Toward the Ultimate Conservative Scheme: Following the Quest

The aim of this paper is to develop a class of numerical schemes that work on triangular finite element type meshes, and which are devoted to the computation of steady transonic flows. The schemes are extensions of the positive streamwise invariant scheme of Struijs and are built directly on the system of the Euler equation for fluid mechanics. They are a blending between a first-order and a second-order scheme, which is realized from entropy considerations. It is formally second-order accurate at steady state. Several numerical examples are shown to demonstrate the stability and accuracy of these schemes.