Artificial Wind—A New Framework to Construct Simple and Efficient Upwind Shock-Capturing Schemes

Using a concept of artificial wind having its roots in the Galilean invariance of hydrodynamic equations, we propose a new framework to design upwind shock-capturing schemes. Its application results in simple, efficient, and accurate schemes retaining their simplicity for a broad range of hydrodynamic problems. The global, local, and differential artificial wind approaches are subsequently elaborated. Test results demonstrate efficiency and accuracy of the new schemes in comparison with the Godunov scheme and its second-order extension. The relationship between the artificial wind approach and some existing schemes is also discussed.