Download or read book High-order, Robust Multidimensional Summation-by-parts Discretizations Applicable to Hp-adaptive Curvilinear Grids written by Siavosh Shadpey and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this thesis is on the development of high-order semi-discrete methods for the Euler equations that are applicable to non-conforming curvilinear grids arising from h-, p-, and hp-refinement. First, we present a method stable for linear differential equations. Second, we present two schemes stable for nonlinear differential equations. These two methods differ in the coupling procedure of neighbouring elements in a mesh: one couples them in a pointwise manner, while the other in a skew-symmetric manner. Finally, we present a fourth scheme which is numerically robust and discretely mimics the kinetic energy equation - an attractive property for simulating turbulent flows. The conservation, accuracy, and stability properties of the methods are first theoretically proven and then numerically verified. Furthermore, preliminary studies comparing all four methods in terms of robustness and computational efficiency are provided.