Tadayasu Takahashi

Conservation properties of vectorial operator splitting

This work is concerned with the conservation properties of a new vectorial operator splitting scheme for solving the incompressible Navier-Stokes equations. It is proven that the difference approximation of the advection operator conserves square of velocity components and the kinetic energy as the differential operator does, while pressure term conserves only the kinetic energy. Some analytical requirements necessary to be satisfied of difference schemes for incompressible Navier-Stokes equations are formulated and discussed. The properties of the methods are illustrated with results from numerical computations for lid-driven cavity flow.

Comparison Between Experimental and Numerical Results of a Mould Filling with Viscous Fluid

Dramatically viscous fluids are required to fill missiles, rockets and the boosters of the Ariane V Rocket. Such a rocket engine is called solid propellant engine, since the dynamic viscosity of the casted material increases in the course of time. At the end of the operation, the propellant becomes solid. Since the geometries we deal with are relatively complex, we solve the three-dimensional Navier-Stokes equations together with the transport of the fluid interface. The rheological behavior of the fluid involved, (the propellant, modelled as a fluid) is Newtonian.

On Some Nonlinear Dispersive Systems and the Associated Nonlinear Evolution Operators

Publisher Summary This chapter discusses the initial-boundary value problem for nonlinear dispersive equations. The technique used here provides a unified method for solving nonlinear dispersive equations in case o f Dirichlet and periodic boundary conditions. It shows via appropriate transformations of unknown functions that the result can be applied to a long wave equation with various time-dependent boundary conditions. This chapter also constructs a nonlinear evolution operator on H10 that provides the solutions of the evolution equation.