Journal ArticleDOI
the immersed interface method for elliptic equations with discontinuous coefficients and singular sources
Randall J. LeVeque,Zhilin Li +1 more
Reads0
Chats0
TLDR
In this paper, the authors developed finite difference methods for elliptic equations of the form \[ \nabla \cdot (\beta (x)) + \kappa (x)u(x) = f(x)) in a region in one or two dimensions.Abstract:
The authors develop finite difference methods for elliptic equations of the form \[ \nabla \cdot (\beta (x)\nabla u(x)) + \kappa (x)u(x) = f(x)\] in a region $\Omega $ in one or two space dimension...read more
Citations
More filters
Journal ArticleDOI
The immersed boundary method
TL;DR: This paper is concerned with the mathematical structure of the immersed boundary (IB) method, which is intended for the computer simulation of fluid–structure interaction, especially in biological fluid dynamics.
Journal ArticleDOI
Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science (2nd edition)
Journal ArticleDOI
Immersed boundary methods
Rajat Mittal,Gianluca Iaccarino +1 more
TL;DR: The term immersed boundary (IB) method is used to encompass all such methods that simulate viscous flows with immersed (or embedded) boundaries on grids that do not conform to the shape of these boundaries.
Journal ArticleDOI
A distributed Lagrange multiplier/fictitious domain method for particulate flows
TL;DR: In this article, a new Lagrange-multiplier based fictitious-domain method is presented for the direct numerical simulation of viscous incompressible flow with suspended solid particles, which uses a finite-element discretization in space and an operator-splitting technique for discretisation in time.
Journal ArticleDOI
Structural Boundary Design via Level Set and Immersed Interface Methods
TL;DR: An algorithmic approach to the boundary design of elastic structures which allows one to rapidly solve the two-dimensional Lam� equations in arbitrary domains and compute, for example, the stresses, and to develop a systematic way of modifying the design to optimize chosen properties.
References
More filters
Journal ArticleDOI
Numerical solution of the Navier-Stokes equations
TL;DR: In this paper, a finite-difference method for solving the time-dependent Navier-Stokes equations for an incompressible fluid is introduced, which is equally applicable to problems in two and three space dimensions.
Journal ArticleDOI
The partition of unity finite element method: Basic theory and applications
Jens Markus Melenk,Ivo Babuška +1 more
TL;DR: In this article, the basic ideas and the mathematical foundation of the partition of unity finite element method (PUFEM) are presented and a detailed and illustrative analysis is given for a one-dimensional model problem.
Journal ArticleDOI
Numerical analysis of blood flow in the heart
TL;DR: In this article, the authors extended previous work on the solution of the Navier-Stokes equations in the presence of moving immersed boundaries which interact with the fluid and introduced an improved numerical representation of the δ-function.
Book
Free and moving boundary problems
TL;DR: In this paper, a front-tracking method is used to solve moving boundary problems and an analytical solution of seepage problems is proposed. But this method is not suitable for solving free boundary problems.