Communication. Cracking of combustion tubes when using a semi-automatic flash-combustion apparatus

Leonard, M. A.; Swindall, W. Jim

doi:10.1039/an9719600749

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Grid-convergence Using Exact Diffusion Terms1

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1994

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“…In fact, the formulation they propose is an 0 ( h 3 ) single-point operator, rewritten in pseudo-flux-difference form. It is only O(h2) accurate in a finite-volume formulation, as seen by equation (4) or in Table I. They (incorrectly) conclude that the QUICK( l/8) operator is an O(hz) accurate finite-volume scheme; in fact, they have shown that QUICK(1/8) is O(h2) accurate when used out of context as a single-point scheme in both their truncation-error analysis and their grid-refinement study.…”

Section: Grid-convergence Using Exact Diffusion Termsmentioning

confidence: 99%

Comments on ‘equivalent versions of the quick scheme for finite‐difference and finite‐volume numerical methods’

Leonard

1994

Commun. Numer. Meth. Engng.

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In Reference 1, Johnson and MacKinnon consider two convection schemes. For ease of reference, call these QUICK(l/8) and QUICK( 1/6). The authors state that the QUICK(1/8) scheme is only O(h2) accurate when used (as originally intended*) as a finite-volume method, and that the alternative QUICK(1/6) scheme is O(h3) in a finite-volume formulation. In fact, exactly the reverse is true: the QUICK(1/8) scheme is O ( h 3 ) accurate in a finite-volume formulation, but only O(hz) accurate in a single-point (finite-difference) formulation; whereas the QUICK (1/6) scheme is O(h3) accurate in the single-point formulation, but only O(h2) when used as a finite-volume method. This can easily be shown in two separate ways: (i) truncation-error analysis, and (ii) gridconvergence using exact diffusive fluxes.

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Section: Grid-convergence Using Exact Diffusion Termsmentioning

confidence: 99%

Comments on ‘equivalent versions of the quick scheme for finite‐difference and finite‐volume numerical methods’

Leonard

1994

Commun. Numer. Meth. Engng.

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Communication. Cracking of combustion tubes when using a semi-automatic flash-combustion apparatus

Cited by 1 publication

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Comments on ‘equivalent versions of the quick scheme for finite‐difference and finite‐volume numerical methods’

Comments on ‘equivalent versions of the quick scheme for finite‐difference and finite‐volume numerical methods’

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