×
Chizari, Hossain; Ismail, Farzad

A grid-insensitive LDA method on triangular grids solving the system of Euler equations. (English) Zbl 06849494

J. Sci. Comput. 71, No. 2, 839-874 (2017).
Summary: The performance of the classic upwind-type residual distribution (RD) methods on skewed triangular grids are rigorously investigated in this paper. Based on an improved signals distribution, an improved second order RD method based on the LDA approach is proposed to faithfully replicate the flow physics on skewed triangular grids. It will be mathematically and numerically shown that the improved LDA method is found to have minimal accuracy variations when grids are skewed compared to classic RD and cell vertex finite volume methods on scalar equations and system of Euler equations.

Cited in 7 Documents

MSC:

65-XX Numerical analysis

Keywords:

residual distribution; LDA; skewed triangular grids; cell-vertex finite volume; hyperbolic conservation laws

Software:

FEAPpv
Cite Review PDF
Full Text: DOI

References:

[1] Hall, M.: Cell vertex multigrid schemes for the solution of the euler equations. Numer. Fluids Fluid Dyn. II, 303-365 (1886)
[2] Morton, K., Crumpton, P., Mackenzie, J.: Cell vertex methods for inviscid and viscous flows. J. Comput. Fluids 22(2,3), 91-102 (1993) · Zbl 0779.76073 · doi:10.1016/0045-7930(93)90042-8
[3] Morton, K., Rudgyard, M.A., Shaw, G.J.: Upwind iteration methods for the cell vertex scheme in one-dimension. J. Comput. Phys. 114(2), 209-226 (1994) · Zbl 0811.65070 · doi:10.1006/jcph.1994.1161
[4] Roe, P. L.: Fluctuations and signals, a framework for numerical evolution problems. Numer. Methods Fluid Dyn. 11, 219-257 (1982) · Zbl 1423.76147
[5] Abgrall, R.: An extension of roe’s upwind scheme to algebraic equilibrium real gas models. Comput. Fluids 19(2), 171-182 (1991) · Zbl 0721.76061 · doi:10.1016/0045-7930(91)90032-D
[6] Abgrall, R.: Toward the ultimate conservative scheme: following the quest. J. Comp. Phys. 167(2), 277-315 (2001) · Zbl 0988.76055 · doi:10.1006/jcph.2000.6672
[7] Abgrall, R.: Residual distribution schemes: current status and future trends. Comput. Fluids 35(7), 641-669 (2006) · Zbl 1177.76205 · doi:10.1016/j.compfluid.2005.01.007
[8] Abgrall, R., Trefilík, J.: An example of high order residual distribution scheme using non-lagrange elements. J. Sci. Comput. 45(1-3), 3-25 (2010) · Zbl 1203.65240 · doi:10.1007/s10915-010-9405-y
[9] Deconinck, H., Struijs, R., Bourgois, G., Roe, P.L.: Compact advection schemes on unstructured grids. In: Computational Fluid Dynamics, VKI LS 1993-04 (1993) · Zbl 1271.76190
[10] Mesaros, L.M.: Fluctuation Splitting Schemes for the Euler Equations on Unstructured Grid, Ph.D. thesis, University of Michigan (1995) · Zbl 0779.76073
[11] Nishikawa, H.: Robust and accurate viscous discretization via upwind scheme I: basic principle. Comput. Fluids 49(1), 62-86 (2011) · Zbl 1271.76190 · doi:10.1016/j.compfluid.2011.04.014
[12] Chizari, H., Ismail, F.: Accuracy variations in residual distribution and finite volume methods on triangular grids. Bull. Malays. Math. Sci. Soc. 22, 1-34 (2015)
[13] Guzik, S., Groth, C.: Comparison of solution accuracy of multidimensional residual distribution and godunov-type finite-volume methods. Int. J. Comp. Fluid Dyn. 22, 61-83 (2008) · Zbl 1388.76176 · doi:10.1080/10618560701748176
[14] De Santis, D.: High-order linear and non-linear residual distribution schemes for turbulent compressible flows. Comput. Methods Appl. Mech. Eng. 285, 1-31 (2015) · Zbl 1423.76147 · doi:10.1016/j.cma.2014.10.045
[15] Koloszar, L., Villedieu, N., Quintino, T., Rambaud, P., Deconinck, H., Anthoine, J.: Residual distribution method for aeroacoustics. AIAA J. 49(5), 1021-1037 (2011) · doi:10.2514/1.J050645
[16] Mazaheri, A., Nishikawa, H.: Improved second-order hyperbolic residual-distribution scheme and its extension to third-order on arbitrary triangular grids. J. Comp. Phys. 300(1), 455-491 (2015) · Zbl 1349.65377 · doi:10.1016/j.jcp.2015.07.054
[17] van der Weide, E.: Compressible flow simulation on unstructured grids using multidimensional upwind schemes, Ph.D. thesis, Delft University of Technology (1998) · Zbl 0474.65066
[18] Zienkiewicz, O.C., Taylor, R.L. Zhu, J.: The finite element method: its basis and fundamentals, 6th edn. Elsevier (2005) · Zbl 1307.74005
[19] Deconinck, H., Sermeus, K., Abgrall, R.: Status of multidimensional upwind residual distribution schemes and applications in aeronautics. Fluids 2000 Conference and Exhibit, Denver · Zbl 1350.76047
[20] Abgrall, R., Mezine, M.: Residual distribution scheme for steady problems. In 33rd Computational Fluid Dynamics Course VKI Lecture Series 2003-20005 (Von Karman Institute for Fluid Dynamics) · Zbl 1067.65505
[21] Dobes, J., Deconinck, H.: Second order blended multidimensional upwind residual distribution scheme for steady and unsteady computations. J. Comput. Appl. Math. 215(2), 378-389 (2008) · Zbl 1350.76047 · doi:10.1016/j.cam.2006.03.046
[22] Abgrall, R.: A review of residual distribution schemes for hyperbolic and parabolic problems: the July 2010 state of the art. Commun. Comp. Phys. 11(4), 1043-1080 (2012) · Zbl 1373.76114 · doi:10.4208/cicp.270710.130711s
[23] Masatsuka, K.: I do like CFD, book, Vol. 1 (2009)
[24] Blazek, J.: Computational fluid dynamics: principles and applications (2001) · Zbl 0995.76001
[25] Roe, P.L.: Approximate Riemann solvers, parameter and difference schemes. J. Comput. Phys. 43, 357-372 (1981) · Zbl 0474.65066 · doi:10.1016/0021-9991(81)90128-5
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.