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/methods/momentbased/momentbasedsimplifications.py

@@ -9,7 +9,7 @@ from itertools import product
 from lbmpy.methods.abstractlbmethod import LbmCollisionRule
 from pystencils import Assignment, AssignmentCollection
 from pystencils.stencil import inverse_direction
-from pystencils.simp.subexpression_insertion import insert_subexpressions
+from pystencils.simp.subexpression_insertion import insert_subexpressions, is_constant
 from pystencils.sympyextensions import extract_most_common_factor, replace_second_order_products, subs_additive
 
 from collections import defaultdict
@@ -328,7 +328,7 @@ def insert_pure_products(ac, symbols, **kwargs):
         if isinstance(rhs, sp.Symbol) and rhs in symbols:
             return True
         elif isinstance(rhs, sp.Mul):
-            if all(arg in symbols for arg in rhs.args):
+            if all((is_constant(arg) or (arg in symbols)) for arg in rhs.args):
                 return True
         return False