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2019 | OriginalPaper | Chapter

An a Posteriori Very Efficient Hybrid Method for Compressible Flows

Authors : Javier Fernández-Fidalgo, Xesús Nogueira, Luis Ramírez, Ignasi Colominas

Published in: Recent Advances in CFD for Wind and Tidal Offshore Turbines

Publisher: Springer International Publishing

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Abstract

In this work we present a framework for a high-order hybrid method made up of an explicit finite-difference scheme and a member of the Weighted Essentially Non-Oscillatory (WENO) family. A new a posteriori switching criterion is developed based on the Multidimensional Optimal Order Detection (MOOD) method. The schemes tested here are chosen to illustrate the process, we select non-standard fourth order finite difference and fifth order compact and non-compact WENO, but any other combination of central finite differences and upwind schemes could be used as well. In this work we present a one-dimensional and a two-dimensional case to illustrate the speed, accuracy and shock-capturing properties of the proposed schemes.

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previous chapter A High-Order Finite Volume Method for the Simulation of Phase Transition Flows Using the Navier–Stokes–Korteweg Equations

Costa B, Don WS (2007) High order hybrid central-WENO finite difference scheme for conservation laws. J Comput Appl Math 204(2):209–218MathSciNetMATHCrossRef

Pirozzoli S (2002) Conservative hybrid compact-WENO schemes for shock-turbulence interaction. J Comput Phys 178(1):81–117MathSciNetMATHCrossRef

Hu XY, Wang B, Adams NA (2015) An efficient low-dissipation hybrid weighted essentially non-oscillatory scheme. J Comput Phys 301:415–424MathSciNetMATHCrossRef

Clain S, Diot S, Loubère R (2011) A high-order finite volume method for systems of conservation laws—multi-dimensional optimal order detection (MOOD). J Comput Phys 230(10):4028–4050MathSciNetMATHCrossRef

Diot S, Clain S, Loubère R (2012) Improved detection criteria for the multi-dimensional optimal order detection (MOOD) on unstructured meshes with very high-order polynomials. Comput Fluids 64:43–63MathSciNetMATHCrossRef

Vinokur M (1974) Conservation equations of gasdynamics in curvilinear coordinate systems. J Comput Phys 14(2):105–125MathSciNetMATHCrossRef

Visbal MR, Gaitonde DV (1999) High-order-accurate methods for complex unsteady subsonic flows. AIAA J 37(10):1231–1239CrossRef

Ghosh D, Baeder JD (2012) Compact reconstruction schemes with weighted eno limiting for hyperbolic conservation laws. SIAM J Sci Comput 34(3):A1678–A1706MathSciNetMATHCrossRef

Jiang GS, Shu CW (1996) Efficient implementation of weighted ENO schemes. J Comput Phys 126(1):202–228MathSciNetMATHCrossRef

10.

Bogey C, Bailly C (2002) A family of low dispersive and low dissipative explicit schemes for computing aerodynamic noise. In: 8th AIAA/CEAS aeroacoustics conference exhibit. American Institute of Aeronautics and Astronautics

11.

Visbal MR, Gaitonde DV (1998) High-order schemes for Navier-Stokes equations: algorithm and implementation into FDL3DI. Air Force Research Lab Wright-Patterson, Air Vehicles Directorate

12.

Johnsen E, Larsson J, Bhagatwala AV, Cabot WH, Moin P, Olson BJ, Rawat PS, Shankar SK, Sjögreen B, Yee HC, Zhong X, Lele SK (2010) Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves. J Comput Phys 229(4):1213–1237MathSciNetMATHCrossRef

13.

Adams NA, Shariff K (1996) A high-resolution hybrid compact-ENO scheme for shock-turbulence interaction problems. J Comput Phys 127(1):27–51MathSciNetMATHCrossRef

14.

Henrick AK, Aslam TD, Powers JM (2005) Mapped weighted essentially non-oscillatory schemes: achieving optimal order near critical points. J Comput Phys 207(2):542–567MATHCrossRef

15.

Dumbser M, Zanotti O, Loubère R, Diot S (2014) A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws. J Comput Phys 278:47–75MathSciNetMATHCrossRef

16.

Nogueira X, Ramírez L, Clain S, Loubère R, Cueto-Felgueroso L, Colominas I (2016) High-accurate SPH method with multidimensional optimal order detection limiting. Comput Methods Appl Mech Eng 310:134–155MathSciNetCrossRef

17.

Fernández-Fidalgo J, Nogueira X, Ramírez L, Colominas I (2018) An a posteriori, efficient, high-spectral resolution hybrid finite-difference method for compressible flows. Comput Methods Appl Mech Eng 335:91–127MathSciNetCrossRef

18.

Figueiredo J, Clain S (2015) Second-order finite volume mood method for the shallow water with dry/wet interface. In: SYMCOMP

19.

Hu XY, Adams NA, Shu CW (2012) Positivity-preserving flux limiters for high-order conservative schemes. J Comput Phys 242:169–180CrossRef

20.

Sod GA (1978) A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. J Comput Phys 27(1):1–31MathSciNetMATHCrossRef

21.

Liepmann HW, Roshko A (1959) Elements of gasdynamics. Wiley, New York. ISBN: 978-0486419633

Title: An a Posteriori Very Efficient Hybrid Method for Compressible Flows
Authors: Javier Fernández-Fidalgo
Xesús Nogueira
Luis Ramírez
Ignasi Colominas
Publisher: Springer International Publishing
Book: Recent Advances in CFD for Wind and Tidal Offshore Turbines
Print ISBN: 978-3-030-11886-0

Electronic ISBN: 978-3-030-11887-7

Copyright Year: 2019
DOI: https://doi.org/10.1007/978-3-030-11887-7_13