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/simplificationfactory.py

@@ -73,7 +73,7 @@ def _moment_space_simplification(split_inner_loop):
     s.add(insert_half_force)
     s.add(insert_aliases)
     s.add(add_subexpressions_for_divisions)
-    s.add(add_subexpressions_for_constants)
+    #s.add(add_subexpressions_for_constants)
     if split_inner_loop:
         s.add(create_lbm_split_groups)
     s.add(lambda ac: ac.new_without_unused_subexpressions())
@@ -90,7 +90,7 @@ def _cumulant_space_simplification(split_inner_loop):
     s.add(insert_aliases)
     s.add(insert_constants)
     s.add(add_subexpressions_for_divisions)
-    s.add(add_subexpressions_for_constants)
+    #s.add(add_subexpressions_for_constants)
     if split_inner_loop:
         s.add(create_lbm_split_groups)
     s.add(lambda ac: ac.new_without_unused_subexpressions())