A gas inside the microsystems or the porous media is in its non-equilibrium state, due to the fact that the molecular mean free path is comparable to the characteristic dimension of the media. The same state of a gas, called rarefied, is found at high altitude or in the vacuum equipment working at low pressure. All these types of flow can be described by the kinetic models derived from the Bolt...

In this paper we review and further develop a class of strong-stability preserving (SSP) high-order time discretizations for semi-discrete method-of-lines approximations of partial di erential equations. Termed TVD (total variation diminishing) time discretizations before, this class of high-order time discretization methods preserves the strong-stability properties of rst-order Euler time step...

Continuously operated clarifier-thickener units can be modeled by a non-linear, scalar conservation law with a flux that involves two parameters that depend discontinuously on the space variable. This paper presents two numerical schemes for the solution of this equation that have formal second-order accuracy in both the time and space variable. One of the schemes is a standard total variation ...

We present a WENO-TVD scheme for the simulation of atmospheric phenomena. The scheme considers a spatial discretization via a second-order TVD flux based upon a flux-centered limiter approach, which makes use of high-order accurate extrapolated values arising from a WENO reconstruction procedure. Time discretization is performed with a third order RK-TVD scheme, and splitting is used for the in...

A new three dimensional Piecewise Parabolic Method (PPM) based hydrodynamic code is utilized to compute the distribution of hot gas in the standard COBE normalized CDM universe. Utilizing periodic boundary conditions, a box with size 85h 1 Mpc having cell size 0:31h 1 Mpc, is followed in a simulation with 270 3 = 10 7:3 cells. Adopting standard parameters determined from COBE and light element ...

In this paper, we developed a class of the fourth order accurate finite volume Hermite weighted essentially non-oscillatory (HWENO) schemes based on the work (Computers & Fluids, 34: 642–663 (2005)) by Qiu and Shu, with Total Variation Diminishing Runge-Kutta time discretization method for the two-dimensional hyperbolic conservation laws. The key idea of HWENO is to evolve both with the solutio...

In this paper we present the analysis for the Runge-Kutta discontinuous Galerkin (RKDG) method to solve scalar conservation laws, where the time discretization is the third order explicit total variation diminishing Runge–Kutta (TVDRK3) method. We use an energy technique to present the L-norm stability for scalar linear conservation laws, and obtain a priori error estimates for smooth solutions...

We study the properties of galaxies at redshift z = 2 in a Λ cold dark matter (ΛCDM) universe, using two different types of hydrodynamic simulation methods (Eulerian TVD and SPH) and a spectrophotometric analysis in the Un, G,R filter set. The simulated galaxies at z = 2 satisfy the color-selection criteria proposed by Adelberger et al. (2004) and Steidel et al. (2004) when we assume Calzetti e...

Three-dimensional numerical simulations of solar surface magnetoconvection using realistic model physics are conducted. The thermal structure of convective motions into the upper radiative layers of the photosphere, the main scales of convective cells and the penetration depths of convection are investigated. We take part of the solar photosphere with size of 60 × 60 Mm in horizontal direction ...

A high-order, conservative, yet efficient method named the spectral volume (SV) method is developed for conservation laws on unstructured grids. The concept of a “spectral volume” is introduced to achieve high-order accuracy in an efficient manner similar to spectral element and multidomain spectral methods. Each spectral volume is further subdivided into control volumes, and cell-averaged data...