This paper deals with the application of a moving mesh method for kinetic/hydrodynamic coupling model in two dimensions. With some criteria, the domain is dynamically decomposed into three parts: kinetic regions where fluids are far from equilibrium, hydrodynamic regions where fluids are near thermodynamical equilibrium and buffer regions which are used as a smooth transition. Boltzmann-BGK equ...

We show that the possibly discontinuous solution of a scalar conservation law in one space dimension may be approximated in i-'(R) to within 0(N~2) by a piecewise linear function with O(N) nodes; the nodes are moved according to the method of characteristics. We also show that a previous method of Dafermos, which uses piecewise constant approximations, is accurate to 0(N~l). These numerical met...

To better accommodate the highly disparate length scales encountered in geophysical flows, we have extended EULAG with a solution-adaptive moving mesh capability [1]. The development builds on [2], where the authors set forth a time-dependent curvilinear coordinate formulation of the governing PDEs to enable dynamic mesh adaptivity in EULAG. Here, the anelastic flux-form dynamical core of EULAG...

We present a splitting moving mesh method for multi-dimensional reaction-diffusion problems with nonlinear forcing terms over rectangular domains. The structure of the adaptive algorithm is an elegant combination of an operator splitting and one-dimensional moving mesh. It is motivated by the nature of splitting method, which splits a multi-dimensional problems into a few one-dimensional proble...

We present a unified analysis of finite element methods for problems with prescribed moving boundaries. In particular, we study an abstract parabolic problem posed on a moving domain with prescribed evolution, discretized in space with a finite element space that is associated with a moving mesh that conforms to the domain at all times. The moving mesh is assumed to evolve smoothly in time, exc...

This work is concerned with developing moving mesh strategies for solving problems defined on a sphere. To construct mappings between the physical domain and the logical domain, it has been demonstrated that harmonic mapping approaches are useful for a general class of solution domains. However, it is known that the curvature of the sphere is positive, which makes the harmonic mapping on a sphe...

The aim of this paper is to study the feasibility of using (irreversible) entropy production as driving force for a moving mesh. Such a method should be able to capture or track physical phenomena such as viscous and thermal boundary layers, shock waves and regions with chemical reactions. A brief outline is given for the FEM-ALE approach, which forms the basis of the moving mesh method. Mesh v...

We perform numerical simulations of several 3D uid-particle interaction problems. We simulate the sedimentation in a liquid lled tube of multiple spheres ranging in number from two to ve. The Navier-Stokes equations for incompressible ow are solved using the stabilized space-time nite element method. This method gives us the exibility to move the mesh to accommodate the motion of the spheres. A...