Advances in Computational Mechanics and Numerical Simulation.-The Splitting Scheme for Mathematical Modeling of the Mixed Region Dynamics in a Stratified Fluid -- Modeling of Some Astrophysical Problems on Supercomputers Using Gasdynamical Model.-Numerical Modeling of the Kolmogorov Flow in a Viscous Media -- On Structures of Supersonic Flow around Plane System of Cylindrical Rods.-Limiting Functions Affecting the Accuracy of Numerical Solution Obtained by Discontinuous Galerkin Method -- Numerical Simulation of Detonation Initiation: The Quest of Grid Resolution -- On the Stability of a Detonation Wave in a Channel of Variable cross Section with Supersonic Input and Output Flows -- Physical and Kinematic Processes Associated with Meteoroid when Falling in the Earth's Atmosphere -- Computational Modeling of Rarefied Plasma and Neutral Gas Effusion into Vacuum. .