2.5.2 Artificial viscosity

Inserting the Lax-Friedrichs flux (115) into the conservative update formula (99) results in

$$\textstyle \rho^{n+1}_i = \underbrace{ \rho^n_i - \frac... ..._{i-1}^n \right] }_{\mbox{artificial viscosity}} \enspace .$$ (119)

The last term looks like a 2nd derivative and is called artificial viscosity. In general, the flux of any scheme can be written in the form

$$f = \underbrace{ f_{\mathrm{FTCS}} }_{\mbox{FTCS flux}} ... ...ight) }_{\mbox{flux due to artificial viscosity}} \enspace .$$ (120)

Sometimes, the Lax-Wendroff flux is used as reference,

$$f = \underbrace{ f_{\mathrm{Lax-Wendroff}} }_{\mbox{Lax-W... ...ight) }_{\mbox{flux due to artificial viscosity}} \enspace .$$ (121)