Fourth-order correction for cumulants

Adds the fourth-order diffusion correction to the D3Q27 cumulants, as proposed in Geier et al. (2017). Also adds the possibility to use limiters for the third-order cumulants in order to increase stability.

This MR depends on the MR pystencils!338 (merged) and can only be merged afterwards.

lbmpy_tests/test_json_serializer.py

+"""
+Test the lbmpy-specific JSON encoder and serializer as used in the Database class.
+"""
+
+import tempfile
+import pystencils as ps
+
+from lbmpy import Stencil, Method, ForceModel
+from lbmpy.advanced_streaming import Timestep
+from lbmpy.creationfunctions import LBMConfig, LBMOptimisation, LBStencil
+from lbmpy.fieldaccess import StreamPullTwoFieldsAccessor
+
+from pystencils.runhelper import Database
+from lbmpy.db import LbmpyJsonSerializer
+
+
+def test_json_serializer():
+
+    stencil = LBStencil(Stencil.D3Q27)
+    q = stencil.Q
+    pdfs, pdfs_tmp = ps.fields(f"pdfs({q}), pdfs_tmp({q}): double[3D]", layout='fzyx')
+    density = ps.fields(f"rho: double[3D]", layout='fzyx')
+
+    from lbmpy.non_newtonian_models import CassonsParameters
+    cassons_params = CassonsParameters(0.2)
+
+    # create dummy lbmpy config
+    lbm_config = LBMConfig(stencil=LBStencil(Stencil.D3Q27), method=Method.CUMULANT, force_model=ForceModel.GUO,
+                           compressible=True, relaxation_rate=1.999, smagorinsky=True, galilean_correction=True,
+                           cassons=cassons_params, density_input=density, kernel_type=StreamPullTwoFieldsAccessor,
+                           timestep=Timestep.BOTH)
+
+    lbm_optimization = LBMOptimisation(cse_pdfs=False, cse_global=False, builtin_periodicity=(True, False, False),
+                                       symbolic_field=pdfs, symbolic_temporary_field=pdfs_tmp)
+
+    # create dummy database
+    temp_dir = tempfile.TemporaryDirectory()
+    db = Database(file=temp_dir.name, serializer_info=('lbmpy_serializer', LbmpyJsonSerializer))
+
+    db.save(params={'lbm_config': lbm_config, 'lbm_optimization': lbm_optimization}, result={'test': 'dummy'})