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Fluid mixture models are essential for describing a wide range of physical phenomena, including wave dynamics and spinodal decomposition. However, there is a lack of consensus in the modeling of compressible mixtures, with limited…
The flow of fluid confined between a heated rotating cylinder and a cooled stationary cylinder is a canonical experiment for the study of heat transfer in engineering. The theoretical treatment of this system is greatly simplified if the…
We consider the governing equations for the motion of compressible fluid on an evolving surface from both energetic and thermodynamic points of view. We employ our energetic variational approaches to derive the momentum equation of our…
One of the fundamental differences of compressible fluid flows from incompressible fluid flows is the involvement of thermodynamics. This difference should be manifested in the design of numerical methods and seems often be neglected in…
This article is a survey concerning the state-of-the-art mathematical theory of the Euler equations of incompressible homogenous ideal fluid. Emphasis is put on the different types of emerging instability, and how they may be related to the…
A closure theory is developed for inhomogeneous turbulent flow, which enables a systematic derivation of the turbulence constitutive relations without relying on any empirical parameters. Renormalized-perturbation approximation is performed…
We consider the governing equations for the motion of the viscous fluids in two moving domains and an evolving surface from both energetic and thermodynamic points of view. We make mathematical models for multiphase flow with surface flow…
We present results of large-scale three-dimensional simulations of supersonic Euler turbulence with the piecewise parabolic method and multiple grid resolutions up to 2048^3 points. Our numerical experiments describe non-magnetized driven…
In recent works, we proposed a hypothesis that the turbulence in gases could be produced by particles interacting via a potential, and examined the proposed mechanics of turbulence formation in a simple model of two particles for a variety…
The ability of streamwise-travelling waves of spanwise velocity to reduce the turbulent skin friction drag is assessed in the compressible regime. Direct numerical simulations are carried out to compare drag reduction in subsonic, transonic…
Many geophysical and astrophysical phenomena are driven by turbulent fluid dynamics, containing behaviors separated by tens of orders of magnitude in scale. While direct simulations have made large strides toward understanding geophysical…
A central obstacle to understanding the route to turbulence in wall-bounded flows is that the flows are composed of complex, highly fluctuating, and strongly nonlinear states. In the case of pipe flow, models have deepened our understanding…
This paper presents a novel methodology for the direct numerical modeling and simulation of turbulent flows. The kinetic model equation is firstly extended to turbulent flow with the account of coupled evolution of kinetic, thermal, and…
We revisit the molecular arguments underpinning the Eulerian model for compressible and diffusive flows, and conclude that a heat diffusive term appears to be missing in the original model. By studying a pure heat transfer problem, we…
Thermodynamic relations are derived from first principles of mechanics for non-equilibrium processes. Since the key role herein is played by the law of increase of entropy, the latter is analyzed at first. It is shown that its derivation…
We study stationary solutions to the continuity equation for weakly compressible flows. These describe non-equilibrium steady states of weakly dissipative dynamical systems. Compressibility is a singular perturbation that changes the steady…
A thermodynamically consistent visco-elastodynamical model at finite strains is derived that also allows for inelasticity (like plasticity or creep), thermal coupling, and poroelasticity with diffusion. The theory is developed in the…
In this article, a suite of physically inconsistent properties of the Navier-Stokes equations, associated with the lack of mass diffusion and the definition of velocity, are presented. We show that these inconsistencies are consequences of…
The concept of continuous topological evolution, based upon Cartan's methods of exterior differential systems, is used to develop a topological theory of non-equilibrium thermodynamics, within which there exist processes that exhibit…
In this paper, two approaches for modeling three-component fluid flows using diffusive interface method are discussed. Thermodynamic consistency of the proposed models is preserved when using an energetic variational framework to derive the…