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A study of curved boundary representations for 2D high order Euler solvers. (English) Zbl 1203.65032
Summary: The present study discusses several approaches of representing curve boundaries with high-order Euler solvers. The aim is to minimize the solution entropy error. The traditional boundary representation based on interpolation polynomials is presented first. A new boundary representation based on the Bezier curve is then developed and analyzed. Several numerical tests are conducted to compare both representations. The new approach is shown to have several advantages for complicated geometries.

65D17 Computer-aided design (modeling of curves and surfaces)
76M25 Other numerical methods (fluid mechanics) (MSC2010)
Full Text: DOI
[1] Bassi, F., Rebay, S.: Accurate 2D computations by means of a high order discontinuous finite element method. In: XIV International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics, vol. 453, pp. 234–240. Springer, Berlin (1994) · Zbl 0850.76344
[2] Bassi, F., Rebay, S.: High order accurate discontinuous finite element solution of 2D Euler equations. J. Comput. Phys. 138, 251–285 (1997) · Zbl 0902.76056 · doi:10.1006/jcph.1997.5454
[3] Cockburn, B., Shu, C.-W.: TVB Runge-Kutta local projections discontinuous Galerkin finite element method for conservation laws II: general framework. Math. Comput. 52, 411–435 (1989) · Zbl 0662.65083
[4] Cockburn, B., Shu, C.-W.: The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems. J. Comput. Phys. 141, 199–224 (1998) · Zbl 0920.65059 · doi:10.1006/jcph.1998.5892
[5] Foley, J.D., van Dam, A., Feiner, S., Hughes, J.: Computer Graphics: Principles and Practice in C, 2nd edn. Addison-Wesley, Reading (1992) · Zbl 0875.68891
[6] Gordon, W.J., Hall, C.A.: Construction of curvilinear co-ordinate systems and applications to mesh generation. Int. J. Numer. Methods Eng. 7, 461–477 (1973) · Zbl 0271.65062 · doi:10.1002/nme.1620070405
[7] Gordon, W.J., Hall, C.A.: Transfinite element methods and blending function interpolation over curved element domains. Numer. Math. 21, 109–129 (1973) · Zbl 0254.65072 · doi:10.1007/BF01436298
[8] Hynh, H.T.: A flux reconstruction approach to high-order schemes including discontinuous Galerkin methods. AIAA-2007-4079
[9] Kopriva, D.A., Kolias, J.H.: A conservative staggered grid Chebychev multi-domain method for compressible flows. J. Comput. Phys. 125, 1 (1996) 244–261 · Zbl 0847.76069 · doi:10.1006/jcph.1996.0091
[10] Krivodonova, L., Berger, M.: High-order accurate implementation of solid wall boundary conditions in curved geometries. J. Comput. Phys. 211, 492–512 (2006) · Zbl 1138.76403 · doi:10.1016/j.jcp.2005.05.029
[11] Liu, Y., Vinokur, M., Wang, Z.J.: Discontinuous spectral difference method for conservation laws on unstructured grids. J. Comput. Phys. 216, 780–801 (2006) · Zbl 1097.65089 · doi:10.1016/j.jcp.2006.01.024
[12] Wang, Z.J., Gao, H.: A unifying collocation penalty formulation for the Euler and Navier–Stokes equations on mixed grids. AIAA-2009-0401 (2009)
[13] Wang, Z.J., Liu, Y.: Spectral (finite) volume method for conservation laws on unstructured grids III: extension to one-dimensional systems. J. Sci. Comput. 20, 137 (2004) · Zbl 1097.65100 · doi:10.1023/A:1025896119548
[14] Wang, Z.J., Liu, Y.: Extension of the spectral volume method to high-order boundary representation. J. Comput. Phys. 211, 154–178 (2006) · Zbl 1161.76536 · doi:10.1016/j.jcp.2005.05.022
[15] Wang, Z.J., Zhang, L., Liu, Y.: Spectral (finite) volume method for conservation laws on unstructured grids III: extension to one-dimensional systems. J. Comput. Phys. 194, 716 (2004) · Zbl 1039.65072 · doi:10.1016/j.jcp.2003.09.012
[16] Wang, Z.J., Liu, Y., May, G., Jameson, A.: Spectral difference method for unstructured grids II: extension to the Euler equations. J. Sci. Comput. 32(1), 45–71 (2007) · Zbl 1151.76543 · doi:10.1007/s10915-006-9113-9
[17] Zienkiewicz, O.C., Taylor, R.L.: The Finite Element Method the Basics, vol. 1. Butterworth-Heinemann, Oxford (2000) · Zbl 0991.74002
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