Kaori Kato

Poisson equation solver with fourth-order accuracy by using interpolated differential operator scheme☆☆☆

Abstract A Poisson equation solver with fourth-order spatial accuracy has been developed by using the interpolated differential operator (IDO) scheme. The number of grids required for obtaining the results of numerical computation with the same accuracy as that by the second-order center finite difference method is drastically reduced. The consistency is confirmed to the use of the multigrid method and the red-black algorithm. The decrease of the CPU time by the multigrid method and by the parallel computing indicates the applicability of the IDO Poisson solver to large scale problems.

Numerical simulation of shockwave by KrF laser ablation

Hydrodynamic simulation code that is based on the cubic interpolated pseudo-particle scheme and the model of the equation of state is developed to analyze the hydrodynamic instabilities in the inertial confinement fusion. Ablation structure, shockwave, and the hydrodynamic instabilities by KrF laser were investigated by the 1D and 2D hydrodynamic simulation.

Parallel Simulation for Strong Blast Wave from TNT Explosion on Large-scale PC-Cluster

For the simulation of strong blast waves, a high-accurate numerical scheme was presented. The fractional step method splits the compressible fluid equation into the advection phase and non-advection phase. The monotone preserving RCIP scheme is used for the density and the internal energy in the advection phase to avoid negative values, and the IDO scheme is adapted with 3-stage Runge-Kutta time integration in the non-advection phase to describe the sound wave accurately. It is noticed that in both the phases, the schemes are based on the cubic Hermite interpolations constructed by the value and the gradient, and the overall numerical accuracy of the scheme keeps 3rd order in space.

Photo-realistic visualization for the blast wave of TNT explosion by grid-based rendering

After the detonation of a solid high explosive, the material has extremely high pressure keeping the solid density and expands rapidly driving strong shock wave. In order to investigate the blast wave propagation driven by the 32-kg TNT explosion of the underground magazine a three-dimensional simulation is performed with a stable and accurate numerical scheme without a special modeling for the expansion process of detonation product gas. The compressible fluid equations are solved by a fractional step procedure which consists of the advection phase and non-advection phase. The former employs the Rational function CIP scheme in order to preserve monotone signals and the latter is solved by IDO (Interpolated Differential Operator) scheme for achieving the accurate calculation. For this simulation results, photo-realistic visualization is achieved with combination of volume rendering with isosurface rendering on grid computer.

Numerical Simulation of Carbon Simple Cubic by Dynamic Compression

An impact scheme of a slab target and flyer with a layered structure is proposed to achieve low-entropy dynamic compression of diamond. The thermodynamic state of diamond during compression is examined using one-dimensional Lagrangian hydrodynamic code and the tabulated equation of state library, SESAME. The use of a material with a small shock impedance for the impact interfaces markedly decreases the strength of the primary shock wave. It is found that a gradient of shock impedance across the thickness of the flyer generates small multiple shock waves into the diamond and is effective for low-entropy compression. The thermodynamic conditions required for carbon simple cubic and low-entropy dynamic compression is achieved.