Browsing by Author "Munz, Claus-Dieter (Prof. Dr. rer. nat.)"

Now showing 1 - 6 of 6

Open Access
Aeroacoustic simulation of turbulent boundary layer induced automotive gap noise
(2021) Erbig, Lars; Munz, Claus-Dieter (Prof. Dr. rer. nat.)
Open Access
An explicit discontinuous Galerkin method for parallel compressible two-phase flow simulations
(2017) Hoffmann, Malte; Munz, Claus-Dieter (Prof. Dr. rer. nat.)
In this thesis an efficient numerical method is presented to enable simulations with cavitating flow for a pure fluid. The simulation of cavitating flow poses various challenges. On the one hand, the phase transition between the vapor and liquid phase must be considered, and on the other hand a high-resolving numerical method is required, which can resolve the occurring spatial and temporal scales. In addition, in the presence of cavitation, the thermodynamic quantities (e.g. density, pressure) can vary by several orders of magnitude over a very short distance. To consider phase change, in this work an accurate equation of state is needed which is able to resolve the vapor, liquid and two-phase regions of such a fluid. CoolProp, a thermodynamic property database for over 100 fluids, is well suited for this task since it uses the most-accurate Helmholtz free energy formulation as equation of state. Assuming thermodynamic equilibrium and using the Maxwell construction in the two-phase region, the compressible Navier-Stokes equations can be closed by the equation of state from the CoolProp library. Compressibility effects need to be considered in the two-phase region as well as in the vapor state. Also friction and the heat flux are represented by the Navier-Stokes equations. From the class of the numerical methods, the discontinuous Galerkin method is a good candidate to resolve the occurring spatial and temporal scales. The here used discontinuous Galerkin spectral element method solves the Navier-Stokes equations with an explicit time integration. This method is known for its low numerical dissipation and good scaling capabilities on state of the art high performance computers. A disadvantage of this method is that it can handle neither shocks nor high gradients. These occurring physical phenomena must be resolved by a method which can deal with these phenomena, but does not affect the good scaling ability. For this case a second order finite volume sub-cell approach is presented. The finite volume method is only active in those elements where the discontinuous Galerkin method is not able to resolve the high gradients or shocks. Since the evaluation of the Helmholtz free energy formulation is linked with high computational effort, the equation of state is stored in a preprocessing step as a polynomial representation on a hierarchically adaptable grid (so-called quadtree). This step is parallelized and performs on an arbitrary number of processors. The data of the equation of state are stored in a polynomial representation with a user-defined error compared to the original solution. During the simulation the stored quadtrees are loaded into the memory of each processor. Then the data of the quadtrees are used to provide the necessary relations between the thermodynamic variables. This approach reduces the computational effort by three orders of magnitude compared to the direct evaluation and is well suited for calculations on state of the art high performance computers. The presented method is validated and it is compared to results in literature for one dimensional simulations. The desired convergence rate is reached and the obtained results are in very good agreement with the reference data from the literature. A two dimensional calculation shows water streaming around a hydrofoil producing cavitation. The strong pressure waves arising during the collapse of the cavitation regions are captured by the simulation and resolved in a numerically stable manner. Finally, the framework developed here is applied to a complex, three-dimensional application from the industry to demonstrate the quality of the method and to show that complex multiscale problems can be calculated on several thousand processors in a reasonable time. For this industrial application also the good scaling on a high performance computer is shown.
Open Access
Explicit discontinuous Galerkin methods for magnetohydrodynamics
(2012) Altmann, Christoph; Munz, Claus-Dieter (Prof. Dr. rer. nat.)
In this work, the explicit space-time expansion discontinuous Galerkin (STE-DG) method is adapted and applied to unsteady ideal and viscous magnetohydrodynamic (MHD) computations. With a special emphasis on shock-capturing and divergence correction of the magnetic field, enhancements to the STE-DG method are proposed that are necessary within the MHD context. Discontinuous Galerkin schemes enjoy continuously growing popularity, since they combine the flexibility in handling complex geometries, a variable adaptivity to the calculated problem and efficiency of parallel implementations. These are big advantages for modern numerical calculations of various fields of interest, also for MHD calculations e.g. in astrophysics or plasma physics. The presented STE-DG scheme can further enhance explicit computations by its local timestepping functionality, allowing each cell to run with its own determined timestep. The necessary local formulation adds additional constraints to the implementation of new equation systems and numerical ingredients and not every method is suitable. On the other hand it enables mechanisms that would generally be considered to be ineffective for explicit numerical schemes, since they would drastically decrease the timestep of the calculation. The proposed use of artificial viscosity for shock capturing falls in this category: Artificial viscosity is used to capture shocks with a high order scheme. The thereby caused strong influence on the scheme's timestep is substantially reduced by the local timestepping. For this purpose, suitable oscillation indicators were found and evaluated. For the divergence correction of the magnetic field, the local timesteps enable a sub-cycling feature to increase the correction efficiency. In addition, postprocessing and data reduction techniques are presented, that are especially of interest for high order schemes. Further more, the parallel efficiency of the STE-DG implementation and code development strategies are considered. To validate the STE-DG implementation for MHD and the proposed ingredients, several multi-dimensional test cases have been set up, including convergence studies and shock tube tests. The scheme is then applied to two- and three-dimensional more complex astrophysical test cases of larger computational scale.
Open Access
High order particle transport for PIC simulations of plasma flows
(2010) Quandt, Martin; Munz, Claus-Dieter (Prof. Dr. rer. nat.)
Numerical simulations of plasma flows based on the Particle in Cell (PIC) technique need a procedure for the integration of Newtons relativistic equation of motion for charged particles. In this work a new explicit single step integration method based on a Taylor series expansion of particles velocity is presented. Up to now the most often used particle push methods are the enhanced leapfrog scheme by J.P. Boris and the classic Runge-Kutta scheme. The special construction of the explicit Boris leapfrog scheme yields to a very efficient and robust integration, but the scheme is limited to a second order convergence rate. For a high order explicit integration the Runge-Kutta method is the only one and achieves its convergence rates by evaluating Newton's equation of motion at different interim stages. The calculation of the these stages with the complete PIC cycle is the most expensive part of this scheme. Both methods serve as a reference in this work. The presented truncated Taylor series expansion applied on Newtons equation of motion for charged particle is the first high order explicit single step integration method. The realization of this expansion up to the desired truncation order yields to higher total derivatives of the relativistic velocity and the inverse Lorentz factor. The dependency of these derivatives in time, space and the relativistic velocity itself leads to a complex differential operator. To compute the higher total derivatives of the relativistic velocity, the hierarchical structure of this procedure is utilized to construct the operators by a rearrangement of previously defined operators. Furthermore the unknown total derivatives of the electromagnetic fields are replaced by the application of simple differentiation rules by the given high order partial derivatives in time and space as well as the mixed derivatives. These higher temporal and spatial derivatives of the electromagnetic fields are a prerequisite of the new integration scheme and have to be calculated by a high order Maxwell solver. To assess and verify this new integration method the Taylor series expansion was tested on different examples in the non-relativistic case on space and time dependent electromagnetic fields and in the relativistic region where the Lorentz factor with all total derivatives are present. For all examples the experimental order corresponds to the selected formal order and a gain in accuracy and efficiency by an increase of the selected formal order is successfully demonstrated.
Open Access
Mehrskalenmodellierung von aeroakustischen Quellen in schwach kompressiblen Strömungen
(2006) Fortenbach, Roland; Munz, Claus-Dieter (Prof. Dr. rer. nat.)
Die Herausforderung der Strömungsakustik im Regime von Strömungen mit kleiner Mach-Zahl M besteht in der Behandlung der deutlich variierenden Skalen. Die Strömung ist gekennzeichnet durch sehr kleine räumliche Strukturen, wie sie beispielsweise in den Wirbeln von turbulenten Strömungen auftreten. Sie breitet sich mit langsamer Konvektion aus und enthält den Haupteil der Energie des Systems. Dagegen sind die akustischen Wellen räumlich langskalig, da sie sich mit der schnellen Schallgeschwindigkeit ausbreiten. Eine weitere Eigenschaft der Akustik ist ihr sehr geringer Energieanteil, der durch ihre kleinen Druckamplituden zum Ausdruck kommt. Um dem beschriebenen Mehrskalenproblem zu begegnen, verwendet die vorliegende Arbeit einen Störungsansatz, der auf den inkompressiblen Strömungsgleichungen basiert und der die Schallerzeugung und ihre Ausbreitung modelliert. Dazu werden die Erkenntnisse aus der inkompressiblen Grenzwertbetrachtung einer kompressiblen Strömungen verwendet. Das motiviert eine Skalierung der Terme einer Entwicklung um die inkompressible Strömungslösung. Der Vorteil der Skalierung besteht darin, dass die physikalisch bedeutenden Terme hervortreten, was sich an der Potenz der Mach-Zahl ablesen läßt, mit welcher der jeweilige Term gewichtet ist. Gerade im Regime sehr kleiner Mach-Zahlen wird eine Mehrskalenbetrachtung den unterschiedlichen räumlichen Skalen gerecht. Denn die Mehrskalenmodellierung führt eine zweite, langskalige Raumvariable ein. Die aus diesem Ansatz resultierenden Störungsgleichungen beinhalten Gradienten der physikalischen Größen, die sich sowohl auf die kurze wie auf die lange Raumskala beziehen. Die Eigenschaften der langskaligen Anteile werden über einen Mittelungsprozeß extrahiert, was in einer inhomogenen Wellengleichung für die akustische Ausbreitung resultiert. Die Quellterme sind durch die Strömungslösung definiert und modellieren die Schallerzeugung. Der konvektive Einfluß der Strömung auf die akustische Ausbreitung wird in Störungen der nächst höheren Ordnung beschrieben. Der Grundgedanke der Mehrskalenmodellierung wird im numerischen Verfahren wieder aufgegriffen. Denn die Strömung wird auf einem feinen Rechengitter diskretisiert, um die kleinen räumlichen Strukturen abzubilden. Dieses ist eingebettet in ein deutlich gröber aufgelöstes Rechengitter, auf dem die akustischen Ausbreitung simuliert und das den langskaligen akustischen Wellen angepaßt ist. Die beiden Rechengebiete für die Strömung und die Akustik kommunizieren über akustische Quellterme. Diese sind durch die schallerzeugende Strömung auf dem feinen CFD-Gitter definiert und regen auf dem groben CAA-Rechengitter die Akustik an. Die Vorschrift für den Transfer der Quellterme zwischen den Rechengebieten wird von der Mehrskalenmodellierung explizit durch einen Mittelungsprozeß geliefert. Die numerischen Ergebnisse bestehen einerseits aus der Validierung der numerischen Methoden für deren aeroakustische Anwendbarkeit, andererseits wurde das aeroakustische Mehrskalenmodell mit dem analytischen Testfall des rotierenden Wirbelpaars getestet.
Open Access
Numerical modeling of compressible two-phase flows with a pressure-based method
(2014) Boger, Markus; Munz, Claus-Dieter (Prof. Dr. rer. nat.)
This work is directed towards the direct numerical simulation (DNS) of compressible and incompressible multiphase flows. The main objective is the extension of an incompressible two-phase solver to the compressible flow regime. The starting point is the existing multiphase solver FS3D for the simulation of three-dimensional, incompressible flows. For this code, the topic of surface tension modeling is looked at in detail with respect to the so-called parasitic currents. These spurious, unphysical velocities are caused by the numerical approximation of surface tension and a balanced-force algorithm is presented that considerably reduces the parasitic currents by several orders of magnitude. The main focus of this thesis is on the extension of an incompressible, pressure-based numerical approach to the simulation of compressible multiphase flows. For this purpose, the physical and mathematical background of the governing equations for incompressible and compressible flows is discussed and the transition from the compressible to the incompressible regime is addressed. In this context, fundamental investigations for the coupling of compressible and incompressible flow regions are presented in one space dimension. On the basis of these considerations, several iterative coupling schemes are derived and validated with the help of generic test cases. The pressure-based Multiple Pressure Variables (MPV) method that allows the extension of an incompressible flow solver to the compressible regime is presented. The numerical scheme builds upon an asymptotic pressure decomposition taking into account the different roles of pressure for incompressible and compressible flows. This avoids the singular incompressible limit of the compressible flow equations. At first, the MPV method is introduced for single-phase flows. Then its extension to compressible two-phase flows is presented. In this context, the treatment of the material interface between the two fluids and the corresponding jump in the material properties and the equations of state play a crucial role. While the present approach numerically smears the density jump between the two phases, the thermodynamic transition is a sharp one. Contrary to many density-based two-phase flow solvers, the MPV scheme does not suffer from oscillations in pressure and velocity at the interface location due to the use of pressure as primary variable. A detailed analysis of this behavior is presented. Finally, the MPV scheme proves to accurately solve one-dimensional single- and two-phase Riemann problems. For the single-phase flows, the focus is on the wave propagation and shock-capturing properties of the MPV method. In three space dimensions, the numerical scheme is successfully applied to the computation of shock-droplet interactions.