It is now over half a century since Keulegan conducted his open channel flow experiments. Over the past decades, many empirical formulae were proposed based on his results, however, there is still not a combined expre...It is now over half a century since Keulegan conducted his open channel flow experiments. Over the past decades, many empirical formulae were proposed based on his results, however, there is still not a combined expression to describe the effects of friction over all hydraulic regions in open channel flows. Therefore, in this letter, based on the analysis of the implicit model and the logarithmic matching method, the results of Keulegan （for authentic experiment data are no longer available, here we adopt the analytical solutions given by Dou） are rescaled into one monotone curve by combining the Reynolds number and the relative roughness of the river bed. A united expression that could cover the entire turbulence regions and be validated with Dou＇s analytical solutions is suggested to estimate the friction factor throughout the turbulent region in open channel flows, with higher accuracy than that of the previous formulas.展开更多
Weighted interior penalty discontinuous Galerkin method is developed to solve the two-dimensional non-equilibrium radiation diffusion equation on unstructured mesh.There are three weights including the arithmetic,the ...Weighted interior penalty discontinuous Galerkin method is developed to solve the two-dimensional non-equilibrium radiation diffusion equation on unstructured mesh.There are three weights including the arithmetic,the harmonic,and the geometric weight in the weighted discontinuous Galerkin scheme.For the time discretization,we treat the nonlinear diffusion coefficients explicitly,and apply the semiimplicit integration factormethod to the nonlinear ordinary differential equations arising from discontinuous Galerkin spatial discretization.The semi-implicit integration factor method can not only avoid severe timestep limits,but also takes advantage of the local property of DG methods by which small sized nonlinear algebraic systems are solved element by element with the exact Newton iteration method.Numerical results are presented to demonstrate the validity of discontinuous Galerkin method for high nonlinear and tightly coupled radiation diffusion equation.展开更多
A high-order accuracy time discretization method is developed in this paper to solve the one-dimensional nonlinear Dirac(NLD)equation.Based on the implicit integration factor(IIF)method,two schemes are proposed.Centra...A high-order accuracy time discretization method is developed in this paper to solve the one-dimensional nonlinear Dirac(NLD)equation.Based on the implicit integration factor(IIF)method,two schemes are proposed.Central differences are applied to the spatial discretization.The semi-discrete scheme keeps the conservation of the charge and energy.For the temporal discretization,second-order IIF method and fourth-order IIF method are applied respectively to the nonlinear system arising from the spatial discretization.Numerical experiments are given to validate the accuracy of these schemes and to discuss the interaction dynamics of the NLD solitary waves.展开更多
基金supported by the National Natural Science Foun-dation of China(Grant Nos.51479007,11172218 and 11372232)the Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20130141110016)
文摘It is now over half a century since Keulegan conducted his open channel flow experiments. Over the past decades, many empirical formulae were proposed based on his results, however, there is still not a combined expression to describe the effects of friction over all hydraulic regions in open channel flows. Therefore, in this letter, based on the analysis of the implicit model and the logarithmic matching method, the results of Keulegan （for authentic experiment data are no longer available, here we adopt the analytical solutions given by Dou） are rescaled into one monotone curve by combining the Reynolds number and the relative roughness of the river bed. A united expression that could cover the entire turbulence regions and be validated with Dou＇s analytical solutions is suggested to estimate the friction factor throughout the turbulent region in open channel flows, with higher accuracy than that of the previous formulas.
基金the National Nature Science Foundation of China(11171038)R.Zhang’s work was also supported by Brazilian Young Talent Attraction Program via National Council for Scientific and Technological Development(CNPq).J.Zhu and A.Loula’s works were partially supported by CNPq.X.Cui’s work was partially supported by the National Natural Science Foundation of China(11271054)+1 种基金the Science Foundation of CAEP(2010A0202010,2012B0202026)the Defense Industrial Technology Development Program(B1520110011).
文摘Weighted interior penalty discontinuous Galerkin method is developed to solve the two-dimensional non-equilibrium radiation diffusion equation on unstructured mesh.There are three weights including the arithmetic,the harmonic,and the geometric weight in the weighted discontinuous Galerkin scheme.For the time discretization,we treat the nonlinear diffusion coefficients explicitly,and apply the semiimplicit integration factormethod to the nonlinear ordinary differential equations arising from discontinuous Galerkin spatial discretization.The semi-implicit integration factor method can not only avoid severe timestep limits,but also takes advantage of the local property of DG methods by which small sized nonlinear algebraic systems are solved element by element with the exact Newton iteration method.Numerical results are presented to demonstrate the validity of discontinuous Galerkin method for high nonlinear and tightly coupled radiation diffusion equation.
基金the National Natural Science Foundation of China(No.11671044)the Science Challenge Project(No.TZ2016001)the Beijing Municipal Education Commission(No.PXM2017014224000020).
文摘A high-order accuracy time discretization method is developed in this paper to solve the one-dimensional nonlinear Dirac(NLD)equation.Based on the implicit integration factor(IIF)method,two schemes are proposed.Central differences are applied to the spatial discretization.The semi-discrete scheme keeps the conservation of the charge and energy.For the temporal discretization,second-order IIF method and fourth-order IIF method are applied respectively to the nonlinear system arising from the spatial discretization.Numerical experiments are given to validate the accuracy of these schemes and to discuss the interaction dynamics of the NLD solitary waves.
