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Showing 1 to 20 of 32 for “"truncation error"”.
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Truncation Error Based Mesh Adaptation and its Application to Multi-Mesh CFD
One of the largest sources of error in a CFD simulation is the discretization error. One of the least computationally expensive ways of reducing the discretization error in a simulation is by performing mesh adaptation. In this work, the mesh adaptation processes are driven by the truncation error, …
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Application of Improved Truncation Error Estimation Techniques to Adjoint Based Error Estimation and Grid Adaptation
… Dynamics (CFD) are subject to discretization error, which is locally generated by truncation error. The discretization error is extremely difficult to properly estimate and this in turn leads to uncertainty over the quality of the numerical solutions obtained via CFD methods and the …
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On the Tightness of the Balanced Truncation Error Bound with an Application to Arrowhead Systems
Balanced truncation model reduction for linear systems yields reduced-order models that satisfy a well-known error bound in terms of a system's Hankel singular values. This bound is known to hold with equality under certain conditions, such as when the full-order system is state-space symmetric. In …
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Residual-based Discretization Error Estimation for Computational Fluid Dynamics
… 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 …
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Application of r-Adaptation Techniques for Discretization Error Improvement in CFD
… 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 …
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Analytic Computation of the Prime -Counting Function
… perform a careful analysis of various sources of truncation error; (3) give choices of parameters which bound the truncation error while keeping computation to a minimum; (4) develop two new methods for enumerating primes in intervals, which require much less memory than previously known sieving …
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On Numerical Error Estimation for the Finite-Volume Method with an Application to Computational Fluid Dynamics
… each CFD result inherently contains numerical errors that can significantly degrade the accuracy of a simulation. Discretization error is typically the largest contributor to the overall numerical error in a given simulation. Discretization error can be very difficult to estimate since the …
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Residual-Based Discretization Error Estimation for Unsteady Flows
… 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 …
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Lie group invariant finite-difference schemes for the neutron diffusion equation
… neutron diffusion equation, the typical local truncation error for standard finite difference approximation is on the order of the mesh spacing squared. To improve the accuracy of the finite difference approximation of the diffusion equation, the invariance properties of the original …
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A Generalization of Linear Multistep Methods
… interpolating and approximating functions. Local truncation error estimates as well as stability analysis is given. Specifically, the class of linear multistep methods of the Adams and BDF type are discussed.</p>
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Discretization Error Estimation Using the Error Transport Equations for Computational Fluid Dynamics Simulations
… methods, and finite-element methods. Error introduced in the discretization process is called discretization error and defined as the difference between the exact solution to the discrete equations and the exact solution to the partial differential or integral equations. For most CFD …
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PARASPICE: A parallel direct circuit simulator for shared-memory multiprocessors
… of sparse linear systems (SOLVE), and local truncation error estimation (TRUNC), which account for at least 95 percent of the total job time. Therefore, it is suitable for a wide range of shared-memory multiprocessors. The implementation of the approach in SPICE2 resulted in a portable …
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The application of high order finite difference methods to the diffusion-convection equation
… 5PFDM. It has fourth order correctness in space truncation error and shows good approximation to the solution of the equation in a normalized, dimensionless fluid system and also in a field size fluid system. Comparisions of the numerical results with the analytical solution of the equation are …
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High-Order and Wavelet-Adaptive Immersed Methods for PDEs on Complex Domain Geometries
… the wavelet and serves as an indicator for local truncation error (LTE), resulting in an adaptive resolution strategy with explicit error control. To address the latter, we introduce a fifth-order upwind finite difference (FD) scheme that sustains numerical stability across any immersed interface …
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Lattice Boltzmann Methods for Diffuse and Mobile Interfaces
… approaches are employed for deriving the truncation error of LB models which approximate Navier-Stokes flows. Improved LB models are formulated and validated through point-by-point comparison with limiting benchmark flows. Finally, the modified LB models are used to study a complex …
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Automatic, Unstructured Mesh Generation for 2D Shelf Based Tidal Models
… process of creating meshes which utilizes local truncation analysis to generate a spatially varied size function. An advancing frontal mesh generation algorithm uses this function to optimize node placement and density. Further analysis to better understand appropriate applications of this …
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Numerical simulation of microwave heating of a target with temperature dependent electrical properties in a single-mode cavity
… grids are refined simply to reduce asymptotic truncation error, our method can retain its advantages by reducing truncation error through higher-order discretization of the Helmholtz operator.
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Error Assessment in FEM Calculations of Flows with Moving Boundaries
… of the calculations is examined through local truncation error analysis and numerical experiments. The two-dimensional flow between two plates separating at a prescribed speed, which admits an analytical solution, is used to verify and illustrate the results. It is determined that the accuracy …
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A Lattice Boltzmann method model of diffusion-weighted magnetic resonance imaging in skeletal muscle
… in both time and space at the theoretical truncation error rate and to agree with analytical solutions of limiting cases. The effect of membrane permeability is investigated and found to be consistent in trend with prior experimental investigations. A simpler two-compartment exchange model …
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Truncated Bayesian nonparametrics
… treatment of sequential representations and truncation in Bayesian nonparametrics. It details three sequential representations of a large class of nonparametric priors, and analyzes their truncation error and computational complexity. The results generalize and improve upon those existing in …
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