A mesh movement scheme is implemented in a multiply nested primitive equation ocean model. Mesh movement can be specified or determined in the course of the model run so as to follow an evolving oceanic feature, such as a wave front or propagating eddy, or atmospheric forcing, such as a tropical cyclone. Mass, heat, and momentum are conserved during the movement. The mesh movement scheme is tes...

Abstract Good mesh moving methods are always part of what makes moving-mesh good in computation flow problems with boundaries and interfaces, including fluid–structure interaction. Moving-mesh methods, such as the space–time (ST) arbitrary Lagrangian–Eulerian (ALE) enable mesh-resolution control near solid surfaces thus high-resolution representation boundary layers. Mesh based on linear elasti...

We introduce a framework for the design of finite element methods for two-dimensional moving boundary problems with prescribed boundary evolution that have arbitrarily high order of accuracy, both in space and in time. At the core of our approach is the use of a universal mesh: a stationary background mesh containing the domain of interest for all times that adapts to the geometry of the immers...

In this paper we present an application of our Bézier-based approach to moving meshes [1] to Navier-Stokes simulations with several immersed elastic membranes. By a moving mesh we mean one that moves with the material and is adapted to maintain good aspect ratio triangles of minimal size. The adaptations we employ include point insertion and removal, as well as edge smoothing. This work is bein...

Subject: The aim of mesh adaptation is to generate automatically the best mesh to perform a specific numerical simulation [1]. It results in a powerful methodology that reduces significantly the size of the mesh required to reach the desired accuracy. Thus, it impacts favorably the simulation CPU time and memory requirement. Moreover, as the generated adapted mesh is in agreement with the physi...

A moving-mesh finite-difference solution of a Lotka-Volterra competition-diffusion model theoretical ecology is described in which the competition sufficiently strong to spatially segregate two populations, leading two-phase problem with coupling condition at moving interface. mesh approach preserves identities species space and time, so that parameters always refer correct population. The impl...

A mesh-free method based on moving least squares approximation (MLS)  and weak form of governing equations including two dimensional equations of motion and Maxwell’s equation is used to analyze the free vibration of functionally graded piezoelectric material (FGPM) beams. Material properties in beam are determined using a power law distribution. Essential boundary conditions are imposed by the...

Moving mesh methods provide an efficient way of solving partial differential equations for which large, localised variations in the solution necessitate locally dense spatial meshes. In one-dimension, meshes are typically specified using the arclength mesh density function. This choice is well-justified for piecewise polynomial interpolants, but it is only justified for spectral methods when mo...

A moving mesh finite element algorithm is proposed for the adaptive solution of nonlinear diffusion equations with moving boundaries in one and two dimensions. The moving mesh equations are based upon conserving a local proportion, within each patch of finite elements, of the total “mass” that is present in the projected initial data. The accuracy of the algorithm is carefully assessed through ...

numerical solutions obtained by the meshless local petrov–galerkin (mlpg) method are presented for two-dimensional steady-state heat conduction problems. the mlpg method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. the penalty method is adopted to efficiently enforce the essential boundary co...