3)(q(sup 1), q(sup 2), t)) is used to specify the instantaneous position, i.e., Lagrangian variable, of the point on the mean position of the wall with curvilinear (Gaussian) co-ordinates (q(sup 1), q(sup 2)). Myers uses a locally orthogonal coordinate system which is somewhat less specific than what is used here.
Linear and quadratic Serendipity hybrid-stress elements are examined in respect of stability, coordinate invariance, and optimality. A formulation based upon symmetry group theory successfully addresses these issues in undistorted geometries and is fully detailed for plane elements. The resulting least-order stable invariant stress polynomials can be applied as astute approximations in distorted cases through a variety of tensor components and variational principles. A distortion sensitivity study for two- and three-dimensional elements provides favorable numerical comparisons with the assumed displacement method.
Topics covered include: (1) initial Cartesian coordinates for rapid precision orbit prediction; (2) accelerating convergence in optimization methods using search routines by applying curvilinear projection ideas; (3) perturbation-magnitude control for difference-quotient estimation of derivatives; and (4) determining the accelerometer bias for in-orbit shuttle trajectories.
In order to effectively analyze the flow in sinuous river channels, a curvilinear grid system was developed for use in the appropriate hydrodynamic code. The CENTERLINE program was designed to generate a two dimensional grid for this purpose. The Cartesian coordinates of a series of points along the boundaries of the sinuous channel represent the primary input to CENTERLINE. The program calculates the location of the river centerline, the distance downstream along the centerline, and both radius of curvature and channel width as a function of such distance downstream. These parameters form the basis for the generation of the curvilinear grid. Based on input values for longitudinal and lateral grid spacing, the corresponding grid system is generated and a file is created containing the appropriate parameters for use in the associated explicit finite difference hydrodynamic programs. Because of the option for a nonuniform grid, grid spacing can be concentrated in areas containing the largest flow gradients.
The spherical means of the solutions of a linear partial differential equation Lu = f in a conical region are studied. The conical region is bounded by a surface generated by curvilinear ti surfaces. The spherical mean is the average of u over a constant ti surface. The conditions on the linear differential operator, L, and on the orthogonal coordinates (ti, eta, zeta) are established so that the spherical mean of the solution subjected to the appropriate boundary and initial conditions can be determined directly as a problem with only space variable. Conditions are then established so that the spherical mean of the solution in one concial region will be proportional to that of a known solution in another conical region. Applications to various problems of mathematical physics and their physical interpretations are presented.
An elliptic grid generation scheme is described which produces a curvilinear, boundary-fitted grid for highly swept wings with sharp leading edges. The three-dimensional integration domain is segmented in successive crossflow sections wherein the physical coordinates are transformed to computational coordinates by solving an elliptic set of two quasi-linear differential equations. Grid points are clustered in the vicinity of the wing surface, especially in the neighborhood of the leading edges. The formulation of the source terms in the equations governing the transformation contains adjustable parameters which are determined from limiting forms of the elliptic equations along the boundaries. The source terms are assigned to each grid point by interpolation of these parameters into the interior domain. The formulation does not depend on the boundary shape or on the distribution of the grid points along the boundaries. For the first time, the discretized governing equations have been solved using a fast AF1 iteration scheme.
The spherical means of the solutions of a linear partial differential equation Lu = f in a conical region are studied. The conical region is bounded by a surface generated by curvilinear xi lines and by two truncating xi surfaces. The spherical mean is the average of u over a constant xi surface. Conditions on the linear differential operator, L, and on the orthogonal coordinates xi, eta, and zeta are established so that the problem for the determination of the spherical mean of the solution subjected to the appropriate boundary and initial conditions can be reduced to a problem with only one space variable. Conditions are then established so that the spherical mean of the solution in one conical region will be proportional to that of a known solution in another conical region. Applications to various problems of mathematical physics and their physical interpretations are presented.
An inverse wing design method was developed around an existing transonic wing analysis code. The original analysis code, TAWFIVE, has as its core the numerical potential flow solver, FLO30, developed by Jameson and Caughey. Features of the analysis code include a finite-volume formulation; wing and fuselage fitted, curvilinear grid mesh; and a viscous boundary layer correction that also accounts for viscous wake thickness and curvature. The development of the inverse methods as an extension of previous methods existing for design in Cartesian coordinates is presented. Results are shown for inviscid wing design cases in super-critical flow regimes. The test cases selected also demonstrate the versatility of the design method in designing an entire wing or discontinuous sections of a wing.
Entity is a new-generation, fully open-source particle-in-cell (PIC) code developed to overcome key limitations in astrophysical plasma modeling, particularly the extreme separation of scales and the performance challenges associated with evolving, GPU-centric computing infrastructures. It achieves hardware-agnostic performance portability across various GPU and CPU architectures using the Kokkos library. Crucially, Entity maintains a high standard for usability, clarity, and customizability, offering a robust and easy-to-use framework for developing new algorithms and grid geometries, which allows extensive control without requiring edits to the core source code. This paper details the core general-coordinate special relativistic module. Entity is the first PIC code designed to solve the Vlasov–Maxwell system in general coordinates, enabling a coordinate-agnostic framework that provides the foundational structure for straightforward extension to arbitrary coordinate geometries. The core methodology achieves numerical stability by solving particle equations of motion in the global orthonormal Cartesian basis, despite using generalized coordinates like Cartesian, axisymmetric spherical, and quasi-spherical grids. Charge conservation is ensured via a specialized current deposition technique using conformal currents. The code exhibits robust scalability and performance portability on major GPU platforms (AMD MI250X, NVIDIA A100, and Intel Max Series), with the 3D particle pusher and the current deposition operating efficiently at about 2 ns per particle per time step. Functionality is validated through a comprehensive suite of standard Cartesian plasma tests and the accurate modeling of relativistic magnetospheres in curvilinear axisymmetric geometries.
The new Structured Mapping At Reduced dimension Topology elements (SMART) method for the accurate calculation of derivatives at multiblock structured grid block interfaces is presented. In the SMART method, a ’local’ curvilinear mapping is defined at each interface point, giving a consistent multidimensional definition of the derivatives. The resulting system of equations is overdetermined, and a least squares method is used to determine the value of the derivatives in the local coordinate system. In the special case of a nonsingular interface point, the SMART method automatically recovers the spatial differencing stencils used at the interior points in the neighboring grid blocks.
We describe a time-explicit finite-difference algorithm for solving the nonlinear fluid equations. The method is similar to existing Eulerian schemes in its use of operator-splitting and artificial viscosity, except that we solve the Lagrangian equations of motion with a predictor-corrector and then remap onto a fixed Eulerian grid. The remap is formulated to eliminate errors associated with coordinate singularities, with a general prescription for remaps of arbitrary order. We perform a comprehensive series of tests on standard problems. Self-convergence tests show that the code has a second-order rate of convergence in smooth, two-dimensional flow, with pressure forces, gravity, and curvilinear geometry included. While not as accurate on idealized problems as high-order Riemann-solving schemes, the predictor-corrector Lagrangian-remap code has great flexibility for application to a variety of astrophysical problems.
A method for generating boundary-fitted, curvilinear, two dimensional grids by the use of the Poisson equations is presented. Grids of C-type and O-type were made about airfoils and other shapes, with circular, rectangular, cascade-type, and other outer boundary shapes. Both viscous and inviscid spacings were used. In all cases, two important types of grid control can be exercised at both inner and outer boundaries. First is arbitrary control of the distances between the boundaries and the adjacent lines of the same coordinate family, i.e., stand-off distances. Second is arbitrary control of the angles with which lines of the opposite coordinate family intersect the boundaries. Thus, both grid cell size (or aspect ratio) and grid cell skewness are controlled at boundaries. Reasonable cell size and shape are ensured even in cases wherein extreme boundary shapes would tend to cause skewness or poorly controlled grid spacing. An inherent feature of the Poisson equations is that lines in the interior of the grid smoothly connect the boundary points (the grid mapping functions are second order differentiable).