Christian Rohde
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View article: Comparison of entropy stable collocation high-order DG methods for compressible turbulent flows
Comparison of entropy stable collocation high-order DG methods for compressible turbulent flows Open
View article: Existence and stability of the Riemann solutions for a non-symmetric Keyfitz--Kranzer type model
Existence and stability of the Riemann solutions for a non-symmetric Keyfitz--Kranzer type model Open
In this article, we develop a new hyperbolic model governing the first-order dynamics of a thin film flow under the influence of gravity and solute transport. The obtained system turns out to be a non-symmetric Keyfitz-Kranzer type system.…
View article: Statistical conservation laws for scalar model problems: Hierarchical evolution equations
Statistical conservation laws for scalar model problems: Hierarchical evolution equations Open
The probability density functions (PDFs) for the solution of the incompressible Navier-Stokes equation can be represented by a hierarchy of linear equations. This article develops new hierarchical evolution equations for PDFs of a scalar c…
View article: Entropy stable high-order discontinuous Galerkin spectral-element methods on curvilinear, hybrid meshes
Entropy stable high-order discontinuous Galerkin spectral-element methods on curvilinear, hybrid meshes Open
Hyperbolic-parabolic partial differential equations are widely used for the modeling of complex, multiscale problems. High-order methods such as the discontinuous Galerkin (DG) scheme are attractive candidates for their numerical approxima…
View article: A generalized Riemann problem solver for a hyperbolic model of two-layer thin film flow
A generalized Riemann problem solver for a hyperbolic model of two-layer thin film flow Open
In this paper, a second-order generalized Riemann problem (GRP) solver is developed for a two-layer thin film model. Extending the first-order Godunov approach, the solver is used to construct a temporal-spatial coupled second-order GRP-ba…
View article: A hyperbolic relaxation approximation of the incompressible Navier-Stokes equations with artificial compressibility
A hyperbolic relaxation approximation of the incompressible Navier-Stokes equations with artificial compressibility Open
View article: Mathematical Justification of a Baer$-$Nunziato Model for a Compressible Viscous Fluid with Phase Transition
Mathematical Justification of a Baer$-$Nunziato Model for a Compressible Viscous Fluid with Phase Transition Open
In this work, we justify a Baer$-$Nunziato system including appropriate closure terms as the macroscopic description of a compressible viscous fluid that can occur in a liquid or a vapor phase in the isothermal framework. As a mathematical…
View article: Two-phase pore-network model for evaporation-driven salt precipitation -- representation and analysis of pore-scale processes
Two-phase pore-network model for evaporation-driven salt precipitation -- representation and analysis of pore-scale processes Open
Evaporation-driven salt precipitation occurs in different contexts and leads to challenges in case of e.g. soil salinization or stress-introducing precipitation in building material. During evaporation, brine in porous media gets concentra…
View article: Data-driven geometric parameter optimization for PD-GMRES
Data-driven geometric parameter optimization for PD-GMRES Open
Restarted GMRES is a robust and widely used iterative solver for linear systems. The control of the restart parameter is a key task to accelerate convergence and to prevent the well-known stagnation phenomenon. We focus on the Proportional…
View article: A phase-field approach to model evaporation from porous media: Modeling and upscaling
A phase-field approach to model evaporation from porous media: Modeling and upscaling Open
View article: A hyperbolic model for two-layer thin film flow with a perfectly soluble anti-surfactant
A hyperbolic model for two-layer thin film flow with a perfectly soluble anti-surfactant Open
We consider the motion of a two-phase thin film that consists of two immiscible viscous fluids and is endowed with an anti-surfactant solute. The presence of such solute particles induces variations of the surface tension and interfacial s…
View article: A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow
A Note on Hyperbolic Relaxation of the Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flow Open
We consider the two-phase dynamics of two incompressible and immiscible fluids. As a mathematical model we rely on the Navier-Stokes-Cahn-Hilliard system that belongs to the class of diffuse-interface models. Solutions of the Navier-Stokes…
View article: A hyperbolic relaxation system of the incompressible Navier-Stokes equations with artificial compressibility
A hyperbolic relaxation system of the incompressible Navier-Stokes equations with artificial compressibility Open
We introduce a new hyperbolic approximation to the incompressible Navier-Stokes equations by incorporating a first-order relaxation and using the artificial compressibility method. With two relaxation parameters in the model, we rigorously…
View article: Muskat-Leverett two-phase flow in thin cylindric porous media: Asymptotic approach
Muskat-Leverett two-phase flow in thin cylindric porous media: Asymptotic approach Open
A reduced-dimensional asymptotic modelling approach is presented for the analysis of two-phase flow in a thin cylinder with aperture of order $\mathcal{O}(\varepsilon),$ where $\varepsilon$ is a small positive parameter. We consider a nonl…
View article: Mathematical Challenges for the Theory of Hyperbolic Balance Laws in Fluid Mechanics: Complexity, Scales, Randomness
Mathematical Challenges for the Theory of Hyperbolic Balance Laws in Fluid Mechanics: Complexity, Scales, Randomness Open
Understanding the dynamics of hyperbolic balance laws is of paramount interest in the realm of fluid mechanics. Nevertheless, fundamental questions on the analysis and the numerics for distinctive hyperbolic features related to turbulent f…
View article: Investigation of Different Throat Concepts for Precipitation Processes in Saturated Pore-Network Models
Investigation of Different Throat Concepts for Precipitation Processes in Saturated Pore-Network Models Open
The development of reliable mathematical models and numerical discretization methods is important for the understanding of salt precipitation in porous media, which is relevant for environmental problems like soil salinization. Models on t…
View article: Reduced-dimensional modelling for nonlinear convection-dominated flow in cylindric domains
Reduced-dimensional modelling for nonlinear convection-dominated flow in cylindric domains Open
The aim of the paper is to construct and justify asymptotic approximations for solutions to quasilinear convection–diffusion problems with a predominance of nonlinear convective flow in a thin cylinder, where an inhomogeneous nonlinear Rob…
View article: A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate
A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate Open
Understanding the dynamics of phase boundaries in fluids requires quantitative knowledge about the microscale processes at the interface. We consider the sharp-interface motion of the compressible two-component flow and propose a heterogen…
View article: Reduced-dimensional modelling for nonlinear convection-dominated flow in cylindric domains
Reduced-dimensional modelling for nonlinear convection-dominated flow in cylindric domains Open
The aim of the paper is to construct and justify asymptotic approximations for solutions to quasilinear convection-diffusion problems with a predominance of nonlinear convective flow in a thin cylinder, where an inhomogeneous nonlinear Rob…
View article: Rigorous derivation of discrete fracture models for Darcy flow in the limit of vanishing aperture
Rigorous derivation of discrete fracture models for Darcy flow in the limit of vanishing aperture Open
We consider single-phase flow in a fractured porous medium governed by Darcy's law with spatially varying hydraulic conductivity matrices in both bulk and fractures. The width-to-length ratio of a fracture is of the order of a small parame…
View article: A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate
A Multiscale Method for Two-Component, Two-Phase Flow with a Neural Network Surrogate Open
Understanding the dynamics of phase boundaries in fluids requires quantitative knowledge about the microscale processes at the interface. We consider the sharp-interface motion of compressible two-component flow, and propose a heterogeneou…
View article: Rigorous Derivation of Discrete Fracture Models for Darcy Flow in the Limit of Vanishing Aperture
Rigorous Derivation of Discrete Fracture Models for Darcy Flow in the Limit of Vanishing Aperture Open
We consider single-phase flow in a fractured porous medium governed by Darcy's law with spatially varying hydraulic conductivity matrices in both bulk and fractures. The width-to-length ratio of a fracture is of the order of a small parame…
View article: Puiseux asymptotic expansions for convection-dominated transport problems in thin graph-like networks: strong boundary interactions
Puiseux asymptotic expansions for convection-dominated transport problems in thin graph-like networks: strong boundary interactions Open
This article completes the study of the influence of the intensity parameter $α$ in the boundary condition $\varepsilon \partial_{\boldsymbolν_\varepsilon} u_\varepsilon - u_\varepsilon \, \overrightarrow{V_\varepsilon}\boldsymbol{\cdot}\b…
View article: Well-posedness for a stochastic Camassa–Holm type equation with higher order nonlinearities
Well-posedness for a stochastic Camassa–Holm type equation with higher order nonlinearities Open
View article: Asymptotic approximations for semilinear parabolic convection-dominated transport problems in thin graph-like networks
Asymptotic approximations for semilinear parabolic convection-dominated transport problems in thin graph-like networks Open
We consider time-dependent convection-diffusion problems with high Péclet number of order $\mathcal{O}(\varepsilon^{-1})$ in thin three-dimensional graph-like networks consisting of cylinders that are interconnected by small domains (nodes…
View article: Nordic Salmon: Value added processing in Nordic aquaculture
Nordic Salmon: Value added processing in Nordic aquaculture Open
The workshop on value added processing of farmed fish in the Nordic explored options and assessed the feasibility of value added production in the region. It brought together 45 participants from various sectors, including salmon farms, …
View article: Nordic Salmon: Value added processing in Nordic aquaculture
Nordic Salmon: Value added processing in Nordic aquaculture Open
<p> </p>\n\n<p>The workshop on value added processing of farmed fish in the Nordic explored options and assessed the feasibility of value added production in the region. It brought together 45 participants from vario…
View article: Towards hybrid two‐phase modelling using linear domain decomposition
Towards hybrid two‐phase modelling using linear domain decomposition Open
The viscous flow of two immiscible fluids in a porous medium on the Darcy scale is governed by a system of nonlinear parabolic equations. If infinite mobility of one phase can be assumed (e.g., in soil layers in contact with the atmosphere…
View article: Asymptotic expansion for convection-dominated transport in a thin graph-like junction
Asymptotic expansion for convection-dominated transport in a thin graph-like junction Open
We consider for a small parameter $\varepsilon >0$ a parabolic convection-diffusion problem with Péclet number of order $\mathcal{O}(\varepsilon^{-1})$ in a three-dimensional graph-like junction consisting of thin curvilinear cylinders wit…
View article: A Relaxation Model for the Non-Isothermal Navier-Stokes-Korteweg Equations in Confined Domains
A Relaxation Model for the Non-Isothermal Navier-Stokes-Korteweg Equations in Confined Domains Open
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…