Taking one-dimensional shallow water wave equation as an example, a comparative analysis on the computational stability related to the short-range motion of atmosphere and ocean is carried out for the conservative and...Taking one-dimensional shallow water wave equation as an example, a comparative analysis on the computational stability related to the short-range motion of atmosphere and ocean is carried out for the conservative and nonconservative scheme, and it is pointed out that the computational stability of conservative scheme is absolutely different from that of the nonconservative scheme. The relationship between the short-range motion of atmosphere and ocean and the conservative and nonconservative scheme is further discussed. The constructed conservative scheme is proved to be stable by the numerical experiment for the short-range motion of atmosphere and ocean while the CTCS scheme is unstable. So that the conservative scheme for the solution of this kind of problem has more advantages.展开更多
A traveling wave solution to the Aw-Rascle traffic flow model that includes the relaxation and diffusion terms is investigated. The model can be approximated by the well-known Kortweg-de Vries （KdV） equation. A nume...A traveling wave solution to the Aw-Rascle traffic flow model that includes the relaxation and diffusion terms is investigated. The model can be approximated by the well-known Kortweg-de Vries （KdV） equation. A numerical simulation is conducted by the first-order accurate Lax-Friedrichs scheme, which is known for its ability to capture the entropy solution to hyperbolic conservation laws. Periodic boundary conditions are applied to simulate a lengthy propagation, where the profile of the derived KdV solution is taken as the initial condition to observe the change of the profile. The simulation shows good agreement between the approximated KdV solution and the numerical solution.展开更多
Direct simulation of 3-D MHD(magnetohydrodynamics) flows in liquid metal fusion blanket with flow channel insert(FCI) has been conducted.Two kinds of pressure equilibrium slot (PES) in FCI,which are used to balance th...Direct simulation of 3-D MHD(magnetohydrodynamics) flows in liquid metal fusion blanket with flow channel insert(FCI) has been conducted.Two kinds of pressure equilibrium slot (PES) in FCI,which are used to balance the pressure difference between the inside and outside of FCI,are considered with a slot in Hartmann wall or a slot in side wall,respectively.The velocity and pressure distribution of FCI made of SiC/SiC_f are numerically studied to illustrate the 3-D MHD flow effects,which clearly show that the flows in fusion blanket with FCI are typical three-dimensional issues and the assumption of 2-D fully developed flows is not the real physical problem of the MHD flows in dual-coolant liquid metal fusion blanket.The optimum opening location of PES has been analyzed based on the 3-D pressure and velocity distributions.展开更多
Some problems of nonlinear computational instability are discussed in this article, which are shown as follows: 1) Three types of representative evolution equations are analyzed, and the close relationship between the...Some problems of nonlinear computational instability are discussed in this article, which are shown as follows: 1) Three types of representative evolution equations are analyzed, and the close relationship between the nonlinear computational stability or instability in their corresponding difference equations and the properties of their solution is revealed. 2) The problem of nonlinear computational instability in conservative differencing equations with the periodic boundary condition is further discussed, and some effective ways to avoid nonlinear computational instability are proposed. 3) The problem of nonlinear computational instability in non-conservative difference equations with the aperiodic boundary condition is focused on by using nonlinear advection equations as examples, and u synthetic analysis method' is given to judge their computational stability.展开更多
基金supported by the National Outstanding Youth Scientist Foundation of China(Grant No.49825109)the Key Innovation Project of the Chinese Academy of Sciences(Grant No.KZCX2-208)+1 种基金the Hundred Talents Project of the Chinese Academy of Sciencesthe National Natura1 Science Foundation of China(Grant No.40275023).
文摘Taking one-dimensional shallow water wave equation as an example, a comparative analysis on the computational stability related to the short-range motion of atmosphere and ocean is carried out for the conservative and nonconservative scheme, and it is pointed out that the computational stability of conservative scheme is absolutely different from that of the nonconservative scheme. The relationship between the short-range motion of atmosphere and ocean and the conservative and nonconservative scheme is further discussed. The constructed conservative scheme is proved to be stable by the numerical experiment for the short-range motion of atmosphere and ocean while the CTCS scheme is unstable. So that the conservative scheme for the solution of this kind of problem has more advantages.
基金Project supported by the National Natural Science Foundation of China (Nos. 11072141 and 11272199)the National Basic Research Program of China (No. 2012CB725404)+1 种基金the University Research Committee, HKU SPACE Research FundFaculty of Engineering Top-up Grant of the University of Hong Kong (No. 201007176059)
文摘A traveling wave solution to the Aw-Rascle traffic flow model that includes the relaxation and diffusion terms is investigated. The model can be approximated by the well-known Kortweg-de Vries （KdV） equation. A numerical simulation is conducted by the first-order accurate Lax-Friedrichs scheme, which is known for its ability to capture the entropy solution to hyperbolic conservation laws. Periodic boundary conditions are applied to simulate a lengthy propagation, where the profile of the derived KdV solution is taken as the initial condition to observe the change of the profile. The simulation shows good agreement between the approximated KdV solution and the numerical solution.
基金supported by National Natural Science Foundation of China with grant Nos.10872212,50936006National Magnetic Confinement Fusion Science Program in China with grant No.2009GB10401
文摘Direct simulation of 3-D MHD(magnetohydrodynamics) flows in liquid metal fusion blanket with flow channel insert(FCI) has been conducted.Two kinds of pressure equilibrium slot (PES) in FCI,which are used to balance the pressure difference between the inside and outside of FCI,are considered with a slot in Hartmann wall or a slot in side wall,respectively.The velocity and pressure distribution of FCI made of SiC/SiC_f are numerically studied to illustrate the 3-D MHD flow effects,which clearly show that the flows in fusion blanket with FCI are typical three-dimensional issues and the assumption of 2-D fully developed flows is not the real physical problem of the MHD flows in dual-coolant liquid metal fusion blanket.The optimum opening location of PES has been analyzed based on the 3-D pressure and velocity distributions.
基金he National Key Planning Development Project for Basic Research (Grant No.1999032801 ) and the National Natural Science Founda
文摘Some problems of nonlinear computational instability are discussed in this article, which are shown as follows: 1) Three types of representative evolution equations are analyzed, and the close relationship between the nonlinear computational stability or instability in their corresponding difference equations and the properties of their solution is revealed. 2) The problem of nonlinear computational instability in conservative differencing equations with the periodic boundary condition is further discussed, and some effective ways to avoid nonlinear computational instability are proposed. 3) The problem of nonlinear computational instability in non-conservative difference equations with the aperiodic boundary condition is focused on by using nonlinear advection equations as examples, and u synthetic analysis method' is given to judge their computational stability.
