We couple together existing ideas,existing results,special structure and novel ideas to accomplish the exact limits and improved decay estimates with sharp rates for all order derivatives of the global weak solutions ...We couple together existing ideas,existing results,special structure and novel ideas to accomplish the exact limits and improved decay estimates with sharp rates for all order derivatives of the global weak solutions of the Cauchy problem for an n-dimensional incompressible Navier-Stokes equations.We also use the global smooth solution of the corresponding heat equation to approximate the global weak solutions of the incompressible Navier-Stokes equations.展开更多
Smoothed particle hydrodynamics (SPH) is a useful meshless method.The first and second orders are the most popular derivatives of the field function in the mechanical governing equations.New methods were proposed to i...Smoothed particle hydrodynamics (SPH) is a useful meshless method.The first and second orders are the most popular derivatives of the field function in the mechanical governing equations.New methods were proposed to improve accuracy of SPH approximation by the lemma proved.The lemma describes the relationship of functions and their SPH approximation.Finally,the error comparison of SPH method with or without our improvement was carried out.展开更多
The smoothed particle hydrodynamics (SPH), as a fully Lagrangian particle method, has been suc- cessfully applied to astrophysical problems and extended to elastic dynamics and computational fluid dynamics. High order...The smoothed particle hydrodynamics (SPH), as a fully Lagrangian particle method, has been suc- cessfully applied to astrophysical problems and extended to elastic dynamics and computational fluid dynamics. High order derivatives have to be approximated when elastic dynamics problems are modeled. However, the approximation errors in SPH could lead to computational failure in the case that the order of derivative is high. A novel method was proposed in order to improve the accuracy of SPH method, which shows the relationship between the selected functions and their SPH approximations. The entire involved system was represented by a finite number of particles that carry individual mass and occupy individual space, and the integral interpo- lation was approximated by a summation interpolation. In addition, error comparison was made between SPH method with and without the present improvement.展开更多
文摘We couple together existing ideas,existing results,special structure and novel ideas to accomplish the exact limits and improved decay estimates with sharp rates for all order derivatives of the global weak solutions of the Cauchy problem for an n-dimensional incompressible Navier-Stokes equations.We also use the global smooth solution of the corresponding heat equation to approximate the global weak solutions of the incompressible Navier-Stokes equations.
基金The National Natural Science Foundation of China(No.50778111)The Key Project of Fund of Science and Technology Development of Shanghai(No.07JC14023)
文摘Smoothed particle hydrodynamics (SPH) is a useful meshless method.The first and second orders are the most popular derivatives of the field function in the mechanical governing equations.New methods were proposed to improve accuracy of SPH approximation by the lemma proved.The lemma describes the relationship of functions and their SPH approximation.Finally,the error comparison of SPH method with or without our improvement was carried out.
基金National Scientific Instrument Major Project of P.R.China(2013YQ220643)Fundamental Research Funds for the Central Universities of China(YS1404)Beijing Natural Science Foundation(4172044)
基金the Key Project of Fund of Science and Technology Development of Shanghai (No. 07JC14023)the National Natural Science Foundation of China(No. 50778111)
文摘The smoothed particle hydrodynamics (SPH), as a fully Lagrangian particle method, has been suc- cessfully applied to astrophysical problems and extended to elastic dynamics and computational fluid dynamics. High order derivatives have to be approximated when elastic dynamics problems are modeled. However, the approximation errors in SPH could lead to computational failure in the case that the order of derivative is high. A novel method was proposed in order to improve the accuracy of SPH method, which shows the relationship between the selected functions and their SPH approximations. The entire involved system was represented by a finite number of particles that carry individual mass and occupy individual space, and the integral interpo- lation was approximated by a summation interpolation. In addition, error comparison was made between SPH method with and without the present improvement.
