Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  is devoted to the construction and analysis of a new smoothness index for WENO interpolation capable of dealing with corner discontinuities. The new smoothness index presented is initially developed for the point-value framework of Harten’s multiresolution. Even so, the ideas about how to extend the results to the cell-average framework are presented. The new smoothness index is inspired by the one proposed in Jiang and Shu (J Comput Phys 126(1):202–228, 1996). This index works very ll for jump discontinuities as it was originally designed for the context of conservation laws in order to deal with problems that contain shocks and complicated fluid-structure interactions. Even so, it is easy to check that the mentioned index does not provide an appropriate performance for corner discontinuities. Our aim is to rise the order of accuracy of WENO interpolation near corner discontinuities. In order to do so,  will modify the original smoothness index proposed by Jiang and Shu such that the discontinuities in the first derivative of the function contribute effectively to the index. The modification proposed will produce a variation in the ights of WENO when dealing with a corner, that do not appear when using the smoothness indexes proposed by Jiang and Shu. The variation in the ights induced by the modification of the smoothness index will allow adaption to corner discontinuities, maintaining the adaption to jumps provided by the original smoothness index proposed by Jiang and Shu. The strategy proposed in Arandiga et al. (SIAM J Numer Anal 49(2):893–915, 2011) can be adapted such that the accuracy is maintained near critical points at smooth zones.
['Sergio Amat', 'Juan Ruiz']
I am writing a research paper on a idea New WENO Smoothness Indicators Computationally Efficient in the Presence of Corner Discontinuities
[{"from": "human", "value": "I am writing a research paper on a idea New WENO Smoothness Indicators Computationally Efficient in the Presence of Corner Discontinuities"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  is devoted to the construction and analysis of a new smoothness index for WENO interpolation capable of dealing with corner discontinuities. The new smoothness index presented is initially developed for the point-value framework of Harten\u2019s multiresolution. Even so, the ideas about how to extend the results to the cell-average framework are presented. The new smoothness index is inspired by the one proposed in Jiang and Shu (J Comput Phys 126(1):202\u2013228, 1996). This index works very ll for jump discontinuities as it was originally designed for the context of conservation laws in order to deal with problems that contain shocks and complicated fluid-structure interactions. Even so, it is easy to check that the mentioned index does not provide an appropriate performance for corner discontinuities. Our aim is to rise the order of accuracy of WENO interpolation near corner discontinuities. In order to do so,  will modify the original smoothness index proposed by Jiang and Shu such that the discontinuities in the first derivative of the function contribute effectively to the index. The modification proposed will produce a variation in the ights of WENO when dealing with a corner, that do not appear when using the smoothness indexes proposed by Jiang and Shu. The variation in the ights induced by the modification of the smoothness index will allow adaption to corner discontinuities, maintaining the adaption to jumps provided by the original smoothness index proposed by Jiang and Shu. The strategy proposed in Arandiga et al. (SIAM J Numer Anal 49(2):893\u2013915, 2011) can be adapted such that the accuracy is maintained near critical points at smooth zones."}]