Related papers: Shock profiles for hydrodynamic models for fluid-p…
This paper is concerned with singular shocks for a system of conservation laws modeling incompressible two-phase fluid flow. We prove the existence of viscous profiles using the Geometric Singular Perturbation Theory. Weak convergence and…
We present a full investigation into shock wave profile description using hydrodynamics models. We identified constitutive equations that provide better agreement for all parameters involved in testing hydrodynamic equations for the…
In this paper, we are interested in the dynamics of charged particles interacting with the incompressible viscous flow. More precisely, we consider the Vlasov-Poisson or Vlasov-Poisson-Fokker-Planck equation coupled with the incompressible…
Viscoelastic rate-type fluid models constitute a fundamental framework for the mathematical description of complex materials exhibiting coupled elastic and viscous effects, with a wide range of applications in engineering, biomaterials, and…
The sensitivity of charge, heat, or momentum transport to the sample geometry is a hallmark of viscous electron flow. Therefore, hydrodynamic electronics requires the detailed understanding of electron flow in finite geometries. The…
We present a shock capturing method for large-eddy simulation of turbulent flows. The proposed method relies on physical mechanisms to resolve and smooth sharp unresolved flow features that may otherwise lead to numerical instability, such…
The system describing the dynamics of a compressible isentropic fluid exhibiting viscosity and internal capillarity in one space dimension and in Lagrangian coordinates, is considered. It is assumed that the viscosity and the capillarity…
We examine the existence of shock profiles for a hyperbolic-elliptic system arising in radiation hydrodynamics. The algebraic-differential system for the wave profile is reduced to a standard two-dimensional form that is analyzed in details…
The derivation of an approximate Class-I model for nonisothermal multicomponent systems of fluids, as the high-friction limit of a Class-II model is justified, by validating the Chapman-Enskog expansion performed from the Class-II model…
Shock solutions for multi-temperature Euler equations are inherently ambiguous due to the loss of microscopic physical detail during model reduction and occurrence of non-conservative terms. This paper presents a detailed analytical study…
We investigate the behavior of a one-dimensional diatomic fluid under a shock wave excitation. We find that the properties of the resulting shock wave are in striking contrast with those predicted by hydrodynamic and kinetic approaches,…
A Type-I model of a multicomponent system of fluids with non-constant temperature is derived as the high-friction limit of a Type-II model via a Chapman-Enskog expansion. The asymptotic model is shown to fit into the general theory of…
Brenner has recently proposed modifications to the Navier-Stokes equations that are based on theoretical arguments but supported only by experiments having a fairly limited range. These modifications relate to a diffusion of fluid volume…
In this paper, thermal-slip coefficients in slip boundary conditions of the Stokes equation are derived using the generalized slip-flow theory, with special interest in the role of near-wall potential in micro- and nanoscale flows. As the…
An overview of recent results pertaining to the hydrodynamic description (both Newtonian and non-Newtonian) of granular gases described by the Boltzmann equation for inelastic Maxwell models is presented. The use of this mathematical model…
The paper investigates shock-induced vortical flows within inhomogeneous media of nonuniform thermodynamic properties. Numerical simulations are performed using an Eularian type mathematical model for compressible multi-component flow…
Polydisperse gas-solid flows, which is notoriously difficult to model due to the complex gas-particle and particle-particle interactions, are widely encountered in industry. In this article, a refined kinetic theory for polydisperse flow is…
This paper shows that in second-order hyperbolic systems of partial differential equations proposed in authors' earlier paper (J. Math. Phys. 59 (2018)) for modelling the relativistic dynamics of barotropic fluids in the presence of…
The physical quantities in a gas should vary continuously across a shock. However, the physics inherent in the compressible Euler equations is insufficient to describe the width or structure of the shock. We demonstrate the existence of…
In this paper we study existence and stability of shock profiles for a 1-D compressible Euler system in the context of Quantum Hydrodynamic models. The dispersive term is originated by the quantum effects described through the Bohm…