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

Abstract

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.

Keywords:

• Linear advection equation
• non-dissipative time-integration schemes
• method of characteristics
• crank-nicolson scheme
• box scheme

C.R. Category:

• G.1.8