Laser-produced plasma ~LPP! devices are being developed as a light source for the extreme ultraviolet ~EUV! lithography applications. One concern of such devices is to increase the conversion efficiency of laser energy to EUV light. A new idea based on the initiation and confinement of cumulative plasma jet inside a hollow laser beam is developed and simulated. The integrated computer model ~HE...

The level set method is one of the most successful methods for the simulation of multi-phase flows. To keep the level set function close the signed distance function, the level set function is constantly reinitialized by solving a Hamilton-Jacobi type of equation during the simulation. When the fluid interface intersects with a solid wall, a moving contact line forms and the reinitialization of...

It was recently shown that for reasonable notions of approximation of states and functions by quantum circuits, almost all states and functions are exponentially hard to approximate 5]. The bounds obtained are asymptotically tight except for the one based on total variation distance (TVD). TVD is the most relevant metric for the performance of a quantum circuit. In this paper we obtain asymptot...

We investigate time-dependent inviscid hydrodynamical accretion flows onto a black hole using numerical simulations. We consider the accretion that consists of hot tenuous gas with low specific angular momentum and cold dense gas with high specific angular momentum. The former accretes continuously and the latter highly intermittently as blobs. The high specific angular momentum gas blobs bounc...

Accurate solutions of the porous media equation that usually occurs in nonlinear problems of heat and mass transfer and in biological systems are obtained using a compact finite difference method in space and a low-storage total variation diminishing third-order Runge-Kutta scheme in time. In the calculation of the numerical derivatives, only a tridiagonal band matrix algorithm is encountered. ...

For Runge–Kutta methods and linear multistep methods, much attention has been paid, in the literature, to special nonlinear stability properties indicated by the terms total-variationdiminishing (TVD), strong-stability-preserving (SSP), and monotonicity. Stepsize conditions, guaranteeing these properties, were studied, e.g., by Shu and Osher [J. Comput. Phys., 77 (1988), pp. 439–471], Gottlieb,...

This article deals with a method, based on total variation diminishing (TVD) scheme, for solving three-dimensional equations of gravitational gas dynamics. For this method a parallel algorithm of the decision is offered. Equations of this kind are a powerful approach to simulating astrophysical problems. Numerical schemes applied for their solving must provide high-resolution capturing of shock...

The alternating evolution (AE) system of Liu [25] ∂tu +∇x · f(v) = 1 2 (v − u), ∂tv +∇x · f(u) = 1 2 (u− v) serves as a refined description of systems of hyperbolic conservation laws ∂tφ +∇x · f(φ) = 0, φ(x, 0) = φ0(x). The solution of conservation laws is precisely captured when two components take the same initial value as φ0, or approached by two components exponentially fast when 2 ↓ 0 if t...

An Eulerian TVD code and a Lagrangian SPH code are used to simulate the off-axis collision of equal-mass main sequence stars in order to address the question of whether stellar mergers can produce a remnant star where the interior has been replenished with hydrogen due to significant mixing. Each parent main sequence star is chosen to be found near the turnoff, with hydrogen depleted in the cor...

The Runge–Kutta discontinuous Galerkin (RKDG) method for solving hyperbolic conservation laws is a high order finite element method, which utilizes the useful features from high resolution finite volume schemes, such as the exact or approximate Riemann solvers, TVD Runge–Kutta time discretizations, and limiters. In this paper, we investigate using the RKDG finite element method for compressible...