- 期刊
- OpenAccess
One-Dimensional Adaptive Grid Procedure via Conservative Monotone Interpolation
並列摘要
Monotone conditions of cubic and fourth order interpolations on one-dimensional adaptive grid procedures are examined in this study. Damping due to interpolation is found when the conservative interpolation is employed in the adaptive procedure. Adaptive limiters are designed to improve compressive characters of the linear, cubic, and fourth order interpolations, respectively. Although new monotone conditions are not as easily satisfied as the classical monotone condition for continuous curves, procedure is proven helpful in reducing the damping due to interpolation. One-dimensional numerical tests show that the linear interpolation with the adaptive limiter works very well in the high gradient region and fairly well in the smooth region in comparison to the cubic and fourth order interpolations. Because the boundary of monotone conditions of the fourth order interpolation method is too complicated to be directly applied, several approximations are made. Consequently, the resulting interpolation is more diffusive than the cubic interpolation. It seems that cubic interpolation provides the best result because it is similar to linear interpolation in the high gradient region and is only slightly worse than the fourth order interpolation in the smooth region.
延伸閱讀
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