3　Method

3.1　Governing equations

2-D Saint-Venant equations were employed as governing equations for lake hydrodynamic modelling,which were shown as follows[1][equation(1)],

where t indicates the time;x and y are Cartesian coordinates;U,E,G and S are vectors of the conserved flow variables,fluxes in the x and y-directions,and source terms,respectively;in which

where h is the water depth;u and v are the depth-averaged velocity components in the x-and y-directions,respectively;g=9.81m/s2 is the gravity acceleration;S0x and S0y are bed slopes in the xand y directions,respectively;Sfx and Sfy are friction slopes in the x-and y directions,respectively.

3.2　Finite volume discretization

The integral form of(1)is

Applying Green's theorem,equation(4)becomes

in whichΩis the control volume;∂Ωdenotes the boundary of the volume;n is the unit outward vector normal to the boundary;dΩand d l are the area and arc elements,respectively.

Fadv=[Eadv,Gadv]T;Fdiff=[Ediff,Gdiff]T.

3.3　Computational grid

Considering the advantages of the triangular mesh such as strong fitting ability of complex boundary,convenient in mesh generation and local encryption,the unstructured triangular element was employed in the study[1-5].A grid is characterized by three vertices,three edges,and three or less immediate neighbor grids.The vertices of each cell Ci have to be numbered in the counter-clockwise direction,as vertices 1-2-3 shown in Fig.1.The edge of each cell are also numbered counterclockwise,as edgeΓi,1-Γi,2-Γi,3 shown in Fig.1.Each edge has a start node,an end node,and a unit outward normal vector.The neighbor cells of each cell should be numbered the same as edges.

Fig.1　Schematic diagram of the unstructured triangular grid