The piecewise-parabolic method in curvilinear coordinates

Mathematics

Scientific paper

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Finite Difference Theory, Interpolation, Spherical Coordinates, Advection, Polynomials, Singularity (Mathematics)

Scientific paper

We derive interpolation formulae for a third-order finite difference method in curvilinear, orthogonal coordinate systems. These formulae serve as a supplement to Colella and Woodward's PPM scheme for problems where the coordinate origin is included in the computational domain. Numerical examples of the improved accuracy of the advection scheme near coordinate singularities are shown.

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