Abstract:
Aiming at high accuracy and high resolution computation for numerical simulation of compressible fluid flows, based on the smoothness measurement of the flux function of the stencil, the new kind of weighted factor is constructed. On the basis, the hybrid scheme (H-WENO7-CD8) combines the characteristics of WENO scheme and central flux scheme, and it improves the resolution of the scheme and the ability to capture the shock wave. The Fourier method is adopted to analysis the mathematical characteristics of the discrete scheme. The adaptive hybrid scheme has low dissipation. By the numerical simulation tests of the Shu-Osher shock-density interference problem, the two-dimensional Rayleigh-Taylor instability problem, and double Mach reflection, compared with the numerical tests of the WENO-JS scheme, the present hybrid scheme can capture the shock wave better, and it has higher resolution for shock waves and small-scale waves with a low computation cost. Therefore, the present scheme lays an algorithm foundation for high resolution numerical simulation of compressible fluid flows such as the shock wave-turbulent layer interaction problem or Richtmyer-Meshkov instability problem.