On the Construction of Kinetic Schemes

A general method for the construction of kinetic schemes of evolutionary equations is illustrated with the simple example of the linear advection equation, where the role of the collision effect is clarified theoretically and numerically. The application to the compressible Euler equation and Navier–Stokes equation is explained. The theoretical backgrounds of the existing kinetic schemes, such as the Pullin scheme for the Euler equation and Chou–Baganoff scheme and modified Prendergast–Xu scheme for the Navier–Stokes equation, are unified and their intrinsic errors are revealed.