Markus Klein

Bio: Markus Klein is an academic researcher from Bundeswehr University Munich. The author has contributed to research in topics: Turbulence & Direct numerical simulation. The author has an hindex of 27, co-authored 145 publications receiving 3529 citations. Previous affiliations of Markus Klein include GM Powertrain Torino & Technische Universität Darmstadt.

Efficient Generation of Initial- and Inflow-Conditions for Transient Turbulent Flows in Arbitrary Geometries

Abstract: A method is presented to artificially generate initial conditions and transient inflow-conditions for DNS and LES. It creates velocity fields that satisfy a given Reynolds-stress-tensor and length-scale. Compared to existing approaches, the new method features greater flexibility, efficiency and applicability. It is well suited for the complex geometries and for the arbitrary grids that occur in technical applications. This is demonstrated in connection with the generation of initial data for an internal combustion engine. To assess the accuracy and efficiency of the new approach, it is applied to the test-case of a non-premixed jet-flame, which is known to be sensitive to transient inflow-data.

An Attempt to Assess the Quality of Large Eddy Simulations in the Context of Implicit Filtering

Abstract: While methods for assessing the uncertainty of Reynolds–Averaged–Navier–Stokes (RANS) simulations have been well established in the past, the verification of Large Eddy Simulations (LES) is more difficult. One reason is that the numerical discretization error as well as the subgrid scale model contribution depend on the grid resolution and that both terms interact. In the present paper the accuracy of single-grid estimators to assess the amount of the unresolved turbulent kinetic energy is studied first. In the second part of the paper the sensitivity of the simulation results on the modeling error as well as the numerical error will be investigated in the context of LES with implicit filtering. This will be achieved by performing a systematic grid and model variation. The analysis is applied to an isothermal, turbulent, plane jet and a turbulent channel flow.

Synthetic turbulence inflow conditions for large-eddy simulation

Abstract: Direct numerical or large-eddy simulations of the majority of spatially inhomogeneous turbulent flows require turbulent inflow boundary conditions. A potential implication is that any results computed may be strongly influenced by the prescribed instantaneous inlet velocity profiles. Such profiles are practically never available, and a usual practice is to generate synthetic inflow data satisfying certain statistical properties, which may, for example, be known from experimental data or empirical correlations. The present paper describes a new method for generating turbulent inflow data based on digital filters that is capable of reproducing specified statistical data. Two variants of the approach are presented: a simple method in which the Reynolds stresses and a single length scale are prescribed, and a more detailed approach that is able to reproduce the complete Reynolds-stress tensor as well as any given, locally defined, spatial and temporal correlation functions. The application of the methods to a plane jet flow and to a developing wall boundary layer serve to demonstrate the applicability of the approach.

Assessment Measures for Engineering LES Applications

Abstract: Anticipating that large eddy simulations will increasingly become the future engineering tool for research, development, and design, it is deemed necessary to formulate some quality assessment measures that can be used to judge the resolution of turbulent scales and the accuracy of predictions. In this context some new and refined measures are proposed and compared with those already published by the authors in the common literature. These measures involve (a) fraction of the total turbulent kinetic energy, (b) relative grid size with respect to Kolmogorov or Taylor scales, and (c) relative effective subgrid/numerical viscosity with respect to molecular viscosity. In addition, an attempt is made to segregate the contributions from numerical and modeling errors. Proposed measures are applied to various test cases and validated against fully resolved large eddy simulation and/or direct numerical simulation whenever possible.

Calculation of Gauss quadrature rules.

Abstract: Most numerical integration techniques consist of approximating the integrand by a polynomial in a region or regions and then integrating the polynomial exactly. Often a complicated integrand can be factored into a non-negative ''weight'' function and another function better approximated by a polynomial, thus $\int_{a}^{b} g(t)dt = \int_{a}^{b} \omega (t)f(t)dt \approx \sum_{i=1}^{N} w_i f(t_i)$. Hopefully, the quadrature rule ${\{w_j, t_j\}}_{j=1}^{N}$ corresponding to the weight function $\omega$(t) is available in tabulated form, but more likely it is not. We present here two algorithms for generating the Gaussian quadrature rule defined by the weight function when: a) the three term recurrence relation is known for the orthogonal polynomials generated by $\omega$(t), and b) the moments of the weight function are known or can be calculated.

New insights into large eddy simulation

Abstract: Fluid dynamic turbulence is one of the most challenging computational physics problems because of the extremely wide range of time and space scales involved, the strong nonlinearity of the governing equations, and the many practical and important applications. While most linear fluid instabilities are well understood, the nonlinear interactions among them makes even the relatively simple limit of homogeneous isotropic turbulence difficult to treat physically, mathematically, and computationally. Turbulence is modeled computationally by a two-stage bootstrap process. The first stage, direct numerical simulation, attempts to resolve the relevant physical time and space scales but its application is limited to diffusive flows with a relatively small Reynolds number (Re). Using direct numerical simulation to provide a database, in turn, allows calibration of phenomenological turbulence models for engineering applications. Large eddy simulation incorporates a form of turbulence modeling applicable when the large-scale flows of interest are intrinsically time dependent, thus throwing common statistical models into question. A promising approach to large eddy simulation involves the use of high-resolution monotone computational fluid dynamics algorithms such as flux-corrected transport or the piecewise parabolic method which have intrinsic subgrid turbulence models coupled naturally to the resolved scales in the computed flow. The physical considerations underlying and evidence supporting this monotone integrated large eddy simulation approach are discussed.

A synthetic-eddy method for generating inflow conditions for large-eddy simulations

Abstract: The generation of inflow data for spatially developing turbulent flows is one of the challenges that must be addressed prior to the application of LES to industrial flows and complex geometries. A new method of generation of synthetic turbulence, suitable for complex geometries and unstructured meshes, is presented herein. The method is based on the classical view of turbulence as a superposition of coherent structures. It is able to reproduce prescribed first and second order one point statistics, characteristic length and time scales, and the shape of coherent structures. The ability of the method to produce realistic inflow conditions in the test cases of a spatially decaying homogeneous isotropic turbulence and of a fully developed turbulent channel flow is presented. The method is systematically compared to other methods of generation of inflow conditions (precursor simulation, spectral methods and algebraic methods).