Total variation diminishing scheme

Summary

A total variation diminishing (TVD) scheme is a numerical scheme for a scalar conservation law in one space dimension. Its discrete total variation never increases from one time step to the next. This copies a property of the exact entropy solutions, and it rules out the creation of new local extrema. So the scheme gives no spurious oscillations near shocks. The notion was introduced by Harten in 1983, and it is the design principle of the high-resolution schemes built with flux limiters.