Application of the Discontinuous Galerkin Method to Wake Vortex Flows

Abstract

A code was developed that utilizes the discontinuous Galerkin method to solve the Euler equations while utilizing a modal arti cial viscosity sensor developed by Klockner [12]. The sensor was augmented for the purpose of this research so that it could be run more quickly as well as having a more robust adaptation to di erent problems and speci cally for this research the vortex burst problem. The sensor had a number of ops reduced from its calculation through the use of a di erent approach for creation of the modes. This new approach was based o of multiplying through by the Vandermonde matrix built from a one dimensional system instead of a three dimensional system. This was done by taking the cube of nodes for a cell and multiplying it by slices of data. The sensor was then made more robust by changing the value by which baseline decay model was added to the modes. The baseline decay model is needed to remove white noise from being sensed upon. Both these changes were re ected in examinations of routine test problems involving the Sod shock tube and the Kelvin-Helmholtz phenomena. With test cases validating the improvements to the sensor, the approach was then used against an element of wake vortex ow to show the sensor's robustness. Through plotting the pressure, vorticity, and total kinetic energy the test case was validated against previous research.