The local inertial equation (LIE) as a simple mathematical model has been widely used for flood simulation. So far, the maximum allowable time step of the discretized LIE with the conventional semi-implicit scheme has been believed to follow the standard Courant-Friedrichs-Lewy condition. However, we demonstrate that this is not true from the viewpoint of a numerical stability analysis considering the model non-linearity. In addition, a fully-implicit variant of the scheme with higher stability is presented, indicating its practical advantages.
This paper presents original mathematical models to simulate formation of dendritic tree networks such as natural river channels. These are referred to as the Poisson Equation Model (PEM) and as the Inhomogeneous Permeability Model (IPM), respectively, where the two-dimensional Poisson equations are solved under the homogeneous or the inhomogeneous condition. Particularly important is the IPM, which assumes that permeability varies depending on the site, which reflects regional fluctuations of geographical properties such as soil, precipitation, and so on. Natural river basins are supposed to realize a kind of optimization principle such that total energy expenditure or flow resistance is minimal, as stated by the Optimal Channel Network (OCN) theory or the Constructal law. From a viewpoint of optimization, possible structures of area-to-point flow systems are explored by use of PEMs and IPMs. According to our numerical simulations, it is supposed that the origin of the fractal structure that characterizes natural fluvial landscapes is heterogeneity in geomorphic conditions. This study indicates that the permeability randomization method can be utilized not only as a practical but also as an instructive tool to reproduce naturally disturbed river network systems.
Two simulation methods, Equivalent-Circuit Model (ECM) simulation and Finite Element Method (FEM) simulation, are proposed for analyzing the time evolution of the shielding current density in a High-Temperature Superconducting (HTS) film that is part of a pellet container moving in an applied magnetic field. In the ECM simulation, Newton's equation of motion for the pellet container is solved together with the circuit equations equivalent to the governing equation of the shielding current density in the HTS film. On the other hand, it is solved together with the governing equation in the FEM simulation. Two numerical codes are developed on the basis of the ECM/FEM and the performance of the Superconducting Linear Acceleration (SLA) system is investigated by using the two codes. The results of computations show that, even for the case with a single electromagnet, the SLA system has a possibility to accelerate a pellet container up to over 140 m/s.