Atsushi Nobe

Bio: Atsushi Nobe is an academic researcher from Chiba University. The author has contributed to research in topics: Toda lattice & Cluster algebra. The author has an hindex of 9, co-authored 37 publications receiving 978 citations. Previous affiliations of Atsushi Nobe include Future University Hakodate & University of Tokyo.

Numerical analysis of breaking waves using the moving particle semi-implicit method

Abstract: SUMMARY The numerical method used in this study is the moving particle semi-implicit (MPS) method, which is based on particles and their interactions. The particle number density is implicitly required to be constant to satisfy incompressibility. A semi-implicit algorithm is used for two-dimensional incompressible non-viscous flow analysis. The particles whose particle number densities are below a set point are considered as on the free surface. Grids are not necessary in any calculation steps. It is estimated that most of computation time is used in generation of the list of neighboring particles in a large problem. An algorithm to enhance the computation speed is proposed. The MPS method is applied to numerical simulation of breaking waves on slopes. Two types of breaking waves, plunging and spilling breakers, are observed in the calculation results. The breaker types are classified by using the minimum angular momentum at the wave front. The surf similarity parameter which separates the types agrees well with references. Breaking waves are also calculated with a passively moving float which is modelled by particles. Artificial friction due to the disturbed motion of particles causes errors in the flow velocity distribution which is shown in comparison with the theoretical solution of a cnoidal wave. © 1998 John Wiley & Sons, Ltd.

Ultradiscretization of a solvable two-dimensional chaotic map associated with the hesse cubic curve

Abstract: We present a solvable two-dimensional piecewise linear chaotic map which arises from the duplication map of a certain tropical cubic curve. Its gener al solution is constructed by means of the ultradiscrete theta function. We show that the map is derived by the ultradiscretization of the duplication map associated with the Hesse cubic curve. We also show that it is possible to obtain the nontrivial ultradiscrete limit of the solutio n in spite of a problem known as “the minus-sign problem.”

Ultradiscrete QRT maps and tropical elliptic curves

Abstract: It is shown that the polygonal invariant curve of the ultradiscrete QRT (uQRT) map, which is a two-dimensional piecewise linear integrable map, is the complement of the tentacles of a tropical elliptic curve on which the curve has a group structure in analogy to classical elliptic curves. Through the addition formula of a tropical elliptic curve, a tropical geometric description of the uQRT map is then presented. This is a natural tropicalization of the geometry of the QRT map found by Tsuda. Moreover, the uQRT map is linearized on the tropical Jacobian of the corresponding tropical elliptic curve in terms of the Abel-Jacobi map. Finally, a formula concerning the period of a point in the uQRT map is given, and an exact solution to its initial-value problem is constructed by using the ultradiscrete elliptic theta function.

On reversibility of cellular automata with periodic boundary conditions

Abstract: Reversibility of one-dimensional cellular automata with periodic boundary conditions is discussed. It is shown that there exist exactly 16 reversible elementary cellular automaton rules for infinitely many cell sizes by means of a correspondence between elementary cellular automaton and the de Bruijn graph. In addition, a sufficient condition for reversibility of three-valued and two-neighbour cellular automaton is given.

Exact solutions for discrete and ultradiscrete modified KdV equations and their relation to box-ball systems

Abstract: A new class of solutions is proposed for discrete and ultradiscrete modified KdV equations. These are directly related to solutions of the box and ball system with a carrier. Moreover, an extended box and ball system and its exact solutions are discussed.

Incompressible sph method for simulating newtonian and non-newtonian flows with a free surface

Abstract: An incompressible smoothed particle hydrodynamics (SPH) method is presented to simulate Newtonian and non-Newtonian flows with free surfaces. The basic equations solved are the incompressible mass conservation and Navier–Stokes equations. The method uses prediction–correction fractional steps with the temporal velocity field integrated forward in time without enforcing incompressibility in the prediction step. The resulting deviation of particle density is then implicitly projected onto a divergence-free space to satisfy incompressibility through a pressure Poisson equation derived from an approximate pressure projection. Various SPH formulations are employed in the discretization of the relevant gradient, divergence and Laplacian terms. Free surfaces are identified by the particles whose density is below a set point. Wall boundaries are represented by particles whose positions are fixed. The SPH formulation is also extended to non-Newtonian flows and demonstrated using the Cross rheological model. The incompressible SPH method is tested by typical 2-D dam-break problems in which both water and fluid mud are considered. The computations are in good agreement with available experimental data. The different flow features between Newtonian and non-Newtonian flows after the dam-break are discussed.

An SPH Projection Method

Abstract: A new formulation is introduced for enforcing incompressibility in Smoothed Particle Hydrodynamics (SPH). The method uses a fractional step with the velocity field integrated forward in time without enforcing incompressibility. The resulting intermediate velocity field is then projected onto a divergence-free space by solving a pressure Poisson equation derived from an approximate pressure projection. Unlike earlier approaches used to simulate incompressible flows with SPH, the pressure is not a thermodynamic variable and the Courant condition is based only on fluid velocities and not on the speed of sound. Although larger time-steps can be used, the solution of the resulting elliptic pressure Poisson equation increases the total work per time-step. Efficiency comparisons show that the projection method has a significant potential to reduce the overall computational expense compared to weakly compressible SPH, particularly as the Reynolds number, Re, is increased. Simulations using this SPH projection technique show good agreement with finite-difference solutions for a vortex spin-down and Rayleigh?Taylor instability. The results, however, indicate that the use of an approximate projection to enforce incompressibility leads to error accumulation in the density field.

Numerical Modeling of Water Waves with the SPH Method

Abstract: Smoothed Particle Hydrodynamics (SPH) is a relatively new method for examining the propagation of highly nonlinear and breaking waves. At Johns Hopkins University, we have been working since 2000 to develop an engineering tool using this technique. However, there have been some difficulties in taking the model from examples using a small number of particles to more elaborate and better resolved cases. Several improvements that we have implemented are presented here to handle turbulence, the fluid viscosity and density, and a different time-stepping algorithm is used. The final model is shown to be able to model breaking waves on beaches in two and three dimensions, green water overtopping of decks, and wave–structure interaction.

A multi-phase SPH method for macroscopic and mesoscopic flows

Abstract: A multi-phase smoothed particle hydrodynamics (SPH) method for both macroscopic and mesoscopic flows is proposed. Since the particle-averaged spatial derivative approximations are derived from a particle smoothing function in which the neighboring particles only contribute to the specific volume, while maintaining mass conservation, the new method handles density discontinuities across phase interfaces naturally. Accordingly, several aspects of multi-phase interactions are addressed. First, the newly formulated viscous terms allow for a discontinuous viscosity and ensure continuity of velocity and shear stress across the phase interface. Based on this formulation thermal fluctuations are introduced in a straightforward way. Second, a new simple algorithm capable for three or more immiscible phases is developed. Mesocopic interface slippage is included based on the apparent slip assumption which ensures continuity at the phase interface. To show the validity of the present method numerical examples on capillary waves, three-phase interactions, drop deformation in a shear flow, and mesoscopic channel flows are considered.