This paper gives a survey on different types of geometric models being suitable for Numerical Simulation techniques. They are classified in coarse- and fine-grain models for topologically 'rigid' and topologically transient structures. For structural problems, these models are linked to the p-version of the finite element method, and for problems in fluid dynamics, the Lattice Boltzmann method is applied.

Rayleigh-Taylor (RT) instability has a growing importance in many fields including aircraft industry and astrophysics. The development and the growth of RT instability were investigated using sinusoidal disturbances with different wavelength at the interface of the two fluids. Numerical Simulations were performed by solving Navier-Stokes unsteady equations with the VOF formulation. Results of the 2D Simulation are compared with experimental results.It is shown that beyond a critical time, not captured experimentally, the mushroom shape of RT instability turns into a helical path or breaks down into a patchy shape depending on the shape of disturbance. Nonlinear instabilities responsible for such behavior are apparent when the wavelength exceeds 10 times the length scale introduced in this study.

In this research, the Supercavitation phenomenon in compressible liquid flows is simulated. The one-fluid method based on a new exact two-phase Riemann solver is used for modeling. The cavitation is considered as an isothermal process and a consistent equation of state with the physical behavior of the water is used. High speed flow of water over a cylinder and a projectile are simulated and the results are compared with the previous Numerical and experimental results. The cavitation bubble profile in both cases agrees well with the previous experimental results reported in the literature. As the result shows, coupling the two-phase Riemann solver with the considered EOS prepares a robust method for simulating the compressible fluid flow with cavitation which can undertake the whole physical behavior of water in a supercavitation process.Furthermore, the influence of the cavitator head and the flow speed on the supercavitation bubble is explored.The results show that cavitators with sharper head results in a smaller supercavitating bubble. Increasing the flow speed beyond a specific limit does not have any significant effect on the cavitation bubble and slightly increases the bubble size.

A two-dimensional Numerical model has been developed to study wave breaking on a sloping beach. The basic elements of Numerical model are Reynolds Averaged Navier-Stokes (RANS) equations that describe the mean flow motion of a turbulent flow; a k turbulence closure model that describes the turbulent transport and dissipation process; an efficient technique (VOF- Volume Of Fluid method) for tracking the free surface motion; and a new scheme developed by Lin and Liu (1999) for wave generation. Shoaling, breaking and overturning of solitary wave on a slope of 1/16 have been studied with the main emphasis on turbulence characteristics. Turbulence characteristics i.e., turbulence kinetic energy, k; turbulence dissipation rate, ; turbulence production, pr; turbulence eddy viscosity, vt; and their spatial distribution during the breaking process have been discussed in great details. Spatial distribution of turbulence characteristics and the order of magnitude have been found to be in agreement with existing experimental and Numerical studies. The main characteristic of plunging breaking waves, the shoreward advective transport of turbulence, has also been investigated and Numerically proved.