Numerical simulations of a spherical shock refraction have been successfully conducted by a front tracking method We demonstrate the e ciency of the front tracking algorithm by comparing the L error of spherical simulations by tracked and untracked methods We nd that the tracked algorithm is about times faster than the correspond ing method without tracking the interface for a d d simulation

We study the autonomous motion of catalytic nanorods in Gibbs monolayers. The catalytic activity of the rods on a hydrogen peroxide aqueous subphase gives rise to anomalous translational and rotational diffusion. The rods perform a Levy-walk superdiffusive motion that can be decomposed into thermal orientation fluctuations and an active motion of the rods with a constant velocity along their lo...

We rigorously derive nonlinear instability of Hele-Shaw flows moving with a constant velocity in the presence of smooth viscosity profiles where the viscosity upstream is lower than the viscosity downstream. This is a single-layer problem without any material interface. The instability of the basic flow is driven by a viscosity gradient as opposed to conventional interfacial Saffman–Taylor inst...

The paper describes the development of the efficient interface sharpening procedure for viscous incompressible flows governed by the Navier–Stokes equations. The moving interface has been captured by a pseudo-concentration method. The solution domain has been discretised by the space-time finite elements, while numerical schemes have been stabilised by the Galerkin least squares method. The dam...

The problem of the vibration of a beam subject to a travelling force is considered. The purpose of the study is to develop simple tools for finding the maximum deflection of a beam for any given velocity of the travelling force. It is shown that, for given boundary conditions, there exists a unique response–velocity dependence function. A technique to determine this function is suggested, which...

We study a two-point free boundary problem for a quasilinear parabolic equation. This problem arises in the model of flame propagation in combustion theory. It also arises in the study of the motion of interface moving with curvature in which the studied problem is confined in the conical region bounded by two straight lines and the interface has prescribed touching angles with these two straig...

The behaviour of a solid-liquid-gas system near the three-phase contact line is considered using a diffuse-interface model with no-slip at the solid and where the fluid phase is specified by a continuous density field. Relaxation of the classical approach of a sharp liquid-gas interface and careful examination of the asymptotic behaviour as the contact line is approached is shown to resolve the...

Public use of information and computer technology (ICT) in disaster response has become a new type of “megacollaboration.” However, government policy is moving in the opposite direction, toward a strict chain-of-command model. The resulting divergence can lead to inefficiency and weakened disaster response. Hence, there is a clear need for an interface that can bridge the gap between these two ...

In many situations of hydrodynamic phenomenon, two-layer fluid is a dominant feature of fluid motion. Such two-layer fluid often contains jumps in the density across the interface of fluid domains. The interface of air and water or salt water and fresh water is obvious example [Tho68]. The density jump may be assumed to occur in an infinitesimally thin interface in the mixture. And, the behavio...

In recent years, there have been extensive efforts to find the numerical methods for solving problems with interface. The main idea of this work is to introduce an efficient truly meshless method based on the weak form for interface problems. The proposed method combines the direct meshless local Petrov–Galerkin method with the visibility criterion technique to solve the interface problems. It ...