Matthias Waidmann

Energy dissipation caused by boundary layer instability at vanishing viscosity

A qualitative explanation for the scaling of energy dissipation by high-Reynolds-number fluid flows in contact with solid obstacles is proposed in the light of recent mathematical and numerical results. Asymptotic analysis suggests that it is governed by a fast, small-scale Rayleigh-Tollmien-Schlichting instability with an unstable range whose lower and upper bounds scale as Re-3/8 and Re-1/2 , respectively. By linear superposition, the unstable modes induce a boundary vorticity flux of order Re-1, a key ingredient in detachment and drag generation according to a theorem of Kato. These predictions are confirmed by numerically solving the Navier-Stokes equations in a two-dimensional periodic channel discretized using compact finite differences in the wall-normal direction, and a spectral scheme in the wall-parallel direction.

Building Blocks for a Strictly Conservative Generalized Finite Volume Projection Method for Zero Mach Number Two-Phase Flows

Building blocks for a generalized fully conservative finite volume projection method for numerical simulation of immiscible zero Mach number two-phase flows on Cartesian grids are presented, focusing on the crucial issues of interface propagation, fluid phase conservation and discretization of the singular contribution due to surface tension, each in a discretely conservative fashion. Additionally, a solution approach for solving Poisson-type equations for two-phase flows at arbitrary ratio of coefficients is sketched. Further, (intermediate) results applying these building blocks are presented and open issues and future developments are proposed.

A Stochastic Closure Approach for LES with Application to Turbulent Channel Flow

The integral conservation laws for mass, momentum and energy of a flow field are universally valid for arbitrary control volumes. Thus, if the associated fluxes across its bounding surfaces are determined exactly, the equations capture the underlying physics of conservation correctly and guarantee an accurate prediction of the time evolution of the integral mean values.

Towards a Stochastic Closure Approach for Large Eddy Simulation

We present a stochastic sub grid scale modeling strategy currently under development for application in Finite Volume Large Eddy Simulation (LES) codes. Our concept is based on the integral conservation laws for mass, momentum and energy of a flow field that are universally valid for arbitrary control volumes. We model the space-time structure of the fluxes to create a discrete formulation. Advanced methods of time series analysis for the data-based construction of stochastic models with inherently non-stationary statistical properties and concepts of information theory for the model discrimination are used to construct stochastic surrogate models for the non-resolved fluctuations. Vector-valued auto-regressive models with external influences (VARX-models) form the basis for the modeling approach. The reconstruction capabilities of the modeling ansatz are tested against fully three dimensional turbulent channel flow data computed by direct numerical simulation (DNS). We present here the outcome of our reconstruction tests.

A Conservative Coupling of Level-Set, Volume-of-Fluid and Other Conserved Quantities

A conservative level-set volume-of-fluid synchronization strategy including coupling to other conserved quantities such as mass or momentum is presented. The scheme avoids mass loss/gain of fluidic structures in zero Mach number two-phase flow while keeping the interface between the two fluid phases sharp. Local level-set correction and a consistent discretization error control using information from the energy equation based divergence constraint allow for application of the presented method to both constant and variable density zero Mach number two-phase flow with or without interfacial mass transport.