Open AccessBook
The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains
Zhilin Li,Kazufumi Ito +1 more
TLDR
The IIM for Stokes and Navier-Stokes equations and some applications of the IIM Bibliography Index are reviewed.Abstract:
Preface 1. Introduction 2. The IIM for one-dimensional elliptic interface problems 3. The IIM for two-dimensional elliptic interface problems 4. The IIM for three-dimensional elliptic interface problems 5. Removing source singularities for certain interface problems 6. Augmented strategies 7. The fourth-order IIM 8. The immersed finite element methods 9. The IIM for parabolic interface problems 10. The IIM for Stokes and Navier-Stokes equations 11. Some applications of the IIM Bibliography Index.read more
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Numerical Methods for Fluid-Structure Interaction — A Review
TL;DR: This article reviews representative numeri- cal methods based on conforming and non-conforming meshes that are currently avail- able for computing fluid-structure interaction problems, with an emphasis on some of the recent developments in the field.
Journal ArticleDOI
An Isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces
Dominik Schillinger,Dominik Schillinger,Luca Dedè,Michael A. Scott,John A. Evans,Michael J. Borden,Ernst Rank,Thomas J. R. Hughes +7 more
TL;DR: It is shown that hierarchical refinement considerably increases the flexibility of this approach by adaptively resolving local features of NURBS, which combines full analysis suitability of the basis with straightforward implementation in tree data structures and simple generalization to higher dimensions.
Journal ArticleDOI
An improved immersed boundary method with direct forcing for the simulation of particle laden flows
Tobias Kempe,Jochen Fröhlich +1 more
TL;DR: It is shown that the basic scheme is inconsistent when moving surfaces are allowed to approach closer than twice the step size, and a remedy is developed based on excluding from the force computation all surface markers whose stencil overlaps with the stencil of a marker located on the surface of a collision partner.
Journal ArticleDOI
The Finite Cell Method: A Review in the Context of Higher-Order Structural Analysis of CAD and Image-Based Geometric Models
Dominik Schillinger,Martin Ruess +1 more
TL;DR: This review article provides a concise introduction to the basics of the finite cell method, and summarizes recent developments of the technology, with particular emphasis on the research topics in which the author has been actively involved.
Journal ArticleDOI
Solving pdes in complex geometries: a diffuse domain approach.
TL;DR: A general approach for solving partial differential equations in complex, stationary, or moving geometries with Dirichlet, Neumann, and Robin boundary conditions with matched asymptotic expansions is presented.
Related Papers (5)
the immersed interface method for elliptic equations with discontinuous coefficients and singular sources
Randall J. LeVeque,Zhilin Li +1 more