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EFFECT OF GRID ASPECT RATIO ON convergence

AIAA JOURNAL 1994年第12期32卷 2401-2408页

作者： BUELOW, PEO VENKATESWARAN, S MERKLE, CL Pennsylvania State University University Park Pennsylvania 16802

The effects of high-aspect-ratio grids on algorithm convergence are considered by means of vector stability theory and computational experiments. The results indicate that approximately factored implicit schemes experience convergence deterioration because of nonoptimum local time-stepping procedures and increased need for viscous preconditioning. Based on this insight, an enhanced algorithm is devised using improved selection of the local time step, appropriate definition of the viscous preconditioning matrix, and proper implementation of the boundary conditions. The new algorithm provides uniformly efficient convergence at all aspect ratios for both Euler and Navier-Stokes computations for a variety of test problems.

关键词： High Aspect Ratio algorithms convergence Turbulent Boundary Layer Navier Stokes Equations Supersonic Flow Mach Numbers Euler Equations Navier Stokes Algorithm Choked Nozzles Computing

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Novel Approach to Improve Stability and convergence of Flowfield Solution Processes: Mode Multigrid

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AIAA JOURNAL 2023年第8期61卷 3496-3506页

作者： Wang, XuKun Liu, Yilang Zhang, Weiwei Northwestern Polytech Univ Sch Aeronaut Natl Key Lab Sci & Technol Aerodynam Design & Res Xian 710072 Peoples R China

In the field of computational fluid dynamics, stability and convergence problems are often encountered when solving the governing equation. This paper studies the effect of the mode multigrid on the stability and convergence of iterative algorithms. By further analyzing the mechanism for accelerating the convergence of mode multigrid, a new adaptive mode multigrid (AMMG) is proposed, and an adaptive selection criterion is formulated for the parameters of dynamic modal decomposition, which can accurately identify and filter out the unstable modes in the flowfield, thus efficiently obtaining the accurate steady solution. In the cases of laminar flow past circular cylinder and turbulent flow past airfoil, the AMMG significantly improves the stability of the iterative algorithm;in the case of transonic flow past airfoil, the AMMG solves the problem of shock wave shaking during the iteration, and the convergence is significantly improved. In summary, the AMMG method significantly enhances the stability and convergence of the iterative algorithm, and can be used as an effective convergence-preserving computation strategy.

关键词： Computational Fluid Dynamics Airfoil Finite Volume Formulation Reynolds Averaged Navier Stokes Numerical algorithms algorithms convergence Numerical Stability

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Tackling Nonconvex Collision Avoidance Constraints for Optimal Trajectory Planning Using Saturation Functions

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2022年第6期45卷 1002-1016页

作者： Zhao, Zichen Shang, Haibin Wei, Bingwei Beijing Inst Technol Sch Aerosp Engn Beijing 100081 Peoples R China Beijing Inst Technol Key Lab Dynam & Control Flight Vehicle Beijing 100081 Peoples R China

The problem of optimal trajectory planning with nonconvex collision avoidance constraints is discussed in this paper. The trajectory planning algorithm aims to generate a feasible trajectory with specified performance indexes to reduce collisions of aerospace vehicles in the presence of second-order smooth obstacles. The algorithm design that manages such mission scenarios is challenging because of the stringent avoidance constraints of various nonconvex types, especially considering the requirements of efficient computation. This problem is addressed within the sequential convex programming (SCP) framework by utilizing the characteristics of saturation functions. The introduction of the saturation function is found to significantly improve the convergence of the SCP algorithm by overcoming the drawbacks of potential interruptions from the iteration process and controlling the search directions for successive solutions. Theoretical analyses are performed to guarantee that the original constraints are satisfied and to ensure the iterative solution searches in the directions of the true optimal solution. Under multiple randomly generated test environments, the applications of the proposed approach in highly constrained aircraft path planning problems and spacecraft rendezvous operations are numerically simulated by comparing two representative conventional SCP-based methods to demonstrate the effectiveness, efficiency, and convergence of the proposed methodology.

关键词： Iterative Solution Path Planning Spacecraft Rendezvous algorithms convergence Nonlinear Programming UAV Fuel Consumption Bang Bang Control Obstacle Avoidance Numerical Simulation

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A VISUAL CUEING MODEL FOR TERRAIN-FOLLOWING APPLICATIONS

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1985年第2期8卷 201-207页

作者： ZACHARIAS, GL CAGLAYAN, AK SINACORI, JB JOHN B SINACORI ASSOCIATES HOLLISTERCA

A model to account for the pilot's processing of visual flowfield cues during low-level flight over uncultured terrain is described. The model is predicated on the notion that the pilot makes noisy, sampled measurements onthe spatially distributed visual flowfield surrounding him, and, on the basis of these measurements, generates estimates of his own linear and angular terrain-relative velocities which optimally satisfy, in a least-squaressense, the visual kinematic flow constraints. A subsidiary but significant output of the model is an "impact time" map, an observer-centered spatially scaled replica of the viewed surface. Simulation results are presented to demonstrate the potential for modeling relevant human visual performance data and evaluating candidate simulator configurations in terms of expected impact on the perceptual performance of the terrain-following pilot. Additional model applications are discussed, including interfacing with other human performance models and modeling other types of visually driven human task performance. © 1985 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Pilot Human Performance Modeling Level Flight Flow Patterns Diminishing Returns Pilot Flying Monte Carlo Simulation algorithms convergence Cost Effectiveness Aircraft Maneuvers

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Formation Establishment and Reconfiguration Using Differential Elements in J2-Perturbed Orbits

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2015年第9期38卷 1725-1740页

作者： Roscoe, Christopher W. T. Westphal, Jason J. Griesbach, Jacob D. Schaub, Hanspeter Appl Def Solut Columbia MD 21044 USA Univ Colorado Dept Aerosp Engn Sci Associate Chair Undergrad Affairs Boulder CO 80309 USA

A computationally efficient algorithm is developed for onboard planning of n-impulse fuel-optimal maneuvers for establishment and reconfiguration of spacecraft formations. The method is valid in circular and elliptic orbits and includes first-order secular J2 effects. The dynamics are expressed in terms of differential mean orbital elements, and relations are provided to allow the formation designer to transform these into intuitive geometric quantities for visualization and analysis. The maneuver targeting problem is formulated as an optimal control problem in both continuous and discrete time. The continuous-time formulation cannot be solved directly in an efficient manner, and the discrete-time formulation, which has an analytical solution, does not directly yield the optimal thrust times. Therefore, a new flight-suitable algorithm is designed by iteratively solving the discrete-time formulation while using the continuous-time necessary conditions to refine the thrust times until they converge to the optimal values. Simulation results illustrate the performance for a variety of reconfiguration maneuvers and reference orbits, including examples for the NASA CubeSat Proximity Operations Demonstration mission.

关键词： Sun Synchronous Orbit Time Optimal Control Nonsingular Orbital Elements CubeSat Spacecraft Formation Formation Flying Argument of Latitude Ballistic Coefficient algorithms convergence Guidance System

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Autonomous Maneuver Targeting Around Small Bodies Using Continuous-Thrust Propulsion

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2022年第3期45卷 499-516页

作者： Kuettel, Donald H. H. McMahon, Jay W. Univ Colorado Orbital Res Cluster Celestial Applicat Smead Dept Aerosp Engn Boulder CO 80303 USA

This paper presents a novel fuel-efficient continuous-thrust maneuver targeting (CTMT) algorithm that is capable of planning finite, continuous maneuvers in a larger autonomous spacecraft guidance architecture. This is accomplished using a constant-thrust bilinear tangent guidance law in conjunction with an optimal Lambert algorithm and a Newton-Raphson predictor-corrector targeting scheme. This simple approach is capable of planning a plethora of different free-time and fixed-time single-burn, burn-coast intercept, or burn-coast-burn bilinear tangent maneuvers from an initial state/orbit to a desired state/orbit. For the study case of asteroid Bennu, when used with thrust levels that are greater than 5% of the surface acceleration of asteroid Bennu, the CTMT algorithm is able to converge on 99% of orbital transfers initiated from a circular, 1.5 km, terminator orbit. Furthermore, many of the continuous-thrust maneuvers calculated by the CTMT algorithm are the optimal constant-thrust trajectories between two states in the small-body dynamical environment, and they are able to be calculated hundreds of times faster with the CTMT algorithm than with state-of-the-art nonlinear optimization algorithms. Ultimately, the CTMT algorithm shows promise as a candidate for future autonomous guidance applications.

关键词： Thrust Propulsion System Optimal Impulsive Maneuvers Broyden Fletcher Goldfarb Shanno Guidance Laws Asteroids Lambert Algorithm Spacecraft Trajectories Sparse Nonlinear Optimizer algorithms convergence

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STRUCTURED AND UNSTRUCTURED REMESHING METHOD FOR HIGH-SPEED FLOWS

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JOURNAL OF SPACECRAFT AND ROCKETS 1991年第2期28卷 158-164页

作者： VEMAGANTI, GR THORNTON, EA WIETING, AR UNIV VIRGINIA DEPT MECH & AEROSP ENGN CHARLOTTESVILLE VA 22901 USA NASA LYNDON B JOHNSON SPACE CTR AEROTHERMAL LOADS BRANCH HOUSTON TX 77058 USA

An adaptive remeshing method using both triangular and quadrilateral elements suitable for high-speed flows is presented. For inviscid flows, the method generates completely unstructured meshes. For viscous flows, the boundary-layer edge is identified adaptively and a structured mesh is generated in the boundary layer;an unstructured mesh is generated in the inviscid region. Examples of inviscid and viscous mesh adaptations for high-speed flows are presented. A comparison is made between first-order and higher-order finite element algorithms when used in association with the remeshing method.

关键词： Flow Separation In Compressible Viscous Flows Mesh Generation High Aspect Ratio algorithms convergence Flux Corrected Transport Heat Flux Distribution Triangular Element Heat Transfer Coefficients Mach Number

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SOLUTION-ADAPTIVE AND QUALITY-ENHANCING GRID GENERATION

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JOURNAL OF AIRCRAFT 1993年第2期30卷 227-234页

作者： LUONG, PV THOMPSON, JF GATLIN, B Mississippi State University Mississippi State Mississippi 39762

A straightforward and effective procedure for converting any CFD code that operates on a block-structured grid into a dynamically adaptive code is presented. Coupling between the grid generation system and the flow solver is through external files, so that only minimal changes are required in the source codes. Adaptive grids are generated using elliptic equation techniques. The mechanism of grid movement is control functions, which form the right side of the system of generating equations. These control functions can be specified to include grid quality measures, flow solutions, solution gradients, solution curvature, or any combination of these. Adaptation can be static, dynamic, or periodic. Typical results for adaptation in compressible and incompressible flows are presented and compared with solutions obtained on static grids.

关键词： Incompressible Viscous Flow CFD Codes Aspect Ratio Pressure Coefficient Poisson's Equation Velocity Profiles Skin Friction Coefficient Friction Coefficient algorithms convergence Euler Equations

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Directional agglomeration multigrid techniques for high-Reynolds-number viscous flows

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AIAA JOURNAL 1999年第10期37卷 1222-1230页

作者： Mavriplis, DJ NASA Langley Res Ctr Hampton VA 23681 USA

A preconditioned directional-implicit agglomeration multigrid algorithm is developed for solving two- and three-dimensional viscous flows an highly anisotropic unstructured meshes of mixed-element types. The multigrid smoother consists of a preconditioned point- or line-implicit solver that operates on lines constructed in the unstructured mesh using a weighted graph algorithm. Directional coarsening or agglomeration is achieved using a similar weighted graph algorithm. A tight coupling of the line construction and directional agglomeration algorithms enables the use of aggressive coarsening ratios in the multigrid algorithm, which in turn reduces the cost of a multigrid cycle. convergence rates that ape independent of the degree of grid stretching are demonstrated In both two and three dimensions. Further improvement of the three-dimensional convergence rates through a Generalized Minimum Residual (GMRES) technique is also demonstrated.

关键词： Freestream Mach Number algorithms convergence Viscous Flow Tetrahedral Element Courant Friedrichs Lewy Turbulence Models Multigrid Methods Unstructured Grid Wing Geometry RAE 2822

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Numerical Solution of a Generalized Wahba Problem for a Spinning Spacecraft

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2012年第3期35卷 764-773页

作者： Psiaki, Mark L. Hinks, Joanna C. Cornell Univ Sibley Sch Mech & Aerosp Engn Ithaca NY 14853 USA

A numerical solution algorithm has been developed to solve a generalization of Wahba's attitude determination problem in the case of unknown attitude and attitude rate. It provides a robust global solution to nonlinear batch attitude and rate estimation problems for spinning spacecraft. The original Wahba problem seeks the attitude that fits a set of unit-normalized direction vector measurements. The generalized problem seeks an initial attitude and rate that, when combined with a torque-free rigid-body attitude dynamics model, tit a time series of direction vector measurements. The new algorithm combines an inner analytic solution for the unknown initial attitude quaternion with an outer numerical solution for the unknown initial rate. The inner problem can be cast in a standard Wahba form, and it is solved in closed form using an adaptation of the q method. The outer problem relies on a trust-region implementation of Newton's method to ensure global convergence. The global solution is determined by re-solving starting from a random set of first guesses of the attitude rate that cover the space of nonaliasing rates. Tests on truth-model simulation data for minor-axis and major-axis spinning spacecraft confirm the new algorithm's ability to achieve global convergence and its estimation accuracy's consistency with its computed estimation error covariance matrix.

关键词： Spinning Spacecraft Singular Value Decomposition Numerical Integration algorithms convergence Attitude Dynamics Optimization Algorithm Extended Kalman Filter Cumulative Distribution Function Numerical Optimization Spacecraft Missions

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