Investigate removing reordered variables to reduce memory usage

[JamieJQuinn]

@semi-h Can you summarise here?

[semi-h]

This is very briefly mentioned in #37. It only requires some changes in the solver class, so completely independent from the backends.

We reserve 3 fields for 3 components of velocity field when we instantiate the solver.

x3d2/src/solver.f90

Lines 80 to 82 in 00d0986

	solver%u => solver%backend%allocator%get_block()
	solver%v => solver%backend%allocator%get_block()
	solver%w => solver%backend%allocator%get_block()

So long as solver lives we have 3 field size equivalent memory with us all the time. It makes sense because after all we need to do a timestep after transeq such that
$u_i = u_i + dt \cdot du_i$
and then after pressure is sorted we need to do a pressure correction such that
$u_i = u_i - p_x \cdot \epsilon ??$

So obviously we can't get rid of them. But inside transeq we can play a trick to limit the total amount of temporary storage transeq requires.

We first use the velocity field components here, and obtain all the derivatives we need in x direction.

x3d2/src/solver.f90

Line 151 in 00d0986

call self%backend%transeq_x(du, dv, dw, u, v, w, self%xdirps)

Then we have to reorder them into y so that y derivatives can be obtained

x3d2/src/solver.f90

Lines 162 to 164 in 00d0986

	call self%backend%reorder(u_y, u, RDR_X2Y)
	call self%backend%reorder(v_y, v, RDR_X2Y)
	call self%backend%reorder(w_y, w, RDR_X2Y)

And this is the key part. Because at this stage we have a copy of velocity field in y orientation as well as the original arrays in x orientation, we can actually get rid of the memory of the original arrays.

If we do this then the reordering below will have to go from y to z.

x3d2/src/solver.f90

Lines 194 to 196 in 00d0986

	call self%backend%reorder(u_z, u, RDR_X2Z)
	call self%backend%reorder(v_z, v, RDR_X2Z)
	call self%backend%reorder(w_z, w, RDR_X2Z)

And then at the very end we'll have to reorder z->x so that the original u, v, and w fields are restrored before returning back to run method in solver.