Related papers: A fully nonlinear iterative solution method for se…
We study the Cauchy problem associated with the equations governing a fluid loaded plate formulated on either the line or the half-line. We show that in both cases the problem can be solved by employing the unified approach to boundary…
A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…
A number of important results of studying large deformations of hyper-elastic shells are obtained using discrete methods of mathematical physics. In the present paper, using the variational method for solving nonlinear boundary problems of…
We introduce an innovative numerical technique based on convex optimization to solve a range of infinite dimensional variational problems arising from the application of the background method to fluid flows. In contrast to most existing…
We develop a framework for analyzing the momentum balance of laminar particle-laden flows based on immersed boundary methods, which solve the Navier-Stokes equations and resolve the particle surfaces. This framework differs from previous…
In a transformation method the numerical solution of a given boundary value problem is obtained by solving one or more related initial value problems. This paper is concerned with the application of the iterative transformation method to…
We present a methodology for simulating three-dimensional flow of incompressible viscoplastic fluids modelled by generalised Newtonian rheological equations. It is implemented in a highly efficient framework for massively parallelisable…
Applied problems of oil and gas recovery are studied numerically using the mathematical models of multiphase fluid flows in porous media. The basic model includes the continuity equations and the Darcy laws for each phase, as well as the…
This brief note addresses the free boundary problem arising from the steady two-dimensional seepage flow through a rectangular dam. The flow problem consists in finding the free boundary location, and the velocity and pressure fields. The…
We study the inverse boundary value problem for the wave equation using the single-layer potential operator as the data. We assume that the data have frequency content in a bounded interval. We prove how to choose classes of nonsmooth…
An important problem that arises in many engineering applications is the boundary value problem for ordinary differential equations. There have been many computational methods proposed for dealing with this problem. The convergence of the…
A fully nonlinear potential Numerical Wave Tank (NWT) is developed in two dimensions, using a combination of the Harmonic Polynomial Cell (HPC) method for solving the Laplace problem on the wave potential and the Immersed Boundary Method…
Many physical systems of interest involve the close interaction of a flow in a domain with complex, time-varying boundaries. Treatment of boundaries of this nature is cumbersome due to the difficulty in explicitly tracking boundaries that…
Interfacial Stokes flow can be efficiently computed using the Boundary Integral Equation method. In 3D, the fluid velocity at a target point is given by a 2D surface integral over all interfaces, thus reducing the dimension of the problem.…
We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a periodic, multiply-connected fluid domain that includes…
We present a spectrally-accurate scheme to turn a boundary integral formulation for an elliptic PDE on a single unit cell geometry into one for the fully periodic problem. Applications include computing the effective permeability of…
In this article we present a goal-oriented adaptive finite element method for a class of subsurface flow problems in porous media, which exhibit seepage faces. We focus on a representative case of the steady state flows governed by a…
We present a set of effective outflow/open boundary conditions and an associated algorithm for simulating the dynamics of multiphase flows consisting of $N$ ($N\geqslant 2$) immiscible incompressible fluids in domains involving outflows or…
Many immersed boundary methods solve for surface stresses that impose the velocity boundary conditions on an immersed body. These surface stresses may contain spurious oscillations that make them ill-suited for representing the physical…
The Immersed Boundary Method (IBM) is one of the popular one-fluid mixed Eulerian-Lagrangian methods to simulate motion of droplets. While the treatment of a moving complex boundary is an extremely time consuming and formidable task in a…