New interpolation technique for the CIP method on curvilinear coordinates

Authors:
Nobuyoshi Fujimatsu;Kojiro Suzuki
Affiliations:
Department of Mechanical Science and Engineering, Aoyama Gakuin University, 5-10-1 Kobuchi, Sagamihara, Kanagawa 229-8558, Japan;Department of Advanced Energy, Graduate School of Frontier Sciences, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 227-8561, Japan
Venue:
Journal of Computational Physics
Year:
2010

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Abstract

We propose a new interpolation technique for the CIP method applied to curvilinear coordinates. The CIP method can hardly maintain third-order accuracy on curvilinear coordinates. The reason for the degeneracy in accuracies has not been discussed in detail. This paper reveals the problems of the CIP method on curvilinear coordinates and presents an improved CIP method to solve the advection equation accurately. The features of the presented method are: (1) the metric computation on the upwind stencil is defined in the same manner as in the advection phase of the CIP method; and (2) gradient values in the physical domain in the computation on the curvilinear coordinates are used. Various test problems show that the improved CIP method has approximate third-order accuracy.