Related papers: Exact and Approximate Solutions for Magnetohydrody…
A collection of arbitrarily-shaped solid objects, each moving at a constant speed, can be used to mix or stir ideal fluid, and can give rise to interesting flow patterns. Assuming these systems of fluid stirrers are two-dimensional, the…
We develop a self-consistent analytical two-fluid framework for plasma evolution in the short-time regime, elucidating the fundamental mechanism underlying the coupled generation of flow and magnetic fields. We show that consistency between…
Weakly ionised plasmas, formed in high enthalpy hypersonic flows, can be actively manipulated via imposed magnetic fields - a concept termed magnetohydrodynamic (MHD) flow control. Imposed MHD effects, within flows which exhibit multiple…
Computational fluid dynamics is a direct modeling of physical laws in a discretized space. The basic physical laws include the mass, momentum and energy conservations, physically consistent transport process, and similar domain of…
Multi-component fluid flow simulations in multi-scale porous structures often involve regions that are under-resolved at practical computational resolutions. Accurately capturing the contributions from these unresolved regions is critical.…
A nonlocal interface equation is derived for two-phase fluid flow, with arbitrary wettability and viscosity contrast c=(mu_1-mu_2)/(mu_1+mu_2), in a model porous medium defined as a Hele-Shaw cell with random gap b_0+delta b. Fluctuations…
Force-free electrodynamics describes the electromagnetic field of the magnetically dominated plasma found near pulsars and active black holes, but gives no information about the underlying particles that ultimately produce the observable…
We discuss conjectural scaling limits of discrete 2-dimensional aggregation models conditioned on a semi-axis considered by Levine and Peres in arXiv:0712.3378. These are certain problems about Hele-Show flows. We study moment properties of…
We present a new connection between the Hele-Shaw flow, also known as two-dimensional (2D) Laplacian growth, and the theory of holomorphic discs with boundary contained in a totally real submanifold. Using this we prove short time existence…
In this paper, the interfacial motion between two immiscible viscous fluids in the confined geometry of a Hele-Shaw cell is studied. We consider the influence of a thin wetting film trailing behind the displaced fluid, which dynamically…
When a viscous fluid partially fills a Hele--Shaw channel, and is pushed by a pressure difference, the fluid interface is unstable due to the Saffman--Taylor instability. We consider the evolution of a fluid region of finite extent, bounded…
Finite volume schemes for hyperbolic conservation laws require a numerical intercell flux. In one spatial dimension the numerical flux can be successfully obtained by solving (exactly or approximately) Riemann problems that are introduced…
We formulate hydrodynamic equations and spectrally accurate numerical methods for investigating the role of geometry in flows within two-dimensional fluid interfaces. To achieve numerical approximations having high precision and level of…
The flow near a moving contact line is primarily governed by three key parameters: viscosity ratio, dynamic contact angle, and inertia. While the behavior of dynamic contact angles has been extensively studied in earlier experimental and…
The magnetohydrodynamic equations system for heavy fluid over an arbitrary surface in shallow water approximation is studied in the present paper. It is shown that simple wave solutions exist only for underlying surfaces that are slopes of…
Understanding fluid flow in wedge-shaped geometries is essential for predicting hydrodynamic interactions in confined systems, such as microfluidic devices and near-corner transport phenomena. This article reviews analytical methods and…
In this paper we deal with the numerical solution of a Hele--Shaw-like system via a cell model with active motion. Convergence of approximations is established for well-posed initial data. These data are chosen in such a way the time…
Time-dependent injection strategies are commonly employed to control the number of viscous fingers emerging at the interface separating two fluids during radial displacement in Hele-Shaw flows. Here we demonstrate theoretically that such a…
Flow birefringence measurement is an emerging technique for visualizing stress fields in fluid flows. This study investigates flow birefringence in the steady radial Hele-Shaw flow. In the radial Hele-Shaw flow, stress is dominant along the…
In models of fast magnetic reconnection, flux transfer occurs within a small portion of a current sheet triggering stored magnetic energy to be thermalized by shocks. When the initial current sheet separates magnetic fields which are not…