A high-order CFD method using successive differentiation

Yang, Hong; Chen, Z.J.; Przekwas, Andrzej; Dudley, Jonathan G.

doi:10.1016/j.jcp.2014.10.046

Cited by 15 publications

(16 citation statements)

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“…This formulation was first proposed by Burg for unstructured FV codes, where a third‐order spatial accuracy was achieved for 2‐dimensional (2D) and 3D problems. Yang et al and Yang and Harris extended the scheme to fourth‐order spacial accuracy. The scheme resembles the MUSCL‐schemes and used here to discretise the convective part of the Navier‐Stokes equations.…”

Section: High‐order Formulationmentioning

confidence: 99%

“…Following Yang et al, the proposed fourth‐order structured MUSCL scheme is written in a similar fashion, where the extrapolation to both sides of the face located at j +1/2 is given as

{boldF}_{j + 1 false/ 2}^{normalL} = \overset{\overset{F_{j} + \frac{k_{1}}{2} false(F_{j + 1} - F_{j} false) + false(1 - k_{1} false) \overset{\nabla}{true} F_{j} • {\overset{r}{true}}_{f_{j}}}{true}}{true} \underset{High‐order corrections for the left state}{\underset{⏟}{+ \frac{1}{2} ([], \frac{k_{2}}{2} ((), \overset{\nabla}{true} F_{j + 1} • {\overset{r}{true}}_{f_{j}} - \overset{\nabla}{true} F_{j} • {\overset{r}{true}}_{f_{j}}) + false(1 - k_{2} false) \overset{\nabla}{true} ((), \overset{\nabla}{true} F_{j} • {\overset{r}{true}}_{f_{j}}) • {\overset{r}{true}}_{f_{j}})}}

\begin{matrix} {boldF}_{j + 1 / 2}^{normalR} = \overset{Standard MUSCL for the right state}{\overset{⏞}{{boldF}_{j + 1} - \frac{k_{1}}{2} ({boldF}_{j + 1} - {boldF}_{j}) - (1 - k_{1}) \vec{\nabla} {boldF}_{j + 1} • {\vec{boldr}}_{f_{j + 1}}}} \\ + \frac{1}{2} [k_{}] \end{matrix}

…”

Section: High‐order Formulationmentioning

confidence: 99%

“…This high‐order method (up to fourth‐order) was presented by Yang et al and Yang and Harris and implemented into an unstructured CFD solver. To the author's knowledge, this is the first time that this kind of scheme is implemented in a structured FV CFD method and demonstrated for rotor flows.…”

Section: Introductionmentioning

confidence: 99%

“…A first classification covers high-order schemes developed either for structured 7,8 or unstructured meshes. [9][10][11][12] The formulation of those methods in finite-difference (FD) 13,14 or finite-volume (FV) 15,16 frameworks is also a means of classification. A more complete classification is given by Ekaterinaris 17 in his review paper on high order CFD methods.…”

Section: Introductionmentioning

confidence: 99%

“…27 This paper demonstrates a high-order method (up to fourth-order), achieved using high-order correction terms through successive differentiation. 11,12 The method can be implemented as a correction to existing Monotonic Upstream-centered Scheme for Conservation Laws (MUSCL) schemes and offers good accuracy with very easy implementation in existing codes. Unlike ENO and WENO schemes, 28-30 (MUSCL) schemes are easier to code and represent a good compromise between level of accuracy and CPU and memory overheads for rotorcraft applications.The structure of this paper is as follows.…”

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confidence: 99%

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Assessment of a high‐order MUSCL method for rotor flows

Jiménez-García

Barakos

2018

Numerical Methods in Fluids

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Summary This work presents the implementation of a high‐order, finite‐volume scheme suitable for rotor flows. The formulation is based on the variable extrapolation MUSCL‐scheme, where high‐order spatial accuracy (up to fourth‐order) is achieved using correction terms obtained through successive differentiation. A variety of results are presented, including 2‐ and 3‐dimensional test cases. Results with the proposed scheme, showed better wake and higher resolution of vortical structures compared with the standard MUSCL, even when coarse meshes were employed. The method was also demonstrated for 3‐dimensional unsteady flows using overset and moving grids for the UH‐60A rotor in forward flight and the Enhanced Rotorcraft Innovative Concept Achievement tiltrotor in aeroplane mode. For medium grids, the present method adds reasonable CPU and memory overheads and offers good accuracy on relatively coarse grids.

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Section: High‐order Formulationmentioning

confidence: 99%

“…Following Yang et al, the proposed fourth‐order structured MUSCL scheme is written in a similar fashion, where the extrapolation to both sides of the face located at j +1/2 is given as