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Showing 1 to 20 of 39 for “"Discretization Error"”.
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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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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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Extrapolation-based Discretization Error and Uncertainty Estimation in Computational Fluid Dynamics
… requires approximations that result in numerical error in the final solution. Of the different types of numerical error in a solution, discretization error is the largest and most difficult error to estimate. In addition, the accuracy of the discretization error estimates relies on the solution …
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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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Discretization Error Estimation Using the Error Transport Equations for Computational Fluid Dynamics Simulations
… nonlinear algebraic equations. Typical spatial discretization schemes include finite-difference methods, finite-volume 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 …
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Discretization Error Estimation and Exact Solution Generation Using the 2D Method of Nearby Problems
… solutions the MNP can be extended for use as an error estimator. The nearby problem can be solved numerically on the same grid as the original problem. The nearby problem discretization error is calculated as the difference between its numerical solution and exact solution (curve fit). This is an …
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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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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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Uncertainty assessment for CFD using error transport equation
… The overall uncertainty (or the global error) involved in CFD results can be due to different sources mainly contributed by (i) discretization error (or solution error due to incomplete grid convergence), (ii) iteration convergence error, (iii) grid generation errors (skewness, grid …
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Application of Improved Truncation Error Estimation Techniques to Adjoint Based Error Estimation and Grid Adaptation
… Fluid 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 …
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A Posteriori Error Analysis of the Discontinuous Galerkin Method for Linear Hyperbolic Systems of Conservation Laws
… an analysis for the discontinuous Galerkin discretization error of multi-dimensional first-order linear symmetric and symmetrizable hyperbolic systems of conservation laws. We explicitly write the leading term of the local DG error, which is spanned by Legendre polynomials of degree p and …
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A Posteriori Error Analysis for a Discontinuous Galerkin Method Applied to Hyperbolic Problems on Tetrahedral Meshes
… a simple and efficient \emph{a posteriori} error estimation procedure for a discontinuous finite element method applied to scalar first-order hyperbolic problems on structured and unstructured tetrahedral meshes. We present a local error analysis to derive a discontinuous Galerkin …
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A posteriori error estimates for the Poisson problem on closed, two-dimensional surfaces
… We then construct an adjoint-based a posteriori error estimate for the problem, discuss some computational issues that arise in solving the problem and show some numerical examples. The major sources of numerical error when solving the Poisson problem are geometric error, discretization error, …
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Unified Multilevel Adaptive Finite Element Methods for Elliptic Problems
… resulting change in the solution is used as an error indicator to determine which triangles to divide. The multigrid iteration uses a red-black Gauss-Seidel relaxation in which the black relaxations are used only locally. The grid transfers use the change between the nodal and hierarchical …
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Accuracy improvement of the second-kind Fredholm integral equations in computational electromagnetics
… of the numerical accuracy is mainly due to the discretization error of the identity operators involved in second-kind IEs. In the past decade, although much effort has been made to improve the numerical accuracy of the second-kind integral equations, no conclusive understandings and final …
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Optimizing Irreversible Perturbations of the Unadjusted Langevin Algorithm
… is anisotropic or multimodal, and persistent discretization bias introduced by numerical schemes. This thesis investigates irreversible perturbations of overdamped Langevin dynamics, aiming to accelerate mixing while controlling discretization error. Irreversible perturbations introduce …
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Statistical Modeling of Simulation Errors and Their Reduction via Response Surface Techniques
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 …
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Verification of Compressible and Incompressible Computational Fluid Dynamics Codes and Residual-based Mesh Adaptation
… model of MFIX. In a CFD simulation, truncation error (TE) is the difference between the continuous governing equation and its discrete approximation. Since TE can be shown to be the local source term for the discretization error, TE is proposed as the criterion for determining which regions of …
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Numerical Simulation of 4th Order Total Variation Flow Problem by using C^0 IPDG Method
… functional. The main results are a priori error estimates of the global discretization error in a mesh dependent C$^0$IPDG-norm and the L$^2$-norm. A documentation of numerical results is provided illustrating the performance of the C$^0$IPDG method and predictor corrector continuation …
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Adaptive Finite Element Methods for Optimization in Partial Differential Equations
A new approach to error control and mesh adaptivity is described for the discretization of optimal control problems governed by (elliptic) partial differential equations. The Lagrangian formalism yields the first-order necessary optimality condition in form of an indefinite boundary value problem …
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