A variationally consistent mesh adaptation method for triangular elements in explicit Lagrangian dynamics

2009 ◽  
Vol 82 (9) ◽  
pp. 1073-1113 ◽  
Author(s):  
Sudeep K. Lahiri ◽  
Javier Bonet ◽  
Jaume Peraire
Keyword(s):  
Mesh Adaptation ◽  
Lagrangian Dynamics ◽  
Triangular Elements ◽  
Adaptation Method

A goal-oriented anisotropic hp-mesh adaptation method for linear convection–diffusion–reaction problems

2019 ◽  
Vol 78 (9) ◽  
pp. 2973-2993 ◽  
Author(s):  
Ondřej Bartoš ◽  
Vít Dolejší ◽  
Georg May ◽  
Ajay Rangarajan ◽  
Filip Roskovec
Keyword(s):  
Mesh Adaptation ◽  
Diffusion Reaction ◽  
Convection Diffusion ◽  
Adaptation Method

scholarly journals Mesh Adaptation Method for Optimal Control With Non-Smooth Control Using Second-Generation Wavelet

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 135076-135086
Author(s):  
Zhiwei Feng ◽  
Qingbin Zhang ◽  
Jianquan Ge ◽  
Wuyu Peng ◽  
Tao Yang ◽  
...  
Keyword(s):  
Optimal Control ◽  
Second Generation ◽  
Mesh Adaptation ◽  
Smooth Control ◽  
Second Generation Wavelet ◽  
Adaptation Method

scholarly journals Entropy dissipation of moving mesh adaptation

2014 ◽  
Vol 11 (03) ◽  
pp. 633-653 ◽  
Author(s):  
Mária Lukáčová-Medvid'ová ◽  
Nikolaos Sfakianakis
Keyword(s):  
Numerical Stability ◽  
Sufficient Conditions ◽  
Mesh Adaptation ◽  
Moving Mesh ◽  
Nonlinear Conservation Laws ◽  
The Past ◽  
Entropy Dissipation ◽  
Uniform Grids ◽  
Mesh Reconstruction ◽  
Adaptation Method

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 analysis of the moving mesh adaptation method, including both the mesh reconstruction and evolution of the solution. We moreover employ this method to extract sufficient conditions — on the adaptation of the mesh — that stabilize a numerical scheme in the sense of the entropy dissipation.

Least-squares finite element solution of Euler equations with H-type mesh refinement and coarsening on triangular elements

2014 ◽  
Vol 24 (7) ◽  
pp. 1487-1503 ◽  
Author(s):  
Hayri Yigit Akargun ◽  
Cuneyt Sert
Keyword(s):  
Finite Element ◽  
Least Squares ◽  
Euler Equations ◽  
Compressible Flows ◽  
Mesh Refinement ◽  
Mesh Adaptation ◽  
Content Type ◽  
Triangular Elements ◽  
Inviscid Compressible Flows ◽  
Mesh Coarsening

Purpose – The purpose of this paper is to demonstrate successful use of least-squares finite element method (LSFEM) with h-type mesh refinement and coarsening for the solution of two-dimensional, inviscid, compressible flows. Design/methodology/approach – Unsteady Euler equations are discretized on meshes of linear and quadratic triangular and quadrilateral elements using LSFEM. Backward Euler scheme is used for time discretization. For the refinement of linear triangular elements, a modified version of the simple bisection algorithm is used. Mesh coarsening is performed with the edge collapsing technique. Pressure gradient-based error estimation is used for refinement and coarsening decision. The developed solver is tested with flow over a circular bump, flow over a ramp and flow through a scramjet inlet problems. Findings – Pressure difference based error estimator, modified simple bisection method for mesh refinement and edge collapsing method for mesh coarsening are shown to work properly with the LSFEM formulation. With the proper use of mesh adaptation, time and effort necessary to prepare a good initial mesh reduces and mesh independency control of the final solution is automatically taken care of. Originality/value – LSFEM is used for the first time for the solution of inviscid compressible flows with h-type mesh refinement and coarsening on triangular elements. It is shown that, when coupled with mesh adaptation, inherent viscous dissipation of LSFEM technique is no longer an issue for accurate shock capturing without unphysical oscillations.

Time Dependent Calculations for Incompressible Flows on Adaptive Unstructured Meshes

2003 ◽  
Author(s):  
Xiang Zhao ◽  
Jun Wang ◽  
Sijun Zhang
Keyword(s):  
Large Scale ◽  
Incompressible Flows ◽  
Computational Cost ◽  
Mesh Adaptation ◽  
Time Dependent ◽  
Reynolds Number Flow ◽  
Viscous Incompressible Flows ◽  
Number Flow ◽  
Time Dependent Problems ◽  
Adaptation Method

An adaptive unstructured method has been developed for simulating two-dimensional unsteady, viscous, incompressible flows. The pressure-based approach coupled with a mesh adaptation method is employed to better capture the details of flow physics for time dependent problems by optimizing computational cost with respect to accuracy. The mesh adaptation for locally refining and coarsening hybrid unstructured grid is based on hanging node approach. The time dependent calculations is further enhanced by virtue of parallel computing which is the most powerful for large scale intensive computation at the present time. The proposed method is validated by comparison with experimental results of low Reynolds number flow over a shedding circular cylinder.

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