In this paper, we apply an AMG prconditioner to solve the unsteady NavierStokes equations with moving mesh finite element method. 4P1 − P1 element pair is selected, which is based on the data structure of hierarchy geometry tree. We choose two-layer nested meshes including velocity mesh and pressure mesh. AMG preconditioners are designed for PDE solver and divergence-interpolation in moving mes...

In this paper we consider several moving mesh partial diierential equations which are related to the equidistribution principle. Several of these are new, and some correspond to discrete moving mesh equations which have been used by others. An analysis of their stability is done. It is seen that a key term for most of these moving mesh PDEs is a source-like term which measures the level of equi...

In this paper, the role of molecular diffusion in mobilization of waterflood residual oil is examined. A moving mesh method is applied to solve the moving interface problem of residual oil blobs swelling by Co2 diffusion through a blocking water phase. The results of this modeling are compared with experimental results of a 2D glass micromodel experiment. Although, the solution method is applie...

A moving mesh strategy for solving high dimensional PDEs is presented along the lines of the moving mesh PDE approach recently developed in one dimension by the authors and their co-workers. With this strategy, a moving mesh PDE is formulated from the Euler-Lagrange equation for a suitable functional using a heat equation, and the underlying physical PDE is replaced with an extended system cons...

Several versions of a moving mesh method are developed based on a mesh spatial smoothing technique and on the moving mesh PDEs derived in a previous paper. These versions are quite simple and easy to program. They are applied to three benchmark one-dimensional problems which show diierent solution behaviour. The numerical results clearly demonstrate that the present methods are capable of accur...

We develop in this paper a moving mesh spectral method for the phase-field model of twophase flows with non-periodic boundary conditions. The method is based on a variational moving mesh PDE for the phase function, coupled with efficient semi-implicit treatments for advancing the mesh function, the phase function and the velocity and pressure in a decoupled manner. Ample numerical results are p...