The use of Richardson extrapolation in PNs solutions of rocket nozzle flow

Dang, Anthony; Kehtarnavaz, H.; Coats, D.

doi:10.2514/6.1989-2895

Cited by 4 publications

(1 citation statement)

References 14 publications

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“…Churchill et al (1981) and de Vahl Davis (1983) applied the method to estimate zero-grid-size solution in natural convection problems. Applications to aerodynamic flows are reported by Dang et al (1989) and Zing (1991), amongst others. The common result is that the Richardson extrapolation method is reliable only when the numerical solutions on the different grids used in the procedure are smooth and display similar characteristics, which presupposes that the grids should be sufficiently fine to resolve all flow features.…”

Section: Introductionmentioning

confidence: 99%

Estimating Uncertainty in Computations of Two-Dimensional Separated Flows

Demuren

Wilson

1994

Journal of Fluids Engineering

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The present paper investigates sources of uncertainties in two-dimensional flow computations and presents methods for estimating them. A sample problem is used for illustration. The following categories are explored in detail: (i) Uncertainty due to truncation error in numerical schemes; (ii) Uncertainty due to discretization error; (iii) Uncertainty due to outflow boundary conditions; (iv) Uncertainty due to incomplete iterative convergence; (v) Uncertainty due to computational grid aspect ratio. The error estimates are based on requirements for internal consistencies in computed results. Therefore, they provide better judgement of the numerical solution integrity than comparisons to experimental data or “benchmark” solutions whose reliability may sometimes be questionable. Ideally, both approaches should be employed. A new method is presented for estimating the optimum grid-cell aspect ratio for computational accuracy and efficiency.

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Section: Introductionmentioning

confidence: 99%

Estimating Uncertainty in Computations of Two-Dimensional Separated Flows

Demuren

Wilson

1994

Journal of Fluids Engineering

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Calculation of Numerical Uncertainty Using Richardson Extrapolation: Application to Some Simple Turbulent Flow Calculations

Çelik

Zhang

1995

Journal of Fluids Engineering

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Richardson extrapolation has been applied to turbulent pipe flow and turbulent flow past a backward facing step. A commercial CFD code is used for this purpose. It is found that the application of the method is not straightforward and some aspects need careful consideration. Some of the problems are elucidated. The particular code used for the present application employs a hybrid scheme, and it does not give monotonic convergence for all the variables in all regions as the grid is refined. The flow regions and the variables which converge monotonically in these regions should be identified first before the method is applied. When this is done Richardson extrapolation gives good results in calculating the apparent order of the numerical procedure used, as well as obtaining grid independent results with which discretization error bounds can be calculated as measures of numerical uncertainty. Even in cases where it does not work, the method can be used as an error indicator for some obscured user mistakes. This paper also demonstrates several shortcomings of using commercial CFD codes. The present findings should help the users of CFD software in general, to quantify discretization errors in their calculations.

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Performance and flow calculations for a gaseous H2/O2 thruster

Kim¹,

Vanoverbeke

1991

Journal of Spacecraft and Rockets

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The use of Richardson extrapolation in PNs solutions of rocket nozzle flow

Cited by 4 publications

References 14 publications

Estimating Uncertainty in Computations of Two-Dimensional Separated Flows

Estimating Uncertainty in Computations of Two-Dimensional Separated Flows

Calculation of Numerical Uncertainty Using Richardson Extrapolation: Application to Some Simple Turbulent Flow Calculations

Performance and flow calculations for a gaseous H2/O2 thruster

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