The capabilities of Summation-by- Parts Operators for Non-linear Stability of Semi- discrete Schemes

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We provide an overview of the SBP technique and its applications for mimicking nonlinearly stable operators. We provide a short review of the SBP operators, non-linear stability with entropy stability. We follow the method of line approach in developing this work. The Burgers equation is used as an example for the development of an entropy stable semi discretizate scheme. Then, a semi-discrete entropy stable implementation of the Eulerian model is presented as an application of non-linear stability in computational fluid dynamics.