论文信息 - Non-dissipative time-integration schemes for the linear advection equation

Non-dissipative time-integration schemes for the linear advection equation

We discuss an application of the class of non-dissipative methods, introduced recently in Chawla and Al-Zanaidi [1], for the time-integration of the linear advection equation: Since spatial discretization affects, often adversely, the property of non-dissipativity, to fully realize the non-dissipativity of these rules, in the present investigation we consider their application to the linear advection equation combined with the method of characteristics. Numerical experiments confirm the non-dissipativity of these time-integration schemes for the important instances of problems in which the initial condition is a pulse with jump discontinuities or steep fronts.

[1] J. W. Thomas. Numerical Partial Differential Equations: Finite Difference Methods , 1995 .

[2] M. M. Chawla,et al. Non-dissipative extended one-step methods for oscillatory problems , 1998, Int. J. Comput. Math..

[3] Gilbert Strang,et al. Accurate partial difference methods , 1964 .

[4] G. Smith,et al. Numerical Solution of Partial Differential Equations: Finite Difference Methods , 1978 .

[5] Edward H. Twizell,et al. Backward difference replacements of the space derivative in first-order hyperbolic equations , 1984 .

[6] B. Wendroff. Theoretical Numerical Analysis , 1966 .

[7] M.Y. Hussaini,et al. Low-Dissipation and Low-Dispersion Runge-Kutta Schemes for Computational Acoustics , 1994 .