A quantitative comparison of the usual and recent numerical treatments which are applied to the Smoothed Particle Hydrodynamics (SPH) method are presented together with a new free-surface treatment. A series of numerical treatments are studied to refine the numerical procedures of the SPH method particularly for violent flows with a free surface. Two dimensional dam-break and sway-sloshing prob...

nowadays, with the industry development, a lot of waste is produced damaging the environment. among wastewater treatment methods, anaerobic techniques have been highly regarded due to numerous advantages. in anaerobic systems, upflow anaerobic sludge blanket (uasb) reactor has many features. in this study using computational fluid dynamics techniques, three-phase reactor hydrodynamics in two an...

in this note we characterize polynomial numerical hulls of matrices $a in m_n$ such that$a^2$ is hermitian. also, we consider normal matrices $a in m_n$ whose $k^{th}$ power are semidefinite. for such matriceswe show that $v^k(a)=sigma(a)$.