Improved upwind discretization of the advection equation

The simplest upwind discretization of the advection equation is only first‐order accurate in time and space and very diffusive. In this article, the first‐order upwind method is improved by changing its basis functions. The resulting scheme, called exponentially fitted, proves to be more accurate in both space and time. In addition, it inherits some qualitative behaviors of the advection equation. The proposed approach is able to be generalized for more complicated problems provided that appropriate relations between the fitting parameters of the method are imposed. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 773–787, 2014