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Author(s):
T. Aoki
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Title:
Interpolated Differential Operator (IDO) Scheme for Solving Partial Differential Equations
Date of publication:
Sep. 1996
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Key words:
Partial Differential Equation, Hermite Interpolation, Non-conservative form, Numerical Scheme
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Abstract:
We present a numerical scheme to apply to wide variety of partial differential equations (PDEs) in space and time. The scheme is based on high accurate interpolation of the profile for independent variables over a local area and repetitive differential operations by regarding PDEs as differential operators. We demonstrate that the scheme is applicable to all of hyperbolic, ellipsoidal and parabolic equations. The equations are solved in terms of the primitive independent variables, so that the scheme has flexibility for various type of equation including source terms. We find that the conservation holds accurate because of the high order scheme when we use a Hermite interpolation. The interface is found to be sharply described by adding an artificial viscosity term.
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