Abstract
An invariant finite difference scheme of the two-phase shallow water equations is extended to the two dimensional case. A two dimensional scheme is first proposed by using a locally one-dimensional scheme to guarantee the stability of the non-symmetric hyperbolic system. The proposed scheme loses the invariance of rotational transformations. To recover the invariance of rotational transformations, two schemes are averaged in which the order of one-dimensional calculations is different. The averaged scheme produces good numerical results.
