This paper presents an adaptive mesh moving technique for three-dimensional (3D) fluid flow problems that involve moving fluid boundaries and fluid–solid interfaces. Such mesh moving techniques are an essential ingredient of fluid–structure interaction methods that typically employ arbitrary Lagrangian– Eulerian (ALE) frameworks. In the ALE frame, the velocity field representing motion of the u...

Maintaining a moving mesh of a deforming surface is widely studied in various disciplines. However, difficulties arise with requirements of topology changes, homeomorphism between mesh and surface, and guarantees of triangle quality. We propose a mesh deformation algorithm to satisfy the above requirements. We employ the skin surface by Edelsbrunner that approximates objects in fields like comp...

objectives: indicators of oral health-related quality of life (ohrqol) in children are widely adopted to evaluate the effects of oral problems. recently, the scale of oral health outcomes for 5-year-old children (soho-5) was developed based on the children’s self-reports. this study aimed to evaluate the validity and reliability of the persian version of the questionnaire in a sample of iranian...

Non-uniform grids and mesh adaptation have become an important part of numerical approximations of differential equations over the past decades. It has been experimentally noted that mesh adaptation leads not only to locally improved solution but also to numerical stability of the underlying method. In this paper we consider nonlinear conservation laws and provide a method to perform the analys...

Three-dimensional real-life simulations are generally unsteady and involve moving geometries. Industries are currently still very far from performing such simulations on a daily basis, mainly due to the robustness of the moving mesh algorithm and their extensive computational cost. The proposed approach is a way to improve these two issues. This paper brings two new ideas. First, it demonstrate...

Adaptive Cartesian mesh methods have demonstrated unique abilities for automated mesh generation and dynamic mesh adaptation to flow solution and moving boundaries. However Navier-Stokes (NS) solvers with Cartesian mesh often produce large fluctuations of surface quantities (pressure, skin friction, and heat flux) at solid boundaries. We show that the Immersed Boundary Method (IBM) with adaptiv...

Universal meshes have recently appeared in the literature as a computationally efficient and robust paradigm for the generation of conforming simplicial meshes for domains with evolving boundaries. The main idea behind a universal mesh is to immerse the moving boundary in a background mesh (the universal mesh), and to produce a mesh that conforms to the moving boundary at any given time by adju...

A framework for adaptive meshes based on the Hamilton–Schoen–Yau theory was proposed by Dvinsky. In a recent work (2001, J. Comput. Phys. 170, 562– 588), we extended Dvinsky’s method to provide an efficient moving mesh algorithm which compared favorably with the previously proposed schemes in terms of simplicity and reliability. In this work, we will further extend the moving mesh methods based...

An r-refinement (moving mesh) method is considered for solving time dependent partial differential equations (PDEs). The resulting coupled system, consisting of the physical PDE and a moving mesh PDE, is solved by a Schwarz waveform relaxation method. In particular, the computational space-time domain is decomposed into overlapping subdomains and the solution obtained by iteratively solving the...

This paper presents a multi‐dimensional high‐order discontinuous Galerkin (DG) method in an arbitrary Lagrangian‐Eulerian (ALE) formulation to simulate flows over variable domains with moving and deforming meshes. It is an extension of the gas‐kinetic DG method proposed by the authors for static domains (X. Ren et al., A multi‐dimensional high‐order discontinuous Galerkin method based on gas ki...