WIP: Fluctuating Equations non-normalized

Non normalized equations for the variances.

Still need to figure out how to get lattice spacing and whether definition for mu should contain lattice time as well.

Related to walberla/walberla!220 (merged) and implements/enhances #2 (closed)

lbmpy/creationfunctions.py

@@ -178,7 +178,7 @@ from lbmpy.fieldaccess import (
     AAEvenTimeStepAccessor, AAOddTimeStepAccessor, CollideOnlyInplaceAccessor, EsoTwistEvenTimeStepAccessor,
     EsoTwistOddTimeStepAccessor, PdfFieldAccessor, PeriodicTwoFieldsAccessor, StreamPullTwoFieldsAccessor,
     StreamPushTwoFieldsAccessor)
-from lbmpy.fluctuatinglb import fluctuation_correction, method_with_rescaled_equilibrium_values
+from lbmpy.fluctuatinglb import fluctuation_correction, fluctuating_variance_equations
 from lbmpy.methods import create_mrt3, create_mrt_orthogonal, create_mrt_raw, create_srt, create_trt, create_trt_kbc
 from lbmpy.methods.creationfunctions import create_generic_mrt
 from lbmpy.methods.cumulantbased import CumulantBasedLbMethod
@@ -309,9 +309,6 @@ def create_lb_collision_rule(lb_method=None, optimization={}, **kwargs):
     if rho_in is not None and isinstance(rho_in, Field):
         rho_in = rho_in.center
 
-    if params['fluctuating']:
-        lb_method = method_with_rescaled_equilibrium_values(lb_method)
-
     if u_in is not None:
         density_rhs = sum(lb_method.pre_collision_pdf_symbols) if rho_in is None else rho_in
         eqs = [Assignment(cqc.zeroth_order_moment_symbol, density_rhs)]
@@ -326,13 +323,22 @@ def create_lb_collision_rule(lb_method=None, optimization={}, **kwargs):
     collision_rule = simplification(collision_rule)
 
     if params['fluctuating']:
-        variances = SymbolGen("variance") if params['fluctuating'] is True else params['fluctuating']
+        variances = [v for v, _ in zip(iter(SymbolGen("variance")), lb_method.moments)] if params['fluctuating'] is True else params['fluctuating']
         correction = fluctuation_correction(lb_method, random_symbol(collision_rule.subexpressions, dim=lb_method.dim),
                                             variances)
+
         for i, corr in enumerate(correction):
             collision_rule.main_assignments[i] = Assignment(collision_rule.main_assignments[i].lhs,
                                                             collision_rule.main_assignments[i].rhs + corr)
 
+        temperature = sp.Symbol("fluctuating_temperature") if params["temperature"] is None else params["temperature"]
+        variance_equations = fluctuating_variance_equations(method=lb_method,
+                                                            temperature=temperature,
+                                                            c_s_sq=params["c_s_sq"],
+                                                            variances=variances)
+        collision_rule.subexpressions += variance_equations
+        collision_rule.topological_sort(sort_subexpressions=True, sort_main_assignments=False)
+
     if params['entropic']:
         if params['smagorinsky']:
             raise ValueError("Choose either entropic or smagorinsky")
@@ -528,6 +534,7 @@ def update_with_default_parameters(params, opt_params=None, fail_on_unknown_para
         'omega_output_field': None,
         'smagorinsky': False,
         'fluctuating': False,
+        'temperature': None,
 
         'output': {},
         'velocity_input': None,

[Michael Kuron]

I don't like the name "fluctuating_temperature". Of course it is the temperature of the fluctuating LB, but the name sounds like it's a bool that specifies whether you want the temperature to fluctuate or not. Why not just name it "temperature"? It's unlikely any future modification will ever require specifying separate temperatures for the LB method and for the fluctuation algorithm, so the distinction is not needed.

[Felix Winterhalter]

I agree with you its not that great. I just didn't want to assume that its the only temperature that will ever be introduced, hence the qualifier. If you also agree that we can just name it "temperature" I'm fine with that.

[Martin Bauer]

I'm a bit hesitant to just name it temperature. How about passing a dict as the fluctuating parameter if additional options are required?

Is it correct that one can either pass variance values or temperature values? Could the user also just call create_lb_*(fluctuating=variance_expressions_from_temperature(temperature))

[Michael Kuron]

This should probably only be called if a temperature has been specified instead of a list of variances.

[Felix Winterhalter]

Might be a useful change. If you do not pass a temperature even in symbolic form there would be no need to generate the variance equations.

@bauer Thoughts on this? Should there be a different option for when variance equations are builtin?