相关论文: Integral methods for shallow free-surface flows wi…

The theory of integrable systems of Hamiltonian PDEs and their near-integrable deformations is used to study evolution equations resulting from vertical-averages of the Euler system for two-layer stratified flows in an infinite 2D channel.…

Interactions between an evolving solid and inviscid flow can result in substantial computational complexity, particularly in circumstances involving varied boundary conditions between the solid and fluid phases. Examples of such…

Hydroelastic solitary waves propagating on the surface of a three-dimensional ideal fluid through the deformation of an elastic sheet are studied. The problem is investigated based on a Benney-Luke-type equation derived via an explicit…

A streamwise-constant model is presented to investigate the basic mechanisms responsible for the change in mean flow occuring during pipe flow transition. Using a single forced momentum balance equation, we show that the shape of the…

The standard analytical approach for studying gravity free-surface waves generated by a moving body often relies upon a linearization of the physical geometry, where the body is considered asymptotically small in one or several of its…

We present the derivation of a new unidirectional model for We present the derivation of a new unidirectional model for unsteady mixed flows in non uniform closed water pipes. We introduce a local reference frame to take into account the…

We present a Lagrangian-Eulerian scheme to solve the shallow water equations in the case of spatially variable bottom geometry. Using a local curvilinear reference system anchored on the bottom surface, we develop an effective first-order…

The laminar-turbulent boundary S is the set separating initial conditions which relaminarise uneventfully from those which become turbulent. Phase space trajectories on this hypersurface in cylindrical pipe flow look to be chaotic and show…

Flow through porous, elastically deforming media is present in a variety of natural contexts ranging from large-scale geophysics to cellular biology. In the case of incompressible constituents, the porefluid pressure acts as a Lagrange…

This paper deals with the two-dimensional incompressible, laminar, steady-state boundary layer equations.First, we determine a family of velocity distributions outside the boundary layer such that these problems may have similarity…

We study an integro-differential equation that describes the slow erosion of granular flow. The equation is a first order non-linear conservation law where the flux function includes an integral term. We show that there exist unique…

Gravity-driven flows of liquid films are frequent in nature and industry, such as in landslides, lava flow, cooling of nuclear reactors, and coating processes. In many of these cases, the liquid is non-Newtonian and has particular…

Meandering instability is familiar to everyone through river meandering or small rivulets of rain flowing down a windshield. However, its physical understanding is still premature, although it could inspire researchers in various fields,…

Models and simulations of the flow of thin films of fluids have many important applications in industrial and natural processes. We consider the motion of a thin layer of an incompressible, Newtonian fluid over an arbitrary solid,…

Fluid deformable surfaces show a solid-fluid duality which establishes a tight interplay between tangential flow and surface deformation. We derive the governing equations as a thin film limit and provide a general numerical approach for…

In this paper, a new method to model solidification of thin liquid films is proposed. \blue{This method is targeted at applications like aircraft icing and tablet coating where the formation of liquid films from impinging droplets on a…

Equations relating the pressure at a horizontal seabed, the free-surface profile and the surface-pressure are derived for two-dimensional irrotational steady water waves with arbitrary pressure at the free surface. Special cases include…

We computationally study the spontaneous phase separation of ternary fluid mixtures using the lattice Boltzmann method, both when all the surface tensions are equal and when they have different values. Previous theoretical works typically…

Linear and weakly nonlinear stability analyses of an externally shear-imposed, gravity-driven falling film over a uniformly heated wavy substrate are studied. The longwave asymptotic expansion technique is utilized to formulate a single…

In this paper, a novel immersed boundary method is developed, validated, and applied. Through devising a second-order three-step flow reconstruction scheme, the proposed method is able to enforce the Dirichlet, Neumann, Robin, and Cauchy…