Abstract
Originally, kinetic schemes have been used as numerical methods to solve the system of compressible Euler equations in gas dynamics. The main idea in the approach is to construct the numerical flux function based on a microscopical description of the gas. In this article the schemes are investigated in the case of isentropic Euler equations and low Mach numbers. Expanding the microscopical velocity distribution naturally leads to new kinetic schemes with strong resemblance to lattice Boltzmann methods. By adjusting the parameters of the kinetic scheme the numerical viscosity can be used to reproduce a given physical viscosity. In this way, a finite difference solver for the incompressible Navier–Stokes equation is obtained. Its close relation to the lattice Boltzmann approach is highlighted.
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