Simulation of Kelvin-Helmholtz instability with high-order finite difference method

The Kelvin-Helmholtz instability in the inviscid fluid was simulated by applying high-order weighted essentially non-oscillatory(WENO) scheme to solve the two-dimensional conservative Euler equations. The simulation adopted the periodic boundary condition for the velocity shear direction and the fringe method as the outflow boundary condition for the disturbance growth direction, where an unstable wavelength contained 64 grids. The linear growth rate of the disturbance amplitude derived from this numerical simulation agrees well with that from the linear stability analysis, which proves the validity and accuracy of the simulation method. The method can provide clear density contours, showing a good capturing ability of interface deformation.