function [Fu Fv] = UVadvect_TVD_mex(Nx, Ny, dx, dy, dt, ui, vi, uj, vj, Nodeu, Nodev, idsu, idsv,Nbcs,NbcsDu,NbcsDv)

% function [Fu Fv] = UVadvect_DO_mex(Nx, Ny, dx, dy, u, v, Nodeu, Nodev, idsu, idsv)

% This function calculates the FV fluxes in a staggered grid for velocity

% advection, and allows for different velocities to be used to determine the

% upwind direction (as required by the DO implementation). QUICK scheme used for

% advection.

%

% INPUTS:

%       Nx:     Number of interior nodes in the x-direction

%       Ny:     Number of interior nodes in the y-direction

%       dx:     Step size in x direction

%       dy:     Step size in y direction

%       ui:     Vector containing the i'th u mode of velocity, including boundary

%                 data

%       vi:     Vector containing the i'th v mode of velocity, including boundary

%                 data

%       uj:     Vector containing the j'th u mode of velocity, including boundary

%                 data

%       vj:     Vector containing the j'th v mode of velocity, including boundary

%                 data

%       Nodeu:  Is the node numbering matrix for the u velocity

%       Nodev:  Is the node numbering matrix for the v velocity

%       idsu:   Location of active u-velocity nodes in interior

%       idsv:   Location of active v-velocity nodes in interior

%       Nbcs:   Number of boundary conditions

%       NbcsDu: Number of Dirichlet u-velocity boundary conditions

%       NbcsDv: Number of Dirichlet v-velocity boundary conditions

%       

% OUTPUTS:

%       Fu:      Output vector:Fu = (Fue-Fuw)*dy/dV+(Fus-Fun)*dx/dV

%       Fv:      Output vector:Fv = (Fve-Fvw)*dy/dV+(Fvs-Fvn)*dx/dV

%

% Authors:   Matt Ueckermann, Themis Sapsis, 

%            Pierre Lermusiaux, Pat Haley for MIT course 2.29

%

% NOTE: In this version of the advection equation, there is no upwind direction.

% This is consistent for the modes which should have no sign attached to them.

%% Call C++ function to do advection. Note the casting to int32's (important)

[Fu Fv]=UVadvect_TVD_mx(int32(Nx),int32(Ny),dx,dy,dt,ui,vi,uj, vj,... 

    int32(Nodeu),int32(Nodev),int32(Nbcs),int32(NbcsDu),int32(NbcsDv));

%Reformat flux for output

Fu=Fu(idsu); 

Fv=Fv(idsv);