We propose a moving mesh adaptive approach for solving time-dependent partial differential equations. The motion of spatial grid points is governed by a moving mesh PDE (MMPDE) in which amesh relaxation time τ is employed as a regularization parameter. Previously reported results on MMPDEs have invariably employed a constant value of the parameter τ . We extend this standard approach by incorpo...

We propose a new moving mesh method suitable for solving timedependent partial differential equations (PDEs) in R which have fine scale solution structures that develop or dissipate. A key feature of the method is its ability to add or remove mesh nodes in a smooth manner and that it is consistent with r-refinement schemes. Central to our approach is an implicit representation of a Lagrangian m...

In this thesis, we introduce and assess a new adaptive method for solving non-linear parabolic partial differential equations with fixed or moving boundaries, using a moving mesh with continuous finite elements. The evolution of the mesh within the interior of the spatial domain is based upon conserving the distribution of a chosen monitor function across the domain throughout time, where the i...

Dynamical processes occurring in geophysical flows are characterised by the nonlinear interaction of various scales of motion. The accurate numerical representation of such flows is limited by the available number of mesh points covering the domain of interest. Numerical simulations applying uniformly distributed grid cells waste mesh points in regions of large motion scales whereas coexisting ...

Abstract. This paper discusses numerical simulation techniques using a moving mesh approach together with the multigrid fictitious boundary method (FBM) for liquid-solid flow configurations. The flow is computed by an ALE formulation with a multigrid finite element solver (FEATFLOW), and the solid particles are allowed to move freely through the computational mesh which can be adaptively aligne...

A hybrid method to simulate unsteady multiphase flows is described. One phase is represented by moving particles and the other phase is defined on stationary mesh. The flow field is discretized by a conservative finite volume approximation on the stationary mesh, and the interface is automatically captured by the distribution of particles moving through the stationary mesh. The effects of surfa...