In this paper, we study the evolving behaviors of the first eigenvalue of the Laplace- Beltrami operator under the normalized backward Ricci flow, construct various quantities which are monotonic under the backward Ri...In this paper, we study the evolving behaviors of the first eigenvalue of the Laplace- Beltrami operator under the normalized backward Ricci flow, construct various quantities which are monotonic under the backward Ricci flow and get upper and lower bounds. We prove that in cases where the backward Ricci flow converges to a sub-Riemannian geometry after a proper rescaling, the eigenvalue evolves toward zero.展开更多
The work deals with numerical modelling of turbulent flows in channels with an expansion of the cross-section where flow separation and reattachment occur. The performance of several eddy viscosity models and an expli...The work deals with numerical modelling of turbulent flows in channels with an expansion of the cross-section where flow separation and reattachment occur. The performance of several eddy viscosity models and an explicit algebraic Reynolds stress model (EARSM) is studied. The used test cases are flows in channels with various backward facing steps where the step is perpendicular or inclined and the top wall is parallel or deflected. Furthermore, a channel with the circular ramp is considered. The numerical solution is achieved by the finite volume method or by the finite element method. The results of both numerical approaches are compared.展开更多
基金Supported by NSFC(Grant No.11001268)Chinese Universities Scientific Fund(Grant No.2014QJ002)
文摘In this paper, we study the evolving behaviors of the first eigenvalue of the Laplace- Beltrami operator under the normalized backward Ricci flow, construct various quantities which are monotonic under the backward Ricci flow and get upper and lower bounds. We prove that in cases where the backward Ricci flow converges to a sub-Riemannian geometry after a proper rescaling, the eigenvalue evolves toward zero.
基金supported by Grant Number 103/09/0977 of Czech Science FoundationResearch Plans of MSMT No. 6840770010 and No. AV0Z207 60514
文摘The work deals with numerical modelling of turbulent flows in channels with an expansion of the cross-section where flow separation and reattachment occur. The performance of several eddy viscosity models and an explicit algebraic Reynolds stress model (EARSM) is studied. The used test cases are flows in channels with various backward facing steps where the step is perpendicular or inclined and the top wall is parallel or deflected. Furthermore, a channel with the circular ramp is considered. The numerical solution is achieved by the finite volume method or by the finite element method. The results of both numerical approaches are compared.
