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A finite-element algorithm for computing free-surface flows driven by arbitrary body forces is presented. The algorithm is primarily designed for the microfluidic parameter range where (i) the Reynolds number is small and (ii) force-driven…
Exact solutions of a classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite strip bounded by the free surface (from above) and (from the…
For problems with multiple bodies, the current integral approach needs the use of auxiliary potential functions in order to have an individual force formula for each body. While the singularity approach, based on an extension of the…
Modeling of wall-bounded turbulent flows is still an open problem in classical physics, with only modest progress made in the last few decades beyond the so-called `log law', which describes only the intermediate region in wall-bounded…
In the classical one-dimensional solution of fluid dynamics equations all unknown functions depend only on time t and Cartesian coordinate x. Although fluid spreads in all directions (velocity vector has three components) the whole picture…
In conventional fluid mechanics, the chemical composition and thermodynamic state of a fluid-solid interface are not considered when establishing velocity-field boundary conditions. As a consequence, fluid simulations are usually not able…
Turbulence problem is often considered as "the last unsolved problem of classical physics". It is due to strong interaction between velocity and/or velocity gradient fluctuations, a high Reynolds number flow is a fascinating mixture of…
High resolution simulations of incompressible flows have become routine across a range of engineering applications. Despite their routine use, due to the high dimensional parameter space present for most practical applications, a…
We revisit the computation of bubble wall friction during a cosmological first-order phase transition, using an extended fluid Ansatz to solve the linearized Boltzmann equation. A singularity is found in the fluctuations of background…
The mechanism for singularity formation in an inviscid wall-bounded fluid flow is investigated. The incompressible Euler equations are numerically simulated in a cylindrical container. The flow is axisymmetric with swirl. The simulations…
This article attempts to use the ideas from the field of complexity sciences to revisit the classical field of fluid mechanics. For almost a century, the mathematical self-consistency of Navier-Stokes equations has remained elusive to the…
The proposed flow in a 3-D cubic cavity is driven by its parallel walls moving in perpendicular directions to create a genuinely three-dimensional highly separated vortical flow yet having simple single-block cubical geometry of…
The principle of multiple solutions of the Navier-Stokes equations discussed in this paper is not directed at any particular problems in fluid dynamics, nor at any specific applications. The non-uniqueness principle states that the Reynolds…
The properties of bubble-laden turbulent flows at different scales are investigated experimentally, focusing on the flow kinetic energy, energy transfer, and extreme events. The experiments employed particle shadow velocimetry measurements…
The lattice Boltzmann method with enhanced collisions and rest particles is used to calculate the flow in a two-dimensional lid-driven cavity. The abilitity of this method to compute the velocity and the pressure of an incompressible fluid…
The internal interactions of fluids occur at all scales therefore the resulting force fields have no reason to be smooth and differentiable. The release of the differentiability hypothesis has important mathematical consequences, like scale…
A particle-based model for mesoscopic fluid dynamics is used to simulate steady and unsteady flows around a circular and a square cylinder in a two-dimensional channel for a range of Reynolds number between 10 and 130. Numerical results for…
We consider the flow of a Newtonian fluid in a three-dimensional domain, rotating about a vertical axis and driven by a vertically invariant horizontal body-force. This system admits vertically invariant solutions that satisfy the 2D…
In this paper, we show that the spatio-temporal evolution of incompressible flows in a long circular pipe can be described by vorticity dynamics. The principal techniques to obtain solutions are similar to those used for flows in the whole…
The paper is devoted to the motion of a body in a fluid under the influence of gravity and drag. Depending on the regime considered, the drag force can exhibit a linear, quadratic or even more general dependence on the velocity of the body…