Related papers: Euler-like modelling of dense granular flows: appl…
The single droplet under shear is a foundational problem in fluid mechanics. In computational fluid dynamics, the two-dimensional (2D) formulation offers advantages in both computational efficiency and relevance, yet its theoretical…
The Euler equations describing two-dimensional steady flows of an inviscid fluid are studied. These equations are reduced to one equation for the stream function and then, using the Hirota function, solutions of three nonlinear elliptic…
The solution of a momentum conservation equation for the gas and liquid stream in the flowing element is obtained on the basis of the modern approach to a problem on contact interaction of bodies and mediums. A flowing element, system are:…
Nonlinear acoustics of wind instruments conducts to study unidimensional fluid flows. From physically relevant approximations that are modelized with the thin layer Navier Stokes equations, we propose a coupled model where perfect fluid…
We develop structure-preserving numerical methods for the compressible Euler equations, employing potential temperature as a prognostic variable. We construct three numerical fluxes designed to ensure the conservation of entropy and total…
We carry out a detailed comparison of soft particle molecular dynamics simulations with the theory of partially fluidized shear granular flows. We verify by direct simulations a constitutive relation based on the separation of the shear…
In this article, we propose a novel conservative diffuse-interface method for the simulation of immiscible compressible two-phase flows. The proposed method discretely conserves the mass of each phase, momentum and total energy of the…
This paper establishes the nonlinear stability of the Couette flow for the 2D Boussinesq equations with only vertical dissipation. The Boussinesq equations concerned here model buoyancy-driven fluids such as atmospheric and oceanographic…
In this work we systematically derive the governing equations of supersonic conical flow by projecting the 3D Euler equations onto the unit sphere. These equations result from taking the assumption of conical invariance on the 3D flow…
This paper presents a streamfunction-vorticity formulation for the Navier--Stokes and Euler equations on general surfaces. Notably, this includes non-simply connected surfaces, on which the harmonic components of the velocity field play a…
We present a symmetry result regarding stationary solutions of the 2D Euler equations in a disk. We prove that in a disk, a steady flow with only one stagnation point and tangential boundary conditions is a circular flow, which confirms a…
The ultra--relativistic Euler equations describe gases in the relativistic case when the thermal energy dominates. These equations for an ideal gas are given in terms of the pressure, the spatial part of the dimensionless four-velocity, and…
In this paper we show that steady states $u$ of the pressureless Euler equation which belong to $L^3_{loc}(\mathbb{R}^2,\mathbb{R}^2)$ are shear flows. This is achieved by combining results of degenerate Monge-Amp\`ere-type equations with…
The temporal evolution of a dilute granular gas, both in a compressible flow (uniform longitudinal flow) and in an incompressible flow (uniform shear flow), is investigated by means of the direct simulation Monte Carlo method to solve the…
Steady simple shear flow of a low-density binary mixture of inelastic smooth hard spheres is studied in the context of the Boltzmann equation. This equation is solved by using two different and complementary approaches: a Sonine polynomial…
We consider rigidity properties of steady Euler flows in two-dimensional bounded domains. We prove that steady Euler flows in a disk with exactly one interior stagnation point and tangential boundary conditions must be circular flows, which…
Neither natural nor laboratory laminar flows are perfectly steady. Instead, they are frequently highly unsteady, as illustrated by experimental studies on B\'{e}nard convection. In the paper, we investigate the transition threshold of the…
Flows of one-dimensional continuum in Lagrangian coordinates are studied in the paper. Equations describing these flows are reduced to a single Euler-Lagrange equation which contains two undefined functions. Particular choices of the…
Bubbly flows, as present in bubble column reactors, can be simulated using a variety of simulation techniques. In order to gain high resolution CFD methods are used to simulate a pseudo 2D bubble column using EL and EE techniques. The…
We report on progress on the free surface flow in the presence of submerged oscillating line sources (2D) or point sources (3D) when a simple shear flow is present varying linearly with depth. Such sources are in routine use as Green…