Journal of Engineering Mathematics
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Droplet impact onto a spring-supported plate: analysis and simulations
Journal of Engineering Mathematics - Tập 128 - Trang 1-27 - 2021
The high-speed impact of a droplet onto a flexible substrate is a highly non-linear process of practical importance, which poses formidable modelling challenges in the context of fluid–structure interaction. We present two approaches aimed at investigating the canonical system of a droplet impacting onto a rigid plate supported by a spring and a dashpot: matched asymptotic expansions and direct nu...... hiện toàn bộ
Unsteady Fully-Developed Flow in a Curved Pipe
Journal of Engineering Mathematics - Tập 34 - Trang 131-141 - 1998
It is shown that the boundary layer which develops from rest in a loosely coiled pipe of circular cross-section, following the imposition of a constant pressure gradient, terminates in singular behaviour at the inside bend after a finite time. This singularity of the boundary-layer equations is interpreted as an eruption of boundary-layer fluid into the interior or core flow. This result complemen...... hiện toàn bộ
A boundary-integral method for the interaction of large-amplitude ocean waves with a compliant floating raft such as a sea-ice floe
Journal of Engineering Mathematics - Tập 62 - Trang 355-372 - 2008
The interaction of large-amplitude water waves with a compliant floating raft such as a sea-ice floe or a pontoon-type VLFS (very large floating structure) is considered. The solution is expressed as a series using a perturbation expansion, the first two components of which are solved inductively using a boundary-integral method. The primary interest of this paper is to the ways in which the secon...... hiện toàn bộ
High- and low-frequency asymptotic consequences of the Kramers-Kronig relations
Journal of Engineering Mathematics - Tập 20 - Trang 293-306 - 1986
This paper examines the high- and low-frequency asymptotic consequences of the Kramers-Kronig relations which hold for the real and imaginary parts of the Fourier transform of the response of any linear causal system. By knowing or assuming the high- or low-frequency expansion of one of these functions, the corresponding asymptotic expansion of the other is easily determined, and furthermore the c...... hiện toàn bộ
Salt-water up-coning during extraction of fresh water from a tropical island
Journal of Engineering Mathematics - Tập 48 - Trang 69-91 - 2004
Rainwater can collect in a lens-shaped region within the rock of a tropical island, and may be separated from the underlying salt water by a sharp interface. This paper presents a nonlinear theory for determining the shape of this interface. The island is assumed to be saturated with rain, and provision is made for the outflow of rain-water through the sides of the island. The effect of a bore wel...... hiện toàn bộ
P-stable singlestep methods for periodic initial-value problems involving second-order differential equations
Journal of Engineering Mathematics - Tập 13 - Trang 317-326 - 1979
A class of P-stable singlestep methods is discussed for solving initial-value problems involving second-order differential equations. The methods depend upon a parameter p>0 and reduce to the classical methods for p=0. A few choices of p have been discussed for which the methods are P-stable. Further, when p is chosen for linear problems as the square of the frequency of the periodic solution, the...... hiện toàn bộ
The stabilized-trigonometric scalar auxiliary variable approach for gradient flows and its efficient schemes
Journal of Engineering Mathematics - Tập 129 - Trang 1-26 - 2021
We develop a trigonometric scalar auxiliary variable (TSAV) approach for constructing linear, totally decoupled, and energy-stable numerical methods for gradient flows. An auxiliary variable r based on the trigonometric form of the nonlinear potential functional removes the bounded-from-below restriction. By adding a positive constant greater than 1, the positivity preserving property of r can be ...... hiện toàn bộ
Large-time behaviour of solutions of the inviscid non-planar Burgers equation
Journal of Engineering Mathematics - Tập 69 - Trang 345-357 - 2010
Large-time behaviour of the entropy solution of an initial-value problem (IVP) for the inviscid non-planar Burgers equation is studied. The initial profile is assumed to be non-negative, bounded and compactly supported. The large-time behaviour of the support function of this entropy solution is also presented. This is achieved via the construction of the entropy solution of the IVP for the invisc...... hiện toàn bộ
Homogeneous ignition for a three-step chain-branching reaction model
Journal of Engineering Mathematics - - 2006
Inversion of the source and vorticity equations for supercavitating hydrofoils
Journal of Engineering Mathematics - Tập 26 - Trang 349-361 - 1992
The problem of a supercavitating hydrofoil of general shape with leading edge cavity detachment is addressed in linear theory in terms of unknown source and vorticity distributions on the foil and cavity. The related singular integral equations are inverted analytically and the cavitation number, the source and vorticity distributions are expressed in terms of integrals of quantities which depend ...... hiện toàn bộ
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