double precision function u_exa(x,y,t,c_x,c_y)

c General information:

c     Function u_exa returns an exact solution to the convection
c     equation:
c
c        u_t + c_x ux + c_y u_y =0.

c     Function u_exa requires an arbitrary two parameter
c        double precision function f(x,y).
c     The returned exact solution will be:
c        f(x-c_x t, y - c_y t)

c Arguments:

c     Avoid typos:
      implicit none

c     Input: the position for which to return the exact solution:
      double precision x,y

c     Input: the time at which to return the exact solution:
      double precision t

c     Input: the components c_x and c_y of the convection velocity:
      double precision c_x,c_y

c External variables:

c     An arbitrary two-parameter function:
      double precision f
      external f

c Executable statements:

c     Return the exact solution:
      u_exa=f(x-c_x*t,y-c_y*t)

c Exit:

      return
      end

c ========================================================================
c ========================================================================

      double precision function f(x,y)

c General information:

c     Function f is an infinitely smooth, bounded, periodic but
c     not harmonic function of two arguments.

c Arguments:

c     Avoid typos:
      implicit none

c     The two arguments of f:
      double precision x,y

c Local variables:

c     Parameters of the function
      double precision c1,c2
      parameter (c1=2.3d0,c2=1.5d0)

c Executable statements:

c     Return the value of f:
      f=sin(sin(c1*x-y))*cos(c2*cos(x+y))

c Exit:

      return
      end