The blood flow model admits the steady state,in which the flux gradient is non-zero and is exactly balanced by the source term.In this paper,we present a high order well-balanced finite difference weighted essentially...The blood flow model admits the steady state,in which the flux gradient is non-zero and is exactly balanced by the source term.In this paper,we present a high order well-balanced finite difference weighted essentially non-oscillatory(WENO)scheme,which exactly preserves the steady state.In order to maintain the wellbalanced property,we propose to reformulate the equation and apply a novel source term approximation.Extensive numerical experiments are carried out to verify the performances of the current scheme such as the maintenance of well-balanced property,the ability to capture the perturbations of such steady state and the genuine high order accuracy for smooth solutions.展开更多
基金The authors would like to thank the support of the Natural Science Foundation of China through Grants Nos.11201254 and 41476101the Natural Science Foundation of Shandong Province of China through Grants Nos.ZR2014DM017 and ZR2015PF002the Project for Scientific Plan of Higher Education in Shandong Province of China through Grant No.J12LI08.
文摘The blood flow model admits the steady state,in which the flux gradient is non-zero and is exactly balanced by the source term.In this paper,we present a high order well-balanced finite difference weighted essentially non-oscillatory(WENO)scheme,which exactly preserves the steady state.In order to maintain the wellbalanced property,we propose to reformulate the equation and apply a novel source term approximation.Extensive numerical experiments are carried out to verify the performances of the current scheme such as the maintenance of well-balanced property,the ability to capture the perturbations of such steady state and the genuine high order accuracy for smooth solutions.
