T. Yabe

Cubic interpolated pseudo-particle method (CIP) for solving hyperbolic-type equations

Abstract A new cubic-polynomial interpolation method, where the gradient of the quantity is a free parameter, is proposed for solving hyperbolic-type equations. Various choices of the gradient are investigated, and a stable and less diffusive scheme is made possible without the clipping or the flux-correction procedure.

The cubic-interpolated Pseudo particle (cip) method: application to nonlinear and multi-dimensional hyperbolic equations

Abstract The basic of CIP, as a method to solve hyperbolic equations, is re-examined from a different viewpoint and the scheme is modified into an explicit finite difeerence form. The method gives a stable and less diffusive result for square wave propagation compared with FCT and a better result for propagation of a sine wave with a discontinuit. The scheme is extended to nonlinear and multi-dimensional problems.

Cubic interpolated propagation scheme for solving the hyper-dimensional Vlasov—Poisson equation in phase space

A new numerical scheme for solving the hyper-dimensional Vlasov—Poisson equation in phase space is described. At each time step, the distribution function and its first derivatives are advected in phase space by the Cubic Interpolated Propagation (CIP) scheme. Although a cell within grid points is interpolated by a cubic-polynomial, any matrix solutions are required. The scheme guarantees exact mass conservation. The numerical results show good agreement with the theory. Even if we reduce the number of grid points in the v-direction, the scheme still gives stable, accurate and reasonable results with memory storage comparable to particle simulations. Owing to this fact, the scheme has succeeded to be generalized in a straightforward way to deal with six-dimensional, or full-dimensional problems.

An Exactly Conservative Semi-Lagrangian Scheme (CIP–CSL) in One Dimension

Abstract Two semi-Lagrangian schemes that guarantee exactly mass conservation are proposed. Although they are in a nonconservative form, the interpolation functions are constructed under the constraint of conservation of cell-integrated value (mass) that is advanced by remapping the Lagrangian volume. Consequently, the resulting schemes conserve the mass for each computational grid cell. One of them (CIP–CSL4) is the direct extension of the original cubic-interpolated propagation (CIP) method in which a cubic polynomial is used as the interpolation function and the gradient is calculated according to the differentiated advection equation. A fourth-order polynomial is employed as the interpolation function in the CIP–CSL4 method and mass conservation is incorporated as an additional constraint on the reconstruction of the interpolation profile. In another scheme (CIP–CSL2), the CIP principle is applied to integrated mass and the interpolation function becomes quadratic. The latter one can be readily extend...

Scalings of implosion experiments for high neutron yield

A series of experiments focused on high neutron yield has been performed with the Gekko‐XII green laser system [Nucl. Fusion 27, 19 (1987)]. Deuterium–tritium (DT) neutron yield of 1013 and pellet gain of 0.2% have been achieved. Based on the experimental data from more than 70 irradiations, the scaling laws of the neutron yield and the related physical quantities have been studied. Comparison of the experimental neutron yield with that obtained by using a one‐dimensional fluid code has led to the conclusion that most of the neutrons produced in the stagnation phase of the computation are not observed in the experiment because of fuel–pusher mixing, possibly induced by the Rayleigh–Taylor instability. The coupling efficiency and ablation pressure have been calculated using the ion temperature measured experimentally. A coupling efficiency of 5.5% and an ablation pressure of 50 Mbar have been obtained.

Constructing oscillation preventing scheme for advection equation by rational function

A numerical scheme for solving advection equations is presented. The scheme is derived from a rational interpolation function. Some properties of the scheme with respect to convex-concave preserving and monotone preserving are discussed. We find that the scheme is attractive in suppressing overshoots and undershoots even in the vicinities of discontinuity. The scheme can also be easily switched as the CIP (Cubic interpolated Pseudo-Particle) method to get a third-order accuracy in smooth region. Numbers of numerical tests are carried out to show the non-oscillatory and less diffusive nature of the scheme.

Constructing exactly conservative scheme in a non-conservative form

A non-conservative scheme that guarantees exact mass conservation is proposed. Although it is in a non-conservative form, the mass of each cell is employed as an additional variable that is advanced in a conservative form. Some numerical tests are carried out to demonstrate the mass conservation and the accurate calculation of the speed of a shock wave even without the viscosity term.

A Multidimensional Cubic-Interpolated Pseudoparticle (CIP) Method without Time Splitting Technique for Hyperbolic Equations

A new numerical method is proposed for multidimensional linear advection equations. The scheme uses a cubic spatial profile within grids, and is described in an explicit form by assuming that both a physical quantity and its spatial derivative obey the given equation. The method gives a stable and less diffusive result without any flux limiter. Its extension to nonlinear equations with nonadvection term is straightforward.

An algorithm for simulating solid objects suspended in stratified flow

Abstract An efficient difference algorithm for computing directly deformationless solid objects suspended in stratified flow in 2D has been developed. The objects are represented by colour functions (or density functions) and predicted by a sharpness preserving scheme that is able to prevent the numerical diffusion across the sharp interface. Pressure distribution is then calculated by a unified solver and the solid object is treated as a mass of material of high sound speed. The motion of the solid object is decomposed into translation and rotation, and the force as well as the torque that cause change in the motion of the solid body are evaluated by an averaging calculation over the region occupied by the solid body. Calculations are conducted on a fixed grid system. Operations for reconstructing moving interfaces or dealing with inner boundary conditions are not necessary.

Constructing a multi-dimensional oscillation preventing scheme for the advection equation by a rational function

We recently developed a numerical scheme for solving advection equations based on a rational interpolation function. The scheme shows properties in suppressing spurious numerical oscillations near great gradients and sharing high accuracy in the smooth region. Results in one dimension were reported in a previous paper (F. Xiao, T. Yabe and T. Ito, Comput. Phys. Commun. 93 (1996) 1). In this paper, we, for completion, present the two- and three-dimensional versions of the scheme without directional splitting. Formula are derived in the way such as to recover the CIP method (T. Yabe, T. Aoki, Comput. Phys. Commun. 60 (1991) 219; T. Yabe, T. Ishikawa, P.Y. Wang, T. Aoki, Y. Kadota and F.Ikeda, Comput. Phys. Commun. 66 (1991) 233) by switching. The oscillation preventing quality of the scheme in two and three dimensions is tested by sample calculations.