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

@@ -75,8 +75,10 @@ LES methods:
 
 Fluctuating LB:
 
-- ``fluctuating=(variance1, variance2, )``: enables fluctuating lattice Boltzmann by randomizing collision process.
-  Pass sequence of variances for each moment, or `True` to use symbolic variances
+- ``fluctuating=dict``: set to a dictionary to enable thermal fluctuations
+    Must pass either ``temperature`` in the dict to set a temperature or ``variances`` which contains number of moment
+    variances for the fluctuations
+    Additional dict parameters are ``rng_node`` to set the random number generator used
 
 
 
@@ -178,7 +180,7 @@ 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
@@ -193,7 +195,7 @@ from pystencils import Assignment, AssignmentCollection, create_kernel
 from pystencils.cache import disk_cache_no_fallback
 from pystencils.data_types import collate_types
 from pystencils.field import Field, get_layout_of_array
-from pystencils.rng import random_symbol
+from pystencils.rng import random_symbol, PhiloxFourFloats
 from pystencils.simp.assignment_collection import SymbolGen
 from pystencils.stencil import have_same_entries
 
@@ -309,9 +311,6 @@ 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)]
@@ -326,9 +325,39 @@ 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']
-        correction = fluctuation_correction(lb_method, random_symbol(collision_rule.subexpressions, dim=lb_method.dim),
+        if not isinstance(params["fluctuating"], dict):
+            raise ValueError("Must pass a dictionary as fluctuating parameter")
+
+        variances = None
+
+        if "variances" in params["fluctuating"]:
+            variances = params["fluctuating"]["variances"]
+
+        elif "temperature" in params["fluctuating"]:
+            variances = [v for v, _ in zip(iter(SymbolGen("variance")), lb_method.moments)]
+            temperature = sp.Symbol("temperature") if params["fluctuating"]["temperature"] is True\
+                else params["fluctuating"]["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)
+        else:
+            raise ValueError("Fluctuating dict must contain temperature or variance key")
+
+        rng_node = PhiloxFourFloats
+
+        if "rng_node" in params["fluctuating"]:
+            rng_node = params["fluctuating"]["rng_node"]
+
+        correction = fluctuation_correction(lb_method,
+                                            random_symbol(collision_rule.subexpressions,
+                                                          rng_node=rng_node,
+                                                          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)
@@ -527,7 +556,7 @@ def update_with_default_parameters(params, opt_params=None, fail_on_unknown_para
         'entropic_newton_iterations': None,
         'omega_output_field': None,
         'smagorinsky': False,
-        'fluctuating': False,
+        'fluctuating': None,
 
         'output': {},
         'velocity_input': None,