| 18 | 18 | Note the ugly, spurious oscillations near the large gradients of the step function. Unfortunately, all monotone schemes (those that do not contain artificial oscillations) are 1st order at best. Thus, the challenge is to reduce these oscillations in regions of discontinuous flow while maximizing accuracy in regions of smooth flow. One such class of schemes are known as 'Total Variation Diminishing' (TVD). These schemes implicitly add artificial viscosity, resulting in smoother flows near large gradients. Such a scheme is the Muscl-Hancock scheme. |
