Implicit CIP (Cubic-Interpolated Propagation) Method in Two Dimensions.

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  • Implicit CIP Cubic-Interpolated Propaga

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Abstract

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 directional-splitting 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.

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