Rework of the Cumulant-Based Method

This MR updates the cumulant-based LB method to better fit into our updated modelling framework. Several components are changed:

Central Moment to Cumulant Transform

• Now derives equations for polynomial cumulants, with monomials as intermediary values
• No longer ignores cumulants of zeroth and first order
• No longer simplifies according to a-priori assumptions about zeroth and first order cumulants, but emits equations containing logarithms and exponentials that need to be simplified later

Cumulant-Based Method

• Renamed to CumulantBasedLbMethod
• Forces are now applied symmetrically in central moment space according to the given force model, no more 'implicit forcing'
• Zeroth and first order cumulants are now treated regularily
• The Galilean correction was extracted as an a-posteriori-modification

Force Models

• Introduced interface method symmetric_central_moment_forcing for use with the cumulant method and implemented it for Simple, Luo, Guo and He

Central Moment Transform

• Introduced BinomialChimeraTransform as a new central moment transform class.

Method Creation

• Cumulant-based methods are now created like all other methods using create_with_equilibrium, and are thus open for use with arbitrary custom equilibria

Simplification

The changes to the derivation did increase the FLOP count of the cumulant method slightly.

• Added insert_logs to eliminate exponentials and logarithms in the cumulant-based method
• Added expand_post_collision_central_moments to simplify post-collision equations
• Added insert_conserved_quantity_products and insert_half_force to simplify expressions in central moment and cumulant based methods that depend only on conserved quantitites or the body force

lbmpy/moment_transforms/centralmomenttransforms.py

@@ -465,6 +465,7 @@ class BinomialChimeraTransform(AbstractCentralMomentTransform):
         backward_simp = SimplificationStrategy()
         backward_simp.add(partial(insert_aliases, skip=bw_skip))
         backward_simp.add(split_pdf_main_assignments_by_symmetry)
+        backward_simp.add(add_subexpressions_for_constants)
 
         return {
             'forward': forward_simp,