Related papers: Numerical solution to a free boundary problem for …
Our aim is to analyse special type of boundary conditions, created to simulate flows like in cardiovascular and respiratory systems. Firstly, we will describe model of viscous, incompressible fluid in a domain consisting many inlets and…
In this work, we present two numerical schemes for a free boundary problem called one phase quadrature domain. In the first method by applying the proprieties of given free boundary problem, we derive a method that leads to a fast iterative…
The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…
A method is proposed for accurately describing arbitrary-shaped free boundaries in single-grid finite-difference schemes for elastodynamics, in a time-domain velocity-stress framework. The basic idea is as follows: fictitious values of the…
This paper shows that the Stokes problem is well-posed when velocity and pressure simultaneously vanish on the domain boundary. This result is achieved by extending Ne\v{c}as' inequality to square-integrable functions that vanish in a small…
The purpose of this survey chapter is to present a transformation technique that can be used in analysis and numerical computation of the early exercise boundary for an American style of vanilla options that can be modelled by class of…
In this article, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A function that has a prescribed value on the domain in which a differential…
Stokes flow equations, used to model creeping flow, are a commonly used simplification of the Navier--Stokes equations. The simplification is valid for flows where the inertial forces are negligible compared to the viscous forces. In…
We present a new energy-stable open boundary condition, and an associated numerical algorithm, for simulating incompressible flows with outflow/open boundaries. This open boundary condition ensures the energy stability of the system, even…
This article is devoted to the analysis of inverse source problems for Stokes systems in unbounded domains where the corresponding velocity flow is observed on a surface. Our main objective is to study the unique determination of general…
This paper describes a novel numerical model aiming at solving moving-boundary problems such as free-surface flows or fluid-structure interaction. This model uses a moving-grid technique to solve the Navier--Stokes equations expressed in…
We prove a stochastic representation formula for the viscosity solution of Dirichlet terminal-boundary value problem for a degenerate Hamilton-Jacobi-Bellman integro-partial differential equation in a bounded domain. We show that the unique…
The incompressible Stokes equations can classically be recast in a boundary integral (BI) representation, which provides a general method to solve low-Reynolds number problems analytically and computationally. Alternatively, one can solve…
In this study we revisit the problem of computing steady Navier-Stokes flows in two-dimensional unbounded domains. Precise quantitative characterization of such flows in the high-Reynolds number limit remains an open problem of theoretical…
A mechanical model and finite element method for the simultaneous solution of Stokes and incompressible Navier-Stokes flows on multiple curved surfaces over a bulk domain are proposed. The two-dimensional surfaces are defined implicitly by…
We develop numerical methods to simulate the fluid-mechanical erosion of many bodies in two-dimensional Stokes flow. The broad aim is to simulate the erosion of a porous medium (e.g. groundwater flow) with grain-scale resolution. Our fluid…
This paper presents a computational approach for finding the optimal shapes of peristaltic pumps transporting rigid particles in Stokes flow. In particular, we consider shapes that minimize the rate of energy dissipation while pumping a…
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a domain in $\R^3$ with compact and smooth boundary, subject to the kinematic and Navier boundary conditions. We first reformulate the…
A numerical method for the Dirichlet initial boundary value problem for the elastic equation in the exterior and unbounded region of a smooth closed simply connected 2-dimensional domain, is proposed and investigated. This method is based…
We consider a boundary value problem for the stationary Stokes problem and the corresponding pressure-Poisson equation. We propose a new formulation for the pressure-Poisson problem with an appropriate additional boundary condition. We…