A new central compact finite difference formula for improving robustness in weighted compact nonlinear schemes

摘要: Abstract The weighted compact nonlinear scheme (WCNS) is a typical well-known finite difference method that shows high-order accuracy and high resolution when applied to problems involving hyperbolic conservation laws. However, flow with severe discontinuities, the original WCNS often suffers from negative densities or pressures. We have found robustness of can be remarkably improved by changing central employed in an alternative one. In this article, new cell-edge- cell-node-type alternate (ACCS) proposed, (i.e., (ACWCNS)) developed combining ACCS reconstruction (weighted interpolation) method. To elucidate basic characteristics ACWCNS, we perform truncation error analysis, wavenumber semi-discrete eigenvalue validation for 1D advection equations. Subsequently, ACWCNS several 2D benchmark compressible flows discontinuities. When solving such problems, it difficult preserve positivity both density pressure using conventional WCNS; nevertheless, able provide stable solutions. smooth regions solutions, spatial deteriorate slightly as improved. compensate this, modified obtained computational results are compared those approaches.