Data from: A Shifted Boundary Method for the compressible Euler equations

The Shifted Boundary Method (SBM) is applied to compressible Euler flows, with and without shock discontinuities. The SBM belongs to the class of unfitted (or immersed, or embedded) finite element methods and avoids integration over cut cells (and the associated implementation/stability issues) by reformulating the original boundary value problem over a surrogate (approximate) computational domain. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. We specifically discuss the advantages the proposed method offers in avoiding spurious numerical artifacts in two scenarios: (a) when curved boundaries are represented by body-fitted polygonal approximations and (b) when the Kutta condition needs to be imposed in immersed simulations of airfoils. An extensive suite of numerical tests is included. The dataset contains numerical results related to all numerical examples in the paper. It includes information of the software that is used to generate the data, all necessary configuration files to generate the dataset using the software, as well as the numerical solution files. Matlab scripts and Paraview scripts used to generate the figures in the paper are also included.

Dr. Scovazzi is supported by the NSF grants DMS-2207164 and DMS-2409919. Dr. Zeng is supported by the NSF grant DMS-2302080. The computation is performed on a HPC cluster funded under the ARO DURIP grant W911NF1510382.