A phase proper orthogonal decomposition (phase POD) method is demonstrated utilizing averaging for the of spatiotemporal behavior statistically non-stationary turbulent flows in an optimized manner. The proposed POD herein applied to a periodically forced lid-driven cavity flow, implemented using snapshot algorithm. Space-phase modes are extracted describe dynamics chaotic which four central fl...

The non-orthogonal boundary-fitted coordinate transformation method is applied to the solution of steady three-dimensional conservation equations of mass, momentum, energy and speciescontinuity to obtain the laminar velocity, temperature and concentration fields for simulation of polymerization of styrene in arbitrary cross-sectional duct reactors. Variable physical properties (except for speci...

In this paper we have discussed different possible orthogonalities in matrices, namely orthogonal, quasiorthogonal, semi-orthogonal and non-orthogonal matrices including completely positive matrices, while giving some of their constructions besides studying some of their properties.