Direct modeling for computational fluid dynamics and the construction of high-order compact scheme for compressible flow simulations

Computational fluid dynamics is a direct modeling of physical laws in discretized space. The basic include the mass, momentum and energy conservations, numerical scale-consistent transport process, similar domain dependence influence wave propagations. Therefore, physically soundable scheme should be compact one which involves closest neighboring cells within for solution update under CFL number (∼1). In order to keep compactness high-order, subcell flow distributions or equivalent degrees freedom beyond cell averaged variables are needed, such as gradients inside each control volume. Under above consideration, use Riemann solver evolution model doesn't provide mechanism. High-order dynamic process used time accurate cell-averaged their gradients. generalized initial condition will developed. reliable data reconstruction, constructed possible discontinuous time-dependent across interface. At same time, flux function at interface can become its process. Same spatial limiter conventional computational methods, total variation diminishing weighted essentially non-oscillatory temporal designed well. method this paper differently on both sides nonlinearly limit high-order derivatives case shock passing through step. unifies concepts nonlinear limiters reconstruction transport. treatment space makes gas-kinetic super robust compressible simulation. 4th 8th-order schemes large (∼0.8) computation, even hypersonic