Colloquium announcement

Faculty of Engineering Technology

Department Engineering Fluid Dynamics
Master programme Mechanical Engineering

As part of his / her masterassignment

Bart Wissink

will hold a speech entitled:

Shock regularization with smoothness increasing accuracy conserving Dirac-delta polynomial kernels



Shocked turbulent flows appear in a wide range of technologies where mixing plays a crucial role, including supersonic and hypersonic combustion and explosions. For the numerical simulation of these complex flows high-resolution schemes are preferred as they offer the possibility to capture small scale flow features on relative coarse grids, thus requiring significantly less computational resources. High-resolution schemes for structured grids are well established. These methods however do not extend well to unstructured spectral meshes. Discontinuous spectral element methods offer the possibility to use unstructured grids for solving shocked turbulent flows in complex geometries. Shock capturing with these methods is however plagued by oscillations in the solution known as the Gibbs phenomena. A common technique for shock capturing in these methods is the use of slope-limiters. The use of limiters is computationally expensive. A cost-effective alternative is the use of artificial viscosity methods. There is however no formal proof of high-order resolution using this method.

A yet to be explored technique for shock capturing is the use of smoothness increasing accuracy conserving (SIAC) filters. This type of filter was developed to use as a postprocessor to improve results obtained in discontinuous spectral element methods. Recently, a regularization technique was developed for Dirac-delta source terms in hyperbolic equations. These high-order Dirac-delta functions are an excellent candidate for a kernel of a SIAC-like regularization and are used to develop filters in this work.

The developed filters are tested in the one-dimensional advection and Burgers’ equation and the one- and two-dimensional Euler equations. Though the main interest is to eventually apply these filters to discontinuous spectral element methods, a single domain spectral method is used as a first step. The filters prove to be effective in capturing shocks and discontinuities while preserving high-resolution away from the shock.