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We present a rigorous mathematical analysis of the modeling of inviscid water waves. The free-surface is described as a parametrized curve. We introduce a numerically stable algorithm which accounts for its evolution with time. The method…
Half-space boundary Kramers' problem about isothermal sliding of moderate dense gas with accomodation boundary conditions along a flat firm surface is solving. The new method of the solution of boundary problems of the kinetic theory is…
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…
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…
The problems of numerical modeling of viscous incompressible fluid flows are widely considered in computational fluid dynamics. Stationary solutions of boundary value problems for the Navier-Stokes equations exist at large Reynolds numbers,…
It is known that the unified transform method may be used to solve any well-posed initial-boundary value problem for a linear constant-coefficient evolution equation on the finite interval or the half-line. In contrast, classical methods…
We consider the Fokas method expression for the solution of the heat equation on the half line with Dirichlet data and we study in detail its boundary behaviour near the spatiotemporal domain boundaries, i.e., the semi-axes, infinity and…
In this paper we discuss a theoretical model for the interfacial profiles of progressive non-linear waves which result from introducing a triangular obstacle, of finite height, attached to the bottom below the flow of a stratified, ideal,…
We study the dynamics of an inextensible, closed interface subject to bending forces and immersed in a two-dimensional and incompressible Stokes fluid. We formulate the problem as a boundary integral equation in terms of the tangent angle…
Inverse design of complex flows is notoriously challenging because of the high cost of high dimensional optimization. Usually, optimization problems are either restricted to few control parameters, or adjoint-based approaches are used to…
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…
We study the immersed boundary problem in 2-D. It models a 1-D elastic closed string immersed and moving in a fluid that fills the entire plane, where the fluid motion is governed by the 2-D incompressible Navier-Stokes equation with a…
This work is concerned with the existence and uniqueness of boundary value problems defined on semi-infinite intervals. These kinds of problems seldom admit exactly known solutions and, therefore, the theoretical information on their…
In this work, an analytical Volume Of Fluid (VOF) implementation of the Generalized Navier Boundary Condition is presented based on the Brackbill surface tension model. The model is validated by simulations of droplets on a smooth surface…
Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…
This paper introduces a fast and numerically stable algorithm for the solution of fourth-order linear boundary value problems on an interval. This type of equation arises in a variety of settings in physics and signal processing. Our method…
We present a novel framework inspired by the Immersed Boundary Method for predicting the fluid-structure interaction of complex structures immersed in flows with moderate to high Reynolds numbers. The main novelties of the proposed…
Cable subsystems characterized by long, slender, and flexible structural elements are featured in numerous engineering systems. In each of them, interaction between an individual cable and the surrounding fluid is inevitable. Such a…
We discuss a numerical method for convection-diffusion-reaction problems with a free boundary in 1D. The method is based on the numerical modelling of the interface evolution, the transformation to a fixed domain problem and the…
An analytical solution based on a diffuse interface model is presented for an isothermal evaporation problem under sub-saturation pressure. The macroscopic equations are derived from the free-energy method, widely recognized in the lattice…