Laplacian computation

[ivan-pi]

Phase-field-Fortran-codes-using-whole-array/comparison/index_array.f90

Lines 82 to 88 in 1741245

	lap_con(i,j) = ( con(ip,j) + con(im,j) + con(i,jm) + con(i,jp) - &
	4.0*con(i,j) ) /( dx*dy )
	dummy_con(i,j) = dfdcon(i,j) - grad_coef*lap_con(i,j)
	lap_dummy(i,j) = ( dummy_con(ip,j) + dummy_con(im,j) + dummy_con(i,jm) &
	+ dummy_con(i,jp) - 4.0*dummy_con(i,j) ) / ( dx*dy )

The calculation of lap_dummy(i,j) depends on values of lap_con which may not have been computed yet. This is different from the whole array version, where you compute the whole Laplacian first:

     dfdcon = A*( 2.0*con*( 1.0 - con )**2 &
          -2.0*con**2*( 1.0 - con ) )
     dummy_con = dfdcon - grad_coef*Laplacian( con )
     con = con + dt*mobility*Laplacian( dummy_con )

[ivan-pi]

Does the Laplacian need to be computed twice or only once? In the main README.md you only compute it once.

[Shahid718]

The main README.md shows the model A which is Allen-Cahn Equation here . model B is Cahn-Hilliard equation and needs laplacian twice there

model A equation is

$$\phi^{n+1}=\phi^n - L \Delta t \left(\frac{\partial f}{\partial \phi^n} - \kappa \nabla^2 \phi^n\right)$$

model B equation is

$$ c^{n+1} = c^n + \nabla^2M \Delta t \left( \frac{\partial f}{\partial {c^{n}}}-\kappa \nabla^2 {c^{n}} \right)$$