Total variation diminishing

In numerical methods, total variation diminishing (TVD) is a property of certain discretization schemes used to solve hyperbolic partial differential equations. The most notable application of this method is in computational fluid dynamics. The concept of TVD was introduced by Ami Harten. In numerical methods, total variation diminishing (TVD) is a property of certain discretization schemes used to solve hyperbolic partial differential equations. The most notable application of this method is in computational fluid dynamics. The concept of TVD was introduced by Ami Harten. In systems described by partial differential equations, such as the following hyperbolic advection equation, the total variation (TV) is given by, and the total variation for the discrete case is, A numerical method is said to be total variation diminishing (TVD) if,