0

We present an efficient mixed finite element method to solve the fourth-order thin film flow equations using moving mesh refinement. The moving mesh strategy is based on harmonic mappings developed by Li et al. [J. Comput. Phys., 170 (2001), pp. 562-588, and 177 (2002), pp. 365-393]. To achieve a high quality mesh, we adopt an adaptive monitor function and smooth it based on a diffusive mechani...

We present a coupled moving mesh and level set method for computing incompressible two-phase flow with surface tension. This work extends a recent work of Di et al. [SIAM J. Sci. Comput., 26 (2005), pp. 1036-1056] where a moving mesh strategy was proposed to solve the incompressible Navier-Stokes equations. With the involvement of the level set function and the curvature of the interface, some ...

The numerical solution of the harmonic heat map flow problems with blowup in finite or infinite time is considered using an adaptive moving mesh method. A properly chosen monitor function is derived so that the moving mesh method can be used to simulate blowup and produce accurate blowup profiles which agree with formal asymptotic analysis. Moreover, the moving mesh method has finite time blowu...

We consider problems involving high-speed moving rigid objects in a fluid flow. Instead of a more traditional deformable mesh approach, we describe a novel fixed mesh approach which use a level set function to implicitly track the fluid-solid interface, therefore no mesh motion or modification is required. The interface boundary conditions are also captured implicitly by combining a Ghost Fluid...

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 ...

Moving mesh partial diierential equations (MMPDEs) are used in the MMPDE moving mesh method to generate adaptive moving meshes for the numerical solution of time dependent problems. How MMPDEs are formulated and solved is crucial to the eeciency and robustness of the method. In this paper, several practical aspects of formulating and solving MMPDEs are studied. They include spatial balance, sca...

A new moving mesh method is introduced for solving time dependent partial diierential equations (PDEs) in divergence form. The method uses a cell-averaging cubic Hermite collocation discretization for the physical PDEs and a three point nite diierence discretization for the PDE which determines the moving mesh. Numerical results are presented for a selection of diicult benchmark problems, inclu...

Moving mesh partial differential equations (MMPDEs) are used in the MMPDE moving mesh method to generate adaptive moving meshes for the numerical solution of time dependent problems. How MMPDEs are formulated and solved is crucial to the efficiency and robustness of the method. In this paper, several practical aspects of formulating and solving MMPDEs are studied. They include spatial balance, ...