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New Immersed Boundary Method on the adaptive cartesian grid Applied to the Local Discontinuous Galerkin Method

Chinese Journal of Mechanical Engineering 2018年第2期31卷 176-185页

作者： Xu-Jiu Zhang Yong-Sheng Zhu Ke Yan You-Yun Zhang Key Laboratory of Education Ministry for Modern Design&Rotor-Bearing System Xi'an Jiaotong University

Currently, many studies on the local discontinuous Galerkin method focus on the cartesian grid with low computational e ciency and poor adaptability to complex shapes. A new immersed boundary method is presented, and this method employs the adaptive cartesian grid to improve the adaptability to complex shapes and the immersed boundary to increase computational e ciency. The new immersed boundary method employs different boundary cells(the physical cell and ghost cell) to impose the boundary condition and the reconstruction algorithm of the ghost cell is the key for this method. The classical model elliptic equation is used to test the method. This method is tested and analyzed from the viewpoints of boundary cell type, error distribution and accuracy. The numerical result shows that the presented method has low error and a good rate of the convergence and works well in complex geometries. The method has good prospect for practical application research of the numerical calculation research.

关键词： Immersed boundary method adaptive cartesian grid Local discontinuous Galerkin method Reconstruction Heat transfer equation

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Positivity-Preserving Runge-Kutta Discontinuous Galerkin Method on adaptive cartesian grid for Strong Moving Shock

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Numerical Mathematics(Theory,Methods and Applications) 2016年第1期9卷 87-110页

作者： Jianming Liu Jianxian Qiu Mikhail Goman Xinkai Li Meilin Liu School of Mathematics and Statistics Jiangsu Normal UniversityXuzhou 221116China Faculty of Technology De Montfort UniversityLeicester LE19BHEngland School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computation Xiamen UniversityXiamen 361005China Shanghai Institute of Satellite Engineering Shanghai 200240China

In order to suppress the failure of preserving positivity of density or pres-sure,a positivity-preserving limiter technique coupled with h-adaptive Runge-Kutta discontinuous Galerkin(RKDG)method is developed in this *** a method is implemented to simulate flows with the large Mach number,strong shock/obstacle interactions and shock *** cartesian grid with ghost cell immersed boundary method for arbitrarily complex geometries is also *** ap-proach directly uses the cell solution polynomial of DG finite element space as the interpolation *** method is validated by the well documented test ex-amples involving unsteady compressible flows through complex bodies over a large Mach *** numerical results demonstrate the robustness and the versatility of the proposed approach.

关键词： Discontinuous Galerkin method adaptive cartesian grid positivity-preserving im-mersed boundary method complex geometry

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Marker-Based,3-D adaptive cartesian grid Method for Multiphase Flow Around Irregular Geometries

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Communications in Computational Physics 2009年第1期5卷 1-41页

作者： Eray Uzgoren Jaeheon Sim Wei Shyy Department of Mechanical Engineering Virginia Polytechnic Institute and State UniversityBlacksburgVA24060USA Department of Aerospace Engineering University of MichiganAnn ArborMI48109USA

Computational simulations of multiphase flow are challenging because many practical applications require adequate resolution of not only interfacial physics associated with moving boundaries with possible topological changes,but also around three-dimensional,irregular solid *** this paper,we highlight recent efforts made in simulating multiphase fluid dynamics around complex geometries,based on an Eulerian-Lagrangian *** approach uses two independent but related grid layouts to track the interfacial and solid boundary conditions,and is capable of capturing interfacial as well as multiphase *** particular,the stationary cartesian grid with time dependent,local adaptive refinement is utilized to handle the computation of the transport equations,while the interface shape and movement are treated by marker-based triangulated surface meshes which freely move and interact with the cartesian *** markers are also used to identify the location of solid boundaries and enforce the no-slip condition *** related to the contact line treatment,topological changes of multiphase fronts during merger or breakup of objects,and necessary data structures and solution techniques are also *** test cases including spacecraft fuel tank flow management and liquid plug flow dynamics are presented.

关键词： Multiphase flows irregular geometry interface tracking adaptive cartesian grid non-conforming boundary methods contact line treatment

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