diff --git a/test/decoupled/2p/CMakeLists.txt b/test/decoupled/2p/CMakeLists.txt
index c9bb0db29529200ba4a65486c02d1d87ed20b907..1142cdace7bf3bb8be89833c54f002fb53df164f 100644
--- a/test/decoupled/2p/CMakeLists.txt
+++ b/test/decoupled/2p/CMakeLists.txt
@@ -65,9 +65,63 @@ add_dumux_test(test_mpfal2padaptive test_mpfa2p test_mpfa2p.cc
-ParameterFile ${CMAKE_CURRENT_SOURCE_DIR}/test_mpfa2p.input
-ModelType MPFALAdaptive)
-add_dumux_test(test_3d2p test_3d2p test_3d2p.cc
+add_dumux_test(test_3d2pfv test_3d2pfv test_3d2p.cc
${CMAKE_SOURCE_DIR}/bin/runTest.sh
${CMAKE_SOURCE_DIR}/bin/fuzzycomparevtu.py
- ${CMAKE_SOURCE_DIR}/test/references/test_3d2p-reference.vtu
- ${CMAKE_CURRENT_BINARY_DIR}/test_3d2p-00012.vtu
- ${CMAKE_CURRENT_BINARY_DIR}/test_3d2p)
+ ${CMAKE_SOURCE_DIR}/test/references/test_3d2pfv-reference.vtu
+ ${CMAKE_CURRENT_BINARY_DIR}/test_3d2pfv-00012.vtu
+ ${CMAKE_CURRENT_BINARY_DIR}/test_3d2pfv
+ -ParameterFile ${CMAKE_CURRENT_SOURCE_DIR}/test_3d2p.input
+ -Problem.OutputName test_3d2pfv
+ -ModelType FV)
+
+add_dumux_test(test_3d2pfvadaptive test_3d2pfvadaptive test_3d2p.cc
+ ${CMAKE_SOURCE_DIR}/bin/runTest.sh
+ ${CMAKE_SOURCE_DIR}/bin/fuzzycomparevtu.py
+ ${CMAKE_SOURCE_DIR}/test/references/test_3d2pfvadaptive-reference.vtu
+ ${CMAKE_CURRENT_BINARY_DIR}/test_3d2pfvadaptive-00012.vtu
+ ${CMAKE_CURRENT_BINARY_DIR}/test_3d2pfvadaptive
+ -ParameterFile ${CMAKE_CURRENT_SOURCE_DIR}/test_3d2p.input
+ -Problem.OutputName test_3d2pfvadaptive
+ -ModelType FVAdaptive)
+
+add_dumux_test(test_3d2pmimetic test_3d2pmimetic test_3d2p.cc
+ ${CMAKE_SOURCE_DIR}/bin/runTest.sh
+ ${CMAKE_SOURCE_DIR}/bin/fuzzycomparevtu.py
+ ${CMAKE_SOURCE_DIR}/test/references/test_3d2pmimetic-reference.vtu
+ ${CMAKE_CURRENT_BINARY_DIR}/test_3d2pmimetic-00012.vtu
+ ${CMAKE_CURRENT_BINARY_DIR}/test_3d2pmimetic
+ -ParameterFile ${CMAKE_CURRENT_SOURCE_DIR}/test_3d2p.input
+ -Problem.OutputName test_3d2pmimetic
+ -ModelType Mimetic)
+
+add_dumux_test(test_3d2pmimeticadaptive test_3d2pmimeticadaptive test_3d2p.cc
+ ${CMAKE_SOURCE_DIR}/bin/runTest.sh
+ ${CMAKE_SOURCE_DIR}/bin/fuzzycomparevtu.py
+ ${CMAKE_SOURCE_DIR}/test/references/test_3d2pmimeticadaptive-reference.vtu
+ ${CMAKE_CURRENT_BINARY_DIR}/test_3d2pmimeticadaptive-00012.vtu
+ ${CMAKE_CURRENT_BINARY_DIR}/test_3d2pmimeticadaptive
+ -ParameterFile ${CMAKE_CURRENT_SOURCE_DIR}/test_3d2p.input
+ -Problem.OutputName test_3d2pmimeticadaptive
+ -ModelType MimeticAdaptive)
+
+add_dumux_test(test_3d2pmpfal test_3d2pmpfal test_3d2p.cc
+ ${CMAKE_SOURCE_DIR}/bin/runTest.sh
+ ${CMAKE_SOURCE_DIR}/bin/fuzzycomparevtu.py
+ ${CMAKE_SOURCE_DIR}/test/references/test_3d2pmpfal-reference.vtu
+ ${CMAKE_CURRENT_BINARY_DIR}/test_3d2pmpfal-00012.vtu
+ ${CMAKE_CURRENT_BINARY_DIR}/test_3d2pmpfal
+ -ParameterFile ${CMAKE_CURRENT_SOURCE_DIR}/test_3d2p.input
+ -Problem.OutputName test_3d2pmpfal
+ -ModelType MPFAL)
+
+add_dumux_test(test_3d2pmpfaladaptive test_3d2pmpfaladaptive test_3d2p.cc
+ ${CMAKE_SOURCE_DIR}/bin/runTest.sh
+ ${CMAKE_SOURCE_DIR}/bin/fuzzycomparevtu.py
+ ${CMAKE_SOURCE_DIR}/test/references/test_3d2pmpfaladaptive-reference.vtu
+ ${CMAKE_CURRENT_BINARY_DIR}/test_3d2pmpfaladaptive-00012.vtu
+ ${CMAKE_CURRENT_BINARY_DIR}/test_3d2pmpfaladaptive
+ -ParameterFile ${CMAKE_CURRENT_SOURCE_DIR}/test_3d2p.input
+ -Problem.OutputName test_3d2pmpfaladaptive
+ -ModelType MPFALAdaptive)
+
diff --git a/test/references/test_3d2pfv-reference.vtu b/test/references/test_3d2pfv-reference.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..ed59d146e243f41ca8a751be70b9a1db9a540572
--- /dev/null
+++ b/test/references/test_3d2pfv-reference.vtu
@@ -0,0 +1,1117 @@
+<?xml version="1.0"?>
+<VTKFile type="UnstructuredGrid" version="0.1" byte_order="LittleEndian">
+ <UnstructuredGrid>
+ <Piece NumberOfCells="512" NumberOfPoints="729">
+ <CellData Scalars="wetting pressure" Vectors="wetting-velocity">
+ <DataArray type="Float32" Name="wetting pressure" NumberOfComponents="1" format="ascii">
+ 1.23805 1.17125 1.15816 1.18328 1.19897 1.16408 1.15381 1.1718 1.14493 1.1294 1.12664 1.14001
+ 1.14271 1.12839 1.12554 1.13809 1.13309 1.12172 1.11442 1.12549 1.13144 1.12051 1.1136 1.12407
+ 1.15743 1.14554 1.13486 1.14178 1.15243 1.14269 1.13274 1.1388 1.17498 1.15546 1.14755 1.15965
+ 1.15933 1.1474 1.14098 1.14927 1.13908 1.12645 1.12341 1.13477 1.13485 1.12379 1.1206 1.13071
+ 1.12837 1.11759 1.11259 1.12126 1.12434 1.11433 1.11185 1.11598 1.14553 1.13806 1.12899 1.13415
+ 1.13848 1.1327 1.12416 1.12877 1.12028 1.1144 1.11282 1.11806 1.11948 1.11332 1.1124 1.11664
+ 1.11226 1.11178 1.11145 1.11188 1.11194 1.11145 1.11106 1.11151 1.11118 1.1108 1.11001 1.11033
+ 1.11072 1.11032 1.10937 1.10975 1.11322 1.1119 1.11096 1.11184 1.11268 1.1115 1.11046 1.11144
+ 1.11778 1.1124 1.11184 1.11418 1.11479 1.11177 1.11119 1.11276 1.1114 1.11091 1.11043 1.1109
+ 1.11078 1.11027 1.10968 1.11019 1.10997 1.10951 1.10827 1.10873 1.10908 1.10854 1.10688 1.10749
+ 1.11205 1.11084 1.10959 1.11074 1.11145 1.11008 1.10857 1.10996 1.13069 1.12561 1.11625 1.12177
+ 1.12835 1.12388 1.11503 1.11881 1.11685 1.11229 1.11132 1.1134 1.11517 1.11188 1.11081 1.11288
+ 1.11242 1.11065 1.11033 1.11196 1.11188 1.11006 1.10968 1.1114 1.11484 1.11397 1.11332 1.11408
+ 1.11424 1.11339 1.11277 1.11353 1.12464 1.12013 1.11362 1.11519 1.11976 1.11487 1.11235 1.11314
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+ 1.11084 1.11006 1.10931 1.11002 1.11032 1.1094 1.10847 1.10935 1.1095 1.1092 1.10852 1.1088
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+ 1.10594 1.10309 1.10009 1.10402 1.10563 1.10253 1.09942 1.10375 1.10002 1.09759 1.09009 1.09507
+ 1.09903 1.09604 1.08692 1.09353 1.08828 1.07691 1.05483 1.08087 1.08557 1.06819 1.0203 1.07576
+ 1.10216 1.09674 1.09401 1.10088 1.1019 1.09588 1.09291 1.10063
+ </DataArray>
+ <DataArray type="Float32" Name="nonwetting pressure" NumberOfComponents="1" format="ascii">
+ 1.23805 1.17125 1.15816 1.18328 1.19897 1.16408 1.15381 1.1718 1.14493 1.1294 1.12664 1.14001
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+ </DataArray>
+ <DataArray type="Float32" Name="capillary pressure" NumberOfComponents="1" format="ascii">
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+ </DataArray>
+ <DataArray type="Float32" Name="wetting saturation" NumberOfComponents="1" format="ascii">
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+ 0.217929 0.2 0.2 0.2 0.200116 0.2 0.2 0.2 0.2 0.2 0.2 0.2
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+ 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
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+ 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
+ 0.2 0.2 0.2 0.2 0.69206 0.671421 0.654326 0.675497 0.640079 0.606402 0.559324 0.618742
+ 0.635486 0.475245 0.297311 0.603451 0.443541 0.204252 0.200017 0.289619 0.43531 0.201243 0.2 0.201905
+ 0.201065 0.2 0.2 0.2 0.650171 0.619806 0.416991 0.584935 0.545661 0.3458 0.200808 0.267857
+ 0.412634 0.273007 0.221338 0.321494 0.20057 0.200002 0.2 0.200031 0.2011 0.2 0.2 0.200006
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diff --git a/test/references/test_3d2pfvadaptive-reference.vtu b/test/references/test_3d2pfvadaptive-reference.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..1c72637b1591c42de8294f6faf9fc0551e3d075f
--- /dev/null
+++ b/test/references/test_3d2pfvadaptive-reference.vtu
@@ -0,0 +1,580 @@
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diff --git a/test/references/test_3d2pmimetic-reference.vtu b/test/references/test_3d2pmimetic-reference.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..7fcfd8741e480b00552f240b5c79afee0ee91b7f
--- /dev/null
+++ b/test/references/test_3d2pmimetic-reference.vtu
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diff --git a/test/references/test_3d2pmimeticadaptive-reference.vtu b/test/references/test_3d2pmimeticadaptive-reference.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..744f51d103d9017f2135d2c8454c417b8176eaed
--- /dev/null
+++ b/test/references/test_3d2pmimeticadaptive-reference.vtu
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diff --git a/test/references/test_3d2p-reference.vtu b/test/references/test_3d2pmpfal-reference.vtu
similarity index 100%
rename from test/references/test_3d2p-reference.vtu
rename to test/references/test_3d2pmpfal-reference.vtu
diff --git a/test/references/test_3d2pmpfaladaptive-reference.vtu b/test/references/test_3d2pmpfaladaptive-reference.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..987462de4d90454e92d29badacb5806747d22324
--- /dev/null
+++ b/test/references/test_3d2pmpfaladaptive-reference.vtu
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