Update BicubicInterpolation.C

Include ddy_dx1_dx2 mixed derivative in the sample2ndDerivative function

framework/src/utils/BicubicInterpolation.C

@@ -168,8 +168,27 @@ BicubicInterpolation::sample2ndDerivative(Real x1, Real x2, unsigned int deriv_v
     return sample_deriv;
   }
 
+  // Take mixed derivative along x1 and x2 axes
+  // Note: sum from i = 1 and j = 1 as the first terms are zero
+  else if (deriv_var == 3)
+  {
+    Real sample_deriv = 0.0;
+    for (const auto i : make_range(1, 4))
+      for (const auto j : make_range(1, 4))
+        sample_deriv += i * j * _bicubic_coeffs[x1l][x2l][i][j] * MathUtils::pow(t, i - 1) *
+                        MathUtils::pow(u, j - 1);
+
+    Real d1 = _x1[x1u] - _x1[x1l];
+    Real d2 = _x2[x2u] - _x2[x2l];
+
+    if (!MooseUtils::absoluteFuzzyEqual(d1, Real(0.0)) && !MooseUtils::absoluteFuzzyEqual(d2, Real(0.0)))
+      sample_deriv /= (d1 * d2);
+
+    return sample_deriv;
+  }
+
   else
-    mooseError("deriv_var must be either 1 or 2 in BicubicInterpolation");
+    mooseError("deriv_var must be either 1, 2 or 3 in BicubicInterpolation");
 }
 
 void