Claus-Dieter Munz

Claus-Dieter Munz
Universität Stuttgart · Institute of Aerodynamics and Gasdynamics

About

367
Publications
60,363
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8,730
Citations
Citations since 2016
97 Research Items
4959 Citations
20162017201820192020202120220200400600800
20162017201820192020202120220200400600800
20162017201820192020202120220200400600800
20162017201820192020202120220200400600800
Introduction

Publications

Publications (367)
Article
In this paper, we consider Riemann solvers with phase transition effects based on the Euler–Fourier equation system. One exact and two approximate solutions of the two-phase Riemann problem are obtained by modelling the phase transition process via the theory of classical irreversible thermodynamics. Closure is obtained by appropriate Onsager coeff...
Article
A core aspect in the simulation of compressible fluid flow is the solution of Riemann problems. The solution is well understood for single-phase flows and is used to define numerical fluxes for finite volume and discontinuous Galerkin schemes. However, the solution of two-phase Riemann problems with phase transitions is still an active field of res...
Preprint
Full-text available
In the last decades, the Arbitrary Lagrangian-Eulerian (ALE) approach has been one of the most popular choices to deal with fluid flows including moving boundaries. The ALE finite volume (FV) method is well-known for its capability of shock capturing. Several ALE discontinuous Galerkin (DG) methods are developed to fully explore the advantages of h...
Article
Full-text available
We present the extension of a discontinuous Galerkin framework to zonal direct-hybrid aeroacoustic simulations. This extension provides the ability to simultaneously perform a zonal large eddy simulation (LES), solving the compressible Navier–Stokes equations, and an acoustic propagation simulation, solving the acoustic perturbation equations. In d...
Chapter
Full-text available
The computation of two-phase flow scenarios in a high pressure and temperature environment is a delicate task, for both the physical modeling and the numerical method. In this article, we present a sharp interface method based on a level-set ghost fluid approach. Phase transition effects are included by the solution of the two-phase Riemann problem...
Chapter
Full-text available
A fundamental understanding of droplet dynamics is important for the prediction and optimization of technical systems involving drops and sprays. The Collaborative Research Center (CRC) SFB-TRR 75 was established in January 2010 to focus on the dynamics of basic drop processes, and in particular on processes involving extreme ambient conditions, fo...
Preprint
The Navier-Stokes-Korteweg (NSK) system is a classical diffuse interface model which is based on van der Waals theory of capillarity. Diffuse interface methods have gained much interest to model two-phase flow in porous media. However, for the numerical solution of the NSK equations two major challenges have to be faced. First, an extended numerica...
Preprint
Full-text available
In this paper, we consider Riemann solvers with phase transition effects based on the Euler-Fourier equation system. One exact and two approximate solutions of the two-phase Riemann problem are obtained by modelling the phase transition process via the theory of classical irreversible thermodynamics. Closure is obtained by appropriate Onsager coeff...
Conference Paper
Hybrid simulation methods are state of the art in computational aeroacoustics. The acoustic sources rely on an accurate prediction of the underlying hydrodynamic field, typically computed with low-fidelity simulation models. In complex flows, low-fidelity models reach their limit. Thus, computationally intense high-fidelity models like wall-resolve...
Article
Full-text available
In this work, we present a novel hybrid Discontinuous Galerkin scheme with hp-adaptivity capabilities for the compressible Euler equations. In smooth regions, an efficient and accurate discretization is achieved via local p-adaptation. At strong discontinuities and shocks, a finite volume scheme on an h-refined element-local subgrid gives robustnes...
Article
Full-text available
Shock‐wave/turbulent boundary‐layer interactions are still a challenge for numerical simulation. The shock capturing needs dissipation to avoid spurious oscillations while turbulence will be falsified by introducing dissipation. Especially, an accurate prediction of quantities such as the skin‐friction coefficient inside the interaction area of sho...
Article
We present a Stochastic Galerkin (SG) scheme for Uncertainty Quantification (UQ) of the compressible Navier-Stokes and Euler equations. For spatial discretization, we rely on the high-order Discontinuous Galerkin Spectral Element Method (DGSEM) in combination with an explicit time-stepping scheme. We simulate complex flow problems in two- and three...
Article
Full-text available
Sliding meshes are a powerful method to treat deformed domains in computational fluid dynamics, where different parts of the domain are in relative motion. In this paper, we present an efficient implementation of a sliding mesh method into a discontinuous Galerkin compressible Navier-Stokes solver and its application to a large eddy simulation of a...
Chapter
Full-text available
Mixing characteristics of supercritical injection studies were analyzed with regard to the necessity to include diffusive fluxes. Therefore, speed of sound data from mixing jets were investigated using an adiabatic mixing model and compared to an analytic solution. In this work, we show that the generalized application of the adiabatic mixing model...
Preprint
Full-text available
Sliding meshes are a powerful method to treat deformed domains in computational fluid dynamics, where different parts of the domain are in relative motion. In this paper, we present an efficient implementation of a sliding mesh method into a discontinuous Galerkin compressible Navier-Stokes solver and its application to a large eddy simulation of a...
Article
The isothermal Navier-Stokes-Korteweg system is a classical diffuse interface model for compressible two-phase flow which grounds in Van Der Waals' theory of capillarity. However, the numerical solution faces two major challenges: due to a third-order dispersion contribution in the momentum equations, extended numerical stencils are required for th...
Preprint
Full-text available
The Riemann problem is one of the basic building blocks for numerical methods in computational fluid mechanics. Nonetheless, there are still open questions and gaps in theory and modelling for situations with complex thermodynamic behavior. In this series, we compare numerical solutions of the macroscopic flow equations with molecular dynamics simu...
Preprint
The quality of the scale resolving domain's inflow condition determines the accuracy of the overall computation when considering a zonal large eddy simulation. However, the generation of scale-and time-resolved turbulence remains a challenging task, and a number of different approaches have been proposed. Within this work, a new turbulent inflow me...
Article
High order (HO) schemes are attractive candidates for the numerical solution of multiscale problems occurring in fluid dynamics and related disciplines. Among the HO discretization variants, discontinuous Galerkin schemes offer a collection of advantageous features which have lead to a strong increase in interest in them and related formulations in...
Chapter
We study Godunov’s method for diffusion and advection-diffusion problems. The numerical fluxes for the finite volume scheme are based on an approximation of the generalized Riemann Problem. Hereby, approximate Riemann solvers are constructed, which approximate the solutions by a space-time discontinuous Galerkin approach. The implementation to a Go...
Chapter
This paper describes improvements of a level-set ghost-fluid algorithm in the scope of sharp interface multi-phase flow simulations. The method is used to simulate drop-drop and shock-drop interactions. Both, the level-set and the bulk phases are discretized by a high order discontinuous Galerkin spectral element method. The multi-phase interface a...
Preprint
Full-text available
In this paper we propose a novel regularization strategy for the local discontinuous Galerkin method to solve the Hamilton-Jacobi equation in the context of level-set reinitialization. The novel regularization idea works in analogy to shock-capturing schemes for discontinuous Galerkin methods, which are based on finite volume sub-cells. In this spi...
Article
Full-text available
We propose a novel $hp$-multilevel Monte Carlo method for the quantification of uncertainties in the compressible Navier--Stokes equations, using the discontinuous Galerkin method as deterministic solver. The multilevel approach exploits hierarchies of uniformly refined meshes while simultaneously increasing the polynomial degree of the ansatz spac...
Preprint
The isothermal Navier-Stokes-Korteweg system is a classical diffuse interface model for compressible two-phase flow. However, the numerical solution faces two major challenges: due to a third-order dispersion contribution in the momentum equations, extended numerical stencils are required for the flux calculation. Furthermore, the equation of state...
Article
We construct an approximate Riemann solver for scalar advection–diffusion equations with piecewise polynomial initial data. The objective is to handle advection and diffusion simultaneously to reduce the inherent numerical diffusion produced by the usual advection flux calculations. The approximate solution is based on the weak formulation of the R...
Preprint
Full-text available
We present a Stochastic Galerkin (SG) scheme for Uncertainty Quantification (UQ) of the com-pressible Navier-Stokes and Euler equations. For spatial discretization, we rely on the high-order Discontinuous Galerkin Spectral Element Method (DGSEM) in combination with an explicit time-stepping scheme. We simulate complex flow problems in two-and three...
Article
Full-text available
The Riemann problem is a fundamental concept in the development of numerical methods for the macroscopic flow equations. It allows the resolution of discontinuities in the solution, such as shock waves, and provides a powerful tool for the construction of numerical flux functions. A natural extension of the Riemann problem involves two phases, a li...
Preprint
Full-text available
High order (HO) schemes are attractive candidates for the numerical solution of multiscale problems occurring in fluid dynamics and related disciplines. Among the HO discretization variants, discontinuous Galerkin schemes offer a collection of advantageous features which have lead to a strong increase in interest in them and related formulations in...
Article
Operating fluids for steering and propulsion of orbital manoeuvring systems are to be changed from toxic substances to environmentally less harmful alternatives. Liquid oxygen (LOX) can be used as oxidizer but the near vacuum conditions of outer space lead to a fast expansion into a superheated state when LOX is injected into the combustion chamber...
Article
Full-text available
In this work, we present a novel data-based approach to turbulence modeling for Large Eddy Simulation (LES) by artificial neural networks. We define the perfect LES formulation including the discretization operators and derive the associated perfect closure terms. We then generate training data for these terms from direct numerical simulations of d...
Article
Full-text available
The use of complex multi-parameter equations of state in computational fluid dynamics is limited due to their expensive evaluation. Tabulation methods help to overcome this limitation. We propose in this work a tabulation approach for real equations of state that is also suitable for multi-component flows and multi-phase flows with phase transition...
Article
Full-text available
A combined approach for the simulation of reactive, neutral, partially or fully ionized plasma flows is presented. This is realized in a code framework named “PICLas” for the approximate solution of the Boltzmann equation by particle based methods. PICLas combines the particle-in-cell method for the collisionless Vlasov–Maxwell system and the direc...
Article
Commonly, severely reduced system models are used to predict the performance of industrial hydraulic systems as injection, brake or pump systems. These simulations are usually based on zero- and one-dimensional mathematical models describing the flow path of the technical system. To take into account parts with inherently three-dimensional flow str...
Chapter
This paper summarizes our progress in the application and feature development of a high-order discontinuous Galerkin (DG) method for scale resolving fluid dynamics simulations on the Cray XC40 Hazel Hen cluster at HLRS. We present the extension to Chimera grid techniques which allow efficient computations on flexible meshes, and discuss data-based...
Article
Common fuel-oxidizer combinations in orbital manoeuvring systems consist of toxic substances but will be replaced in the future. Liquid oxygen (LOX) is one potential oxidizer but it rapidly superheats under the initial low-pressure conditions in the combustion chamber. Bubble nucleation and growth dominate the efficient disintegration of the liquid...
Article
The simulation of laser-plasma interaction via three- dimensional Particle-In-Cell methods based on higher-order schemes is considered. High-order methods allow for drastically reducing the required number of degrees of freedom while still capturing the complex physical nature of non-linear processes. The suitability of high-order methods for the a...
Article
A high-order hybridizable discontinuous Galerkin spectral element method (HDGSEM) for Particle-In-Cell (PIC) schemes is presented for the simulation of electrostatic applications on three-dimensional unstructured curved meshes. The electrostatic Poisson equation is solved and optionally a Boltzmann relation for the electron species can be used whic...
Chapter
Die Approximation bestimmter Integrale tritt bei der numerischen Simulation von praktischen Ingenieurproblemen häufig auf. Auch die Lösung der einfachsten Differenzialgleichungen, bei denen die rechte Seite nicht von der gesuchten Funktion abhängt, führt auf die Berechnung eines bestimmten Integrals. Eine exakte Integration durch die Angabe einer S...
Chapter
Bei der mathematischen Modellierung von ingenieur- oder naturwissenschaftlichen Problemen treten oft Differenzialgleichungen auf. Überall dort, wo die gesuchte Größe und deren Änderung in das mathematische Modell eingehen, wird sich eine solche ergeben. Ist der Anfangszustand bekannt und die Differenzialgleichung beschreibt die zeitliche oder räuml...
Chapter
Qualitätskriterien für Näherungsverfahren sind Konsistenz, Stabilität und Konvergenz. Diese Begriffe wurden schon für die numerischen Methoden für gewöhnliche Differenzialgleichungen eingeführt und werden in diesem Kapitel auf partielle Differenzialgleichungen übertragen. Dies wird so allgemein ausgeführt, dass diese Begriffe für die drei wichtigst...
Chapter
Für die numerischen Verfahren bei partiellen Differenzialgleichungen ist es wichtig, die grundlegenden Eigenschaften der beschriebenen physikalischen Prozesse und die daraus resultierenden Lösungseigenschaften zu kennen. Nur so gelingt es, gute und effiziente numerische Verfahren zu entwickeln. Darum ist eine Übersicht über physikalische Eigenschaf...
Chapter
Auch die Klasse der Finiten-Elemente-Verfahren kann auf den mehrdimensionalen Fall übertragen werden. Die Näherungslösung ist wie bei den Randwertproblemen für gewöhnliche Differenzialgleichungen eine einfache Funktion, die man als Linearkombination von Basisfunktionen darstellt. Dies sind auch hier stückweise Polynome. Für verschiedene Gitterzelle...
Chapter
Neben Anfangswertproblemen stellen sich bei praktischen Anwendungen oft auch Randbedingungen auf beiden Seiten des Rechenintervalls. Statt einem eingespannten Balken und der Lösung eines Anfangswertproblems liegt der Balken auf beiden Seiten auf. Diese beidseitige Lagerung führt auf zwei Randwerte für das Problem. Zur numerische Lösung von Randwert...
Chapter
Die dritte Klasse von numerischen Methoden für partielle Differenzialgleichungen sind die Finite-Volumen-Verfahren, die für hyperbolische Erhaltungsgleichungen abgeleitet werden. Diese Verfahren sind eine direkte Approximation von integralen Mittelwerten in den Gitterzellen. Man benötigt hier keine Voraussetzung an die Stetigkeit der Lösung. Der ze...
Chapter
Die grundlegende Idee bei der Klasse von Differenzenverfahren ist die in der Differenzialgleichung auftretenden Ableitungen durch Differenzenquotienten zu ersetzen. Diese Vorgehensweise ist motiviert durch die Definition der Ableitung als Grenzwert eines Differenzenquotienten. Ist die Schrittweite klein, dann sollte der Differenzenquotient eine gut...
Book
Das Lehrbuch vermittelt die Herleitung numerischer Algorithmen zur Lösung von Differenzialgleichungen und gibt einen Einblick in die praktische Implementierung. Anhand von Beispielen und Übungsaufgaben mit Problemstellungen aus dem Ingenieurbereich werden Eigenschaften und Einsatzbereiche der verschiedenen Verfahren erläutert. Für die Beispiele und...
Chapter
Full-text available
Supercritical fluids are suggested as one of the potential candidates for the next generation nuclear reactor by Generation IV nuclear forum to improve the thermal efficiency. But, supercritical fluids suffer from the deteriorated heat transfer under certain conditions. This deteriorated heat transfer phenomenon is a result of peculiar attenuation...
Preprint
Full-text available
We present a load balancing strategy for hybrid particle-mesh methods that is based on domain decomposition and element-local time measurement. This new strategy is compared to our previous approach, which assumes a constant weighting factor for each particle to determine the computational load. The timer-based load balancing is applied to a plasma...
Preprint
Full-text available
In the context of the validation of PICLas, a kinetic particle suite for the simulation of rarefied, non-equilibrium plasma flows, the biased hypersonic nitrogen flow around a blunted cone was simulated with the Direct Simulation Monte Carlo method. The setup is characterized by a complex flow with strong local gradients and thermal non-equilibrium...
Article
Many particle-based methods require a coupling between particle motion and fluid flows or fields. The particle motion is approximated in phase space, while the fluid flows or fields are calculated on a fixed Eulerian frame of reference. In this work, we present algorithms for locating and tracing particles through curvilinear and unstructured hexah...
Article
Full-text available
In this work, we consider the efficient approximation of low-Mach flows by a high-order scheme. This scheme is a coupling of a discontinuous Galerkin (DG) discretization in space and an implicit/explicit (IMEX) dis-cretization in time. The splitting into linear implicit and nonlinear explicit parts relies heavily on the incompressible solution. The...
Preprint
Full-text available
We propose a novel $hp$-Multilevel Monte Carlo method for the quantification of uncertainties in compressible flows using the Discontinuous Galerkin method as de-terministic solver. The multilevel approach exploits hierarchies of uniformly refined meshes jointly with an increasing polynomial degree for the ansatz space. It allows for a very large r...
Article
We investigate the influence of uncertain input parameters on the aeroacoustic feedback of cavity flows. The so-called Rossiter feedback requires a direct numerical computation of the acoustic noise, which solves hydrodynamics and acoustics simultaneously, in order to capture the interaction of acoustic waves and the hydrodynamics of the ow. Due to...
Chapter
Full-text available
In this chapter, we discuss some of the challenges that arise for the direct numerical computation of noise generation and transport. Noise sources are associated with the non-linearities of the underlying hydrodynamics, i.e. with the turbulent fluctuations across the energy spectrum. Thus, the numerical resolution of these sound sources not only i...
Preprint
Full-text available
In this work, we present a novel data-based approach to turbulence modelling for Large Eddy Simulation (LES) by artificial neural networks. We define the exact closure terms including the discretization operators and generate training data from direct numerical simulations of decaying homogeneous isotropic turbulence. We design and train artificial...
Presentation
The main object of this presentation are Entropy- and kinetic-energy stable discontinuous Galerkin schemes for multi-phase and multi-component flows.
Preprint
Full-text available
In this work, we present a novel, data-based approach to turbulence modelling for Large Eddy Simulation. We define the exact closure terms including the discretization operators and generate training data from direct numerical simulations of decaying homogeneous isotropic turbulence. We design and train artificial neural networks based on local con...
Chapter
This paper summarizes our progress in the application of a high-order discontinuous Galerkin (DG) method for scale resolving fluid dynamics simulations on the Cray XC40 Hazel Hen cluster at HLRS. We present the large eddy simulation (LES) of flow around a wall mounted cylinder, a LES of flow around an airfoil at realistic Reynolds number using a re...
Preprint
Full-text available
We investigate the influence of uncertain input parameters on the aeroacoustic feedback of cavity flows. The so-called Rossiter feedback requires a direct numerical computation of the acoustic noise, which solves hydrodynamics and acoustics simultaneously, in order to capture the interaction of acoustic waves and the hydrodynamics of the flow. Due...
Article
Full-text available
This paper presents a high order hybrid discontinuous Galerkin/finite volume scheme for solving the equations of the magnetohydrodynamics (MHD) and of the relativistic hydrodynamics (SRHD) on quadrilateral meshes. In this approach, for the spatial discretization, an arbitrary high order discontinuous Galerkin spectral element (DG) method is combine...
Conference Paper
The present work analyses the growth of multiple bubbles in superheated liquid jets by means of direct numericalsimulations (DNS). A discontinuous Galerkin approach is used to solve the Euler equations and an adequate in- terface resolution is ensured by applying finite-volume sub-cells in cells with interfaces. An approximate Riemann solver has be...