diff --git a/lbmpy/macroscopic_value_kernels.py b/lbmpy/macroscopic_value_kernels.py
index bcfc9422c22fc3e353cc4bd73bb14eb6344823b5..4ec4f31ae4e44f0468ec58a191ea9843c8072a97 100644
--- a/lbmpy/macroscopic_value_kernels.py
+++ b/lbmpy/macroscopic_value_kernels.py
@@ -8,11 +8,11 @@ from lbmpy.advanced_streaming.utility import get_accessor, Timestep
 
 
 def pdf_initialization_assignments(lb_method, density, velocity, pdfs,
-                                   streaming_pattern='pull', timestep=Timestep.BOTH,
+                                   streaming_pattern='pull', previous_timestep=Timestep.BOTH,
                                    set_pre_collision_pdfs=False):
     """Assignments to initialize the pdf field with equilibrium"""
     if isinstance(pdfs, Field):
-        accessor = get_accessor(streaming_pattern, timestep)
+        accessor = get_accessor(streaming_pattern, previous_timestep)
         if set_pre_collision_pdfs:
             field_accesses = accessor.read(pdfs, lb_method.stencil)
         else:
@@ -32,10 +32,10 @@ def pdf_initialization_assignments(lb_method, density, velocity, pdfs,
 
 
 def macroscopic_values_getter(lb_method, density, velocity, pdfs,
-                              streaming_pattern='pull', timestep=Timestep.BOTH,
+                              streaming_pattern='pull', previous_timestep=Timestep.BOTH,
                               use_pre_collision_pdfs=False):
     if isinstance(pdfs, Field):
-        accessor = get_accessor(streaming_pattern, timestep)
+        accessor = get_accessor(streaming_pattern, previous_timestep)
         if use_pre_collision_pdfs:
             field_accesses = accessor.read(pdfs, lb_method.stencil)
         else:
diff --git a/lbmpy_tests/advanced_streaming/test_fully_periodic_flow.py b/lbmpy_tests/advanced_streaming/test_fully_periodic_flow.py
index 4b52a17416ce505889cb1d085c815d38c173bfe8..4dc7b6b1a5fde034c49c59c3d82fcd22f8c89699 100644
--- a/lbmpy_tests/advanced_streaming/test_fully_periodic_flow.py
+++ b/lbmpy_tests/advanced_streaming/test_fully_periodic_flow.py
@@ -105,14 +105,14 @@ def test_fully_periodic_flow(target, stencil, streaming_pattern):
 
     setter = macroscopic_values_setter(
         lb_method, density, velocity, pdfs,
-        streaming_pattern=streaming_pattern, timestep=zeroth_timestep)
+        streaming_pattern=streaming_pattern, previous_timestep=zeroth_timestep)
     setter_kernel = create_kernel(setter, ghost_layers=1, target=target).compile()
 
     getter_kernels = []
     for t in timesteps:
         getter = macroscopic_values_getter(
             lb_method, density_field, velocity_field, pdfs,
-            streaming_pattern=streaming_pattern, timestep=t)
+            streaming_pattern=streaming_pattern, previous_timestep=t)
         getter_kernels.append(create_kernel(getter, ghost_layers=1, target=target).compile())
 
     #   Periodicity
diff --git a/lbmpy_tests/advanced_streaming/test_periodic_pipe_with_force.py b/lbmpy_tests/advanced_streaming/test_periodic_pipe_with_force.py
index 1cc3526386d1db65b6e5416e7bd02a06045139c2..cafd293b2ddb34e44fbe06f22aca35c05ac167b6 100644
--- a/lbmpy_tests/advanced_streaming/test_periodic_pipe_with_force.py
+++ b/lbmpy_tests/advanced_streaming/test_periodic_pipe_with_force.py
@@ -106,14 +106,14 @@ class PeriodicPipeFlow:
 
         setter = macroscopic_values_setter(
             self.lb_method, self.density, self.velocity, self.pdfs,
-            streaming_pattern=self.streaming_pattern, timestep=self.zeroth_timestep)
+            streaming_pattern=self.streaming_pattern, previous_timestep=self.zeroth_timestep)
         self.init_kernel = create_kernel(setter, ghost_layers=1, target=self.target).compile()
 
         self.getter_kernels = []
         for t in self.timesteps:
             getter = macroscopic_values_getter(
                 self.lb_method, self.density_field, self.velocity_field, self.pdfs,
-                streaming_pattern=self.streaming_pattern, timestep=t)
+                streaming_pattern=self.streaming_pattern, previous_timestep=t)
             self.getter_kernels.append(create_kernel(getter, ghost_layers=1, target=self.target).compile())
 
         #   Periodicity
diff --git a/lbmpy_tests/centeredcumulant/test_flow_around_sphere.py b/lbmpy_tests/centeredcumulant/test_flow_around_sphere.py
index beb2d3db62db48ef7328815909913b449a9112fd..686eb0f60e14fc3c88098b30d143f910aab8c84f 100644
--- a/lbmpy_tests/centeredcumulant/test_flow_around_sphere.py
+++ b/lbmpy_tests/centeredcumulant/test_flow_around_sphere.py
@@ -104,7 +104,7 @@ def flow_around_sphere(stencil, galilean_correction, L_LU, total_steps):
 
     init_eqs = pdf_initialization_assignments(lb_method, 1.0, initial_velocity, pdf_field,
                                               streaming_pattern=streaming_pattern,
-                                              timestep=timesteps[0])
+                                              previous_timestep=timesteps[0])
     init_kernel = create_kernel(init_eqs, target=target).compile()
 
     output = {
diff --git a/lbmpy_tests/centeredcumulant/test_periodic_pipe_flow.ipynb b/lbmpy_tests/centeredcumulant/test_periodic_pipe_flow.ipynb
index eb5562c460dd46558353b7bc7b43ebb485c9cab3..8076fdd2cdc9de4588dc54b8b8359bbfd234ebc6 100644
--- a/lbmpy_tests/centeredcumulant/test_periodic_pipe_flow.ipynb
+++ b/lbmpy_tests/centeredcumulant/test_periodic_pipe_flow.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 1,
    "source": [
     "import pytest\n",
     "pytest.importorskip('pycuda')"
@@ -16,33 +16,24 @@
       ]
      },
      "metadata": {},
-     "execution_count": 7
+     "execution_count": 1
     }
    ],
    "metadata": {}
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 2,
    "source": [
     "%load_ext autoreload\n",
     "%autoreload 2"
    ],
-   "outputs": [
-    {
-     "output_type": "stream",
-     "name": "stdout",
-     "text": [
-      "The autoreload extension is already loaded. To reload it, use:\n",
-      "  %reload_ext autoreload\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "metadata": {}
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 3,
    "source": [
     "import sympy as sp\n",
     "import numpy as np\n",
@@ -70,7 +61,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 4,
    "source": [
     "class PeriodicPipeFlow:\n",
     "    def __init__(self, method_params, optimization=dict()):\n",
@@ -132,14 +123,14 @@
     "\n",
     "        setter = macroscopic_values_setter(\n",
     "            self.lb_method, self.density, self.velocity, self.pdfs,\n",
-    "            streaming_pattern=self.streaming_pattern, timestep=self.zeroth_timestep)\n",
+    "            streaming_pattern=self.streaming_pattern, previous_timestep=self.zeroth_timestep)\n",
     "        self.init_kernel = create_kernel(setter, ghost_layers=1, target=self.target).compile()\n",
     "\n",
     "        self.getter_kernels = []\n",
     "        for t in self.timesteps:\n",
     "            getter = macroscopic_values_getter(\n",
     "                self.lb_method, self.density_field, self.velocity_field, self.pdfs,\n",
-    "                streaming_pattern=self.streaming_pattern, timestep=t)\n",
+    "                streaming_pattern=self.streaming_pattern, previous_timestep=t)\n",
     "            self.getter_kernels.append(create_kernel(getter, ghost_layers=1, target=self.target).compile())\n",
     "\n",
     "        #   Periodicity\n",
@@ -219,7 +210,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 5,
    "source": [
     "stencil = get_stencil('D3Q19')\n",
     "dim = len(stencil[0])\n",
@@ -243,7 +234,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 6,
    "source": [
     "srt_params = {\n",
     "    'stencil': stencil,\n",
@@ -263,7 +254,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 7,
    "source": [
     "srt_u = srt_flow.get_trimmed_velocity_array()\n",
     "ps.plot.vector_field_magnitude(srt_u[30,:,:,:])\n",
@@ -274,11 +265,11 @@
      "output_type": "execute_result",
      "data": {
       "text/plain": [
-       "<matplotlib.colorbar.Colorbar at 0x7faa51244c40>"
+       "<matplotlib.colorbar.Colorbar at 0x7fd9a51311c0>"
       ]
      },
      "metadata": {},
-     "execution_count": 13
+     "execution_count": 7
     },
     {
      "output_type": "display_data",
@@ -310,7 +301,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 8,
    "source": [
     "cm_method_params = {\n",
     "    'method' : 'monomial_cumulant',\n",
@@ -333,7 +324,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 9,
    "source": [
     "lb_method = cm_impl_f_flow.lb_method\n",
     "assert all(rr == 2 for rr in lb_method.relaxation_rates[1:4])\n",
@@ -344,7 +335,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 10,
    "source": [
     "cm_impl_f_flow.init()\n",
     "cm_impl_f_flow.run(400)"
@@ -354,7 +345,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 11,
    "source": [
     "cm_impl_f_u = cm_impl_f_flow.get_trimmed_velocity_array()\n",
     "ps.plot.vector_field_magnitude(cm_impl_f_u[30,:,:,:])\n",
@@ -365,11 +356,11 @@
      "output_type": "execute_result",
      "data": {
       "text/plain": [
-       "<matplotlib.colorbar.Colorbar at 0x7faa5077ed30>"
+       "<matplotlib.colorbar.Colorbar at 0x7fd9a40bd5e0>"
       ]
      },
      "metadata": {},
-     "execution_count": 17
+     "execution_count": 11
     },
     {
      "output_type": "display_data",
@@ -388,7 +379,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 12,
    "source": [
     "assert_allclose(cm_impl_f_u, srt_u, rtol=1, atol=1e-4)"
    ],
@@ -404,7 +395,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 13,
    "source": [
     "from lbmpy.forcemodels import Simple\n",
     "\n",
@@ -429,7 +420,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 14,
    "source": [
     "lb_method = cm_expl_f_flow.lb_method\n",
     "assert all(rr == 0 for rr in lb_method.relaxation_rates[1:4])\n",
@@ -440,7 +431,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 15,
    "source": [
     "cm_expl_f_flow.init()\n",
     "cm_expl_f_flow.run(400)"
@@ -450,7 +441,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 16,
    "source": [
     "cm_expl_f_u = cm_expl_f_flow.get_trimmed_velocity_array()\n",
     "ps.plot.vector_field_magnitude(cm_expl_f_u[30,:,:,:])\n",
@@ -461,11 +452,11 @@
      "output_type": "execute_result",
      "data": {
       "text/plain": [
-       "<matplotlib.colorbar.Colorbar at 0x7faa506476a0>"
+       "<matplotlib.colorbar.Colorbar at 0x7fd99ddf0e20>"
       ]
      },
      "metadata": {},
-     "execution_count": 22
+     "execution_count": 16
     },
     {
      "output_type": "display_data",
@@ -484,7 +475,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 17,
    "source": [
     "assert_allclose(cm_expl_f_u, srt_u, rtol=1, atol=1e-4)\n",
     "assert_allclose(cm_expl_f_u, cm_impl_f_u, rtol=1, atol=1e-4)"
diff --git a/lbmpy_tests/test_compiled_in_boundaries.ipynb b/lbmpy_tests/test_compiled_in_boundaries.ipynb
index 3ea3e793df5ad8b371c39515e4968d09369197b3..97a0cbfd822c08941b3f9ed6bd093c169391064a 100644
--- a/lbmpy_tests/test_compiled_in_boundaries.ipynb
+++ b/lbmpy_tests/test_compiled_in_boundaries.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 8,
    "source": [
     "from lbmpy.session import *\n",
     "from lbmpy.boundaries.boundaries_in_kernel import update_rule_with_push_boundaries\n",
@@ -22,7 +22,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 9,
    "source": [
     "domain_size = (32, 32, 32)\n",
     "relaxation_rate = 1.8\n",
@@ -34,7 +34,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 10,
    "source": [
     "dh = create_data_handling(domain_size, default_target='cpu')\n",
     "pdfs = dh.add_array('pdfs', values_per_cell=19)\n",
@@ -46,7 +46,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 11,
    "source": [
     "boundaries = OrderedDict((\n",
     "    ((0, 1, 0), UBB([lid_velocity, 0, 0])),    \n",
@@ -65,7 +65,7 @@
     "getter_assignments = macroscopic_values_getter(update_rule_aa_even.method, velocity=u.center_vector,\n",
     "                                               pdfs=pdfs, density=None,\n",
     "                                               streaming_pattern=streaming_pattern, \n",
-    "                                               timestep=Timestep.EVEN)\n",
+    "                                               previous_timestep=Timestep.EVEN)\n",
     "\n",
     "getter_kernel = ps.create_kernel(getter_assignments, target=dh.default_target).compile()\n",
     "even_kernel = ps.create_kernel(update_rule_aa_even, target=dh.default_target, ghost_layers=1).compile()\n",
@@ -76,7 +76,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 12,
    "source": [
     "def init():\n",
     "    dh.fill(pdfs.name, 0, ghost_layers=True)\n",
@@ -95,7 +95,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 13,
    "source": [
     "init()\n",
     "aa_time_loop(time_steps)\n",
@@ -108,11 +108,11 @@
      "output_type": "execute_result",
      "data": {
       "text/plain": [
-       "<matplotlib.colorbar.Colorbar at 0x7f7c316778e0>"
+       "<matplotlib.colorbar.Colorbar at 0x7f0cfc8f5b50>"
       ]
      },
      "metadata": {},
-     "execution_count": 10
+     "execution_count": 13
     },
     {
      "output_type": "display_data",
@@ -138,7 +138,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 14,
    "source": [
     "ldc = create_lid_driven_cavity(domain_size, relaxation_rate=relaxation_rate, lid_velocity=lid_velocity)\n",
     "ldc.run(time_steps)\n",
@@ -152,11 +152,11 @@
      "output_type": "execute_result",
      "data": {
       "text/plain": [
-       "<matplotlib.colorbar.Colorbar at 0x7f7c30fd9d60>"
+       "<matplotlib.colorbar.Colorbar at 0x7f0cfca3ceb0>"
       ]
      },
      "metadata": {},
-     "execution_count": 11
+     "execution_count": 14
     },
     {
      "output_type": "display_data",