Christian Rohde
Prof. Dr.
Christian
Rohde


Phone 
0049 711 68565524

Fax 
0049 711 68565599

Room 
7.131 
Email address 
Link

Address

Universität Stuttgart
Institut für Angewandte Analysis und numerische Simulation, Lehrstuhl für Angewandte Mathematik
Pfaffenwaldring 57
70569
Stuttgart
Germany

Consultation 
Friday: 1  2 pm 
Research Interests
 Analysis and numerics for systems of conservation laws
 Finite volume and DiscontinuousGalerkin schemes
 Domain decomposition/Schwarz waveform relaxation
 Heterogenous multiscale methods
 Numerical methods for dynamical systems
 Analysis and numerics for stochastic partial differential equations
 Integrodifferential equations
Fields of applications:
 Shock waves in fluidmechanical applications
 Chemosensitive dynamics of cell populations
 Phase transitions in solid materials
 Phase transitions in liquidvapour systems
 Magnetohydrodynamics in astrophysics and plasmaphysics
 Porous media flow
Recent Preprints
Kuhn, T.; Dürrwächter, J.; Beck, A.; Munz, C.D.; Meyer, F. & Rohde, C.:
Uncertainty Quantification for Direct Aeroacoustic Simulations of Cavity Flows,
2018, (submitted).
@techreport
{Kuhn2018,
author = {Kuhn, T. and Dürrwächter, J. and Beck, A. and Munz, C.D. and Meyer, F. and Rohde, C.}
,
title = {Uncertainty Quantification for Direct Aeroacoustic Simulations of Cavity Flows}
,
year = {2018}
,
volume = {(submitted)}
,
url = {http://www.simtech.unistuttgart.de/publikationen/prints.php?ID=1891}
}
Abstract: We investigate the influence of uncertain input parameters on the aeroacoustic feedback of cavity flows. The socalled 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 to the large bandwidth of spatial and temporal scales, a high order numerical scheme with low dissipation and dispersion error is necessary to preserve important small scale information. Therefore, the opensource CFD solver FLEXI, which is based on a highorder discontinuous Galerkin spectral element method, is used to perform the aforementioned direct simulations of an open cavity configuration with a laminar upstream boundary layer.
To analyse the precision of the deterministic cavity simulation with respect to random input parameters we establish a framework for uncertainty quantification. In particular, a nonintrusive spectral projection method with Legendre and Hermite polynomial basis functions is employed in order to treat uniform and normal probability distributions of the uncertain input. The results indicate a strong, nonlinear dependency of the acoustic feedback mechanism on the investigated uncertain input parameters. An analysis of the stochastic results offers new insights into the noise generation process of open cavity flows and reveals the strength of the implemented uncertainty quantification framework.
Raja Sekhar, G. P.; Sharanya, V. & Rohde, C.:
Effect of surfactant concentration and interfacial slip on the flow past a viscous drop at low surface Péclet number,
erscheint bei Int. J. Multiph. Flow,
2018.
@article
{Rohde,
author = {Raja Sekhar, G. P. and Sharanya, V. and Rohde, Christian}
,
title = {Effect of surfactant concentration and interfacial slip on the flow past a viscous drop at low surface Péclet number}
,
journal = {erscheint bei Int. J. Multiph. Flow}
,
year = {2018}
,
url = {http://arxiv.org/abs/1609.03410}
}
Abstract: The motion of a viscous drop is investigated when the interface is fully covered with a stagnant layer of surfactant in an arbitrary unsteady Stokes flow for the low surface Péclet number limit. The effect of the interfacial slip coefficient on the behavior of the flow field is also considered. The hydrodynamic problem is solved by the solenoidal decomposition method and the drag force is computed in terms of Faxen's laws using a perturbation ansatz in powers of the surface Péclet number. The analytical expressions for the migration velocity of the drop are also obtained in powers of the surface Péclet number. Further instances corresponding to a given ambient flow as uniform flow, Couette flow, Poiseuille flow are analyzed. Moreover, it is observed that, a surfactantinduced crossstream migration of the drop occur towards the centreline in both Couette flow and Poiseuille flow cases. The variation of the drag force and migration velocity is computed for different parameters such as Péclet number, Marangoni number etc.
ArmitiJuber, A. & Rohde, C.:
On Darcyand BrinkmanType Models for TwoPhase Flow in Asymptotically Flat Domains,
2017.
@article
{Armiti2017,
author = {ArmitiJuber, A. and Rohde, C.}
,
title = {On Darcyand BrinkmanType Models for TwoPhase Flow in Asymptotically Flat Domains}
,
year = {2017}
,
url = {https://arxiv.org/abs/1712.07470 }
}
Giesselmann, J.; Meyer, F. & Rohde, C.:
A posteriori error analysis for random scalar conservation laws using the Stochastic Galerkin method.,
2017, (submitted).
@techreport
{Giesselmann2017,
author = {Giesselmann, J. and Meyer, F. and Rohde, C.}
,
title = {A posteriori error analysis for random scalar conservation laws using the Stochastic Galerkin method.}
,
year = {2017}
,
volume = {(submitted)}
,
url = {https://arxiv.org/abs/1709.04351}
}
Abstract: In this article we present an a posteriori error estimator for the spatialstochastic error of a Galerkintype discretisation of an initial value problem for a random hyperbolic conservation law. For the stochastic discretisation we use the Stochastic Galerkin method and for the spatialtemporal discretisation of the Stochastic Galerkin system a RungeKutta Discontinuous Galerkin method. The estimator is obtained using smooth reconstructions of the discrete solution. Combined with the relative entropy stability framework of Dafermos tedafermos2005hyperbolic, this leads to computable error bounds for the spacestochastic discretisation error. \ Moreover, it turns out that the error estimator admits a splitting into one part representing the spatial error, and a remaining term, which can be interpreted as the stochastic error. This decomposition allows us to balance the errors arising from spatial and stochastic discretisation. We conclude with some numerical examples confirming the theoretical findings.
Köppel, M.; Franzelin, F.; Kröker, I.; Oladyshkin, S.; Santin, G.; Wittwar, D.; Barth, A.; Haasdonk, B.; Nowak, W.; Pflüger, D. & Rohde, C.:
Comparison of datadriven uncertainty quantification methods for a carbon dioxide storage benchmark scenario,
2017.
@techreport
{UQcomparison2017,
author = {Köppel, M. and Franzelin, F. and Kröker, I. and Oladyshkin, S. and Santin, G. and Wittwar, D. and Barth, A. and Haasdonk, B. and Nowak, W. and Pflüger, D. and Rohde, C.}
,
title = {Comparison of datadriven uncertainty quantification methods for a carbon dioxide storage benchmark scenario}
,
year = {2017}
,
url = {http://www.simtech.unistuttgart.de/publikationen/prints.php?ID=1759}
}
Abstract: A variety of methods is available to quantify uncertainties arising within the modeling of flow and transport in carbon dioxide storage, but there is a lack of thorough comparisons. Usually, raw data from such storage sites can hardly be described by theoretical statistical distributions since only very limited data is available. Hence, exact information on distribution shapes for all uncertain parameters is very rare in realistic applications. We discuss and compare four different methods tested for datadriven uncertainty quantification based on a benchmark scenario of carbon dioxide storage. In the benchmark, for which we provide data and code, carbon dioxide is injected into a saline aquifer modeled by the nonlinear capillarityfree fractional flow formulation for two incompressible fluid phases, namely carbon dioxide and brine. To cover different aspects of uncertainty quantification, we incorporate various sources of uncertainty such as uncertainty of boundary conditions, of conceptual model definitions and of material properties. We consider recent versions of the following nonintrusive and intrusive uncertainty quantification methods: arbitary polynomial chaos, spatially adaptive sparse grids, kernelbased greedy interpolation and hybrid stochastic Galerkin. The performance of each approach is demonstrated assessing expectation value and standard deviation of the carbon dioxide saturation against a reference statistic based on Monte Carlo sampling. We compare the convergence of all methods reporting on accuracy with respect to the number of model runs and resolution. Finally we offer suggestions about the methods’ advantages and disadvantages that can guide the modeler for uncertainty quantification in carbon dioxide storage and beyond.
Magiera, J. & Rohde, C.:
A Particlebased Multiscale Solver for Compressible LiquidVapor Flow,
erscheint bei Springer Proc. Math. Stat.,
2017.
@article
{MagieraRohdeHyp,
author = {Magiera, J. and Rohde, C.}
,
title = {A Particlebased Multiscale Solver for Compressible LiquidVapor Flow}
,
journal = {erscheint bei Springer Proc. Math. Stat.}
,
year = {2017}
,
note = {submitted}
,
url = {https://arxiv.org/abs/1804.01411}
}
Rohde, C.:
Fully Resolved Compressible TwoPhase Flow: Modelling, Analytical and Numerical Issues,
2017.
@article
{Rohde2017,
author = {Rohde, C.}
,
title = {Fully Resolved Compressible TwoPhase Flow: Modelling, Analytical and Numerical Issues}
,
year = {2017}
}
Seus, D.; Radu, F. A. & Rohde, C.:
A linear domain decomposition method for twophase flow in porous media,
2017.
@inproceedings
{SeusEnumath2017,
author = {Seus, David and Radu, Florin A. and Rohde, Christian}
,
title = {A linear domain decomposition method for twophase flow in porous media}
,
year = {2017}
,
url = {http://arxiv.org/abs/1712.04869}
,
doi = {arXiv:1712.04869}
}
Recent Publications
Raja Sekhar, G. P.; Sharanya, V. & Rohde, C.:
Effect of surfactant concentration and interfacial slip on the flow past a viscous drop at low surface Péclet number,
erscheint bei Int. J. Multiph. Flow,
2018.
@article
{Rohde,
author = {Raja Sekhar, G. P. and Sharanya, V. and Rohde, Christian}
,
title = {Effect of surfactant concentration and interfacial slip on the flow past a viscous drop at low surface Péclet number}
,
journal = {erscheint bei Int. J. Multiph. Flow}
,
year = {2018}
,
url = {http://arxiv.org/abs/1609.03410}
}
Abstract: The motion of a viscous drop is investigated when the interface is fully covered with a stagnant layer of surfactant in an arbitrary unsteady Stokes flow for the low surface Péclet number limit. The effect of the interfacial slip coefficient on the behavior of the flow field is also considered. The hydrodynamic problem is solved by the solenoidal decomposition method and the drag force is computed in terms of Faxen's laws using a perturbation ansatz in powers of the surface Péclet number. The analytical expressions for the migration velocity of the drop are also obtained in powers of the surface Péclet number. Further instances corresponding to a given ambient flow as uniform flow, Couette flow, Poiseuille flow are analyzed. Moreover, it is observed that, a surfactantinduced crossstream migration of the drop occur towards the centreline in both Couette flow and Poiseuille flow cases. The variation of the drag force and migration velocity is computed for different parameters such as Péclet number, Marangoni number etc.
Rohde, C. & Zeiler, C.:
On Riemann Solvers and Kinetic Relations for Isothermal TwoPhase Flows with Surface Tension,
erscheint bei Z. Angew. Math. Phys.,
2018.
@article
{Rohde2016,
author = {Rohde, C. and Zeiler, C.}
,
title = {On Riemann Solvers and Kinetic Relations for Isothermal TwoPhase Flows with Surface Tension}
,
journal = {erscheint bei Z. Angew. Math. Phys.}
,
year = {2018}
,
url = {http://arxiv.org/abs/1611.02243}
}
Seus, D.; Mitra, K.; Pop, I. S.; Radu, F. A. & Rohde, C.:
A linear domain decomposition method for partially saturated flow in porous media ,
Comp. Methods in Appl. Mech. Eng,
2018, 333, 331355.
@article
{SeusMitra2018,
author = {David Seus and Koondanibha Mitra and Iuliu Sorin Pop and Florin Adrian Radu and Christian Rohde}
,
title = {A linear domain decomposition method for partially saturated flow in porous media }
,
journal = {Comp. Methods in Appl. Mech. Eng}
,
year = {2018}
,
volume = {333}
,
pages = {331355}
,
url = {https://www.sciencedirect.com/science/article/pii/S0045782518300318}
,
doi = {https://doi.org/10.1016/j.cma.2018.01.029}
}
Abstract: Abstract The Richards equation is a nonlinear parabolic equation that is commonly used for modelling saturated/unsaturated flow in porous media. We assume that the medium occupies a bounded Lipschitz domain partitioned into two disjoint subdomains separated by a fixed interface Γ . This leads to two problems defined on the subdomains which are coupled through conditions expressing flux and pressure continuity at Γ . After an Euler implicit discretisation of the resulting nonlinear subproblems, a linear iterative ( L type) domain decomposition scheme is proposed. The convergence of the scheme is proved rigorously. In the last part we present numerical results that are in line with the theoretical finding, in particular the convergence of the scheme under mild restrictions on the time step size. We further compare the scheme to other approaches not making use of a domain decomposition. Namely, we compare to a Newton and a Picard scheme. We show that the proposed scheme is more stable than the Newton scheme while remaining comparable in computational time, even if no parallelisation is being adopted. After presenting a parametric study that can be used to optimise the proposed scheme, we briefly discuss the effect of parallelisation and give an example of a fourdomain implementation.
Chalons, C.; Magiera, J.; Rohde, C. & Wiebe, M.:
A FiniteVolume Tracking Scheme for TwoPhase Compressible Flow,
erscheint bei Springer Proc. Math. Stat.,
2017.
@article
{MariaHyp,
author = {Chalons, C. and Magiera, J. and Rohde, C. and Wiebe, M.}
,
title = {A FiniteVolume Tracking Scheme for TwoPhase Compressible Flow}
,
journal = {erscheint bei Springer Proc. Math. Stat.}
,
year = {2017}
,
note = {submitted}
}
Chalons, C.; Rohde, C. & Wiebe, M.:
A Finite Volume Method for Undercompressive Shock Waves in Two Space Dimensions,
ESAIM Math. Model. Numer. Anal.,
2017, 51, 19872015.
@article
{Chalons2016,
author = {Chalons, Christophe. and Rohde, Christian and Wiebe, Maria}
,
title = {A Finite Volume Method for Undercompressive Shock Waves in Two Space Dimensions}
,
journal = {ESAIM Math. Model. Numer. Anal.}
,
year = {2017}
,
volume = {51}
,
number = {5}
,
pages = {19872015}
,
url = {https://www.esaimm2an.org/component/article?access=doi&doi=10.1051/m2an/2017027}
,
doi = {https://doi.org/10.1051/m2an/2017027}
}
Fechter, S.; Munz, C.D.; Rohde, C. & Zeiler, C.:
A sharp interface method for compressible liquidvapor flow with phase transition and surface tension,
J. Comput. Phys.,
2017, 336, 347374.
@article
{Zeiler2015,
author = {Stefan Fechter and ClausDieter Munz and Christian Rohde and Christoph Zeiler}
,
title = {A sharp interface method for compressible liquidvapor flow with phase transition and surface tension}
,
journal = {J. Comput. Phys.}
,
year = {2017}
,
volume = {336}
,
pages = {347374}
,
url = {http://www.sciencedirect.com/science/article/pii/S0021999117300943}
,
doi = {10.1016/j.jcp.2017.02.001}
}
Abstract: The numerical approximation of nonisothermal liquidvapor flow within the compressible regime is a difficult task because complex physical effects at the phase interfaces can govern the global flow behavior. We present a sharp interface approach which treats the interface as a shockwave like discontinuity. Any mixing of fluid phases is avoided by using the flow solver in the bulk regions only, and a ghostfluid approach close to the interface. The coupling states for the numerical solution in the bulk regions are determined by the solution of local multiphase Riemann problems across the interface. The Riemann solution accounts for the relevant physics by enforcing appropriate jump conditions at the phase boundary. A wide variety of interface effects can be handled in a thermodynamically consistent way. This includes surface tension or mass/energy transfer by phase transition. Moreover, the local normal speed of the interface, which is needed to calculate the time evolution of the interface, is given by the Riemann solution. The interface tracking itself is based on a levelset method. The focus in this paper is the description of the multiphase Riemann solver and its usage within the sharp interface approach. Onedimensional problems are selected to validate the approach. Finally, the threedimensional simulation of a wobbling droplet and a shock droplet interaction in two dimensions are shown. In both problems phase transition and surface tension determine the global bulk behavior.
Fechter, S.; Munz, C.D.; Rohde, C. & Zeiler, C.:
Approximate Riemann solver for compressible liquid vapor flow with phase transition and surface tension,
Comput. & Fluids,
2017.
@article
{FZMR,
author = {Stefan Fechter and ClausDieter Munz and Christian Rohde and Christoph Zeiler}
,
title = {Approximate Riemann solver for compressible liquid vapor flow with phase transition and surface tension}
,
journal = {Comput. & Fluids}
,
year = {2017}
,
url = {http://www.sciencedirect.com/science/article/pii/S004579301730107X}
,
doi = {10.1016/j.compfluid.2017.03.026}
}
Köppel, M.; Kröker, I. & Rohde, C.:
Intrusive Uncertainty Quantification for HyperbolicElliptic Systems Governing TwoPhase Flow in Heterogeneous Porous Media,
Comput. Geosci.,
2017, 21, 807832.
@article
{Koeppel2016,
author = {Köppel, Markus and Kröker, Ilja and Rohde, Christian}
,
title = {Intrusive Uncertainty Quantification for HyperbolicElliptic Systems Governing TwoPhase Flow in Heterogeneous Porous Media}
,
journal = {Comput. Geosci.}
,
year = {2017}
,
volume = {21}
,
pages = {807832}
,
url = {https://link.springer.com/article/10.1007%2Fs105960179662z}
,
doi = {10.1007/s105960179662z}
}
Kutter, M.; Rohde, C. & Sändig, A.M.:
WellPosedness of a Two Scale Model for Liquid Phase Epitaxy with Elasticity,
Contin. Mech. Thermodyn.,
2017, 29, 9891016.
@article
{KRS2014,
author = {Kutter, Michael and Rohde, Christian and Sändig, AnnaMargarete}
,
title = {WellPosedness of a Two Scale Model for Liquid Phase Epitaxy with Elasticity}
,
journal = {Contin. Mech. Thermodyn.}
,
year = {2017}
,
volume = {29}
,
number = {4}
,
pages = {9891016}
,
url = {http://dx.doi.org/10.1007/s0016101504621}
,
doi = {10.1007/s0016101504621}
}
Magiera, J. & Rohde, C.:
A Particlebased Multiscale Solver for Compressible LiquidVapor Flow,
erscheint bei Springer Proc. Math. Stat.,
2017.
@article
{MagieraRohdeHyp,
author = {Magiera, J. and Rohde, C.}
,
title = {A Particlebased Multiscale Solver for Compressible LiquidVapor Flow}
,
journal = {erscheint bei Springer Proc. Math. Stat.}
,
year = {2017}
,
note = {submitted}
,
url = {https://arxiv.org/abs/1804.01411}
}
Teaching
Winter term 2017:
Further information
Complete list of Preprints and Publications
.