diff --git a/foamlib/_cases/_async.py b/foamlib/_cases/_async.py
index dae4011..83f7117 100644
--- a/foamlib/_cases/_async.py
+++ b/foamlib/_cases/_async.py
@@ -3,7 +3,7 @@
 import os
 import sys
 from contextlib import asynccontextmanager
-from typing import Any, Callable, Optional, TypeVar, Union
+from typing import Any, Callable, Optional, TypeVar, Union, overload
 
 if sys.version_info >= (3, 9):
     from collections.abc import (
@@ -23,6 +23,8 @@
 
 import aioshutil
 
+from .._files import FoamFieldFile
+from ._base import FoamCaseBase
 from ._run import FoamCaseRunBase
 from ._subprocess import run_async
 from ._util import ValuedGenerator, awaitableasynccontextmanager
@@ -42,6 +44,20 @@ class AsyncFoamCase(FoamCaseRunBase):
     :param path: The path to the case directory.
     """
 
+    class TimeDirectory(FoamCaseRunBase.TimeDirectory):
+        @property
+        def _case(self) -> "AsyncFoamCase":
+            return AsyncFoamCase(self.path.parent)
+
+        async def cell_centers(self) -> FoamFieldFile:
+            """Write and return the cell centers."""
+            calls = ValuedGenerator(self._cell_centers_calls())
+
+            for coro in calls:
+                await coro
+
+            return calls.value
+
     max_cpus = multiprocessing.cpu_count()
     """
     Maximum number of CPUs to use for running `AsyncFoamCase`s concurrently. Defaults to the number of CPUs on the system.
@@ -106,6 +122,23 @@ async def clean(self, *, check: bool = False) -> None:
         for coro in self._clean_calls(check=check):
             await coro
 
+    @overload
+    def __getitem__(
+        self, index: Union[int, float, str]
+    ) -> "AsyncFoamCase.TimeDirectory": ...
+
+    @overload
+    def __getitem__(self, index: slice) -> Sequence["AsyncFoamCase.TimeDirectory"]: ...
+
+    def __getitem__(
+        self, index: Union[int, slice, float, str]
+    ) -> Union["AsyncFoamCase.TimeDirectory", Sequence["AsyncFoamCase.TimeDirectory"]]:
+        ret = super().__getitem__(index)
+        if isinstance(ret, FoamCaseBase.TimeDirectory):
+            return AsyncFoamCase.TimeDirectory(ret)
+        else:
+            return [AsyncFoamCase.TimeDirectory(r) for r in ret]
+
     async def run(
         self,
         cmd: Optional[Union[Sequence[Union[str, "os.PathLike[str]"]], str]] = None,
diff --git a/foamlib/_cases/_base.py b/foamlib/_cases/_base.py
index b86769f..bec3307 100644
--- a/foamlib/_cases/_base.py
+++ b/foamlib/_cases/_base.py
@@ -40,6 +40,10 @@ class TimeDirectory(Set[FoamFieldFile]):
         def __init__(self, path: Union["os.PathLike[str]", str]):
             self.path = Path(path).absolute()
 
+        @property
+        def _case(self) -> "FoamCaseBase":
+            return FoamCaseBase(self.path.parent)
+
         @property
         def time(self) -> float:
             """The time that corresponds to this directory."""
@@ -58,7 +62,7 @@ def __getitem__(self, key: str) -> FoamFieldFile:
 
         def __contains__(self, obj: object) -> bool:
             if isinstance(obj, FoamFieldFile):
-                return obj.path.parent == self.path
+                return obj.path.parent == self.path and obj.path.is_file()
             elif isinstance(obj, str):
                 return (self.path / obj).is_file() or (
                     self.path / f"{obj}.gz"
diff --git a/foamlib/_cases/_run.py b/foamlib/_cases/_run.py
index 2d5ba95..e2c2098 100644
--- a/foamlib/_cases/_run.py
+++ b/foamlib/_cases/_run.py
@@ -40,11 +40,34 @@
 else:
     from typing_extensions import Self
 
+from .._files import FoamFieldFile
 from ._base import FoamCaseBase
 from ._subprocess import DEVNULL, STDOUT
 
 
 class FoamCaseRunBase(FoamCaseBase):
+    class TimeDirectory(FoamCaseBase.TimeDirectory):
+        @abstractmethod
+        def cell_centers(
+            self,
+        ) -> Union[FoamFieldFile, Coroutine[None, None, FoamFieldFile]]:
+            raise NotImplementedError
+
+        @property
+        @abstractmethod
+        def _case(self) -> "FoamCaseRunBase":
+            raise NotImplementedError
+
+        def _cell_centers_calls(self) -> Generator[Any, None, FoamFieldFile]:
+            ret = self["C"]
+
+            if ret not in self:
+                yield self._case.run(
+                    ["postProcess", "-func", "writeCellCentres", "-time", self.name]
+                )
+
+            return ret
+
     def __delitem__(self, key: Union[int, float, str]) -> None:
         shutil.rmtree(self[key].path)
 
diff --git a/foamlib/_cases/_sync.py b/foamlib/_cases/_sync.py
index 4208631..2c95ffb 100644
--- a/foamlib/_cases/_sync.py
+++ b/foamlib/_cases/_sync.py
@@ -3,13 +3,7 @@
 import sys
 from pathlib import Path
 from types import TracebackType
-from typing import (
-    Any,
-    Callable,
-    Optional,
-    Type,
-    Union,
-)
+from typing import Any, Callable, Optional, Type, Union, overload
 
 if sys.version_info >= (3, 9):
     from collections.abc import Collection, Sequence
@@ -21,6 +15,8 @@
 else:
     from typing_extensions import Self
 
+from .._files import FoamFieldFile
+from ._base import FoamCaseBase
 from ._run import FoamCaseRunBase
 from ._subprocess import run_sync
 from ._util import ValuedGenerator
@@ -37,6 +33,22 @@ class FoamCase(FoamCaseRunBase):
     :param path: The path to the case directory.
     """
 
+    class TimeDirectory(FoamCaseRunBase.TimeDirectory):
+        @property
+        def _case(self) -> "FoamCase":
+            return FoamCase(self.path.parent)
+
+        def cell_centers(self) -> FoamFieldFile:
+            """Write and return the cell centers."""
+            calls = ValuedGenerator(self._cell_centers_calls())
+
+            for _ in calls:
+                pass
+
+            print(calls.value)
+
+            return calls.value
+
     def __init__(self, path: Union["os.PathLike[str]", str] = Path()):
         super().__init__(path)
 
@@ -67,6 +79,23 @@ def _copytree(
     ) -> None:
         shutil.copytree(src, dest, symlinks=symlinks, ignore=ignore)
 
+    @overload
+    def __getitem__(
+        self, index: Union[int, float, str]
+    ) -> "FoamCase.TimeDirectory": ...
+
+    @overload
+    def __getitem__(self, index: slice) -> Sequence["FoamCase.TimeDirectory"]: ...
+
+    def __getitem__(
+        self, index: Union[int, slice, float, str]
+    ) -> Union["FoamCase.TimeDirectory", Sequence["FoamCase.TimeDirectory"]]:
+        ret = super().__getitem__(index)
+        if isinstance(ret, FoamCaseBase.TimeDirectory):
+            return FoamCase.TimeDirectory(ret)
+        else:
+            return [FoamCase.TimeDirectory(r) for r in ret]
+
     def __enter__(self) -> Self:
         return self
 
diff --git a/tests/test_cases/test_cavity.py b/tests/test_cases/test_cavity.py
index ea29dda..ec62ecf 100644
--- a/tests/test_cases/test_cavity.py
+++ b/tests/test_cases/test_cavity.py
@@ -56,3 +56,10 @@ def test_double_clean(cavity: FoamCase) -> None:
     cavity.clean()
     cavity.clean(check=True)
     cavity.run(parallel=False)
+
+
+def test_cell_centers(cavity: FoamCase) -> None:
+    cavity.block_mesh()
+    C = cavity[0].cell_centers()
+    assert isinstance(C.internal_field, list)
+    assert len(C.internal_field) == 400
diff --git a/tests/test_cases/test_cavity_async.py b/tests/test_cases/test_cavity_async.py
index f3b1bb6..151d74f 100644
--- a/tests/test_cases/test_cavity_async.py
+++ b/tests/test_cases/test_cavity_async.py
@@ -61,6 +61,14 @@ async def test_double_clean(cavity: AsyncFoamCase) -> None:
     await cavity.run(parallel=False)
 
 
+@pytest.mark.asyncio
+async def test_cell_centers(cavity: AsyncFoamCase) -> None:
+    await cavity.block_mesh()
+    C = await cavity[0].cell_centers()
+    assert isinstance(C.internal_field, list)
+    assert len(C.internal_field) == 400
+
+
 def test_map(cavity: AsyncFoamCase) -> None:
     async def f(x: Sequence[float]) -> float:
         async with cavity.clone() as clone: