An efficient high-order finite difference gas-kinetic scheme for the Euler and Navier-Stokes equations

The time-accurate solution of the gas distribution function permits the FDGKS to be a one-step high-order scheme without multi-step Runge-Kutta temporal matching, which significantly reduces the computational time. Many numerical tests in solving one and two-dimensional Euler and Navier-Stokes equations demonstrate that FDGKS is a highly stable, accurate, and efficient scheme, which captures discontinuities without oscillations.