Compact Implicit MacCormack-Type Schemes with High Accuracy

Analysis of central and upwind compact schemes

“…The early work on compact differencing scheme can be seen in [8][9][10]. Such methods have been optimized to solve the time-domain Maxwell equations in [11] and for problems relating to acoustics in [12,13,28]. In [12] the important concept of dispersion relation preservation (DRP) is discussed with respect to high accuracy schemes for acoustics problems.…”

Symmetrized compact scheme for receptivity study of 2D transitional channel flow

“…If we discretize the time derivative by the leap frog scheme and the spatial derivative by applying the S-OUCS3 scheme, as given by Eq. (14), then the difference equation is obtained as…”

“…Since then, it has gained in importance and has been extensively used to solve problems of fluid dynamics [21,2,38,27] and wave propagation [11,8,37,27,14]. Various compact schemes have been shown to possess enhanced accuracy and resolution in solving model problems with periodic boundary conditions [11].…”

Multidimensional optimization of finite difference schemes for Computational Aeroacoustics

“…[7,11]) are combined with optimized spatial differencing schemes (see, e.g. [1,2,6,9,13,15,16,22]) and proper boundary conditions (see, e.g. [5,8,10,23]).…”