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Designing Several Types of Oscillation-Less and High-Resolution Hybrid Schemes on Block-Structured Grids

  • Zhenhua Jiang (a1), Chao Yan (a1), Jian Yu (a1) and Boxi Lin (a1)

An idea of designing oscillation-less and high-resolution hybrid schemes is proposed and several types of hybrid schemes based on this idea are presented on block-structured grids. The general framework, for designing various types of hybrid schemes, is established using a Multi-dimensional Optimal Order Detection (MOOD) method proposed by Clain, Diot and Loubère [1]. The methodology utilizes low dissipation or dispersion but less robust schemes to update the solution and then implements robust and high resolution schemes to deal with problematic situations. A wide range of computational methods including central scheme, MUSCL scheme, linear upwind scheme and Weighted Essentially Non Oscillatory (WENO) scheme have been applied in the current hybrid schemes framework. Detailed numerical studies on classical test cases for the Euler system are performed, addressing the issues of the resolution and non-oscillatory property around the discontinuities.

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*Corresponding author. Email addresses: (Z. Jiang), (C. Yan), (J. Yu), (B. Lin)
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[1] S. Clain , S. Diot and R. Loubère , A high-order finite volume method for systems of conservation lawsmulti-dimensional optimal order detection (MOOD), J. Comput. Phys., 230(10) (2011), 40284050.

[2] B. van Leer , Towards the ultimate conservation difference scheme V: A second-order sequal to Godunov's method, J. Comput. Phys., 32(1) (1979), 101136.

[3] X. D. Liu , S. Osher and T. Chan , Weighted essentially non-oscillatory schemes, J. Comput. Phys., 115 (1994), 200212.

[4] G. Jiang and C. W. Shu , Efficient implementation of weighted ENO schemes, J. Comput. Phys., 126(1) (1996), 202228.

[7] D. Balsara and C. W. Shu , Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy, J. Comput. Phys., 160 (2000), 405452.

[8] J. Yu , C. Yan and Z. Jiang , A hybrid high resolution low dissipation scheme for compressible flows, Chinese Journal of Aeronautics, 24 (2011), 417424.

[9] N. A. Adams and K. Shariff , A high-resolution hybrid compact-ENO scheme for shock-turbulence interaction problems, J. Comput. Phys., 127 (1996), 2746.

[10] S. Pirozzoli , Conservative hybrid compact-WENO schemes for shock-turbulence interaction, J. Comput. Phys., 178 (2002), 81117.

[11] Y. Ren , M. Liu and H. Zhang , A characteristic-wise hybrid compact-WENO scheme for solving hyperbolic conservation laws, J. Comput. Phys., 192 (2003), 365386.

[12] D. J. Hill and D. I. Pullin , Hybrid tuned center-difference-WENO method for large eddy simulations in the presence of strong shocks, J. Comput. Phys., 194 (2004), 435450.

[13] B. Cosat and W. S. Don , High order hybrid central-WENO finite difference scheme for conservation laws, J. Comput. Appl. Math., 204 (2007), 209218.

[14] G. Li and J. Qiu , Hybrid weighted essentially non-oscillatory schemes with different indicators, J. Comput. Phys., 229 (2010), 81058129.

[15] S. Diot , S. Clain and R. Loubère , Improved detection criteria for the multi-dimensional optimal order detection (MOOD) on unstructured meshes with very high-order polynomials, Comput. Fluids, 64 (2012), 4363.

[16] S. Diot , R. Loubère and S. Clain , The MOOD method in the three-dimensional case: very-high-order finite volume method for hyperbolic systems, Int. J. Numer. Meth. Fluids, 73 (2013), 362392.

[17] R. Loubre , M. Dumbser and S. Diot , A new family of high order unstructured MOOD and ADER finite volume schemes for multidimensional systems of hyperbolic conservation laws, Commun. Comput. Phys., 16 (2014), 718763.

[18] M. Dumbser , O. Zanotti , R. Loubère and S. Diot , A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws, J. Comput. Phys., 278 (2014), 4775.

[20] P. L. Roe , Approximate Riemann solvers, parameter vectors, and difference schemes, J. Comput. Phys., 43 (1981), 357372.

[21] W. J. Rider , Methods for extending high-resolution schemes to non-linear systems of hyperbolic conservation laws, Int. J. Numer. Meth. Fluids, 17(10) (1993), 861885.

[22] R. H. Nichols , R. W. Tramel and P. G. Buning , Evaluation of two high-order weighted essentially nonoscillatory schemes, AIAA J., 46(12) (2008), 30903102.

[23] P. Woodward and P. Colella , Numerical simulation of two-dimensional fluid flows with strong shocks, J. Comput. Phys., 54 (1984), 115173.

[24] E. F. Toro , Riemann Solvers and Numerical Methods for Fluid Dynamics, second ed., Springer Berlin, 1999.

[25] D. S. Balsara , Self-adjusting, positivity preserving high order schemes for hydrodynamics and magnetohydrodynamics, J. Comput. Phys., 231 (2012), 75047517.

[26] V. Titarev and E. Toro , Finite-volume WENO schemes for three-dimensional conservation laws, J. Comput. Phys., 201 (2004), 238260.

[27] C. W. Shu , High order weighted essentially nonoscillatory schemes for convection dominated problems, SIAM Review, 51(1) (2009), 82126.

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Communications in Computational Physics
  • ISSN: 1815-2406
  • EISSN: 1991-7120
  • URL: /core/journals/communications-in-computational-physics
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