An Adaptive Moving Mesh Method for Forced Curve Shortening Flow

An Adaptive Mesh Projection Method for Viscous Incompressible Flow

Many uid ow problems of practical interest|particularly at high Reynolds num-ber|are characterized by small regions of complex and rapidly-varying uid motion surrounded by larger regions of relatively smooth ow. EEcient solution of such problems requires an adaptive mesh reenement capability to concentrate computational eeort where it is most needed. We present in this paper a fractional-step v...

Moving mesh finite element method for unsteady Navier-Stokes flow

In this paper, we use moving mesh fintie element method based upon 4P1 − P1 element to solve the time-dependent Navier-Stokes equations in 2D. Twolayer nested meshes are used including velocity mesh and pressure mesh, and velocity mesh can be obtained by globally refining pressure mesh. We use hierarchy geometry tree to store the nested meshes. This data structure make convienence for adaptive ...

An Introduction to Curve-Shortening and the Ricci Flow

Curve Shortening Flow in a Riemannian Manifold

In this paper, we systemally study the long time behavior of the curve shortening flow in a closed or non-compact complete locally Riemannian symmetric manifold. Assume that we have a global flow. Then we can exhibit a a limit for the global behavior of the flow. In particular, we show the following results. 1). Let M be a compact locally symmetric space. If the curve shortening flow exists for...

Spectral implementation of an adaptive moving mesh method for phase-field equations

Phase-field simulations have been extensively applied to modeling microstructure evolution during various materials processes. However, large-scale simulations of three-dimensional (3D) microstructures are still computationally expensive. Among recent efforts to develop advanced numerical algorithms, the semi-implicit Fourier spectral method is found to be particularly efficient for systems inv...