메뉴 건너뛰기




Volumn 45, Issue 7, 2004, Pages 751-773

Linear and non-linear stability analysis for finite difference discretizations of high-order Boussinesq equations

Author keywords

Boussinesq equations; Finite differences; Local non linear analysis; Method of lines; Pseudospectra; Stability analysis

Indexed keywords

CALCULATIONS; DISPERSION (WAVES); EIGENVALUES AND EIGENFUNCTIONS; FOURIER TRANSFORMS; NUMERICAL ANALYSIS; WATER WAVES;

EID: 3042702711     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/fld.713     Document Type: Article
Times cited : (17)

References (30)
  • 1
    • 0037055049 scopus 로고    scopus 로고
    • A new boussinesq method for fully nonlinear waves from shallow to deep water
    • Madsen PA, Bingham HB, Liu H. A new Boussinesq method for fully nonlinear waves from shallow to deep water. Journal of Fluid Mechanics 2002; 462:1-30.
    • (2002) Journal of Fluid Mechanics , vol.462 , pp. 1-30
    • Madsen, P.A.1    Bingham, H.B.2    Liu, H.3
  • 2
    • 0141848956 scopus 로고    scopus 로고
    • Boussinesq-type formulations for fully nonlinear and extremely dispersive water waves: Derivation and analysis
    • Madsen PA, Bingham HB, Schäffer HA. Boussinesq-type formulations for fully nonlinear and extremely dispersive water waves: derivation and analysis. Proc. R. Soc. Lond A 2003; 459:1075-1104.
    • (2003) Proc. R. Soc. Lond A , vol.459 , pp. 1075-1104
    • Madsen, P.A.1    Bingham, H.B.2    Schäffer, H.A.3
  • 3
    • 0942278089 scopus 로고    scopus 로고
    • Numerical solutions of fully non-linear and highly dispersive Boussinesq equations in two horizontal dimensions
    • Fuhrman DR, Bingham HB. Numerical solutions of fully non-linear and highly dispersive Boussinesq equations in two horizontal dimensions. International Journal for Numerical Methods in Fluids 2004; 44:231-255.
    • (2004) International Journal for Numerical Methods in Fluids , vol.44 , pp. 231-255
    • Fuhrman, D.R.1    Bingham, H.B.2
  • 4
    • 34250447917 scopus 로고
    • Stability of periodic waves of finite amplitude on the surface of a deep fluid
    • Zakharov VE. Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 1968; 9:190-194.
    • (1968) J. Appl. Mech. Tech. Phys. , vol.9 , pp. 190-194
    • Zakharov, V.E.1
  • 5
    • 0037465217 scopus 로고    scopus 로고
    • Accuracy and convergence of velocity formulations for water waves in the framework of Boussinesq theory
    • Madsen PA, Agnon Y. Accuracy and convergence of velocity formulations for water waves in the framework of Boussinesq theory. Journal of Fluid Mechanics 2003; 477:285-319.
    • (2003) Journal of Fluid Mechanics , vol.477 , pp. 285-319
    • Madsen, P.A.1    Agnon, Y.2
  • 6
    • 0002037267 scopus 로고    scopus 로고
    • A review of Boussinesq-type equations for gravity waves
    • Liu P (ed). World Scientific: Singapore
    • Madsen PA, Schäffer HA. A review of Boussinesq-type equations for gravity waves. In Advances in Coastal and Ocean Engineering, vol. 5, Liu P (ed). World Scientific: Singapore, 1999; 1-95.
    • (1999) Advances in Coastal and Ocean Engineering , vol.5 , pp. 1-95
    • Madsen, P.A.1    Schäffer, H.A.2
  • 7
    • 3042780786 scopus 로고    scopus 로고
    • A Boussinesq-type method for fully nonlinear waves interacting with a rapidly varying bathymetry
    • submitted
    • Madsen PA, Fuhrman DR, Wang B. A Boussinesq-type method for fully nonlinear waves interacting with a rapidly varying bathymetry. Journal of Fluid Mechanics, submitted.
    • Journal of Fluid Mechanics
    • Madsen, P.A.1    Fuhrman, D.R.2    Wang, B.3
  • 14
    • 0002753571 scopus 로고
    • A description of DDASSL: A differential/algebraic system solver
    • Petzold LR. A description of DDASSL: a differential/algebraic system solver. IMACS Transactions on Scientific Computation 1983; 1:65-68.
    • (1983) IMACS Transactions on Scientific Computation , vol.1 , pp. 65-68
    • Petzold, L.R.1
  • 17
    • 0008435580 scopus 로고
    • A numerical method for tidal computations in inner seas
    • in German
    • Fischer G. A numerical method for tidal computations in inner seas (in German). Tellus 1959; 11:60-76.
    • (1959) Tellus , vol.11 , pp. 60-76
    • Fischer, G.1
  • 19
    • 0042553279 scopus 로고
    • Smoothing and differentiation of data by simplified least squares procedures
    • Savitzky A, Golay MJE. Smoothing and differentiation of data by simplified least squares procedures. Analytical Chemistry 1964; 36:1627-1639.
    • (1964) Analytical Chemistry , vol.36 , pp. 1627-1639
    • Savitzky, A.1    Golay, M.J.E.2
  • 23
    • 0031238062 scopus 로고    scopus 로고
    • Pseudospectra of linear operators
    • Trefethen LN. Pseudospectra of linear operators. SIAM Review 1997; 39:383-406.
    • (1997) SIAM Review , vol.39 , pp. 383-406
    • Trefethen, L.N.1
  • 26
    • 0031126310 scopus 로고    scopus 로고
    • Low-dimensional models of subcritical transition to turbulence
    • Baggett JS, Trefethen LN. Low-dimensional models of subcritical transition to turbulence. Physics of Fluids 1997; 9:1043-1053.
    • (1997) Physics of Fluids , vol.9 , pp. 1043-1053
    • Baggett, J.S.1    Trefethen, L.N.2
  • 30
    • 0000048673 scopus 로고
    • GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems
    • Saad Y, Schultz MH. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific Computing 1986; 7:856-869.
    • (1986) SIAM Journal on Scientific Computing , vol.7 , pp. 856-869
    • Saad, Y.1    Schultz, M.H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.