| Author | Jared Crean, Kinshuk Panda, Anthony Ashley, Jason E. Hicken |
|---|---|
| Title | Investigation of Stabilization Methods for Multi-Dimensional Summation-by-parts Discretizations of the Euler Equations |
| Year | 2016 |
| Journal | 54th AIAA Aeorspace Sciences Meeting |
| Publisher | American Institute for Aeronautics and Astronautics |
| School | Rensselaer Polytechnic Institute |
| Abstract | We present an extensible Julia-based solver for the Euler equations that uses a summation- by-parts (SBP) discretization on unstructured triangular grids. While SBP operators have been used for tensor-product discretizations for some time, they have only recently been extended to simplices. Here we investigate the accuracy and stability properties of simplex- based SBP discretizations of the Euler equations. Non-linear stabilization is a particular concern in this context, because SBP operators are nearly skew-symmetric. We consider an edge-based stabilization method, which has previously been used for advection-diffusion- reaction problems and the Oseen equations, and apply it to the Euler equations. Addi- tionally, we discuss how the development of our software has been facilitated by the use of Julia, a new, fast, dynamic programming language designed for technical computing. By taking advantage of Julia’s unique capabilities, code that is both efficient and generic can be written, enhancing the extensibility of the solver. |
| DOI Link | 10.2514/6.2016-1328 |