Curvilinear grids for WENO methods in astrophysical simulations

作者: H. Grimm-Strele , F. Kupka , H.J. Muthsam

DOI: 10.1016/J.CPC.2013.11.005

关键词:

摘要: Abstract We investigate the applicability of curvilinear grids in context astrophysical simulations and WENO schemes. With non-smooth mapping functions from Calhoun et al. (2008), we can tackle many problems which were out scope with standard numerical astrophysics. describe difficulties occurring when implementing coordinates into our code, how overcome them. illustrate theoretical results data. The finite difference scheme works only for high Mach number flows smooth functions, whereas volume gives accurate even low on grids.

参考文章(45)
Barry Merriman, Understanding the Shu–Osher Conservative Finite Difference Form Journal of Scientific Computing. ,vol. 19, pp. 309- 322 ,(2003) , 10.1023/A:1025312210724
C. Wayne Mastin, Joe F. Thompson, Z. U.A. Warsi, Numerical Grid Generation: Foundations and Applications ,(1985)
Philip Mocz, Mark Vogelsberger, Debora Sijacki, Rüdiger Pakmor, Lars Hernquist, A discontinuous Galerkin method for solving the fluid and magnetohydrodynamic equations in astrophysical simulations Monthly Notices of the Royal Astronomical Society. ,vol. 437, pp. 397- 414 ,(2014) , 10.1093/MNRAS/STT1890
David I. Ketcheson, Colin B. Macdonald, Sigal Gottlieb, Optimal implicit strong stability preserving Runge--Kutta methods Applied Numerical Mathematics. ,vol. 59, pp. 373- 392 ,(2009) , 10.1016/J.APNUM.2008.03.034
Rui Zhang, Mengping Zhang, Chi-Wang Shu, On the Order of Accuracy and Numerical Performance of Two Classes of Finite Volume WENO Schemes Communications in Computational Physics. ,vol. 9, pp. 807- 827 ,(2011) , 10.4208/CICP.291109.080410S
Chi-Wang Shu, Stanley Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes,II Journal of Computational Physics. ,vol. 83, pp. 32- 78 ,(1989) , 10.1016/0021-9991(89)90222-2
Jay Casper, H.L. Atkins, A Finite-Volume High-Order ENO Scheme for Two-Dimensional Hyperbolic Systems Journal of Computational Physics. ,vol. 106, pp. 62- 76 ,(1993) , 10.1006/JCPH.1993.1091
Donna A. Calhoun, Christiane Helzel, Randall J. LeVeque, Logically Rectangular Grids and Finite Volume Methods for PDEs in Circular and Spherical Domains Siam Review. ,vol. 50, pp. 723- 752 ,(2008) , 10.1137/060664094