On artificial viscosity

Abstract It is shown that the usual analysis for the implicit artificial viscosity of finite difference analogs of the linear advection equation is ambiguous, with different results obtained for transient and steady-state problems. The ambiguity is easily resolved for the inviscid equation, but for the advection-diffusion equation, the steady-state analysis is shown to be applicable to steady-state problems. It is demonstrated that the currently most popular methods, touted as having no artificial viscosity, actually do have such when applied to steady-state problems.