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Efficient Parallel Dynamic Overset Unstructured Grid for Flow Simulation with Moving Bodies

AIAA JOURNAL 2023年第5期61卷 2135-2166页

作者： Tian, Shu-Ling Xu, Ke Xia, Jian Chen, Long Nanjing Univ Aeronaut & Astronaut Coll Aerosp Engn Nanjing 210016 Peoples R China

The overset grid method for simulation of unsteady flow with moving bodies faces several issues, including low assembly efficiency for a large number of bodies, difficult parallel implementation, and the requirement of manual intervention. To address these issues, in this paper, we develop an efficient, automatic, and robust parallel dynamic overset-unstructured-grid assembly method. It is achieved by parallelizing its two main steps: hole cutting, and identification of interpolation stencils. The hole cutting is simply implemented in parallel by identifying the active zone of each grid with a criterion of the global minimum wall distance. The global minimum wall distance is efficiently calculated on each process with the oriented-bounding-box-based k-dimensional (k-D) trees of the wall surface grids. For identification of the interpolation stencil, we use the results of the first step, optimally define the interpolation boundary nodes, and determine their candidate donor partitions in each process. This efficiently minimizes the number of query nodes and their donor cell candidates. The donor cell search is efficiently performed in parallel in each candidate donor partition by using the oriented-bounding-box-based k-D tree of the field volume grid. Several cases are adopted to test the efficiency and capability of the proposed parallel dynamic overset-unstructured-grid assembly approach.

关键词： Unstructured Grid Two Dimensional Flow Computational Fluid Dynamics Projectiles Aerodynamic Coefficients Aerodynamic Performance algorithms and data structures Reynolds Averaged Navier Stokes Search Algorithm Flight Testing

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ADDITIVE WEIGHTS UNDER THE BALANCED PROBABILITY MODEL

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COMPUTING 1995年第3期54卷 241-250页

作者： TRIER, U Fachbereich Informatik (20) Professur Syntaxanalyse & Diskrete Strukturen Wissenschaftlicher Mitarbeiter Johann Wolfgang Goethe-Universität Frankfurt/Main 11 Federal Republic of Germany

We compute the average behaviour of additive weights over the family F-t(n) of unlabelled rooted planar t-ary trees with n nodes under the so-called Balanced Probability Model, introduced by R. Casas, J. Diaz and C. Martinet. The generating function related to a particular additive weight with polynomial weight functions always satisfies an ordinary inhomogeneous differential equation, which can be solved explicitly by the variation of constant - method. These coefficients are estimated using singularity analysis. The so-called occupancy, a parameter which is analyzed in the paper of Casas et al., turns out to be additive, hence, the methods presented here are applicable to it.

关键词： algorithms and data structures MATHEMATICS OF COMPUTATION

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METRIC DIMENSION OF BOUNDED TREE-LENGTH GRAPHS

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SIAM JOURNAL ON DISCRETE MATHEMATICS 2017年第2期31卷 1217-1243页

作者： Belmonte, Remy Fomin, Fedor V. Golovach, Petr A. Ramanujan, M. S. Kyoto Univ Dept Architecture & Architectural Engn Kyoto Japan Univ Bergen Dept Informat Bergen Norway TU Wien A-1040 Vienna Austria

The notion of resolving sets in a graph was introduced by Slater [Proceedings of the Sixth Southeastern Conference on Combinatorics, Graph Theory, and Computing, Util. Math., Winnipeg, 1975, pp. 549-559] and Harary and Melter [Ars Combin., 2 (1976), pp. 191-195] as a way of uniquely identifying every vertex in a graph. A set of vertices in a graph is a resolving set if for any pair of vertices x and y there is a vertex in the set which has distinct distances to x and y. A smallest resolving set in a graph is called a metric basis and its size, the metric dimension of the graph. The problem of computing the metric dimension of a graph is a well-known NP-hard problem and while it was known to be polynomial time solvable on trees, it is only recently that efforts have been made to understand its computational complexity on various restricted graph classes. In recent work, Foucaud [Algorithmica, 2016, pp. 1-31] showed that this problem is NP-complete even on interval graphs. They complemented this result by also showing that it is fixed-parameter tractable (FPT) parameterized by the metric dimension of the graph. In this work, we show that this FPT result can in fact be extended to all graphs of bounded tree-length. This includes well-known classes like chordal graphs, AT-free graphs, and permutation graphs. We also show that this problem is FPT parameterized by the modular-width of the input graph.

关键词： algorithms and data structures graph algorithms parameterized algorithms

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Numerical Investigation of the Dynamic Instability of a Reentry Capsule in Transonic Flow

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AIAA JOURNAL 2024年第2期62卷 449-459页

作者： Han, Seoeum Lee, Bok Jik Furudate, Michiko Ahn Nagai, Hiroki Seoul Natl Univ Dept Aerosp Engn Seoul 08826 South Korea Chungnam Natl Univ Dept Mechatron Engn Daejeon 34134 South Korea Tohoku Univ Dept Aerosp Engn Sendai Miyagi 9808579 Japan

This study presents a numerical investigation of transonic flow characteristics over a reentry capsule at Mach 1.05, employing a detached eddy simulation. The simulated flowfields demonstrate that the recompression shock wave oscillates back and forth at a Strouhal number of the order of 0.01. Frequency analysis of fluctuations in the drag coefficient and base pressure reveals that these fluctuations can be predominantly attributed to oscillations in the recompression shock wave. While the recompression shock wave propagates upstream, local shock waves occur alternately in the upper and lower free-shear layers, with a Strouhal number of the order 0.1, due to the instability of free-shear layers. The repeated occurrence of these local shock waves causes the recirculation region to shrink, resulting in a decrease in the base pressure. Conversely, while the recompression shock wave propagates downstream, no local shock wave occurs and the recirculation region expands, leading to an increase in the base pressure. These results suggest that the interactions among the recompression shock wave, local shock wave, and free shear layer give rise to fluctuations in the base pressure of the capsule, which in turn can affect its dynamic instability.

关键词： Numerical Investigation Compressible Flow Shock Waves Boundary Layers Strouhal Number Freestream Conditions Improved Delayed Detached Eddy Simulation Fluid Flow Properties algorithms and data structures Reynolds Averaged Navier Stokes

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Spectral Sparsification in the Semi-streaming Setting

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THEORY OF COMPUTING SYSTEMS 2013年第2期53卷 243-262页

作者： Kelner, Jonathan A. Levin, Alex MIT Dept Math Cambridge MA 02139 USA

Let G be a graph with n vertices and m edges. A sparsifier of G is a sparse graph on the same vertex set approximating G in some natural way. It allows us to say useful things about G while considering much fewer than m edges. The strongest commonly-used notion of sparsification is spectral sparsification;H is a spectral sparsifier of G if the quadratic forms induced by the Laplacians of G and H approximate one another well. This notion is strictly stronger than the earlier concept of combinatorial sparsification. In this paper, we consider a semi-streaming setting, where we have only storage space, and we thus cannot keep all of G. In this case, maintaining a sparsifier instead gives us a useful approximation to G, allowing us to answer certain questions about the original graph without storing all of it. We introduce an algorithm for constructing a spectral sparsifier of G with O(nlogn/I mu (2)) edges (where I mu is a parameter measuring the quality of the sparsifier), taking time and requiring only one pass over G. In addition, our algorithm has the property that it maintains at all times a valid sparsifier for the subgraph of G that we have received. Our algorithm is natural and conceptually simple. As we read edges of G, we add them to the sparsifier H. Whenever H gets too big, we resparsify it in time. Adding edges to a graph changes the structure of its sparsifier's restriction to the already existing edges. It would thus seem that the above procedure would cause errors to compound each time that we resparsify, and that we should need to either retain significantly more information or reexamine previously discarded edges in order to construct the new sparsifier. However, we show how to use the information contained in H to perform this resparsification using only the edges retained by earlier steps in nearly linear time.

关键词： algorithms and data structures Graph algorithms Spectral graph theory Sub-linear space algorithms Spectral sparsification

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Aeroacoustic Liner Impedance Metamodel from Simulation and Experimental data Using Probabilistic Learning

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AIAA JOURNAL 2023年第11期61卷 4926-4934页

作者： Sinha, Amritesh Soize, Christian Desceliers, Christophe Cunha, Guilherme Gustave Eiffel Univ MSME UMR 8208 F-77454 Marne La Vallee 2 France Airbus Operat SAS F-31300 Toulouse France

To be able to calculate a parameterized aeroacoustic liner impedance, a robust statistical metamodel is constructed as a function of the frequency and of the control parameters that are the percentage of open area and the sound pressure level. This construction is based on the use of simulated data generated with a computationally expensive aeroacoustic model, which translates to a very small training dataset. This means that the learning process has to be used and the probabilistic learning on manifolds algorithm is chosen. Although the aeroacoustic simulation is conducted on a large aeroacoustic computational model, some approximations are introduced, generating model errors that are taken into account by a probability model in the constructed training dataset. This probability model is calibrated using dimensionless experiments available from the open literature. Despite the fact that only a small amount of data is available, a novel statistical metamodel is successfully developed for which the predictions are consistent. This statistical framework allows for exhibiting a confidence region of the parameterized aeroacoustic liner impedance, which gives an information about the level of uncertainties as a function of the frequency and the control parameters.

关键词： Computational Modeling Sound Pressure Level Cumulative Distribution Function algorithms and data structures Computing and Informatics Hamiltonian Monte Carlo Probabilistic learning

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Numerical Investigations on Phase Cancelation of Interaction Noise for Counter-Rotating Propellers

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AIAA JOURNAL 2024年第5期62卷 1826-1839页

作者： Lyu, Changhao Liu, Peiqing Hu, Tianxiang Qu, Qiulin Geng, Xin Sun, Tao Guo, Hao Akkermans, Rinie A. D. Beihang Univ Sch Aeronaut Sci & Engn Key Lab Aeroacoust Minist Ind & Informat TechnolLu Shijia Lab Beijing 100191 Peoples R China Beihang Univ Sch Aeronaut Sci & Engn Key Lab Fluid Mech Minist Educ Beijing 100191 Peoples R China Hamburg Univ Appl Sci Dept Automot & Aeronaut Engn D-20099 Hamburg Germany

The large interaction tonal noise of counter-rotating propellers significantly restricts their application in civil aviation. A pair of counter-rotating propellers was simulated by the lattice Boltzmann method, and the far-field noise was predicted by the Ffowcs Williams and Hawkings analogy. Dynamic mode decomposition was introduced to analyze the surface pressure contribution to far-field noise and to provide insights on the cancellation mechanism of the noise source distribution for the interaction tone. It was found that the cancellation effect is closely related to the relative position between the front blade wake and rear blade element. By adjusting the rear blade sweep and, hence, changing the relative position, the interaction tone can be reduced effectively.

关键词： Counter Rotating Propellers algorithms and data structures Thermal Lattice Boltzmann Method Civil Aviation Vortex Dynamics Overall Sound Pressure Level Frequency Domain Beamforming Aerodynamic Center Tracking and Positioning Systems China Aerodynamics Research and Development Center

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Lower Bounds on Performance of Metric Tree Indexing Schemes for Exact Similarity Search in High Dimensions

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ALGORITHMICA 2013年第2期66卷 310-328页

作者： Pestov, Vladimir Univ Ottawa Dept Math & Stat Ottawa ON K1N 6N5 Canada

Within a mathematically rigorous model, we analyse the curse of dimensionality for deterministic exact similarity search in the context of popular indexing schemes: metric trees. The datasets X are sampled randomly from a domain Omega, equipped with a distance, rho, and an underlying probability distribution, mu. While performing an asymptotic analysis, we send the intrinsic dimension d of Omega to infinity, and assume that the size of a dataset, n, grows superpolynomially yet subexponentially in d. Exact similarity search refers to finding the nearest neighbour in the dataset X to a query point omega a Omega, where the query points are subject to the same probability distribution mu as datapoints. Let denote a class of all 1-Lipschitz functions on Omega that can be used as decision functions in constructing a hierarchical metric tree indexing scheme. Suppose the VC dimension of the class of all sets {omega:f(omega)a parts per thousand yena}, aaa"e is o(n (1/4)/log(2) n). (In view of a 1995 result of Goldberg and Jerrum, even a stronger complexity assumption d (O(1)) is reasonable.) We deduce the Omega(n (1/4)) lower bound on the expected average case performance of hierarchical metric-tree based indexing schemes for exact similarity search in (Omega,X). In paricular, this bound is superpolynomial in d.

关键词： algorithms and data structures Indexing schemes Similarity search Vapnik-Chernonenkis theory Algorithm performance

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data-Driven Control-Oriented Modeling for Response of Fluidic Thrust Vectoring

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AIAA JOURNAL 2024年第10期62卷 3789-3802页

作者： Zhou, Kaiwen Cheng, Changming Wen, Xin Shanghai Jiao Tong Univ Gas Turbine Res Inst Sch Mech Engn Key Lab Educ Minist Power Machinery & Engn 800 Dongchuan Rd Shanghai 200240 Peoples R China

Response to control input is of significance to the application of real-time active flow control (AFC). In this paper, a novel data-driven framework is used to discover the underlying physics of the dynamic response process of fluidic thrust vectoring (FTV), a typical application of AFC. In the proposed framework, sparse identification of a nonlinear dynamics (SINDy) algorithm is used to identify the governing equations of the flow control responses of sets of noisy measurement data. The clustering algorithm is then used to seek the generalized coefficients of basis functions for different sets of data, which improve the robustness of the model to noisy measurement data. First, a simulated mechanical system is used to validate the effect of the framework. To simplify the modeling, control performance and characteristics are investigated in a detailed manner. Then a dimensionless parameter Delta Cp based on the pressure coefficient is found to exhibit a linear relationship with the vector angle under different working conditions. This parameter is introduced in the proposed framework to model the dynamic process of response to control input. The obtained governing equations can describe the dynamic process accurately based on the validation of testing data. The form of the governing equation is rewritten and analyzed based on the control theory, revealing the physics of this process, which is significant to practical AFC implementation.

关键词： Active Flow Control State Estimation algorithms and data structures Fluid Dynamics

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Unified Control of Flight Dynamics and Actuators Using Local Accelerations

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2024年第9期47卷 1920-1938页

作者： Meyer-Bruegel, Wolfram Silvestre, Flavio J. Tech Univ Berlin Chair Flight Mech Flight Control & Aeroelast Marchstr 12 D-10587 Berlin Germany

Control surface actuators usually come with their own servo control algorithm, which ensures that the deflection commanded by the flight control laws is quickly achieved. Therefore, flight control and servo control together form a cascaded control structure. Traditionally, the flight control laws (outer loop) and servo control laws (inner loop) are designed independently. However, recent applications demand an increasingly dynamic design of flight control, with actuator dynamics becoming a limiting factor. In this paper, a unified control design for actuators and flight dynamics is investigated. The local acceleration at the lifting surface (empennages and wing), close to the actuator, is fed back within an inner actuator control loop, allowing for faster compensation. The theoretical properties of the suggested control structure are discussed analytically first. Later, the concept is applied to a linear model for longitudinal aircraft motion. A classical state controller serves as a reference for comparison of the proposed strategy against the standard one with the actuator internal control law. Both controllers are designed using eigenstructure assignment, and the pole locations are numerically optimized. The closed-loop behavior is assessed in the time and frequency domains. The results promise significant improvements in terms of disturbance rejection and robustness.

关键词： Flight Path Angle Actuators Aircraft Flight Control System Closed Loop Transfer Function algorithms and data structures Flight Control Law Signal Processing Aircraft Components and Structure Flight Control Surfaces Aerodynamic Coefficients

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