2. Given that $A, B, C, D$ are four non-coplanar points on a sphere, and $A B=B C=A D=1, B D=A C=\sqrt{2}, B C \perp$ $A D$, then the volume of the sphere is $\qquad$ .
As shown in the figure, by supplementing the tetrahedron $D-ABC$ to form a cube, we can see that the diameter of its circumscribed sphere is $\sqrt{3}$, so the volume of this sphere is
$$
V=\frac{4}{3} \pi \cdot\left(\frac{\sqrt{3}}{2}\right)^{3}=\frac{\sqrt{3}}{2} \pi
$$