A Natural BEM on Non-Uniform Grids and its Coupling Method with their Moving Mesh Applications

2013 ◽  
Vol 385-386 ◽  
pp. 1913-1916
Author(s):  
Quan Zheng ◽  
Xiu Hui Guo
Keyword(s):  
Laplace Equation ◽  
Convergence Theorem ◽  
Unbounded Domains ◽  
Numerical Results ◽  
Coupling Method ◽  
Moving Mesh ◽  
Uniform Grid ◽  
Uniform Grids ◽  
Moving Mesh Methods

For solving Laplace equation in 2D unbounded domains, a natural BEM on non-uniform grid is derived and its convergence theorem is proved. The moving mesh methods for the NBEM and the NBE-FE coupling method are also studied. Numerical results confirm the efficiency of the methods.

scholarly journals Numerical Results of Crank-Nicolson and Implicit Schemes to Laplace Equation with Uniform and Non-Uniform Grids

2021 ◽  
Vol 3 (2) ◽  
pp. 122-135
Author(s):  
Mohammad Ghani
Keyword(s):  
Analytical Solution ◽  
Laplace Equation ◽  
Absolute Error ◽  
Numerical Results ◽  
Implicit Method ◽  
Implicit Schemes ◽  
Separable Variable ◽  
Uniform Grids ◽  
The Absolute ◽  
Crank Nicolson

AbstractIn this paper, we investigate the numerical results between Implicit and Crank-Nicolson method for Laplace equation. Based on the numerical results obtained, we get the conclusion that the absolute error of Crank-Nicolson method is smaller than the absolute error of Implicit method for uniform and non-uniform grids which both refer to the analytical solution of Laplace equation obtained by separable variable method.Keywords: Crank-Nicolson; Implicit; Laplace equation; separable variable method; uniform and non-uniform grids. AbstrakDalam makalah ini, kami menyelidiki hasil numerik antara etode Implisit dan Crank-Nicolson untuk persamaan Laplace. Berdasarkan hasil numerik yang diperoleh, kita mendapatkan kesimpulan bahwa kesalahan absolut metode Crank-Nicolson lebih kecil daripada kesalahan absolut metode Implisit untuk grid seragam dan tak-seragam yang keduanya mengacu pada solusi analitik persamaan Laplace yang diperoleh dengan metode separable.Kata kunci: Crank-Nicolson; Implisit; persamaan Laplace; metode variable terpisah; grid seragam dan tak-seragam.

scholarly journals A linear-elasticity-based mesh moving method with no cycle-to-cycle accumulated distortion

2021 ◽  
Author(s):  
Patrícia Tonon ◽  
Rodolfo André Kuche Sanches ◽  
Kenji Takizawa ◽  
Tayfun E. Tezduyar
Keyword(s):  
Linear Elasticity ◽  
Solid Surfaces ◽  
Moving Mesh ◽  
Test Case ◽  
Half Cycle ◽  
Arbitrary Lagrangian Eulerian ◽  
Interface Motion ◽  
Mesh Motion ◽  
Ale Methods ◽  
Moving Mesh Methods

AbstractGood mesh moving methods are always part of what makes moving-mesh methods good in computation of flow problems with moving boundaries and interfaces, including fluid–structure interaction. Moving-mesh methods, such as the space–time (ST) and arbitrary Lagrangian–Eulerian (ALE) methods, enable mesh-resolution control near solid surfaces and thus high-resolution representation of the boundary layers. Mesh moving based on linear elasticity and mesh-Jacobian-based stiffening (MJBS) has been in use with the ST and ALE methods since 1992. In the MJBS, the objective is to stiffen the smaller elements, which are typically placed near solid surfaces, more than the larger ones, and this is accomplished by altering the way we account for the Jacobian of the transformation from the element domain to the physical domain. In computing the mesh motion between time levels $$t_n$$ t n and $$t_{n+1}$$ t n + 1 with the linear-elasticity equations, the most common option is to compute the displacement from the configuration at $$t_n$$ t n . While this option works well for most problems, because the method is path-dependent, it involves cycle-to-cycle accumulated mesh distortion. The back-cycle-based mesh moving (BCBMM) method, introduced recently with two versions, can remedy that. In the BCBMM, there is no cycle-to-cycle accumulated distortion. In this article, for the first time, we present mesh moving test computations with the BCBMM. We also introduce a version we call “half-cycle-based mesh moving” (HCBMM) method, and that is for computations where the boundary or interface motion in the second half of the cycle consists of just reversing the steps in the first half and we want the mesh to behave the same way. We present detailed 2D and 3D test computations with finite element meshes, using as the test case the mesh motion associated with wing pitching. The computations show that all versions of the BCBMM perform well, with no cycle-to-cycle accumulated distortion, and with the HCBMM, as the wing in the second half of the cycle just reverses its motion steps in the first half, the mesh behaves the same way.

Numerical Simulation of the Supersonic Disk-Gap-Band Parachute by Using Implicit Coupling Method

2017 ◽  
Vol 18 (5) ◽  
pp. 343-349
Author(s):  
Xue Yang ◽  
Li Yu ◽  
Cheng Shen ◽  
Xiao Shun Zhao
Keyword(s):  
Wind Tunnel Test ◽  
Numerical Results ◽  
Coupling Method ◽  
Test Results ◽  
Governing Equations ◽  
Time Step ◽  
Projected Area ◽  
Newmark Scheme ◽  
Canopy Area ◽  
Shock Oscillation

AbstractThe implicit coupling method is applied to model the 0.8 m disk-band-gap parachute at Mach 2.0. The fluid and structure governing equations are solved by the Lower-Upper Symmetric Gauss-Seidel (LU-SGS) algorithm and Newmark scheme, respectively. By exchanging the numerical results of the coupling surface with Gauss-Seidel algorithm, high accuracy solutions at every physical time step are obtained. The numerical results of the canopy drag coefficient and projected area fit well with the wind tunnel test results. The simulation reproduces the shock oscillation and breathing phenomenon of the canopy that are usually observed in these systems at Mach 2.0. Furthermore, it is found that the unstable saddle point is the main reason for the shock oscillation of the canopy. And the unsynchronized phases of the canopy area and shock oscillation curves lead to the drag of the canopy oscillate in irregular state.

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.

scholarly journals Efficient Moving Mesh Methods for $Q$-Tensor Models of Nematic Liquid Crystals

2015 ◽  
Vol 37 (2) ◽  
pp. B215-B238 ◽  
Author(s):  
Craig S. MacDonald ◽  
John A. Mackenzie ◽  
Alison Ramage ◽  
Christopher J. P. Newton
Keyword(s):  
Liquid Crystals ◽  
Nematic Liquid Crystals ◽  
Moving Mesh ◽  
Tensor Models ◽  
Moving Mesh Methods
Sign in / Sign up

Export Citation Format

Share Document