Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement...Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement of tetrahedral meshes using bisection. This algorithm is used in PHG, Parallel Hierarchical Grid Chttp：//lsec. cc. ac. cn/phg/）, a toolbox under active development for parallel adaptive finite element solutions of partial differential equations. The algorithm proposed is characterized by allowing simukaneous refinement of submeshes to arbitrary levels before synchronization between submeshes and without the need of a central coordinator process for managing new vertices. Using the concept of canonical refinement, a simple proof of the independence of the resulting mesh on the mesh partitioning is given, which is useful in better understanding the behaviour of the biseetioning refinement procedure.展开更多
Primary breakup in a liquid-liquid pintle injector element at different radial jet velocities is investigated to elucidate the impingement morphology,the formation of primary breakup spray half cone angle,the pressure...Primary breakup in a liquid-liquid pintle injector element at different radial jet velocities is investigated to elucidate the impingement morphology,the formation of primary breakup spray half cone angle,the pressure distribution,the liquid diameter distribution,and the liquid velocity distribution.With a sufficient mesh resolution,the liquid morphology can be captured in a physically sound way.A mushroom tip is triggered by a larger radial jet velocity and breakup happens at the tip edge first.Different kinds of ligament breakup patterns due to aerodynamic force and surface tension are captured on the axial sheet.A high pressure core is spotted at the impinging point region.A larger radial jet velocity can feed more disturbances into the impinging point and the axial sheet,generate stronger vortices to promote the breakup process at a longer distance,and form a larger spray half cone angle.Because of the re-collision phenomenon the axial sheet diameter does not decrease monotonically.The inner rim on the axial sheet shows a larger diameter magnitude and a lower velocity magnitude due to surface tension.This paper is expected to provide a reference for the optimum design of a liquid-liquid pintle injector.展开更多
Based on the fact that 3-D model discretization by artificial could not always be successfully implemented especially for large-scaled problems when high accuracy and efficiency were required, a new adaptive multigrid...Based on the fact that 3-D model discretization by artificial could not always be successfully implemented especially for large-scaled problems when high accuracy and efficiency were required, a new adaptive multigrid finite element method was proposed. In this algorithm, a-posteriori error estimator was employed to generate adaptively refined mesh on a given initial mesh. On these iterative meshes, V-cycle based multigrid method was adopted to fast solve each linear equation with each initial iterative term interpolated from last mesh. With this error estimator, the unknowns were nearly optimally distributed on the final mesh which guaranteed the accuracy. The numerical results show that the multigrid solver is faster and more stable compared with ICCG solver. Meanwhile, the numerical results obtained from the final model discretization approximate the analytical solutions with maximal relative errors less than 1%, which remarkably validates this algorithm.展开更多
基金supported by the 973 Program of China 2005CB321702China NSF 10531080.
文摘Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement of tetrahedral meshes using bisection. This algorithm is used in PHG, Parallel Hierarchical Grid Chttp：//lsec. cc. ac. cn/phg/）, a toolbox under active development for parallel adaptive finite element solutions of partial differential equations. The algorithm proposed is characterized by allowing simukaneous refinement of submeshes to arbitrary levels before synchronization between submeshes and without the need of a central coordinator process for managing new vertices. Using the concept of canonical refinement, a simple proof of the independence of the resulting mesh on the mesh partitioning is given, which is useful in better understanding the behaviour of the biseetioning refinement procedure.
基金supported by the National Natural Science Foundation of China(No.11572346)。
文摘Primary breakup in a liquid-liquid pintle injector element at different radial jet velocities is investigated to elucidate the impingement morphology,the formation of primary breakup spray half cone angle,the pressure distribution,the liquid diameter distribution,and the liquid velocity distribution.With a sufficient mesh resolution,the liquid morphology can be captured in a physically sound way.A mushroom tip is triggered by a larger radial jet velocity and breakup happens at the tip edge first.Different kinds of ligament breakup patterns due to aerodynamic force and surface tension are captured on the axial sheet.A high pressure core is spotted at the impinging point region.A larger radial jet velocity can feed more disturbances into the impinging point and the axial sheet,generate stronger vortices to promote the breakup process at a longer distance,and form a larger spray half cone angle.Because of the re-collision phenomenon the axial sheet diameter does not decrease monotonically.The inner rim on the axial sheet shows a larger diameter magnitude and a lower velocity magnitude due to surface tension.This paper is expected to provide a reference for the optimum design of a liquid-liquid pintle injector.
基金Projects(2006AA06Z105, 2007AA06Z134) supported by the National High-Tech Research and Development Program of ChinaProjects(2007, 2008) supported by China Scholarship Council (CSC)
文摘Based on the fact that 3-D model discretization by artificial could not always be successfully implemented especially for large-scaled problems when high accuracy and efficiency were required, a new adaptive multigrid finite element method was proposed. In this algorithm, a-posteriori error estimator was employed to generate adaptively refined mesh on a given initial mesh. On these iterative meshes, V-cycle based multigrid method was adopted to fast solve each linear equation with each initial iterative term interpolated from last mesh. With this error estimator, the unknowns were nearly optimally distributed on the final mesh which guaranteed the accuracy. The numerical results show that the multigrid solver is faster and more stable compared with ICCG solver. Meanwhile, the numerical results obtained from the final model discretization approximate the analytical solutions with maximal relative errors less than 1%, which remarkably validates this algorithm.
