A Fourth-Order Compact Implicit Scheme for Solving the Non-Linear Shallow-Water Equations in Conservation-Law Form
作者： IM Navon , None
DOI: 10.1007/978-3-322-86146-7_22
关键词:
摘要: A Fourth-order compact implicit finite-difference scheme is applied for solving numerically the nonlinear shallow-water equations in conservation-law form. The algorithm second-order time accurate, while fourth-order differencing implemented a spatially factored (ADI) Third-order uncentered boundary conditions which preserve overall convergence are experimented with and compared. Von Neuman linearized stability analysis as well Kreiss-type normal-mode performed. integral invariants of conserved during numerical integration. Accuracy tests confirm accuracy scheme.
springer.com
sci-hub.st 参考文章(19)
Jim Douglas, James E. Gunn, A general formulation of alternating direction methods Numerische Mathematik. ,vol. 6, pp. 428- 453 ,(1964) , 10.1007/BF01386093
S. G. Rubin, P. K. Khosla, Numerical methods based on polynomial spline interpolation Some Methods of Resolution of Free Surface Problems. ,vol. 59, pp. 370- 377 ,(1979) , 10.1007/3-540-08004-X_341
Bertil Gustafsson, The convergence rate for difference approximations to mixed initial boundary value problems Mathematics of Computation. ,vol. 29, pp. 396- 406 ,(1975) , 10.1090/S0025-5718-1975-0386296-7
Joseph Oliger, Fourth Order Difference Methods for the Initial Boundary-Value Problem for Hyperbolic Equations Mathematics of Computation. ,vol. 28, pp. 15- 25 ,(1974) , 10.1090/S0025-5718-1974-0359344-7
S.G. Rubin, P.K. Khosla, Higher-Order Numerical Solutions Using Cubic Splines AIAA Journal. ,vol. 14, pp. 851- 858 ,(1976) , 10.2514/3.61427
Blair Swartz, Burton Wendroff, The Relative Efficiency of Finite Difference and Finite Element Methods. I: Hyperbolic Problems and Splines SIAM Journal on Numerical Analysis. ,vol. 11, pp. 979- 993 ,(1974) , 10.1137/0711076
ARNE GRAMMELTVEDT, A SURVEY OF FINITE-DIFFERENCE SCHEMES FOR THE PRIMITIVE EQUATIONS FOR A BAROTROPIC FLUID Monthly Weather Review. ,vol. 97, pp. 384- 404 ,(1969) , 10.1175/1520-0493(1969)097<0384:ASOFSF>2.3.CO;2
David Gottlieb, Bertil Gustafsson, Generalized Du Fort-Frankel methods for parabolic initial-boundary value problems SIAM Journal on Numerical Analysis. ,vol. 13, pp. 129- 144 ,(1976) , 10.1137/0713015
Melvyn Ciment, Stephen H. Leventhal, Higher order compact implicit schemes for the wave equation Mathematics of Computation. ,vol. 29, pp. 985- 994 ,(1975) , 10.1090/S0025-5718-1975-0416049-2
Richard M Beam, R.F Warming, An implicit finite-difference algorithm for hyperbolic systems in conservation-law form Journal of Computational Physics. ,vol. 22, pp. 87- 110 ,(1976) , 10.1016/0021-9991(76)90110-8