On Wednesday, 5 February 2020 at 11:00 Lea Miko Versbach will talk on the topic “Implicit DG solvers and multigrid preconditioners” 

Location: Gyrhofstraße 8a (Gebäude 158a), Room 1.105 (1st floor), 50931

Abstract: In this talk I will give an introduction to implicit DG solvers and the challenges which arise when solving the large nonlinear systems coming from the implicit temporal discretization. We will solve these system using a Jacobian-free Newton-Krylov method. The problem with this method is that the Krylov subspace method converges slowly for discretized PDEs. In order to speed up computations, we need to construct preconditioners. This can be done using iterative methods. Carefully constructed multigrid methods are cheap and effective preconditioners. I will explain more details about the construction of these preconditioners and show some numerical results. 

On Tuesday, 4 February 2020 at 11:00 Bernhard Müller will talk on the topic “Immersed Boundary Method for the Compressible Navier-Stokes Equations Using High Order Summation-By-Parts Operators” based on a joint work with M. Ehsan Khalili and Knut Emil Ringstad, NTNU, and Martin Larsson, Sportradar AS, Trondheim.

Location: Gyrhofstraße 8a (building 158a), Room 1.105 (1st floor), 50931 Cologne

Abstract: An efficient and versatile immersed boundary method (IBM) for simulating compressible viscous flows with complex and moving convex boundaries has been developed. The compressible Navier-Stokes equations are discretized by globally fourth order summation-by-parts (SBP) difference operators with in-built stability properties and the classical fourth order explicit Runge-Kutta method. The proposed Cartesian grid based IBM builds on the ghost point approach in which the solid wall boundary conditions are applied as sharp interface conditions. The interpolation of the flow variables at image points and the solid wall boundary conditions are used to determine the flow variables at three layers of ghost points within the solid body in order to introduce the presence of the body interface in the flow computation and to maintain the overall high order of accuracy of the flow solver. Two different reconstruction procedures, bilinear interpolation and weighted least squares method, are implemented to obtain the values at the ghost points. A robust high order immersed boundary method is achieved by using a hybrid approach in which the first layer of ghost points is treated by using a third order polynomial combined with the weighted least squares method and the second and third layers of ghost points are treated by using bilinear interpolation to find the values at the image points of the corresponding ghost points. After demonstrating the accuracy of the present IBM for low Mach number flow around a circular cylinder, it is applied to simulate flow in the cross-section of the upper airways of a specific obstructive sleep apnea patient. The IBM solver has been further verified and validated for moving boundaries by applying it to a transversely oscillating cylinder in freestream flow and an in-line oscillating cylinder in an initially quiescent fluid. Sound waves generated by the in-line oscillation of the cylinder exhibit both quadrupole and monopole types. The present IBM is also verified for fluid-structure interaction of an elastically mounted circular cylinder in freestream flow at Reynolds number 200, and the rate of energy transferred between the fluid and the structure is investigated.

On Friday, 31 January 2020 at 14:00 Ruediger Pakmor will talk on the topic “The numerical schemes behind the moving mesh code Arepo”

Location: Weyertal 86-90, Seminar room 1 (ground floor), 50931 Cologne

Abstract: I will present the schemes behind the moving mesh magnetohydrodynamics code Arepo and discuss in particular the finite volume scheme on a moving mesh and its time integration. I will then show an example of an anisotropic diffusion solver on the unstructured Voronoi mesh used in Arepo and discuss general properties of the Arepo code.

On Tuesday, 28 January 2020 at 11.00 Cedrick Ansorge will talk on the topic “Turbulent Ekman flow as virtual lab in geophysical fluid dynamics”

Location:  Gyrhofstraße 8a (Gebäude 158a), Room 1.105 (1st floor), 50931 Cologne

Abstract: The atmospheric boundary layer (ABL) is the lowest part of the atmosphere that is directly linked to the surface through vertical turbulent exchange, typically the lowest 100 to 1000m. There, turbulent mixing is the main vertical transport mechanism for heat, water, momentum and any kind of air constituent. Besides turbulence, the ABL is a multi-physical system comprising also radiative, miro-physical, chemical and other processes on scales from the multi-kilometre range down to the Kolmogorov scale of turbulent motion at the sub-millimetre range in three spatial dimensions. Both the multiphysical complexity and the broad-scale nature are prohibitive for a brute-force approach to numerical modelling of the system. Truncated representations of the ABL are thus inevitable when numerically modeling the ABL.
I will introduce turbulent Ekman flow–the doubly periodic flow over a flat rotating plate—that physically truncates the ABL to its fluid-mechanical core, the Navier–Stokes equations with appropriate boundary conditions. The governing equations are solved by a highly scalable numerical algorithm that is being used on up to 250,000 compute cores to represent the turbulent flow on grids that routinely use 3 × 230 collocation points in space. The reduced physical complexity allows for high-fidelity turbulence simulations where the entire range of turbulent motion is represented directly–without need for turbulence closure. We can thus study the ABL under conditions for which classical approaches to represent turbulence fail–such as partial or complete laminarization and transitional flows.

On Friday, 13 December 2019 at 14.00 Almut Gassman will talk on the topic “Entropy production in numerical modeling of a moist atmosphere”

Location: Weyertal 86 – 90, Seminar room 1 (ground floor), 50931 Cologne

Abstract: Atmospheric models are based on basic physical laws, like mass conservation, momentum conservation or sometimes energy conservation. In this talk, another law is inspected, namely the second law of thermodynamics which says that the internal entropy production has to be positive. This law has hardly been checked by modellers. But this law determines the direction (but not the strength) of subgrid-scale parameterized fluxes. Furthermore, the choice of numerical schemes for advection is also limited, because the inherent diffusion of those schemes must be downgradient with respect to the gradients of special measures, which are determined by the second law. The formulation of energetically and entropically consistent numerical schemes will be outlined. Examples of failure of contemporary schemes with respect to the second law will be shown. For instance, conventional (non-entropy-consistent) heat flux parameterizations in the mesosphere will amplify waves instead of allowing them to break and dissipate. Or, as another example, entropy-law-inconsistent higher order or TVD advection schemes for temperature might give rise to accelerations of the wind in the wrong direction. When inspecting the different entropy production (or dissipation) rates in the atmosphere, four types of those rates are distinguished, namely (i) dissipation due to friction, (ii) dissipation due to heat fluxes, (iii) dissipation due to mixing of constituents, and (iv) dissipation due to phase changes. The most important among them are the dissipation due to friction and the dissipation due to falling rain, which can be seen as a special case of mixing of moist air and precipitation.

From September 16th through September 27th, Dr. Viktor Linders from Lund University is going to visit the NumSim group by invitation of Dr. Michael Schlottke-Lakemper. Together with researchers from RWTH Aachen University, they are working on high-order methods with optimized dispersive properties for aeroacoustics simulations. During his stay in Cologne, Dr. Linders will share some of his previous results on summation-by-parts methods in a talk at the Workshop on Efficiency in Computational Science.