Assessment of Characteristic Boundary Conditions Based on the Artificial Compressibility Method in Generalized Curvilinear Coordinates for Solution of the Euler Equations

References

[1] Y. Adam, A Hermitian finite difference method for the solution of parabolic equations Comput. Math. Appl. 1 (1975), 393–406. 10.1016/0898-1221(75)90041-3Suche in Google Scholar

[2] T. Amro, A. Arnold and M. Ehrhardt, Optimized far field boundary conditions for hyperbolic systems, preprint BUW-IMACM 12.02 (2012). Suche in Google Scholar

[3] A. Bayliss and E. Turkel, Radiation boundary conditions for wave-like equations, Comm. Pure Appl. Math. 33 (1980), no. 6, 707–725. 10.1002/cpa.3160330603Suche in Google Scholar

[4] E. Bécache and A. Prieto, Remarks on the stability of Cartesian PMLs in corners, Appl. Numer. Math. 62 (2012), no. 11, 1639–1653. 10.1016/j.apnum.2012.05.003Suche in Google Scholar

[5] J.-P. Berenger, A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys. 114 (1994), no. 2, 185–200. 10.1006/jcph.1994.1159Suche in Google Scholar

[6] M. H. Carpenter, D. Gottlieb and S. Abarbanel, Stable and accurate boundary treatments for compact, high-order finite-difference schemes, Appl. Numer. Math. 12 (1993), no. 1–3, 55–87. 10.1016/0168-9274(93)90112-5Suche in Google Scholar

[7] S. R. Chakravarthy, Euler equations-implicit schemes and boundary conditions, AIAA J. 21 (1983), no. 5, 699–706. 10.2514/6.1982-228Suche in Google Scholar

[8] A. J. Chorin, A numerical method for solving incompressible viscous flow problems, J. Comput. Phys. 2 (1967), no. 1, 12–26. 10.1016/0021-9991(67)90037-XSuche in Google Scholar

[9] T. Colonius, Modeling artificial boundary conditions for compressible flow, Annu. Rev. Fluid Mech. 36 2004, 315–345. 10.1146/annurev.fluid.36.050802.121930Suche in Google Scholar

[10] R. Corral, A. Escribano, F. Gisbert, A. Serrano and C. Vasco, Validation of a linear multigrid accelerated unstructured Navier–Stokes solver for the computation of turbine blades on hybrid grids, AIAA Paper 3326 (2003), no. 9. 10.2514/6.2003-3326Suche in Google Scholar

[11] J. R. Dea, An experimental adaptation of Higdon-type non-reflecting boundary conditions to linear first-order systems, J. Comput. Appl. Math. 235 (2011), no. 5, 1354–1366. 10.1016/j.cam.2010.08.023Suche in Google Scholar

[12] D. Drikakis, P. A. Govatsos and D. E. Papantonis, A characteristic-based method for incompressible flows, Internat. J. Numer. Methods Fluids 19 (1994), no. 8, 667–685. 10.1002/fld.1650190803Suche in Google Scholar

[13] K. Duru and G. Kreiss, On the accuracy and stability of the perfectly matched layer in transient waveguides, J. Sci. Comput. 53 (2012), no. 3, 642–671. 10.1007/s10915-012-9594-7Suche in Google Scholar

[14] B. Engquist and L. Halpern, Far field boundary conditions for computation over long time, Appl. Numer. Math. 4 (1988), no. 1, 21–45. 10.1016/S0168-9274(88)80004-7Suche in Google Scholar

[15] B. Engquist and A. Majda, Absorbing boundary conditions for numerical simulation of waves, Proc. Natl. Acad. Sci. USA 74 (1977), no. 5, 1765–1766. 10.1073/pnas.74.5.1765Suche in Google Scholar

[16] B. Engquist and A. Majda, Radiation boundary conditions for acoustic and elastic wave calculations, Comm. Pure Appl. Math. 32 (1979), no. 3, 314–358. 10.1002/cpa.3160320303Suche in Google Scholar

[17] D. V. Gaitonde, J. Shang and J. L. Young, Practical aspects of higher-order numerical schemes for wave propagation phenomena, Internat. J. Numer. Methods Engrg. 45 (1999), no. 12, 1849–1869. 10.1002/(SICI)1097-0207(19990830)45:12<1849::AID-NME657>3.0.CO;2-4Suche in Google Scholar

[18] A. Gelb, Z. Jackiewicz and B. D. Welfert, Absorbing boundary conditions of the second order for the pseudospectral Chebyshev methods for wave propagation, J. Sci. Comput. 17 (2002), no. 1–4, 501–512. 10.1023/A:1015158227243Suche in Google Scholar

[19] M. B. Giles, Nonreflecting boundary conditions for Euler equation calculations, AIAA J. 28 (1990), no. 12, 2050–2058. 10.2514/3.10521Suche in Google Scholar

[20] D. Givoli and B. Neta, High-order nonreflecting boundary conditions for the dispersive shallow water equations, J. Comput. Appl. Math. 158 (2003), no. 1, 49–60. 10.1016/S0377-0427(03)00462-XSuche in Google Scholar

[21] D. Givoli and B. Neta, High-order nonreflecting boundary scheme for time-dependent waves, J. Comput. Phys. 186 (2003), no. 1, 24–46. 10.1016/S0021-9991(03)00005-6Suche in Google Scholar

[22] T. Hagstrom and S. I. Hariharan, A formulation of asymptotic and exact boundary conditions using local operators, Appl. Numer. Math. 27 (1998), no. 4, 403–416. 10.1016/S0168-9274(98)00022-1Suche in Google Scholar

[23] M. Y. Hashemi and K. Zamzamian, Efficient and non-reflecting far-field boundary conditions for incompressible flow calculations, Appl. Math. Comput. 230 (2014), 248–258. 10.1016/j.amc.2013.12.089Suche in Google Scholar

[24] M. E. Hayder, F. Q. Hu and M. Y. Hussaini, Toward perfectly absorbing boundary conditions for Euler equations, AIAA J. 37 (1999), no. 8, 912–918. 10.2514/6.1997-2075Suche in Google Scholar

[25] G. W. Hedstrom, Nonreflecting boundary conditions for nonlinear hyperbolic systems, J. Comput. Phys. 30 (1979), no. 2, 222–237. 10.1016/0021-9991(79)90100-1Suche in Google Scholar

[26] K. Hejranfar and R. Kamali-Moghadam, Preconditioned characteristic boundary conditions for solution of the preconditioned Euler equations at low Mach number flows, J. Comput. Phys. 231 (2012), no. 12, 4384–4402. 10.1016/j.jcp.2012.01.040Suche in Google Scholar

[27] D. Heubes, A. Bartel and M. Ehrhardt, Characteristic boundary conditions in the lattice Boltzmann method for fluid and gas dynamics, J. Comput. Appl. Math. 262 (2014), 51–61. 10.1016/j.cam.2013.09.019Suche in Google Scholar

[28] R. L. Higdon, Radiation boundary conditions for dispersive waves, SIAM J. Numer. Anal. 31 (1994), no. 1, 64–100. 10.1137/0731004Suche in Google Scholar

[29] R. S. Hirsh, Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique, J. Comput. Phys. 19 (1975), no. 1, 90–109. 10.1016/0021-9991(75)90118-7Suche in Google Scholar

[30] K. A. Hoffmann and S. T. Chiang, Computational Fluid Dynamics. Vol. 1, Engineering Education System, Wichita, 2000. Suche in Google Scholar

[31] F. Q. Hu, Absorbing boundary conditions, Int. J. Comput. Fluid Dyn. 18 (2004), no. 6, 513–522. 10.1080/10618560410001673524Suche in Google Scholar

[32] M. Huet, One-dimensional characteristic boundary conditions using nonlinear invariants, J. Comput. Phys. 283 (2015), 312–328. 10.1016/j.jcp.2014.12.010Suche in Google Scholar

[33] A. Jameson, W. Schmidt and E. Turkel, Numerical solutions of the Euler equations by finite volume methods using Runge–Kutta time-stepping schemes, AIAA Paper 1259 (1981), urlhttps://doi.org/10.2514/6.1981-1259. 10.2514/6.1981-1259Suche in Google Scholar

[34] J. W. Kim and D. J. Lee, Generalized characteristic boundary conditions for computational aeroacoustics, AIAA J. 38 (2000), no. 11, 2040–2049. 10.2514/2.891Suche in Google Scholar

[35] S. K. Lele, Compact finite difference schemes with spectral-like resolution, J. Comput. Phys. 103 (1992), no. 1, 16–42. 10.1016/0021-9991(92)90324-RSuche in Google Scholar

[36] K. Mahesh, A family of high order finite difference schemes with good spectral resolution, J. Comput. Phys. 145 (1998), no. 1, 332–358. 10.1006/jcph.1998.6022Suche in Google Scholar

[37] M. Meinke, W. Schröder, E. Krause and T. Rister, A comparison of second-and sixth-order methods for large-eddy simulations, Comput. & Fluids 31 (2002), no. 4, 695–718. 10.1016/S0045-7930(01)00073-1Suche in Google Scholar

[38] W. Polifke, C. Wall and P. Moin, Partially reflecting and non-reflecting boundary conditions for simulation of compressible viscous flow, J. Comput. Phys. 213 (2006), no. 1, 437–449. 10.1016/j.jcp.2005.08.016Suche in Google Scholar

[39] S. E. Rogers and D. Kwak, An upwind differencing scheme for the incompressible Navier–Stokes equations, Appl. Numer. Math. 8 (1991), no. 1, 43–64. 10.1016/0168-9274(91)90097-JSuche in Google Scholar

[40] Z.-S. Sun, Y.-X. Ren, B.-L. Zha and S.-Y. Zhang, High order boundary conditions for high order finite difference schemes on curvilinear coordinates solving compressible flows, J. Sci. Comput. 65 (2015), no. 2, 790–820. 10.1007/s10915-015-9988-4Suche in Google Scholar

[41] K. W. Thompson, Time-dependent boundary conditions for hyperbolic systems, J. Comput. Phys. 68 (1987), no. 1, 1–24. 10.1016/0021-9991(87)90041-6Suche in Google Scholar

[42] K. W. Thompson, Time-dependent boundary conditions for hyperbolic systems. II, J. Comput. Phys. 89 (1990), no. 2, 439–461. 10.1016/0021-9991(90)90152-QSuche in Google Scholar

[43] S. V. Tsynkov and V. N. Vatsa, Improved treatment of external boundary conditions for three-dimensional flow computations, AIAA J. 36 (1998), no. 11, 1998–2004. 10.2514/2.327Suche in Google Scholar

[44] M. R. Visbal and D. V. Gaitonde, High-order-accurate methods for complex unsteady subsonic flows, AIAA J. 37 (1999), no. 10, 1231–1239. 10.2514/2.591Suche in Google Scholar

[45] D. L. Whitfield and L. K. Taylor, Numerical solution of the two-dimensional time-dependent incompressible Euler equations, Technical Report NASA-CR-195775, 1994. Suche in Google Scholar