diff --git a/sbp/src/operators.rs b/sbp/src/operators.rs
index 70d8fea..4aa79ef 100644
--- a/sbp/src/operators.rs
+++ b/sbp/src/operators.rs
@@ -169,6 +169,72 @@ pub(crate) fn diff_op_1d(
     }
 }
 
+#[inline(always)]
+pub(crate) fn diff_op_row(
+    block: &[&[Float]],
+    diag: &[Float],
+    symmetric: bool,
+    is_h2: bool,
+    prev: ArrayView2<Float>,
+    mut fut: ArrayViewMut2<Float>,
+) {
+    assert_eq!(prev.shape(), fut.shape());
+    let nx = prev.shape()[1];
+    assert!(nx >= 2 * block.len());
+
+    assert_eq!(prev.strides()[1], 1);
+    assert_eq!(fut.strides()[1], 1);
+
+    let dx = if is_h2 {
+        1.0 / (nx - 2) as Float
+    } else {
+        1.0 / (nx - 1) as Float
+    };
+    let idx = 1.0 / dx;
+
+    for (prev, mut fut) in prev
+        .axis_iter(ndarray::Axis(0))
+        .zip(fut.axis_iter_mut(ndarray::Axis(0)))
+    {
+        let prev = prev.as_slice().unwrap();
+        let fut = fut.as_slice_mut().unwrap();
+
+        for (bl, f) in block.iter().zip(fut.iter_mut()) {
+            let diff = bl
+                .iter()
+                .zip(prev.iter())
+                .map(|(x, y)| x * y)
+                .sum::<Float>();
+            *f = diff * idx;
+        }
+
+        // The window needs to be aligned to the diagonal elements,
+        // based on the block size
+        let window_elems_to_skip = block.len() - ((diag.len() - 1) / 2);
+
+        for (window, f) in prev
+            .windows(diag.len())
+            .into_iter()
+            .skip(window_elems_to_skip)
+            .zip(fut.iter_mut().skip(block.len()))
+            .take(nx - 2 * block.len())
+        {
+            let diff = diag.iter().zip(window).map(|(&x, &y)| x * y).sum::<Float>();
+            *f = diff * idx;
+        }
+
+        for (bl, f) in block.iter().zip(fut.iter_mut().rev()) {
+            let diff = bl
+                .iter()
+                .zip(prev.iter().rev())
+                .map(|(x, y)| x * y)
+                .sum::<Float>();
+
+            *f = idx * if symmetric { diff } else { -diff };
+        }
+    }
+}
+
 mod upwind4;
 pub use upwind4::Upwind4;
 mod upwind9;
diff --git a/sbp/src/operators/traditional4.rs b/sbp/src/operators/traditional4.rs
index e1018c6..2221966 100644
--- a/sbp/src/operators/traditional4.rs
+++ b/sbp/src/operators/traditional4.rs
@@ -1,6 +1,6 @@
-use super::*;
+use super::{diff_op_row, SbpOperator1d, SbpOperator2d};
 use crate::Float;
-use ndarray::{ArrayView1, ArrayViewMut1};
+use ndarray::{ArrayView1, ArrayView2, ArrayViewMut1, ArrayViewMut2};
 
 #[derive(Debug, Copy, Clone)]
 pub struct SBP4;
@@ -33,6 +33,26 @@ impl SbpOperator1d for SBP4 {
     }
 }
 
+impl<SBP: SbpOperator1d> SbpOperator2d for (&SBP, &SBP4) {
+    fn diffxi(&self, prev: ArrayView2<Float>, mut fut: ArrayViewMut2<Float>) {
+        assert_eq!(prev.shape(), fut.shape());
+        assert!(prev.shape()[1] >= 2 * SBP4::BLOCK.len());
+
+        match (prev.strides(), fut.strides()) {
+            ([_, 1], [_, 1]) => {
+                diff_op_row(SBP4::BLOCK, SBP4::DIAG, false, false, prev, fut);
+            }
+            ([_, _], [_, _]) => {
+                // Fallback, work row by row
+                for (r0, r1) in prev.outer_iter().zip(fut.outer_iter_mut()) {
+                    SBP4.diff(r0, r1);
+                }
+            }
+            _ => unreachable!("Should only be two elements in the strides vectors"),
+        }
+    }
+}
+
 #[test]
 fn test_trad4() {
     use super::testing::*;
diff --git a/sbp/src/operators/traditional8.rs b/sbp/src/operators/traditional8.rs
index 84ec3ab..062d134 100644
--- a/sbp/src/operators/traditional8.rs
+++ b/sbp/src/operators/traditional8.rs
@@ -1,6 +1,6 @@
-use super::*;
+use super::{diff_op_row, SbpOperator1d, SbpOperator2d};
 use crate::Float;
-use ndarray::{ArrayView1, ArrayViewMut1};
+use ndarray::{ArrayView1, ArrayView2, ArrayViewMut1, ArrayViewMut2};
 
 #[derive(Debug, Copy, Clone)]
 pub struct SBP8;
@@ -37,6 +37,26 @@ impl SbpOperator1d for SBP8 {
     }
 }
 
+impl<SBP: SbpOperator1d> SbpOperator2d for (&SBP, &SBP8) {
+    fn diffxi(&self, prev: ArrayView2<Float>, mut fut: ArrayViewMut2<Float>) {
+        assert_eq!(prev.shape(), fut.shape());
+        assert!(prev.shape()[1] >= 2 * SBP8::BLOCK.len());
+
+        match (prev.strides(), fut.strides()) {
+            ([_, 1], [_, 1]) => {
+                diff_op_row(SBP8::BLOCK, SBP8::DIAG, false, false, prev, fut);
+            }
+            ([_, _], [_, _]) => {
+                // Fallback, work row by row
+                for (r0, r1) in prev.outer_iter().zip(fut.outer_iter_mut()) {
+                    SBP8.diff(r0, r1);
+                }
+            }
+            _ => unreachable!("Should only be two elements in the strides vectors"),
+        }
+    }
+}
+
 #[test]
 fn test_trad8() {
     use super::testing::*;
diff --git a/sbp/src/operators/upwind4.rs b/sbp/src/operators/upwind4.rs
index 42a958c..6e9afb5 100644
--- a/sbp/src/operators/upwind4.rs
+++ b/sbp/src/operators/upwind4.rs
@@ -1,4 +1,4 @@
-use super::*;
+use super::{SbpOperator1d, SbpOperator2d, UpwindOperator1d, UpwindOperator2d};
 use crate::Float;
 use ndarray::{ArrayView1, ArrayView2, ArrayViewMut1, ArrayViewMut2, Axis};
 
@@ -284,7 +284,7 @@ impl SbpOperator1d for Upwind4 {
     }
 }
 
-impl<SBP: SbpOperator1d> SbpOperator2d for (&Upwind4, &SBP) {
+impl<SBP: SbpOperator1d> SbpOperator2d for (&SBP, &Upwind4) {
     fn diffxi(&self, prev: ArrayView2<Float>, mut fut: ArrayViewMut2<Float>) {
         assert_eq!(prev.shape(), fut.shape());
         assert!(prev.shape()[1] >= 2 * Upwind4::BLOCK.len());
@@ -405,7 +405,7 @@ impl UpwindOperator1d for Upwind4 {
     }
 }
 
-impl<SBP: UpwindOperator1d> UpwindOperator2d for (&Upwind4, &SBP) {
+impl<UO: UpwindOperator1d> UpwindOperator2d for (&UO, &Upwind4) {
     fn dissxi(&self, prev: ArrayView2<Float>, mut fut: ArrayViewMut2<Float>) {
         assert_eq!(prev.shape(), fut.shape());
         assert!(prev.shape()[1] >= 2 * Upwind4::BLOCK.len());
diff --git a/sbp/src/operators/upwind4h2.rs b/sbp/src/operators/upwind4h2.rs
index ede6b04..a8d3dd3 100644
--- a/sbp/src/operators/upwind4h2.rs
+++ b/sbp/src/operators/upwind4h2.rs
@@ -1,6 +1,6 @@
-use super::*;
+use super::{diff_op_row, SbpOperator1d, SbpOperator2d, UpwindOperator1d, UpwindOperator2d};
 use crate::Float;
-use ndarray::{ArrayView1, ArrayViewMut1};
+use ndarray::{ArrayView1, ArrayView2, ArrayViewMut1, ArrayViewMut2};
 
 #[derive(Debug, Copy, Clone)]
 pub struct Upwind4h2;
@@ -49,6 +49,53 @@ impl SbpOperator1d for Upwind4h2 {
     }
 }
 
+impl<SBP: SbpOperator1d> SbpOperator2d for (&SBP, &Upwind4h2) {
+    fn diffxi(&self, prev: ArrayView2<Float>, mut fut: ArrayViewMut2<Float>) {
+        assert_eq!(prev.shape(), fut.shape());
+        assert!(prev.shape()[1] >= 2 * Upwind4h2::BLOCK.len());
+
+        match (prev.strides(), fut.strides()) {
+            ([_, 1], [_, 1]) => {
+                diff_op_row(Upwind4h2::BLOCK, Upwind4h2::DIAG, false, true, prev, fut);
+            }
+            ([_, _], [_, _]) => {
+                // Fallback, work row by row
+                for (r0, r1) in prev.outer_iter().zip(fut.outer_iter_mut()) {
+                    Upwind4h2.diff(r0, r1);
+                }
+            }
+            _ => unreachable!("Should only be two elements in the strides vectors"),
+        }
+    }
+}
+
+impl<UO: UpwindOperator1d> UpwindOperator2d for (&UO, &Upwind4h2) {
+    fn dissxi(&self, prev: ArrayView2<Float>, mut fut: ArrayViewMut2<Float>) {
+        assert_eq!(prev.shape(), fut.shape());
+        assert!(prev.shape()[1] >= 2 * Upwind4h2::BLOCK.len());
+
+        match (prev.strides(), fut.strides()) {
+            ([_, 1], [_, 1]) => {
+                diff_op_row(
+                    Upwind4h2::DISS_BLOCK,
+                    Upwind4h2::DISS_DIAG,
+                    true,
+                    true,
+                    prev,
+                    fut,
+                );
+            }
+            ([_, _], [_, _]) => {
+                // Fallback, work row by row
+                for (r0, r1) in prev.outer_iter().zip(fut.outer_iter_mut()) {
+                    Upwind4h2.diss(r0, r1);
+                }
+            }
+            _ => unreachable!("Should only be two elements in the strides vectors"),
+        }
+    }
+}
+
 #[test]
 fn upwind4h2_test() {
     let nx = 20;
diff --git a/sbp/src/operators/upwind9.rs b/sbp/src/operators/upwind9.rs
index f5c775d..cb9abaf 100644
--- a/sbp/src/operators/upwind9.rs
+++ b/sbp/src/operators/upwind9.rs
@@ -1,6 +1,6 @@
-use super::*;
+use super::{diff_op_row, SbpOperator1d, SbpOperator2d, UpwindOperator1d, UpwindOperator2d};
 use crate::Float;
-use ndarray::{ArrayView1, ArrayViewMut1};
+use ndarray::{ArrayView1, ArrayView2, ArrayViewMut1, ArrayViewMut2};
 
 #[derive(Debug, Copy, Clone)]
 pub struct Upwind9;
@@ -54,6 +54,26 @@ impl SbpOperator1d for Upwind9 {
     }
 }
 
+impl<SBP: SbpOperator1d> SbpOperator2d for (&SBP, &Upwind9) {
+    fn diffxi(&self, prev: ArrayView2<Float>, mut fut: ArrayViewMut2<Float>) {
+        assert_eq!(prev.shape(), fut.shape());
+        assert!(prev.shape()[1] >= 2 * Upwind9::BLOCK.len());
+
+        match (prev.strides(), fut.strides()) {
+            ([_, 1], [_, 1]) => {
+                diff_op_row(Upwind9::BLOCK, Upwind9::DIAG, false, false, prev, fut);
+            }
+            ([_, _], [_, _]) => {
+                // Fallback, work row by row
+                for (r0, r1) in prev.outer_iter().zip(fut.outer_iter_mut()) {
+                    Upwind9.diff(r0, r1);
+                }
+            }
+            _ => unreachable!("Should only be two elements in the strides vectors"),
+        }
+    }
+}
+
 impl UpwindOperator1d for Upwind9 {
     fn diss(&self, prev: ArrayView1<Float>, fut: ArrayViewMut1<Float>) {
         super::diff_op_1d(Self::DISS_BLOCK, Self::DISS_DIAG, true, false, prev, fut)
@@ -64,6 +84,33 @@ impl UpwindOperator1d for Upwind9 {
     }
 }
 
+impl<UO: UpwindOperator1d> UpwindOperator2d for (&UO, &Upwind9) {
+    fn dissxi(&self, prev: ArrayView2<Float>, mut fut: ArrayViewMut2<Float>) {
+        assert_eq!(prev.shape(), fut.shape());
+        assert!(prev.shape()[1] >= 2 * Upwind9::BLOCK.len());
+
+        match (prev.strides(), fut.strides()) {
+            ([_, 1], [_, 1]) => {
+                diff_op_row(
+                    Upwind9::DISS_BLOCK,
+                    Upwind9::DISS_DIAG,
+                    true,
+                    false,
+                    prev,
+                    fut,
+                );
+            }
+            ([_, _], [_, _]) => {
+                // Fallback, work row by row
+                for (r0, r1) in prev.outer_iter().zip(fut.outer_iter_mut()) {
+                    Upwind9.diss(r0, r1);
+                }
+            }
+            _ => unreachable!("Should only be two elements in the strides vectors"),
+        }
+    }
+}
+
 #[test]
 fn test_upwind9() {
     use super::testing::*;
diff --git a/sbp/src/operators/upwind9h2.rs b/sbp/src/operators/upwind9h2.rs
index 51def84..a070893 100644
--- a/sbp/src/operators/upwind9h2.rs
+++ b/sbp/src/operators/upwind9h2.rs
@@ -1,6 +1,6 @@
-use super::*;
+use super::{diff_op_row, SbpOperator1d, SbpOperator2d, UpwindOperator1d, UpwindOperator2d};
 use crate::Float;
-use ndarray::{ArrayView1, ArrayViewMut1};
+use ndarray::{ArrayView1, ArrayView2, ArrayViewMut1, ArrayViewMut2};
 
 #[derive(Debug, Copy, Clone)]
 pub struct Upwind9h2;
@@ -57,6 +57,26 @@ impl SbpOperator1d for Upwind9h2 {
     }
 }
 
+impl<SBP: SbpOperator1d> SbpOperator2d for (&SBP, &Upwind9h2) {
+    fn diffxi(&self, prev: ArrayView2<Float>, mut fut: ArrayViewMut2<Float>) {
+        assert_eq!(prev.shape(), fut.shape());
+        assert!(prev.shape()[1] >= 2 * Upwind9h2::BLOCK.len());
+
+        match (prev.strides(), fut.strides()) {
+            ([_, 1], [_, 1]) => {
+                diff_op_row(Upwind9h2::BLOCK, Upwind9h2::DIAG, false, true, prev, fut);
+            }
+            ([_, _], [_, _]) => {
+                // Fallback, work row by row
+                for (r0, r1) in prev.outer_iter().zip(fut.outer_iter_mut()) {
+                    Upwind9h2.diff(r0, r1);
+                }
+            }
+            _ => unreachable!("Should only be two elements in the strides vectors"),
+        }
+    }
+}
+
 #[test]
 fn upwind9h2_test() {
     let nx = 30;
@@ -90,3 +110,30 @@ impl UpwindOperator1d for Upwind9h2 {
         self
     }
 }
+
+impl<UO: UpwindOperator1d> UpwindOperator2d for (&UO, &Upwind9h2) {
+    fn dissxi(&self, prev: ArrayView2<Float>, mut fut: ArrayViewMut2<Float>) {
+        assert_eq!(prev.shape(), fut.shape());
+        assert!(prev.shape()[1] >= 2 * Upwind9h2::BLOCK.len());
+
+        match (prev.strides(), fut.strides()) {
+            ([_, 1], [_, 1]) => {
+                diff_op_row(
+                    Upwind9h2::DISS_BLOCK,
+                    Upwind9h2::DISS_DIAG,
+                    true,
+                    true,
+                    prev,
+                    fut,
+                );
+            }
+            ([_, _], [_, _]) => {
+                // Fallback, work row by row
+                for (r0, r1) in prev.outer_iter().zip(fut.outer_iter_mut()) {
+                    Upwind9h2.diss(r0, r1);
+                }
+            }
+            _ => unreachable!("Should only be two elements in the strides vectors"),
+        }
+    }
+}