The hierarchical reconstruction （HR） [Liu, Shu, Tadmor and Zhang, SINUM ＇07] has been successfully applied to prevent oscillations in solutions computed by finite volume, Runge-Kutta discontinuous Galerkin, spectra...The hierarchical reconstruction （HR） [Liu, Shu, Tadmor and Zhang, SINUM ＇07] has been successfully applied to prevent oscillations in solutions computed by finite volume, Runge-Kutta discontinuous Galerkin, spectral volume schemes for solving hyperbolic conservation laws. In this paper, we demonstrate that HR can also be combined with spectral/hp element method for solving hyperbolic conservation laws. An orthogonal spectral basis written in terms of Jacobi polynomials is applied. High computational efficiency is obtained due to such matrix-free algorithm. The formulation is conservative, and essential nomoscillation is enforced by the HR limiter. We show that HR preserves the order of accuracy of the spectral/hp element method for smooth solution problems and generate essentially non-oscillatory solutions profiles for capturing discontinuous solutions without local characteristic decomposition. In addition, we introduce a postprocessing technique to improve HR for limiting high degree numerical solutions.展开更多
HPS(History, Philosophy and Sociology of Science)教育是把科学史、科学哲学、科学社会学的有关内容纳入科学课程中,其根本目的是帮助学生更好的理解科学的本质。本文以“无机化学”课程教学为基础进行研究,从激发学生学习化学的兴...HPS(History, Philosophy and Sociology of Science)教育是把科学史、科学哲学、科学社会学的有关内容纳入科学课程中,其根本目的是帮助学生更好的理解科学的本质。本文以“无机化学”课程教学为基础进行研究,从激发学生学习化学的兴趣、训练学生科学思维的能力、培养学生求真务实的科学精神、提升学生协同合作交流的品质四个方面论述HPS教育模式在“无机化学”课程教学中的重要作用。基于这一教学理念,本课程凝练出多个基于HPS理念的教学案例,学生对本课程进行评价,结果表明该教育理念教学效果良好。展开更多
本文公开了一种适用于HP-RTM(High Pressure Resin Transfer Molding)工艺的高强度阻燃环氧树脂组合物,包含A、B两个组分,其中A组分包含基体树脂、阻燃剂、稀释剂和助剂,B组分包含胺类固化剂和促进剂,阻燃剂为磷酸酯类化合物和四溴双酚...本文公开了一种适用于HP-RTM(High Pressure Resin Transfer Molding)工艺的高强度阻燃环氧树脂组合物,包含A、B两个组分,其中A组分包含基体树脂、阻燃剂、稀释剂和助剂,B组分包含胺类固化剂和促进剂,阻燃剂为磷酸酯类化合物和四溴双酚A环氧树脂的组合物。研究了基体树脂、阻燃剂、稀释剂的种类和含量对HP-RTM环氧树脂强度和阻燃性的影响,以及胺类固化剂的种类和含量对HP-RTM环氧树脂凝胶时间的影响。结果表明,基体树脂、反应型阻燃剂、稀释剂对力学强度共同影响,阻燃剂对阻燃性能起主要影响作用,固化剂对凝胶时间起主要影响作用。展开更多
The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomia...The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials,modified to accommodate a C~0-continuous expansion. Computationally and theoretically, by increasing the polynomial order p,high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hp element method in more complex science and engineering applications are discussed.展开更多
基金Research was supported in part by NSF grant DMS-0800612Research was supported by Applied Mathematics program of the US DOE Office of Advanced Scientific Computing ResearchThe Pacific Northwest National Laboratory is operated by Battelle for the U.S. Department of Energy under Contract DE-AC05-76RL01830
文摘The hierarchical reconstruction （HR） [Liu, Shu, Tadmor and Zhang, SINUM ＇07] has been successfully applied to prevent oscillations in solutions computed by finite volume, Runge-Kutta discontinuous Galerkin, spectral volume schemes for solving hyperbolic conservation laws. In this paper, we demonstrate that HR can also be combined with spectral/hp element method for solving hyperbolic conservation laws. An orthogonal spectral basis written in terms of Jacobi polynomials is applied. High computational efficiency is obtained due to such matrix-free algorithm. The formulation is conservative, and essential nomoscillation is enforced by the HR limiter. We show that HR preserves the order of accuracy of the spectral/hp element method for smooth solution problems and generate essentially non-oscillatory solutions profiles for capturing discontinuous solutions without local characteristic decomposition. In addition, we introduce a postprocessing technique to improve HR for limiting high degree numerical solutions.
文摘HPS(History, Philosophy and Sociology of Science)教育是把科学史、科学哲学、科学社会学的有关内容纳入科学课程中,其根本目的是帮助学生更好的理解科学的本质。本文以“无机化学”课程教学为基础进行研究,从激发学生学习化学的兴趣、训练学生科学思维的能力、培养学生求真务实的科学精神、提升学生协同合作交流的品质四个方面论述HPS教育模式在“无机化学”课程教学中的重要作用。基于这一教学理念,本课程凝练出多个基于HPS理念的教学案例,学生对本课程进行评价,结果表明该教育理念教学效果良好。
文摘本文公开了一种适用于HP-RTM(High Pressure Resin Transfer Molding)工艺的高强度阻燃环氧树脂组合物,包含A、B两个组分,其中A组分包含基体树脂、阻燃剂、稀释剂和助剂,B组分包含胺类固化剂和促进剂,阻燃剂为磷酸酯类化合物和四溴双酚A环氧树脂的组合物。研究了基体树脂、阻燃剂、稀释剂的种类和含量对HP-RTM环氧树脂强度和阻燃性的影响,以及胺类固化剂的种类和含量对HP-RTM环氧树脂凝胶时间的影响。结果表明,基体树脂、反应型阻燃剂、稀释剂对力学强度共同影响,阻燃剂对阻燃性能起主要影响作用,固化剂对凝胶时间起主要影响作用。
文摘The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials,modified to accommodate a C~0-continuous expansion. Computationally and theoretically, by increasing the polynomial order p,high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hp element method in more complex science and engineering applications are discussed.
