The numerical solution of one-dimensional phase change problems using an adaptive moving mesh method. An adaptive moving mesh method is developed for the numerical solution of an enthalpy formulation of heat conduction problems with a phase change. The algorithm is based on a very simple mesh modiication strategy that allows the smooth evolution of mesh nodes to track interfaces. At each time s...

In computation of fluid-structure interactions, we use mesh update methods consisting of mesh-moving and remeshing-as-needed. When the geometries are complex and the structural displacements are large, it becomes even more important that the mesh moving techniques are designed with the objective to reduce the frequency of remeshing. To that end, we present here mesh moving techniques where the ...

In this paper, we investigate the numerical simulation of rigid particulate flows using a new moving mesh method combined with the multigrid fictitious boundary method (FBM) [9, 10]. With this approach, the mesh is dynamically relocated through a special partial differential equation to capture the region near the surface of the moving particles with high accuracy. The complete system is realiz...

A moving window technique for the finite element time domain (FETD) method is developed to simulate the propagation of electromagnetic waves induced by the transit of a charged particle beam inside large and long structures. The window moving along with the beam in the computational domain adopts high-order finite-element basis functions through p refinement and/or a high-resolution mesh throug...

In this paper, we develop an efficient moving mesh weighted essentially nonoscillatory (WENO) method for one-dimensional hyperbolic conservation laws. The method is based on the quasi-Lagrange approach of the moving mesh strategy in which the mesh is considered to move continuously in time. Several issues arising from the implementation of the scheme, including mesh smoothness, mesh movement re...

In this article we describe the basic dynamics of a moving meshes as part of an r-adaptive adaptive method. We firstly examine the possible geometry of a moving mesh and strategies for disretising a partial differential equation on such a mesh. We then look in more detail (with many examples) at strategies for implementing both position based and velocity based moving meshes. We finally look at...

An adaptive moving mesh method is presented for numerical simulation of two dimensional groundwater flow and transport problems. A selection of problems are considered, including advection dominated chemical transport and reaction, solute transport from contamination sources, transport of nonaqueous phase liquids (NAPLs) in an aquifer, and coupling of groundwater flow with NAPL transport. Numer...

It is well known that if the solution of flow equations has regions of high spatial activity, a standard fixed mesh technique is ineffective, since it should contain a very large number of mesh points. In case of hyperbolic problems of gas dynamics there are domains containing shock waves and contact discontinuities. A moving mesh adaptation algorithm is applied to reduce computational costs in...

Finite volume moving mesh methods are developed for unsteady one-dimensional partial diierential equations. The methods can be viewed as conservative discretisations of the Lagrangian form of the original diier-ential equations. Grid points are moved using the idea of mesh equidistri-bution. The coupled unsteady diierential equations and grid movement equations are solved using a robust and eec...

Adaptive mesh methods are valuable tools in improving the accuracy and efficiency of the numerical solution of evolutionary systems of partial differential equations. If the mesh moves to track fronts and large gradients in the solution, then larger time steps can be taken than if it were to remain stationary. We derive explicit differential equations for moving the mesh so that the time variat...