TVD schemes and their relation to artificial dissipation

The Burgers and Euler fluid dynamics equations are presently solved by incorporating recent dissipations models into modified explicit Runge-Kutta schemes. An effort is made to ascertain the fundamental mechanism underlying the various dissipation models. It is established that the TVD models capture discontinuities much more accurately than the nonlinear dissipation models; their major disadvantages are that they reduce the time step required for a stable solution and require more numerical operations per time-step than the nonlinear dissipation model.