Abstract
High accuracy of numerical schemes is one of the most important requirements to simulate complex flow phenomena. A conservative form of the interpolated differential operator (IDO-CF) scheme is a multi-moment Eulerian scheme explicitly solving all the moments with higher spectral resolution than the conventional finite difference method (FDM). A compact difference (CD) scheme is one of high-order FDMs implicitly solving additional spatial derivatives as non-time-integrated variables. We propose multi-moment compact schemes combining both the concept of the multi-moment schemes and the CD scheme. The proposed schemes have very high-order accuracy and spectral like resolution in Fourier space. In addition, the spatial derivative matrix is reduced to half size so that computational cost gets much smaller than the same-order CD scheme with the same number of independent variables. A linear wave propagation is examined and the results are dramatically improved to compare to the conventional multi-moment scheme. In a non-linear problem, we carry out the direct numerical simulation (DNS) of two-dimensional homogeneous isotropic turbulence, and it is found that the high-order multi-moment compact scheme improves the energy spectral at high wave number region.
