Finite-difference method for the stabilization of the solution of the transport equation for an unstable difference scheme

摘要

We present explicit three-layer difference schemes for the transport equation with the use of adaptive artificial viscosity. These schemes have the third-order approximation with respect to time and the first-order approximation with respect to space for the unstable case of forward differences. We compare these schemes with their known analogs on a series of standard tests in various norms.