We discuss the application of complex variable methods to Hele-Shaw flows and twodimensional Stokes flows, both with free boundaries. We outline the theory for the former, in the case where surface tension effects at the moving boundary are ignored. We review the application of complex variable methods to Stokes flows both with and without surface tension, and we explore the parallels between t...

In the past several years, continuous effort has been made in RIAM, Kyushu University to develop an efficient Cartesian grid method for violent free surface problems in ship and ocean engineering. Our researches have been focused on (1) Accurate and robust flow solver for multi-phase flows with solid bodies. (2) Conservative and smearingless interface capturing scheme. In the numerical method, ...

A model for the simulation of complex three-dimensional free surface flows is presented. An incompressible liquid interacts with a compressible gas. The incompressible Navier-Stokes equations are solved only in the liquid domain while the dynamical effects in the gas are neglected. The compressibility effects of the gas are taken into account by computing its pressure. Surface tension effects a...

The water wave generation by wave paddle and a freely falling rigid body are examined by using an Incompressible Smoothed Particle Hydrodynamics (ISPH). In the current ISPH method, the pressure was evaluated by solving pressure Poisson equation using a semi-implicit algorithm based on the projection scheme and the source term of pressure Poisson equation contains both of divergence free velocit...

In a previous study [DD07b] we presented a novel visco-potential free surface flows formulation. The governing equations contain local and nonlocal dissipative terms. From physical point of view, local dissipation terms come from molecular viscosity but in practical computations, rather eddy viscosity should be used. On the other hand, nonlocal dissipative term represents a correction due to th...

A large collection of particles can behave collectively like a fluid. In this work, we examine the fluid behavior of a large collection of particles in the absence of a background gas phase. The use of granular fluids, as opposed to liquids, has several advantages for free-surface plasma-facing coolants: low vapor pressure, absence of electromagnetic interactions, and chemical inertness, to nam...

A new approach based on the finite-difference technique has been developed to study the steady incompressible Navier-Stokes equations in the laminar region, where the domain is partially bounded by a free surface. The nonstaggered fractional step method is used to solve the flow equations written in terms of primitive variables. The physical domain is transformed to a rectangle by means of a nu...

In this paper the method of Smoothed Particle Hydrodynamics (SPH) is extended to include an adaptive density kernel estimation (ADKE) procedure. It is shown that for a van der Waals (vdW) fluid, this method can be used to deal with free-surface phenomena without difficulties. In particular, arbitrary moving boundaries can be easily handled because surface tension is effectively simulated by the...

The problem of stability of a water-coated ice layer is investigated for a free-surface flow of a thin water film down an inclined plane. An asymptotic (double-deck) theory is developed for a flow with large Reynolds and Froude numbers which is then used to investigate linear two-dimensional, three-dimensional and nonlinear two-dimensional stability characteristics. A new mode of upstream-propa...

In this thesis a model for the simulation of floating objects on free surfaces is presented. Free surfaces arise at the transition between two fluids with a large density difference, e.g. between water and air. This effect is important for a lot of technical applications, such as metal foaming or molding. Fluid flows around obstacles or flows involving solid bodies is a phenomenon, of equally n...