Implicit CIP (Cubic-Interpolated Propagation) method in two dimensions

An implicit cubic-interpolated propagation (CIP) method for 2D hyperbolic equations is developed. By reconsidering the derivation of a 1D implicit solver, extension to multi-dimensions becomes straightforward. The two-dimensional form is numerically solved by two different approaches, that is, by adopting a directionalsplitting technique and by deriving an implicit formulation directly without using directional-splitting. We found that higher order correction terms proportional to Δt² are required in a non-splitting case, while these terms are already included intrinsically in a splitting scheme. Furthermore, we have pointed out that the determination of a profile becomes quite important for implicit calculation, and the interpolation function must be carefully selected to obtain a symmetric profile.