Compressible flows and gas dynamics

Exemplary topics

We investigate the problem of aerodynamic sound generation and propagation in modeled engineering shear flows. To date, neither phenomenon is fully understood, although regions with (constant) shear of velocity are ubiquitous in engineering flow systems. The definite understanding is of major importance when it comes, e.g., to the design process of turbojet engines, as noise regulations make it imperative to consider aeroacoustic properties to meet airworthiness requirements. In the acoustic realm, analyzing small amplitude perturbation dynamics yields the basic understanding. Thus, we initially analyze the linearized compressible Euler equations in the light of the breakthrough achieved by the hydrodynamic stability community in understanding shear flow phenomena in the 1990s. The methods involve Lie symmetry analysis, normal mode analysis and direct numerical simulations.

Contact: Yi Zhang, M.Sc.

Shock-capturing methods are essential in order to obtain robust and stable solutions for compressible flows with large Mach numbers, e.g. consider an airplane flying at supersonic speed. In such flow configurations, discontinuities of the physical quantities (e.g., shocks) can occur. Without the application of suitable techniques, we will not be able to calculate an accurate and non-oscillating high-order approximation. There are different approaches in literature, such as limiting and filtering approaches. In contrast, we employ a so-called artificial viscosity approach combined with a shock sensor in order to achieve a sharp sub-cell representation of the shock. This approach maintains the favourable properties of the DG method (high-order accuracy, cell-locality, efficiently parallelizable, applicable to arbitrary geometries).

Recently, we coupled this approach with an adaptive local time stepping strategy and an immersed boundary solver based on cut cells: Link to article

Contact: Markus Geisenhofer, M.Sc.

Goal of this project is to develop a high order Discontinuous Galerkin solver for compressible flows with immersed boundaries. Building blocks are a compressible Navier-Stokes solver based on the HLLC and SIPG flux formulations, which has been extensively verified and validated. Further, our cut cell approach, using the HMF quadrature rule to integrate over implicit given domains, is used to incorporate the immersed boundaries. The correctness of the solver has been verified and validated by various test cases in 2D. In addition, a new conservative local time stepping (LTS) formulation has been developed to alleviate the severe CFL restriction due to the existence of cut cells.

Contact: Stephan Krämer-Eis, M.Sc.

Within this projects, we are aiming at the development of novel numerical methods for compressible flows with moving immersed boundaries and/or interfaces. That is, we study flows where some part of the domain boundary is given implicitly via at the zero iso-contour of a level set function. This allows us to use simple meshes for the background geometry, even for complicated immersed geometries. Cells intersected by the zero level set are treated via special quadrature techniques, which allows us to keep the discretization almost as simple as for standard calculations.

Currently, we are foscussing on a extension to moving immersed boundaries. Here, classical splitting aproaches (move interface first, then calculate flow field) lead to sub-optimal schemes. We strive at alleviating this problem by employing new, “moving-mesh” time-integrators of higher order

Contact: Dr.-Ing. Björn Müller