def Generate_Grid(Lx, Ly, Nx, Ny, x_s, y_s):

"""Generates a 2D staggered Grid

Params:

-------

Lx, Ly float, length of grid in x and y

Nx, Ny float, number of points in x and y not includeing ghost cells

xs, ys float, starting points in x and y

Returns:

-------

dx, dy float, step size in x and y

x, y 1D array of float, x and y points

xp, yp 1D array of float, pressure point grid in x and y

p_exact 2D array of float, array for exact pressure

xu, yu 1D array of float, u velocity grid in x and y

u_exact 2D array of float, array for exact u

ut 2D array of float, array for time varying u

xv, yv 1D array of float, v velocity grid in x and y

v_exact 2D array of float, array for exact v

vt 2D array of float, array for time varying v

"""

import numpy

dx = Lx/(Nx)

dy = Ly/(Ny)

#test3

x = numpy.zeros((Nx+2,1), dtype=float)

y = numpy.zeros((Ny+2,1), dtype=float)

# Pressure Points

xp = numpy.zeros(Nx, dtype=float)

yp = numpy.zeros(Ny, dtype=float)

p_exact = numpy.zeros((Ny,Nx), dtype=float)

# u velocity points

xu = numpy.zeros(Nx+3, dtype=float)

yu = numpy.zeros(Ny+2, dtype=float)

u_exact = numpy.zeros((Ny+2,Nx+3), dtype=float)

#ut = numpy.zeros_like((Ny+2,Nx+3,nt), dtype=float)

# v velocity points

xv = numpy.zeros(Nx+2, dtype=float)

yv = numpy.zeros(Ny+3, dtype=float)

v_exact = numpy.zeros((Ny+3,Nx+2), dtype=float)

#vt = numpy.zeros_like((Ny+3,Nx+2,nt), dtype=float)

#Pressure

#for i in range(0,Nx+2):

xp = numpy.linspace(dx/2.0,Lx-dx/2.0,Nx)

yp = numpy.linspace(dy/2.0,Ly-dy/2.0,Ny)

#u Velocity

xu = numpy.linspace(-dx,Lx+dx,Nx+3)

yu = numpy.linspace(-dy/2.0,Ly+dy/2.0,Ny+2)

#v Velocity

xv = numpy.linspace(-dx/2.0,Lx+dx/2.0,Nx+2)

yv = numpy.linspace(-dy,Ly+dy,Ny+3)

return x, y, xp, yp, p_exact, xu, yu, u_exact, xv, yv, v_exact, dx, dy