Attempt of Evaluating Numerical Errors in CFD Code

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  • CFDにおける数値誤差解析の試み
  • CFD ニ オケル スウチ ゴサ カイセキ ノ ココロミ

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Abstract

The importance of CFD validation has been recognized, as needs of CFD has currently increased. Several international workshops and meetings on CFD validation have been held for this purpose. Many researchers discussed general philosophy for CFD validation from the view point of the user, and concluded that the achievement of a high-level confidence in CFD for applying it to practical design problems, in turn, requires experiments focussing the verification of the accuracy of CFD codes. The difference between a measured value of flow phenomena and a computational result by CFD is roughly separated into two kinds of errors ; those are a measurement error and a CFD error that includes a modelling error and numerical errors. Therefore, it is important for CFD validation to estimate the numerical errors. Some kinds of numerical errors may arise in the computation itself such as the errors due to mathematical modelling, discretization, approximate solution algorithm, and digital operation. There are two approaches in numerical error analysis, i.e., sensitivity and uncertainty analyses. The sensitivity analysis deals with the sensitivities of various parameters, i.e., the topology and spacing of grids, etc., to numerical solutions, while in the uncertainty analysis, the total numerical error is estimated by summing up the above elemental errors. The present study follows the latter method. We thus classify numerical errors arising in the processes of computation and propose a procedure to verify the accuracy of a CFD code only by slightly modifying the CFD code itself. The procedure applied to an unsteady incompressible Navier-Stokes equation gives both the solution and the bounds of its errors at the same time. The discretization method used here is based on the finite-volume method with geometric conservation. The bounds of the discretization error are estimated from the contribution of the lowest-order truncated terms on the discretized equation. We also investigated their propagation both in time and space domains. A numerical test is performed for the simulation of viscous flows around a sinusoidally oscillating circular cylinder to demonstrate the validity of this procedure.

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