Relevant bibliographies by topics / Nonuniform discretization

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Nonuniform discretization'

Author: Grafiati
Published: 4 June 2021
Last updated: 16 February 2022

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Journal articles on the topic "Nonuniform discretization"

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Tölke, Jonas, Manfred Krafczyk, Manuel Schulz, Ernst Rank, and Rodolfo Berrios. "Implicit discretization and nonuniform mesh refinement approaches for FD discretizations of LBGK Models." International Journal of Modern Physics C 09, no. 08 (December 1998): 1143–57. http://dx.doi.org/10.1142/s0129183198001059.

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After a short discussion of recent discretization techniques for the lattice-Boltzmann equations we motivate and discuss some alternative approaches using implicit, nonuniform FD discretization and mesh refinement techniques. After presenting results of a stability analysis we use an implicit approach to simulate a boundary layer test problem. The numerical results compare well to the reference solution when using strongly refined meshes. Some basic ideas for a nonuniform mesh refinement (with non-cartesian mesh topology) are introduced using the standard discretization procedure of alternating collision and propagation.
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Qiu, Ruofan, Rongqian Chen, and Yancheng You. "An implicit-explicit finite-difference lattice Boltzmann subgrid method on nonuniform meshes." International Journal of Modern Physics C 28, no. 04 (April 2017): 1750045. http://dx.doi.org/10.1142/s0129183117500450.

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In this paper, an implicit-explicit finite-difference lattice Boltzmann method with subgrid model on nonuniform meshes is proposed. The implicit-explicit Runge–Kutta scheme, which has good convergence rate, is used for the time discretization and a mixed difference scheme, which combines the upwind scheme with the central scheme, is adopted for the space discretization. Meanwhile, the standard Smagorinsky subgrid model is incorporated into the finite-difference lattice Boltzmann scheme. The effects of implicit-explicit Runge–Kutta scheme and nonuniform meshes of present lattice Boltzmann method are discussed through simulations of a two-dimensional lid-driven cavity flow on nonuniform meshes. Moreover, the comparison simulations of the present method and multiple relaxation time lattice Boltzmann subgrid method are conducted qualitatively and quantitatively.
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Reif, John H., and Hongyan Wang. "Nonuniform Discretization for Kinodynamic Motion Planning and its Applications." SIAM Journal on Computing 30, no. 1 (January 2000): 161–90. http://dx.doi.org/10.1137/s0097539798331975.

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Di Francescantonio, P., and D. Casalino. "Green's Function Discretization Scheme for Sound Propagation in Nonuniform Flows." AIAA Journal 37, no. 10 (October 1999): 1161–72. http://dx.doi.org/10.2514/2.609.

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Di Francescantonio, P., and D. Casalino. "Green's function discretization scheme for sound propagation in nonuniform flows." AIAA Journal 37 (January 1999): 1161–72. http://dx.doi.org/10.2514/3.14305.

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Ghayesh, Mergen H., Ali Farajpour, and Hamed Farokhi. "Asymmetric Oscillations of AFG Microscale Nonuniform Deformable Timoshenko Beams." Vibration 2, no. 2 (June 14, 2019): 201–21. http://dx.doi.org/10.3390/vibration2020013.

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A nonlinear vibration analysis is conducted on the mechanical behavior of axially functionally graded (AFG) microscale Timoshenko nonuniform beams. Asymmetry is due to both the nonuniform material mixture and geometric nonuniformity. Using the Timoshenko beam theory, the continuous models for translation/rotation are developed via an energy balance. Size-dependence is incorporated via the modified couple stress theory and the rotation via the Timoshenko beam theory. Galerkin’s method of discretization is applied and numerical simulations are conducted for a size-dependent vibration of the AFG microscale beam. Effects of material gradient index and axial change in the cross-sectional area on the force and frequency diagrams are investigated.
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Chen, Xu, Wenli Du, Huaglory Tianfield, Rongbin Qi, Wangli He, and Feng Qian. "Dynamic Optimization of Industrial Processes With Nonuniform Discretization-Based Control Vector Parameterization." IEEE Transactions on Automation Science and Engineering 11, no. 4 (October 2014): 1289–99. http://dx.doi.org/10.1109/tase.2013.2292582.

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Muller-Gronbach, Thomas, and Klaus Ritter. "Lower Bounds and Nonuniform Time Discretization for Approximation of Stochastic Heat Equations." Foundations of Computational Mathematics 7, no. 2 (January 5, 2006): 135–81. http://dx.doi.org/10.1007/s10208-005-0166-6.

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Yi, Tae-Hyeong, and Francis X. Giraldo. "Vertical Discretization for a Nonhydrostatic Atmospheric Model Based on High-Order Spectral Elements." Monthly Weather Review 148, no. 1 (December 27, 2019): 415–36. http://dx.doi.org/10.1175/mwr-d-18-0283.1.

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Abstract This study addresses the treatment of vertical discretization for a high-order, spectral element model of a nonhydrostatic atmosphere in which the governing equations of the model are separated into horizontal and vertical components by introducing a coordinate transformation, so that one can use different orders and types of approximations in both directions. The vertical terms of the decoupled governing equations are discretized using finite elements based on either Lagrange or basis-spline polynomial functions in the sigma coordinate, while maintaining the high-order spectral elements for the discretization of the horizontal terms. This leads to the fact that the high-order model of spectral elements with a nonuniform grid, interpolated within an element, can be easily accommodated with existing physical parameterizations. Idealized tests are performed to compare the accuracy and efficiency of the vertical discretization methods, in addition to the central finite differences, with those of the standard high-order spectral element approach. Our results show, through all the test cases, that the finite element with the cubic basis-spline function is more accurate than the other vertical discretization methods at moderate computational cost. Furthermore, grid dependency studies in the tests with and without orography indicate that the convergence rate of the vertical discretization methods is lower than the expected level of discretization accuracy, especially in the Schär mountain test, which yields approximately first-order convergence.
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Ali, Wondwosen, and Girum Urgessa. "Computational Model for Internal Relative Humidity Distributions in Concrete." Journal of Computational Engineering 2014 (March 9, 2014): 1–7. http://dx.doi.org/10.1155/2014/539850.

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A computational model is developed for predicting nonuniform internal relative humidity distribution in concrete. Internal relative humidity distribution is known to have a direct effect on the nonuniform drying shrinkage strains. These nonuniform drying shrinkage strains result in the buildup of internal stresses, which may lead to cracking of concrete. This may be particularly true at early ages of concrete since the concrete is relatively weak while the difference in internal relative humidity is probably high. The results obtained from this model can be used by structural and construction engineers to predict critical drying shrinkage stresses induced due to differential internal humidity distribution. The model uses finite elment-finite difference numerical methods. The finite element is used to space discretization while the finite difference is used to obtain transient solutions of the model. The numerical formulations are then programmed in Matlab. The numerical results were compared with experimental results found in the literature and demonstrated very good agreement.
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Dissertations / Theses on the topic "Nonuniform discretization"

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Yu, Mingzhao. "Model Reduction and Nonlinear Model Predictive Control of Large-Scale Distributed Parameter Systems with Applications in Solid Sorbent-Based CO2 Capture." Research Showcase @ CMU, 2017. http://repository.cmu.edu/dissertations/887.

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This dissertation deals with some computational and analytic challenges for dynamic process operations using first-principles models. For processes with significant spatial variations, spatially distributed first-principles models can provide accurate physical descriptions, which are crucial for offline dynamic simulation and optimization. However, the large amount of time required to solve these detailed models limits their use for online applications such as nonlinear model predictive control (NMPC). To cope with the computational challenge, we develop computationally efficient and accurate dynamic reduced order models which are tractable for NMPC using temporal and spatial model reduction techniques. Then we introduce an input and state blocking strategy for NMPC to further enhance computational efficiency. To improve the overall economic performance of process systems, one promising solution is to use economic NMPC which directly optimizes the economic performance based on first-principles dynamic models. However, complex process models bring challenges for the analysis and design of stable economic NMPC controllers. To solve this issue, we develop a simple and less conservative regularization strategy with focuses on a reduced set of states to design stable economic NMPC controllers. In this thesis, we study the operation problems of a solid sorbent-based CO2 capture system with bubbling fluidized bed (BFB) reactors as key components, which are described by a large-scale nonlinear system of partial-differential algebraic equations. By integrating dynamic reduced models and blocking strategy, the computational cost of NMPC can be reduced by an order of magnitude, with almost no compromise in control performance. In addition, a sensitivity based fast NMPC algorithm is utilized to enable the online control of the BFB reactor. For economic NMPC study, compared with full space regularization, the reduced regularization strategy is simpler to implement and lead to less conservative regularization weights. We analyze the stability properties of the reduced regularization strategy and demonstrate its performance in the economic NMPC case study for the CO2 capture system.
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Book chapters on the topic "Nonuniform discretization"

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Wesseling, Pieter. "Finite volume and finite difference discretization on nonuniform grids." In Principles of Computational Fluid Dynamics, 81–109. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-05146-3_3.

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"Nonuniform Structured Meshes." In Mimetic Discretization Methods, 145–52. Chapman and Hall/CRC, 2013. http://dx.doi.org/10.1201/b14575-14.

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Glatzmaier, Gary A. "Spatial Discretizations." In Introduction to Modeling Convection in Planets and Stars. Princeton University Press, 2013. http://dx.doi.org/10.23943/princeton/9780691141725.003.0009.

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This chapter considers two ways of employing a spatial resolution that varies with position within a finite-difference method: using a nonuniform grid and mapping to a new coordinate variable. It first provides an overview of nonuniform grids before discussing coordinate mapping as an alternative way of achieving spatial discretization. It then describes an approach for treating both the vertical and horizontal directions with simple finite-difference methods: defining a streamfunction, which automatically satisfies mass conservation, and solving for vorticity via the curl of the momentum conservation equation. It also explains the use of the Chebyshev–Fourier method to simulate the convection or gravity wave problem by employing spectral methods in both the horizontal and vertical directions. Finally, it looks at the basic ideas and some issues that need to be addressed with respect to parallel processing as well as choices that need to be made when designing a parallel code.
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C. Mehta, Rakhab. "Influence of Input Parameters on the Solution of Inverse Heat Conduction Problem." In Inverse Heat Conduction and Heat Exchangers. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.91000.

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A one-dimensional transient heat conduction equation is solved using analytical and numerical methods. An iterative technique is employed which estimates unknown boundary conditions from the measured temperature time history. The focus of the present chapter is to investigate effects of input parameters such as time delay, thermocouple cavity, error in the location of thermocouple position and time- and temperature-dependent thermophysical properties. Inverse heat conduction problem IHCP is solved with and without material conduction. A two-time level implicit finite difference numerical method is used to solve nonlinear heat conduction problem. Effects of uniform, nonuniform and deforming computational grids on the estimated convective heat transfer are investigated in a nozzle of solid rocket motor. A unified heat transfer analysis is presented to obtain wall heat flux and convective heat transfer coefficient in a rocket nozzle. A two-node exact solution technique is applied to estimate aerodynamic heating in a free flight of a sounding rocket. The stability of the solution of the inverse heat conduction problem is sensitive to the spatial and temporal discretization.
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Conference papers on the topic "Nonuniform discretization"

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Kassas, Zaher M., and Ricardo Dunia. "Discretization of MIMO Systems with Nonuniform Input and Output Fractional Time Delays." In Proceedings of the 45th IEEE Conference on Decision and Control. IEEE, 2006. http://dx.doi.org/10.1109/cdc.2006.376965.

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Haspel, N., J. F. Mayer, and H. Stetter. "Prediction of Invsicid Flow in Axial Turbines in Comparison With Measurements." In ASME 1993 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/93-gt-112.

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A CFD code for simulation of 3D inviscid throughflow in turbine stages will be presented in this paper. The discretization is realized by a finite difference method applying a transformation procedure. The time dependent Enter equations are solved by the explicit time marching method of Lax, Wendroff and Richtmyer. The coupling between stator and rotor flow is achieved by circumferentially averaged flow data, enabling the simulation of low frequency flow fluctuations. The flow through a gas turbine stator is simulated by the code. In this case secondary flow phenomena caused by a nonuniform inlet flow are of special interest. A throughflow calculation of the last stage of a LP steam turbine shows that the program is able to manage 3D complex transonic flows as well. The CFD results are compared in both cases with experimental data.
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Wang, Wenyi, Liguo Zhang, Jianzhu Cao, and Feng Xie. "Optimization of the Radiation Shielding Program QAD." In 2016 24th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/icone24-60938.

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The QAD program, based on the point kernel integration method, is widely used in the radiation shielding design of nuclear power plants and related fields. However, QAD-CGA, as the latest version of QAD program, still has some problems, which may affect calculation results and limit the application range. In this paper, the features, principles, and algorithms of QAD-CGA program will be described and several optimization will be introduced. The quantity of γ rays considered in each calculation has been expanded, which can supply more accurate results than those from the original program. Furthermore, the number of dose receivers has been increased, which can provide detailed distribution of the dose field. In addition, a method has been put forward to realize the discretization of source intensity automatically which can simplify the input of the program. Meanwhile, the compartmentalization of the discrete source in the program has been improved. If the size of the discrete source can be minimized small enough to be served as an ideological core, the accuracy of calculations of QAD-CGA program would be guaranteed. However, with the increase of the radius of a sphere or cylinder, the volume of the discrete source will be enlarged and the precondition “small enough” will be lost gradually which can result in the increase of the inaccuracy of calculations. A superior algorithm to solve the coordinate distribution of point kernel which is nonuniform has been proposed. It can reduce the inaccuracy from the discretization of the source intensity in spherical and cylindrical geometry effectively. The optimization of QAD-CGA program has been implemented, analyzed and compared to the original edition with a numerical example.
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Fiore, Maxime, Nicolas Gourdain, Jean-François Boussuge, and Eric Lippinois. "Numerical Study of a Linear Cascade With Upstream Cavity Using Various Rim-Seal Geometries and Purge Rates." In ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-76615.

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This paper introduces numerical investigation of a low-speed linear cascade rig with upstream cavity at Reynolds number commonly observed in modern low-pressure turbine stage. This configuration was tested experimentally during the EU project MAGPI (2007–2011) focused on the impact of secondary air systems on gas turbine performance. Three different purge mass flow rate have been tested numerically using three different rim-seal geometry (axial clearance, simple and double radial overlap). The mechanisms and influence of these two parameters on loss generation for the main annulus flow is investigated. The ability of high-fidelity numerical methods to deal with such kind of configuration is assessed by comparing several unsteady codes over the axial geometry at three purge mass flow rate available. Two Large-Eddy Simulation (LES) solvers based respectively on structured and unstructured meshes and a LES-LBM approach in which equations discretization is based upon a Lattice-Boltzmann Method (LBM) and a Sub-Grid Scale (SGS) model from LES developments are used. The comparison against MAGPI experiments and previous Reynolds Averaged Navier-Stokes (RANS) simulation show that despite a variety of flow dynamics modelling, discretization and numerical parameters, the different unsteady codes are well able to recover aerodynamic quantities into the mainstream passage in which purge flow blows at various rate and different rim-seal geometry. Further results obtained from such high-fidelity methods exhibit strong interaction of separated hub boundary at rim-seal interface with nonuniform pressure field imposed by downstream blade leading to a strong in-depth of mainstream flow into the cavity for the axial clearance. Simple and double overlap damper this phenomenon due to localized recirculation zone into the rim-seal. In addition, hub passage vortex and blade suction side unsteadiness are shown to be strongly related to the vortex shedding process occurring at rim-seal interface.
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Hellum, Aren M., Ranjan Mukherjee, and Andrew J. Hull. "Dynamics of Pipes Conveying Fluid With a Non-Uniform Velocity Profile." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-12858.

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Previous work on stability of fluid-conveying cantilever pipes assumed a uniform velocity profile for the conveyed fluid. In real fluid flows, the presence of viscosity leads to a sheared region near the wall. Earlier studies correctly note that viscous forces drop out of the system’s dynamics since the force of fluid shear on the wall is precisely balanced by pressure drop in the conveyed fluid. The effect of shear has therefore not been ignored in these studies. However, a uniform velocity profile assumes that the sheared region is infinitely thin. Prior analysis was extended to account for a fully developed non-uniform profile such as would be encountered in real fluid flows. A modified equation of motion was derived to account for the reduced momentum carried by the sheared fluid. Numerical analysis was carried out to determine a number of velocity profiles over the Reynolds number range of interest and a simple set of curve fits was used when finer discretization was required. Stability analysis of a pipe conveying fluid with these profiles was performed, and the results were compared to a uniform profile. The mass ratio, β, is the ratio of the fluid mass to the total system mass. At β = 0.2, the non-uniform case becomes unstable at a critical velocity, ucr, that is 5.4% lower than the uniform case. The critical frequency, fcr, is 0.36% higher than the uniform case. A more sensitive region exists near β = 0.32. There, the nonuniform velocity ucr is 23% lower than the uniform case and the non-uniform critical frequency fcr is 49% of the uniform case.
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Goulos, Ioannis, and Vassilios Pachidis. "Real-Time Simulation of Rotor Blade Aeroelasticity for the Multidisciplinary Design of Rotorcraft." In ASME Turbo Expo 2014: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/gt2014-26882.

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This paper elaborates on the theoretical development of a mathematical approach, targeting the real-time simulation of aeroelastic rotor blade dynamics for the multidisciplinary design of rotorcraft. A Lagrangian approach is formulated for the rapid estimation of natural vibration characteristics of rotor blades with nonuniform structural properties. Modal characteristics obtained from classical vibration analysis methods, are utilized as assumed deformation functions. Closed form integral expressions are incorporated, describing the generalized centrifugal forces and moments acting on the blade. The treatment of three-dimensional elastic blade kinematics in the time-domain is thoroughly discussed. In order to ensure robustness and establish applicability in real-time, a novel, second-order accurate, finite-difference scheme is utilized for the temporal discretization of elastic blade motion. The developed mathematical approach is coupled with a finite-state induced flow model, an unsteady blade element aerodynamics model, and a dynamic wake distortion model. The combined aeroelastic rotor formulation is implemented in a helicopter flight mechanics code. The aeroelastic behavior of a full-scale hingeless helicopter rotor has been investigated. Results are presented in terms of rotor blade resonant frequencies, airframe–rotor trim performance, oscillatory structural blade loads, and transient rotor response to control inputs. Extensive comparisons are carried out with wind tunnel and flight test measurements found in the open literature, as well as with non-real-time comprehensive analysis methods. It is shown that, the proposed approach exhibits good agreement with flight test data regarding trim performance and transient rotor response characteristics. Accurate estimation of structural blade loads is demonstrated, in terms of both amplitude and phase, up to the third harmonic component of oscillatory loading. It is shown that, the developed model can be utilized for real-time simulation on a modern personal computer. The proposed methodology essentially constitutes an enabling technology for the multidisciplinary design of rotorcraft, when a compromise between simulation fidelity and computational efficiency has to be sought for in the model development process.
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Ergul, Ozgur, Bariscan Karaosmanoglu, Manouchehr Takrimi, and Vakur B. Erturk. "Broadband multilevel fast multipole algorithm for large-scale problems with nonuniform discretizations." In 2016 URSI International Symposium on Electromagnetic Theory (EMTS). IEEE, 2016. http://dx.doi.org/10.1109/ursi-emts.2016.7571375.

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