Quadratic-reconstruction finite volume scheme for compressible flows on unstructured adaptive grids

Delanaye, Michel; Essers, J. A.

doi:10.2514/3.13559

Cited by 15 publications

(17 citation statements)

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“…5,12 We use Equation 6, which detects uniform flow to switch on the high-order terms only in uniform flow regions. As discussed theoretically in Section IV.A, the results demonstrate that this method violates monotonicity in certain regions.…”

Section: Vb Transonic Flowmentioning

confidence: 99%

“…Transonic and supersonic solutions have been computed in some of these works by various extensions of second-order limiters. However, the work of Barth 9 presents a limiting approach which causes difficulties in steady-state convergence, while other works 5,12 present approaches that do not strictly enforce monotonicity and therefore allow some undesirable oscillations to occur.…”

mentioning

confidence: 99%

“…Higher-order finite-volume methods on unstructured grids, although well known, [3][4][5] have not effectively been applied to large scale aerodynamics problems. An outstanding issue with these methods is how to deal with discontinuities, such as shocks in the flow, while maintaining good accuracy and convergence.…”

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confidence: 99%

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Limiters for Unstructured Higher-Order Accurate Solutions of the Euler Equations

Michalak

Ollivier‐Gooch

2008

46th AIAA Aerospace Sciences Meeting and Exhibit

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Higher-order finite-volume methods have been shown to be more efficient than secondorder methods. However no consensus has been reached on how to eliminating the oscillations caused by solution discontinuities. Essentially non-oscillatory (ENO) schemes provide a solution but are computationally expensive to implement and may not converge well for steady-state problems. This work studies the application of limiters used for second-order methods to the higher-order case. Requirements for accuracy and efficient convergence are discussed. A new limiting procedure is proposed. Results for the fourth-order accurate solution of transonic and supersonic flows demonstrate good convergence properties and significant qualitative improvement of the solution relative the second-order method. Subsonic results demonstrate the superiority of the scheme in smooth flows by the reduction in entropy production. Some aspects of the new limiter can also be successfully applied to reduce the dissipation of second-order schemes with minimal sacrifices in convergence properties.

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Section: Vb Transonic Flowmentioning

confidence: 99%

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confidence: 99%

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Limiters for Unstructured Higher-Order Accurate Solutions of the Euler Equations

Michalak

Ollivier‐Gooch

2008

46th AIAA Aerospace Sciences Meeting and Exhibit

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“…Although there are other alternatives for second-order schemes (notably Green-Gauss reconstruction), obtaining higher than second-order accuracy requires an explicit polynomial reconstruction. In this work, we will focus on k-exact least-squares reconstruction (see, 2,5,14 for instance); the use of ENO 3 or WENO 7,8 reconstruction would alter the approach taken to compute reconstruction polynomials, though not the need to properly ensure conservation of the mean, as described below.…”

Section: Solution Reconstructionmentioning

confidence: 99%

“…Since Barth and Frederickson's pioneering work, 1 a number of researchers have studied high-order (by which we mean third-and fourth-order accurate) finite-volume methods for computational aerodynamics using unstructured meshes [2][3][4][5][6][7][8][9] For the most part, however, these researchers tend to content themselves primarily with showing that highorder schemes are superior in accuracy to second-order schemes without quantifying the order of accuracy of their scheme. Some of the research described in the literature also explicitly fails to implement all terms to high-order accuracy.…”

Section: Introductionmentioning

confidence: 99%

On Obtaining High-Order Finite-Volume Solutions to the Euler Equations on Unstructured Meshes

Ollivier‐Gooch

Nejat

Michalak

2007

18th AIAA Computational Fluid Dynamics Conference

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High-order finite volume schemes for unstructured meshes first appeared in the literature at least as early as Barth and Frederickson's 1990 paper. 1 However, the approach has not gained a wide following, perhaps because of the difficulties in achieving a genuinely high-order accurate solution, especially when dealing with curved boundaries. In this paper, we document in detail our approach to constructing a high-order solver. In addition to reconstruction, we discuss flux integration and curved boundary treatment. We describe how we tackle each of these issues, provide useful testing procedures to verify code correctness, and illustrate the results of mis-handling various small but important details.

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Two‐dimensional flow past circular cylinders using finite volume lattice Boltzmann formulation

Patil

Lakshmisha

2011

Numerical Methods in Fluids

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SUMMARY In this article, an extension to the total variation diminishing finite volume formulation of the lattice Boltzmann equation method on unstructured meshes was presented. The quadratic least squares procedure is used for the estimation of first‐order and second‐order spatial gradients of the particle distribution functions. The distribution functions were extrapolated quadratically to the virtual upwind node. The time integration was performed using the fourth‐order Runge–Kutta procedure. A grid convergence study was performed in order to demonstrate the order of accuracy of the present scheme. The formulation was validated for the benchmark two‐dimensional, laminar, and unsteady flow past a single circular cylinder. These computations were then investigated for the low Mach number simulations. Further validation was performed for flow past two circular cylinders arranged in tandem and side‐by‐side. Results of these simulations were extensively compared with the previous numerical data. Copyright © 2011 John Wiley & Sons, Ltd.

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Quadratic-reconstruction finite volume scheme for compressible flows on unstructured adaptive grids

Cited by 15 publications

References 0 publications

Limiters for Unstructured Higher-Order Accurate Solutions of the Euler Equations

Limiters for Unstructured Higher-Order Accurate Solutions of the Euler Equations

On Obtaining High-Order Finite-Volume Solutions to the Euler Equations on Unstructured Meshes

Two‐dimensional flow past circular cylinders using finite volume lattice Boltzmann formulation

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