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Relevant bibliographies by topics / Discretization errors

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Academic literature on the topic 'Discretization errors'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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Journal articles on the topic "Discretization errors"

1

Geurts, Bernard J. "Analysis of errors occurring in large eddy simulation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 367, no. 1899 (2009): 2873–83. http://dx.doi.org/10.1098/rsta.2009.0001.

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We analyse the effect of second- and fourth-order accurate central finite-volume discretizations on the outcome of large eddy simulations of homogeneous, isotropic, decaying turbulence at an initial Taylor–Reynolds number Re λ =100. We determine the implicit filter that is induced by the spatial discretization and show that a higher order discretization also induces a higher order filter, i.e. a low-pass filter that keeps a wider range of flow scales virtually unchanged. The effectiveness of the implicit filtering is correlated with the optimal refinement strategy as observed in an error-lands

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Nilsen, Halvor M., K. A. A. Lie, and Jostein R. Natvig. "Accurate Modeling of Faults by Multipoint, Mimetic, and Mixed Methods." SPE Journal 17, no. 02 (2012): 568–79. http://dx.doi.org/10.2118/149690-pa.

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Summary The predominant way of modeling faults in industry-standard flow simulators is to introduce so-called transmissibility multipliers in the underlying two-point discretization. Although this approach provides adequate accuracy in many practical cases, two-point discretizations are only consistent for K-orthogonal grids and may introduce significant discretization errors for grids that severely depart from being K-orthogonal. Such grid-distortion errors can be avoided by lateral or vertical stair-stepping of deviated faults at the expense of errors in the geometrical fault description. In

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Zhang, Peng, Jie Wang, Yihao Yang, Shuai Liu, and Jingtao Huang. "On Full-Order Flux Observer and Its Discretization for Induction Motor Control." Electronics 14, no. 5 (2025): 916. https://doi.org/10.3390/electronics14050916.

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Accurate flux observation is crucial for the high-performance control of induction motors (IMs). Implementing a full-order flux observer algorithm in digital controllers requires discretizing the continuous-domain full-order flux observer. However, the errors introduced by discretization increase with rising rotor speed. In the field-weakening region, inappropriate discretization methods can lead to significant flux estimation errors, severely affecting the performance of model predictive control-based induction motors and potentially causing system instability. To enhance the convergence spee

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Carmon, G., N. Mamman, and M. Feingold. "Discretization errors in particle tracking." Physica A: Statistical Mechanics and its Applications 376 (March 2007): 117–32. http://dx.doi.org/10.1016/j.physa.2006.10.048.

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Li, Long-yuan, and Peter Bettess. "Adaptive Finite Element Methods: A Review." Applied Mechanics Reviews 50, no. 10 (1997): 581–91. http://dx.doi.org/10.1115/1.3101670.

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The adaptive finite element method (FEM) was developed in the early 1980s. The basic concept of adaptivity developed in the FEM is that, when a physical problem is analyzed using finite elements, there exist some discretization errors caused owing to the use of the finite element model. These errors are calculated in order to assess the accuracy of the solution obtained. If the errors are large, then the finite element model is refined through reducing the size of elements or increasing the order of interpolation functions. The new model is re-analyzed and the errors in the new model are recal

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Kyei, Yaw. "Effective Source Term Discretizations for Higher Accuracy Finite Volume Discretization of Parabolic Equations." International Journal for Innovation Education and Research 9, no. 8 (2021): 366–92. http://dx.doi.org/10.31686/ijier.vol9.iss8.3305.

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A finite volume method is applied to develop space-time discretizations for parabolic equations based on an equation error method.A space-time expansion of the local equation error based on flux integral formulation of the equation is first designed using a desiredframework of neighboring quadrature points for the solution and local source terms. The quadrature weights are then determined through aminimization process for the error which constitutes all local compact fluxes about each centroid within the computational domain.In utilizing a local source term distribution to account for diffusiv

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Mao, Meiliang, Huajun Zhu, Xiaogang Deng, Yaobing Min, and Huayong Liu. "Effect of Geometric Conservation Law on Improving Spatial Accuracy for Finite Difference Schemes on Two-Dimensional Nonsmooth Grids." Communications in Computational Physics 18, no. 3 (2015): 673–706. http://dx.doi.org/10.4208/cicp.250614.060215a.

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AbstractIt is well known that grid discontinuities have significant impact on the performance of finite difference schemes (FDSs). The geometric conservation law (GCL) is very important for FDSs on reducing numerical oscillations and ensuring free-stream preservation in curvilinear coordinate system. It is not quite clear how GCL works in finite difference method and how GCL errors affect spatial discretization errors especially in nonsmooth grids. In this paper, a method is developed to analyze the impact of grid discontinuities on the GCL errors and spatial discretization errors. A violation

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Kahla, Nabil Ben, Saeed AlQadhi, and Mohd Ahmed. "Radial Point Interpolation-Based Error Recovery Estimates for Finite Element Solutions of Incompressible Elastic Problems." Applied Sciences 13, no. 4 (2023): 2366. http://dx.doi.org/10.3390/app13042366.

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Error estimation and adaptive applications help to control the discretization errors in finite element analysis. The study implements the radial point interpolation (RPI)-based error-recovery approaches in finite element analysis. The displacement/pressure-based mixed approach is used in finite element formulation. The RPI approach considers the radial basis functions (RBF) and polynomials basis functions together to interpolate the finite element solutions, i.e., displacement over influence zones to recover the solution errors. The energy norm is used to represent global and local errors. The

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Kinoshita, Hiroshi, and Hiroshi Nakai. "New Methods for Long-Time Numerical Integration of Planetary Orbits." Symposium - International Astronomical Union 152 (1992): 395–406. http://dx.doi.org/10.1017/s0074180900091439.

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When planetary orbits are numerically integrated for a long time by conventional integrators, the most serious problem is secular errors in the energy and the angular momentum of the planetary system due to discretization (truncation) errors. The secular errors in the energy and the angular momentum mean that the semi-major axes, the eccentricities, and the inclinations of planetary orbits have a secular error which grows linearly with time. Recently symplectic integrators and linear symmetric multistep integrators are found not to produce the secular errors in the energy and the angular momen

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Braack, Malte, and Alexandre Ern. "A Posteriori Control of Modeling Errors and Discretization Errors." Multiscale Modeling & Simulation 1, no. 2 (2003): 221–38. http://dx.doi.org/10.1137/s1540345902410482.

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Dissertations / Theses on the topic "Discretization errors"

1

Domschke, Pia [Verfasser]. "Adjoint-Based Control of Model and Discretization Errors for Gas Transport in Networked Pipelines / Pia Domschke." München : Verlag Dr. Hut, 2011. http://d-nb.info/1016531443/34.

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Kim, Hongman. "Statistical Modeling of Simulation Errors and Their Reduction via Response Surface Techniques." Diss., Virginia Tech, 2001. http://hdl.handle.net/10919/28390.

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Errors of computational simulations in design of a high-speed civil transport (HSCT) are investigated. First, discretization error from a supersonic panel code, WINGDES, is considered. Second, convergence error from a structural optimization procedure using GENESIS is considered along with the Rosenbrock test problem. A grid converge study is performed to estimate the order of the discretization error in the lift coefficient (CL) of the HSCT calculated from WINGDES. A response surface (RS) model using several mesh sizes is applied to reduce the noise magnification problem associa

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Jain, Abhishek. "Modeling of turbulent mixing in combustion LES." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1502969701311144.

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Karouma, Abdulrahman. "A Class of Contractivity Preserving Hermite-Birkhoff-Taylor High Order Time Discretization Methods." Thesis, Université d'Ottawa / University of Ottawa, 2015. http://hdl.handle.net/10393/32403.

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In this thesis, we study the contractivity preserving, high order, time discretization methods for solving non-stiff ordinary differential equations. We construct a class of one-step, explicit, contractivity preserving, multi-stage, multi-derivative, Hermite-Birkhoff-Taylor methods of order p=5,6, ..., 15, that we denote by CPHBT, with nonnegative coefficients by casting s-stage Runge-Kutta methods of order 4 and 5 with Taylor methods of order p-3 and p-4, respectively. The constructed CPHBT methods are implemented using an efficient variable step algorithm and are compared to other well-kno

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Gautham, Tejaswini. "Residual-Based Discretization Error Estimation for Unsteady Flows." Thesis, Virginia Tech, 2020. http://hdl.handle.net/10919/96400.

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Computational fluid dynamics (CFD) is a tool that is widely used in most industries today. It is important to have rigorous techniques to estimate the error produced when using CFD. This thesis develops techniques to estimate discretization error for unsteady flows using the unsteady error transport equation (ETE) as well as defect correction. A framework to obtain exact truncation error and estimated truncation error is also presented. The technique and results for the steady-state cases are given and the algorithm used for the steady case is extended for the unsteady case. Numerical results

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Phillips, Tyrone. "Residual-based Discretization Error Estimation for Computational Fluid Dynamics." Diss., Virginia Tech, 2014. http://hdl.handle.net/10919/50647.

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The largest and most difficult numerical approximation error to estimate is discretization error. Residual-based discretization error estimation methods are a category of error estimators that use an estimate of the source of discretization error and information about the specific application to estimate the discretization error using only one grid level. The higher-order terms are truncated from the discretized equations and are the local source of discretization error. The accuracy of the resulting discretization error estimate depends solely on the accuracy of the estimated truncation error

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Jalali, Alireza. "Truncation error analysis of unstructured finite volume discretization schemes." Thesis, University of British Columbia, 2012. http://hdl.handle.net/2429/42429.

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Numerical experiments have proved that numerical errors are at least as large as other sources of error in numerical simulation of fluid flows. Approximating the continuous partial differential equations that govern the behavior of a fluid with discrete relations results in truncation error which is the initial source of numerical errors. Reducing numerical error requires the ability to quantify and reduce the truncation error. Although the truncation error can be easily found for structured mesh discretizations, there is no generic methodology for the truncation error analysis of unstructured

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Tyson, William Conrad. "Application of r-Adaptation Techniques for Discretization Error Improvement in CFD." Thesis, Virginia Tech, 2015. http://hdl.handle.net/10919/78061.

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Computational fluid dynamics (CFD) has proven to be an invaluable tool for both engineering design and analysis. As the performance of engineering devices become more reliant upon the accuracy of CFD simulations, it is necessary to not only quantify and but also to reduce the numerical error present in a solution. Discretization error is often the primary source of numerical error. Discretization error is introduced locally into the solution by truncation error. Truncation error represents the higher order terms in an infinite series which are truncated during the discretization of the continu

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Hardering, Hanne [Verfasser]. "Intrinsic Discretization Error Bounds for Geodesic Finite Elements / Hanne Hardering." Berlin : Freie Universität Berlin, 2015. http://d-nb.info/1074871022/34.

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Niesen, Jitse. "On the global error of discretization methods for ordinary differential equations." Thesis, University of Cambridge, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.616182.

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Books on the topic "Discretization errors"

1

Diskin, Boris. Solving upwind-biased discretizations II: Multigrid solver using semicoarsening. National Aeronautics and Space Administration, Langley Research Center, 1999.

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Center, Langley Research, ed. Solving upwind-biased discretizations II: Multigrid solver using semicoarsening. National Aeronautics and Space Administration, Langley Research Center, 1999.

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Center, Langley Research, ed. Solving upwind-biased discretizations II: Multigrid solver using semicoarsening. National Aeronautics and Space Administration, Langley Research Center, 1999.

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Center, Langley Research, ed. Solving upwind-biased discretizations II: Multigrid solver using semicoarsening. National Aeronautics and Space Administration, Langley Research Center, 1999.

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5

Barth, Timothy J., and Herman Deconinck, eds. Error Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-05189-4.

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6

Herman, Deconinck, ed. Error Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics. Springer Berlin Heidelberg, 2003.

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Diskin, Boris. New factorizable discretizations for the Euler equations. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 2002.

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8

Kunert, Gerd. Advances in a posteriori error estimation on anisotropic finite element discretizations. Logos, 2003.

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9

1952-, Thomas James L., and Institute for Computer Applications in Science and Engineering., eds. Solving upwind-biased discretizations: Defect-correction iterations. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1999.

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1952-, Thomas James L., and Institute for Computer Applications in Science and Engineering., eds. Solving upwind-biased discretizations: Defect-correction iterations. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1999.

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Book chapters on the topic "Discretization errors"

1

Taheri, Nicole, Fabian R. Wirth, Bradley J. Eck, Martin Mevissen, and Robert N. Shorten. "Robustness to Time Discretization Errors in Water Network Optimization." In Operations Research Proceedings. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-28697-6_81.

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Sampson, Myles B., and Larry Sass. "Interlocking Units for Robotically Fabricated Architectural Structures." In Computational Design and Robotic Fabrication. Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-99-8405-3_37.

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AbstractThroughout this paper, we introduce a novel design-driven method for the robotic assembly of unit-based structures. The goal of this research is to establish a method to robotically fabricate discrete structures, using pick-and-place robotic manipulation and customized 3D-printed geometric units. Thus, the methodology allows for the bespoke discretization of architectural solid models into interlocking architectural units. Investigating how design can reduce error in the robotic fabrication process, a significant feature of this research is the application of mechanical coupling for th

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3

Viré, A., and B. Knaepen. "Discretization errors and subgrid scale implementations in Large Eddy Simulations." In Springer Proceedings in Physics. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03085-7_192.

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Visonneau, M., M. Schmid, G. Deng, and M. Perić. "Analysis of Discretization and Modeling Errors in Complex Three-Dimensional Flows." In Numerical Flow Simulation II. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-540-44567-8_19.

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Domschke, Pia, Oliver Kolb, and Jens Lang. "Adjoint-Based Control of Model and Discretization Errors for Gas and Water Supply Networks." In Studies in Computational Intelligence. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20986-4_1.

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Jacod, Jean, and Philip Protter. "Integrated Discretization Error." In Discretization of Processes. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-24127-7_6.

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Hartmann, Friedel. "The Discretization Error." In Green's Functions and Finite Elements. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-29523-2_4.

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Stein, E., K. H. Lambertz, and L. Plank. "Error Estimators and Mesh Adaptation for Thin-Walled Structures at Finite Rotations." In Discretization Methods in Structural Mechanics. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-49373-7_1.

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Zienkiewicz, O. C., B. Boroomand, and J. Z. Zhu. "Recovery Procedures in Error Estimation and Adaptivity." In IUTAM Symposium on Discretization Methods in Structural Mechanics. Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4589-3_1.

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Giles, Michael B., and Niles A. Pierce. "Adjoint Error Correction for Integral Outputs." In Error Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-05189-4_2.

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Conference papers on the topic "Discretization errors"

1

Foster, Norman. "High-Order Overset Methods for Rotorcraft CFD." In Vertical Flight Society 71st Annual Forum & Technology Display. The Vertical Flight Society, 2015. http://dx.doi.org/10.4050/f-0071-2015-10090.

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It has been shown that for overset CFD calculations that utilize high order accurate inviscid flux discretization schemes, solution accuracy can be increased by using high-order overset interpolation. This can be critically relevant in many cases, such as those where it is important to accurately track vortical structures through the domain because of fluid-structure interactions, for example. Many block structured overset CFD solutions employ variants of Lagrangian interpolation to determine overset donor weights and, of these, most use 2nd order accurate interpolation stencils. This paper de

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Datta, Anubhav, and Wayne Johnson. "Integrated Aeromechanics with Three-Dimensional Solid-Multibody Structures." In Vertical Flight Society 70th Annual Forum & Technology Display. The Vertical Flight Society, 2014. http://dx.doi.org/10.4050/f-0070-2014-9502.

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A full three-dimensional finite element-multibody structural dynamic solver is coupled to a three-dimensional Reynolds-averaged Navier-Stokes solver for the prediction of integrated aeromechanical stresses and strains on a rotor blade in forward flight. The objective is to lay the foundations of all major pieces of an integrated three-dimensional rotor dynamic analysis - from model construction to aeromechanical solution to stress/strain calculation. The primary focus is on the aeromechanical solution. Two types of three-dimensional CFD/CSD interfaces are constructed for this purpose with an e

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Hoffmann, Christian, Erik Esche, and Jens-Uwe Repke. "Integration of Design and Operation with Discretization Error Control." In Foundations of Computer-Aided Process Design. PSE Press, 2024. http://dx.doi.org/10.69997/sct.141459.

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Optimization-based process design is a central task of process systems engineering. However, solely relying on steady-state models may potentially lead to dynamic constraint violations, hinder robust performance, or simply reduce the controllability of a process. This has led to the consideration of process dynamics in the design phase, which is commonly termed integration of design and operation / control. Recently, we proposed a framework to carry out this integrative task by formulating a large-scale nonlinear programming problem that is solved simultaneously. To this end, the dynamic proce

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Sablok, R., and K. Aziz. "Upscaling and Discretization Errors in Reservoir Simulation." In SPE Reservoir Simulation Symposium. Society of Petroleum Engineers, 2005. http://dx.doi.org/10.2118/93372-ms.

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Celik, Ismail B., Zhiyuan Ma, and Sofiane Benyahia. "Discretization Error Estimation in Transient Flow Simulations." In ASME 2016 Fluids Engineering Division Summer Meeting collocated with the ASME 2016 Heat Transfer Summer Conference and the ASME 2016 14th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/fedsm2016-7919.

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Most methods presented in the literature for estimation of discretization errors focus primarily on steady flows. The transport of error in strongly transient flow has not been adequately addressed. Issues related to transient error calculations are discussed and some methods that are viable for such applications are proposed. Examples are presented on simple flows such as transient Burgers equation followed by applications to more complex flows, e.g. two-phase gas-solid flow relevant fluidized beds. It is demonstrated that error estimation can be made with reasonable accuracy using a combinat

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TIBURZI, B. C. "LATTICE DISCRETIZATION ERRORS IN CHIRAL EFFECTIVE FIELD THEORIES." In Proceedings of the 5th International Workshop on Chiral Dynamics, Theory and Experiment. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812790804_0078.

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Sommer, Rainer, Leonardo Chimirri, and Nikolai Husung. "Log-enhanced discretization errors in integrated correlation functions." In The 39th International Symposium on Lattice Field Theory. Sissa Medialab, 2023. http://dx.doi.org/10.22323/1.430.0358.

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Brock, Jerry. "Isolating Temporal-Discretization Errors for Separate-Verification Analyses." In 42nd AIAA Aerospace Sciences Meeting and Exhibit. American Institute of Aeronautics and Astronautics, 2004. http://dx.doi.org/10.2514/6.2004-741.

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Rumschinski, Philipp, Dina Shona-Laila, Steffen Borchers, and Rolf Findeisen. "Influence of discretization errors on set-based parameter estimation." In 2010 49th IEEE Conference on Decision and Control (CDC). IEEE, 2010. http://dx.doi.org/10.1109/cdc.2010.5717519.

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Weinmeister, Justin, and Devina P. Sanjaya. "Successive Procedure for Solution Verification Based on User Needs." In ASME 2024 Verification, Validation, and Uncertainty Quantification Symposium. American Society of Mechanical Engineers, 2024. http://dx.doi.org/10.1115/vvuq2024-127747.

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Abstract This paper discusses a revised solution verification procedure for computational fluid dynamics simulations to estimate the uncertainties in the quantities of interest based on discretization error models. This proposed procedure builds upon current procedures described in ASME V&V 20 but provides more guidance in determining the necessary number of mesh levels to build reliable discretization error models. Such guidance is particularly useful for practicing engineers without prior experience in solution verification. The key features of this proposed solution verification procedu

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Reports on the topic "Discretization errors"

1

Larsen, Edward. The Suppression of Energy Discretization Errors in Multigroup Transport Calculations. Office of Scientific and Technical Information (OSTI), 2013. http://dx.doi.org/10.2172/1087139.

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Chen, X., J. M. Connors, and C. H. Tong. A flexible method to calculate the distributions of discretization errors in operator-split codes with stochastic noise in problem data. Office of Scientific and Technical Information (OSTI), 2014. http://dx.doi.org/10.2172/1119920.

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Sinclair, Andrew J., Anil Raju, Matthew J. Kurzen, Christopher John Roy, and Tyrone S. Phillips. Discretization error estimation and exact solution generation using the method of nearby problems. Office of Scientific and Technical Information (OSTI), 2011. http://dx.doi.org/10.2172/1029791.

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Hart, Nathan, and Yousry Azmy. High Order Implicit Residual-Based Spatial Discretization Error Estimation for S_N Neutron Transport. Office of Scientific and Technical Information (OSTI), 2020. http://dx.doi.org/10.2172/1647197.

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