Making a flux positivity-preserving: A general purpose filter for the euler equations

A general purpose positivity-preserving filter is here presented which transforms any non-positivity-preserving flux into one that is positivity preserving. The method consists of recasting a flux at the interface in terms of a left and right flux, with the left flux having positive eigenvalues, and the right flux having negative eigenvalues. Such can be proven to be positivity-preserving (density and temperature maintained positive) for the Euler equations of gas dynamics. Several test cases show that the positivity-preserving filter can be deployed successfully to viscous and inviscid flows integrated using either explicit or implicit schemes.