**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

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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.