This book is about adaptive mesh generation and moving mesh methods for the numerical
solution of time-dependent partial differential equations. It presents a general framework and …

Aquatic and aerial animals have developed their superior and complete mechanisms of
swimming and flight. These mechanisms bring excellent locomotion performances to natural …

In this article we survey r-adaptive (or moving grid) methods for solving time-dependent
partial differential equations (PDEs). Although these methods have received much less …

A new immersed boundary (IB) technique for the simulation of flow interacting with solid
boundary is presented. The present formulation employs a mixture of Eulerian and …

The vortex structure of the two-dimensional steady flow in a lid-driven rectangular cavity at
different depth-to-width ratios and Reynolds numbers is investigated using a lattice …

In this paper, we present a new optimal interpolation error estimate in $ L^ p $ norm ($1\leq
p\leq\infty $) for finite element simplicial meshes in any spatial dimension. A sufficient …

We construct high-order semidiscrete-in-time, and fully discrete (with Fourier--Galerkin in
space) schemes for the incompressible Navier--Stokes equations with periodic boundary …

This article presents a time-accurate numerical method using high-order accurate compact
finite difference scheme for the incompressible Navier–Stokes equations. The method relies …

As more powerful computing hardware enables higher resolution simulations, a fast and
flexible mesh optimization method is becoming increasingly indispensable for …

We generalize the implicit-explicit (IMEX) second-order backward difference (BDF2) scalar
auxiliary variable (SAV) scheme for Navier–Stokes equation with periodic boundary …