A new combined stable and dispersion relation preserving compact scheme for non-periodic problems

Further improvement and analysis of CCD scheme: Dissipation discretization and de-aliasing properties

“…Combined compact difference (CCD) schemes are very high accuracy methods where first and second derivatives are evaluated simultaneously, from implicit relations between the dependent variable and its derivatives obtained using Hermitian polynomials [1][2][3][4]. This method belongs to the family of compact schemes and hence affords near-spectral accuracy in solving convection-diffusion dominated flows, as noted in [5][6][7][8].…”

“…In [5], methods are indicated to obtain first and second derivatives separately by using compact schemes. CCD schemes [2][3][4]8] provide second derivatives simultaneously, that makes computations faster, increasing the efficiency via enhanced resolution of dissipation terms for convection-diffusion dominated problems. This makes the method very attractive, however only when one works in the physical plane with uniform grids.…”

“…In [11], a comprehensive analysis is made to understand what constitutes error in a signal propagation problem establishing the correct error analysis, as opposed to the existing von Neumann analysis. The application of this analysis technique for solving uni-and bi-directional wave problems was also provided in [4], while investigating an improved CCD scheme. The same scheme is analyzed and compared with other methods for their dissipation discretization and de-aliasing properties.…”

Analysis and application of high order implicit Runge–Kutta schemes to collocated finite volume discretization of the incompressible Navier–Stokes equations

“…This problem has been studied for example in [28,29]. The critical Reynolds number has been reported in [28] to be close to Re ¼ 8000, though this varies to some degree in the literature, mainly due to the chosen numerical method [29]. Here, the lid driven cavity flow at the Reynolds number of Re ¼ 8200 is considered.…”

Development of a symplectic and phase error reducing perturbation finite-difference advection scheme

“…Similar to other high-order schemes, compact schemes need a special approximation treatment near and at boundary nodes, in particular, for the simulation of thin boundary-layer flows [14].…”