Search results for "Compressibility"
showing 10 items of 125 documents
Equilibrium real gas computations using Marquina's scheme
2003
Marquina's approximate Riemann solver for the compressible Euler equations for gas dynamics is generalized to an arbitrary equilibrium equation of state. Applications of this solver to some test problems in one and two space dimensions show the desired accuracy and robustness
Effect of the mineralogical composition on the elastoplastic hydromechanical response of Opalinus Clay shale
2021
Abstract Opalinus Clay is the shale currently under investigation as the host formation for geological radioactive waste disposal in Switzerland. Its hydromechanical response has been widely studied, and the experimental results show a range of values whose dispersion needs to be clarified. This work aims to explain the dispersion in the literature results by correlating the hydro-mechanical response to the mineralogical variability of the tested specimens . Based on published microstructural studies, the Opalinus Clay shale is herein schematised as a sequence of two kinds of layers: the shaly (high in clay-mineral content) and the sandy (low in clay-mineral content) layers. The mineralogic…
Capturing blast waves in granular flow
2007
Abstract In this paper we continue the analysis of compressible Euler equations for inelastic granular gases described by a granular equation of state due to Goldshtein and Shapiro [Goldshtein A, Shapiro M. Mechanics of collisional motion of granular materials. Part 1: General hydrodynamic equations. J Fluid Mech 1995;282:75–114], and an energy loss term accounting for inelastic collisions. We study the hydrodynamics of blast waves in granular gases by means of a fifth-order accurate scheme that resolves the evolution under different restitution coefficients. We have observed and analyzed the formation of a cluster region near the contact wave using the one-dimensional and two-dimensional v…
A flux-split algorithm applied to conservative models for multicomponent compressible flows
2003
In this paper we consider a conservative extension of the Euler equations for gas dynamics to describe a two-component compressible flow in Cartesian coordinates. It is well known that classical shock-capturing schemes applied to conservative models are oscillatory near the interface between the two gases. Several authors have addressed this problem proposing either a primitive consistent algorithm [J. Comput. Phys. 112 (1994) 31] or Lagrangian ingredients (Ghost Fluid Method by Fedkiw et al. [J. Comput. Phys. 152 (1999) 452] and [J. Comput. Phys. 169 (2001) 594]). We solve directly this conservative model by a flux-split algorithm, due to the first author (see [J. Comput. Phys. 125 (1996) …
High order accurate shock capturing schemes for two-component Richtmyer-Meshkov instabilities in compressible magnetohydrodynamics
2011
We design a conservative and entropy satisfying numerical scheme to perform numerical simulations of two component Richtmyer-Meshkov (RM) instabilities in compressible magnetohydrodynamics (MHD). We first formulate a conservative model of a two-component compressible MHD fluid ruled under two ideal gases with different adiabatic exponents. The formulation includes a level set function that allows to evolve the two components of the plasma in a conservative and consistent way. We present a set of examples including two-component Riemann problems and high Mach shock wave interactions with entropy contact waves that validate the high order accurate numerical scheme. We observe that turbulent r…
The Mean-Field Limit for Solid Particles in a Navier-Stokes Flow
2008
We propose a mathematical derivation of Brinkman's force for a cloud of particles immersed in an incompressible viscous fluid. Specifically, we consider the Stokes or steady Navier-Stokes equations in a bounded domain Omega subset of R-3 for the velocity field u of an incompressible fluid with kinematic viscosity v and density 1. Brinkman's force consists of a source term 6 pi rvj where j is the current density of the particles, and of a friction term 6 pi vpu where rho is the number density of particles. These additional terms in the motion equation for the fluid are obtained from the Stokes or steady Navier-Stokes equations set in Omega minus the disjoint union of N balls of radius epsilo…
Size and shape effects on the thermodynamic properties of nanoscale volumes of water
2017
Small systems are known to deviate from the classical thermodynamic description, among other things due to their large surface area to volume ratio compared to corresponding big systems. As a consequence, extensive thermodynamic properties are no longer proportional to the volume, but are instead higher order functions of size and shape. We investigate such functions for second moments of probability distributions of fluctuating properties in the grand-canonical ensemble, focusing specifically on the volume and surface terms of Hadwiger's theorem, explained in Klain, Mathematika, 1995, 42, 329–339. We resolve the shape dependence of the surface term and show, using Hill's nanothermodynamics…
Surface sulci in squeezed soft solids
2013
The squeezing of soft solids, the constrained growth of biological tissues, and the swelling of soft elastic solids such as gels can generate large compressive stresses at their surfaces. This causes the otherwise smooth surface of such a solid to become unstable when its stress exceeds a critical value. Previous analyses of the surface instability have assumed two-dimensional plane-strain conditions, but in experiments isotropic stresses often lead to complex three-dimensional sulcification patterns. Here we show how such diverse morphologies arise by numerically modeling the lateral compression of a rigidly clamped elastic layer. For incompressible solids, close to the instability thresho…
Characterization of V-doped SnO2 nanoparticles at ambient and high pressures
2018
Nanoparticles of V-doped SnO2 with stoichiometry Sn1-xO2Vx (x = 0.05, 0.075, 0.125) have been synthesized by a co-precipitation method. Their structural, vibrational, and nuclear properties have been characterized by x-ray Diffraction, Transmission Electron Microscopy, Energy Dispersive x-ray Spectroscopy, Raman Spectroscopy, and Mössbauer Spectroscopy (with 119Sn probe) at ambient pressure. We also performed high-pressure synchrotron x-ray diffraction experiments. The structural behaviour was studied up to ∼10 GPa under quasi-hydrostatic conditions. It has been found that tin dioxide nanoparticles with V are more compressible than un-doped tin dioxide nanoparticles. Fil: Ferrari, S. Consej…
Thermodynamic class II Szekeres-Szafron solutions. Singular models
2019
A family of parabolic Szekeres-Szafron class II solutions in local thermal equilibrium is studied and their associated thermodynamics are obtained. The subfamily with the hydrodynamic behavior of a generic ideal gas (defined by the equation of state $p = k n \Theta$) results to be an inhomogeneous generalization of flat FLRW $\gamma$-law models. Three significative interpretations that follow on from the choice of three specific thermodynamic schemes are analyzed in depth. First, the generic ideal gas in local thermal equilibrium; this interpretation leads to an inhomogeneous temperature $\Theta$. Second, the thermodynamics with homogeneous temperature considered by Lima and Tiomno (CQG 6 1…