## About

52

Publications

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Introduction

My name is Maurits Silvis and I am a guest researcher at the Chair of Fluid Dynamics of the Technical University of Darmstadt, Germany. Previously, I was a PhD student at the University of Groningen, The Netherlands. I focused on improving turbulence models for large-eddy simulations of incompressible flows. In particular, I devised a framework of constraints for the construction of physics-based subgrid-scale models. I also worked on a new subgrid-scale model for rotating turbulent flows.

## Publications

Publications (52)

We study the construction of subgrid-scale models for large-eddy simulation of incompressible turbulent flows. In particular, we aim to consolidate a systematic approach of constructing subgrid-scale models, based on the idea that it is desirable that subgrid-scale models are consistent with the mathematical and physical properties of the Navier-St...

We focus on subgrid-scale modeling for large-eddy simulation of incompressible turbulent flows. In particular, we follow a systematic approach that is based on the idea that subgrid-scale models should preserve fundamental properties of the Navier–Stokes equations and turbulent stresses. To that end, we discuss the symmetries and conservation laws...

Direct numerical simulations of the incompressible Navier-Stokes equations are not feasible yet for most practical turbulent flows. Therefore, dynamically less complex mathematical formulations are necessary for coarse-grained simulations. In this regard, eddy-viscosity models for Large-Eddy Simulation (LES) are probably the most popular example th...

Rotating turbulent flows form a challenging test case for large-eddy simulation (LES). We, therefore, propose and validate a new subgrid-scale (SGS) model for such flows. The proposed SGS model consists of a dissipative eddy viscosity term as well as a nondissipative term that is nonlinear in the rate-of-strain and rate-of-rotation tensors. The two...

Fluid flows are everywhere. Consider, for example, rivers, the flow of air in the atmosphere and the blood that is flowing through our veins. Most fluid flows are very chaotic, or turbulent, and the prediction of their behavior is essential for many applications, including the design of cars, boats and airplanes. However, accurately predicting turb...

Predicting the behavior of turbulent flows using large-eddy simulation requires a modeling of the subgrid-scale stress tensor. This tensor can be approximated using mixed models, which combine the dissipative nature of functional models with the capability of structural models to approximate out-of-equilibrium effects. We propose a mathematical bas...

Predicting the behavior of turbulent flows using large-eddy simulation requires modeling of the subgrid-scale stress tensor. This tensor can be approximated using mixed models, which combine the dissipative nature of functional models with the capability of structural models to approximate out-of-equilibrium effects. The currently existing mixed mo...

Rotating turbulent flows form a challenging test case for large-eddy simulation (LES). We, therefore, propose and validate a new subgrid-scale (SGS) model for such flows. The proposed SGS model consists of a dissipative eddy viscosity term as well as a nondissipative term that is nonlinear in the rate-of-strain and rate-of-rotation tensors. The two...

We aim to design subgrid-scale models for large-eddy simulation of rotating turbulent flows. Rotating turbulent flows form a challenging test case for eddy viscosity models due to the presence of the conservative Coriolis force. We therefore propose a new subgrid-scale model that, in addition to a dissipative eddy viscosity term, contains a nondiss...

The Navier-Stokes equations describe the motion of viscous fluids. In order to predict turbulent flows with reasonable computational time and accuracy, these equations are spatially filtered according to the large-eddy simulation (LES) approach. The current work applies a volume filtering procedure according to Schumann (1975). To demonstrate the p...

The Navier-Stokes equations describe the motion of viscous fluids. In order to predict turbulent flows with reasonable computational time and accuracy, these equations are spatially filtered, resulting in the large-eddy simulation equations, which are not closed. The closure of these equations is carried out by modeling. The subgrid-scale stress te...

The Navier-Stokes equations describe the motion of viscous fluids. In order to predict turbulent flows with reasonable computational time and accuracy, these equations are spatially filtered according to the large-eddy simulation (LES) approach. The current work applies a volume filtering procedure according to Schumann. To demonstrate the procedur...

It is well known that the governing equations of fluid dynamics, the Navier-Stokes equations, are invariant under certain transformations, such as instantaneous rotations of the coordinate system and the Galilean transformation. It has since long been realized that it is desirable that these symmetries are satisfied in large-eddy simulations of tur...

It is well known that the governing equations of fluid dynamics, the Navier-Stokes equations, are invariant under certain transformations, such as instantaneous rotations of the coordinate system and the Galilean transformation. It has since long been realized that it is desirable that these symmetries are satisfied in large-eddy simulations of tur...

Numerical solution of the equations of fluid dynamics, the Navier-Stokes equations, is not feasible for most practical turbulent flows, due to high resolution requirements. Therefore, usually turbulence models are employed. We present a framework of constraints for the assessment and creation of turbulence models, based on the idea of preserving th...

We studied the construction of subgrid-scale models for large-eddy simulation of incom-pressible turbulent flows, focusing on consistency with important mathematical and physical properties. In particular, we considered the symmetries of the Navier-Stokes equations, and the near-wall scaling and dissipation behavior of the turbulent stresses. After...

Rotating turbulent flows form a challenging test case for large-eddy simulations with commonly employed eddy viscosity models. We therefore propose a new subgrid-scale model that, in addition to an eddy viscosity term, contains a term that is nonlinear in the local velocity gradient through the rate-of-strain and rate-of-rotation tensors. The nonli...

Rotating turbulent flows form a challenging test case for large-eddy simulations with commonly employed eddy viscosity models. We therefore propose a new subgrid-scale model that, in addition to an eddy viscosity term, contains a term that is nonlinear in the local velocity gradient through the rate-of-strain and rate-of-rotation tensors. The nonli...

A new definition of the subgrid characteristic length, δ, for large-eddy simulation (LES) is proposed with the aim to answer the following research question: can we find a simple and robust definition of δ that minimizes the effect of mesh anisotropies on the performance of subgrid scale (SGS) models?

We aim to design subgrid-scale models for large-eddy simulation of rotating turbulent flows. Rotating turbulent flows form a challenging test case for large-eddy simulation due to the presence of the Coriolis force. The Coriolis force conserves the total kinetic energy while transporting it from small to large scales of motion, leading to the forma...

We aim to design subgrid-scale models for large-eddy simulation of rotating turbulent flows. Rotating turbulent flows form a challenging test case for large-eddy simulation due to the presence of the Coriolis force. The Coriolis force conserves the total kinetic energy while transporting it from small to large scales of motion, leading to the forma...

We aim to design subgrid-scale models for large-eddy simulation of rotating turbulent flows. Rotating turbulent flows form a challenging test case for large-eddy simulation due to the presence of the Coriolis force. The Coriolis force conserves the total kinetic energy while transporting it from small to large scales of motion, leading to the forma...

Rotating turbulent flows form a challenging test case for large-eddy simulations with commonly used eddy viscosity models. We therefore consider subgrid-scale models with an additional term, which is nonlinear in the local velocity gradient.

Rotating turbulent flows form a challenging test case for large-eddy simulations with commonly used eddy viscosity models. We therefore consider subgrid-scale models with an additional term, which is nonlinear in the local velocity gradient.

Rotating turbulent flows form a challenging test case for commonly used eddy viscosity models. We therefore consider subgrid-scale models with an additional term, which is nonlinear in the local velocity gradient. We show that this nonlinear model term leads to improved predictions of energy transfer in rotating homogeneous isotropic turbulence. We...

Rotating turbulent flows form a challenging test case for
commonly used eddy viscosity models. We therefore consider
subgrid-scale models with an additional term, which is nonlinear
in the local velocity gradient. We show that this nonlinear
model term leads to improved predictions of energy transfer
in rotating homogeneous isotropic turbulence. We...

We study subgrid-scale modeling for large-eddy simulation (LES) of anisotropic turbulent flows on anisotropic grids. In particular, we show how the addition of a velocity-gradient-based nonlinear model term to an eddy viscosity model provides a better representation of energy transfer. This is shown to lead to improved predictions of rotating and n...

This paper discusses subgrid models for large-eddy simulation of anisotropic flows using anisotropic grids. In particular, we are looking into ways to model not only the subgrid dissipation, but also transport processes, since these are expected to play an important role in rotating turbulent flows. We therefore consider the use of nonlinear subgri...

This paper discusses subgrid models for large-eddy simulation of anisotropic flows using anisotropic grids. In particular, we are looking into ways to model not only the subgrid dissipation, but also transport processes, since these are expected to play an important role in rotating turbulent flows. We therefore consider subgrid-scale models of the...

Most practical turbulent flows cannot be computed directly from the Navier-Stokes equations, because not enough resolution is available to resolve all relevant scales of motion. We therefore turn to large-eddy simulation (LES), in which the large scales of motion in a flow are explicitly computed, whereas effects of small-scale motions have to be m...

Most practical turbulent flows cannot be computed directly from the Navier-Stokes equations, because not enough resolution is available to resolve all relevant scales of motion. We therefore turn to large-eddy simulation (LES), in which the large scales of motion in a flow are explicitly computed, whereas effects of small-scale motions have to be m...

Using a symmetry adapted polaron transformation of the Holstein Hamiltonian, we study the interplay of electronic excitation-vibration couplings, resonance excitation transfer interactions, and temperature in the linear absorption spectra of molecular J-aggregates. Semi-analytical expressions for the spectra are derived and compared with results ob...

Most practical turbulent flows cannot be computed directly from the Navier-Stokes equations, because not enough resolution is available to resolve all relevant scales of motion. We therefore turn to large-eddy simulation (LES), in which the large scales of motion in a flow are explicitly computed, whereas effects of small-scale motions have to be m...

This paper discusses novel relaxation models for large eddy simulation (LES) of turbulent flows. To verify that the scales of motion are truncated properly by the LES-model an explicit box filter is introduced. The relaxation parameter is then determined such that the production of all box-fitting scales is counterbalanced by the dissipation associ...

In the current study we aim to go beyond the dissipative description of turbulent flows that is provided by eddy viscosity models for large-eddy simulation. We further aim to make this description consistent with a number of physical constraints. Starting from a general subgrid-scale model that is nonlinear in the velocity gradient, we show how a f...

In the current study we aim to go beyond the dissipative description of turbulent flows that is provided by eddy viscosity models for large-eddy simulation. We further aim to make this description consistent with a number of physical constraints. Starting from a general subgrid-scale model that is nonlinear in the velocity gradient, we show how a f...

Assuming a general constitutive relation for the turbulent stresses in terms of the local large-scale velocity gradient, we constructed a class of subgrid-scale models for large-eddy simulation that are consistent with important physical and mathematical properties. In particular, they preserve symmetries of the Navier-Stokes equations and exhibit...

In the current study we aim to go beyond the purely dissipative description of turbulent flows that is provided by eddy viscosity models for large-eddy simulation. We further aim to make this description physically consistent. Starting from a general subgrid-scale model that is nonlinear in the velocity gradient, we show how both dissipative and no...

In the current study we aim to go beyond the dissipative description of turbulent flows that is provided by eddy viscosity models for large-eddy simulation. As a starting point, we consider a general subgrid-scale model that is nonlinear in the velocity gradient. To reduce the number of degrees of freedom of the model, we propose a first-principles...

In the current study we aim to go beyond the dissipative description of turbulent flows that is provided by eddy viscosity models for large-eddy simulation. As a starting point, we consider a general subgrid-scale model that is nonlinear in the velocity gradient. To reduce the number of degrees of freedom of the model, we propose a first-principles...

In the current study we aim to go beyond the dissipative description of turbulent flows that is provided by eddy viscosity models for large-eddy simulation. As a starting point, we consider a general subgrid-scale model that is nonlinear in the velocity gradient. To reduce the number of degrees of freedom of the model, we propose a first-principles...

Osborne Reynolds can be seen as one of the founding fathers of modern
turbulence research. During his almost-40-year-long academic career he worked
on an wide range of physics and engineering problems, publishing more
than 70 papers along the way. Two of these papers have had a very profound
impact on the way we think about turbulence, and we’ll lo...

In the current study we aim to go beyond the dissipative description of turbulent flows provided by eddy viscosity models for large-eddy simulation. As a starting point, we consider a general subgrid-scale model that is nonlinear in the velocity gradient. To reduce the number of degrees of freedom of the model, we propose a first-principles-based p...

We study a general subgrid-scale model that is nonlinear in the velocity gradient. As this model forms an extension of the commonly used eddy-viscosity and gradient models, we wonder whether it captures the transfer of energy from large to small scales and vice versa, as well as the effects of small-scale motions on the distribution of energy among...

In the current presentation we will look at large-eddy simulation (LES) as a means to describe and predict the behavior of turbulent flows. After an introduction into LES, we focus on ways to tackle the closure problem that comes with it. In particular, we will consider a closure model called the gradient (or Clark) model. Following from an approxi...

In the current presentation we will look at large-eddy simulation (LES) as a means to describe and predict the behavior of turbulent flows. After an introduction into LES, we focus on ways to tackle the closure problem that comes with it. In particular, we will consider a closure model called the gradient (or Clark) model. Following from an approxi...

In this paper, we address the question: when does the LES model stop the production of smaller scales of motion from continuing at the filter scale?

Motivated by suggestions that exciton-phonon coupling plays an important role in determining the electronic and optical properties of molecular aggregates, in the current research project we have aimed at modeling such dynamical vibrational effects. Taking the Holstein Hamiltonian as a starting point, a new method that utilizes a variational polaro...

Ever since the discovery of molecular aggregates by Jelley and Scheibe in the 1930s, much study has been devoted to their fascinating optical and energy transport properties. These features have inspired the development of complex molecular systems, having potential applications as light-harvesting systems or nanowires. Both the optical and energy...

We investigate the influence of a dynamical environment on the optical properties of molecular aggregates by using a polaron transformation approach that accounts for both weak and strong exciton-phonon coupling regimes as well as thermal effects. Ever since the discovery of molecular aggregates by Jelley and Scheibe in the 1930s much study has bee...

The remarkable spectral signatures and outstanding energy transport properties of molecular aggregates arise from the collective nature of the excitations. Crucial in understanding and ultimately control of these fascinating features, is the interplay between intermolecular resonance interactions, disorder and coupling to a dynamical environment. W...

In this thesis the formalisms of quaternions and biquaternions have been employed to reformulate
Dirac’s relativistic wave equation and to investigate claims concerning elegance, intuitiveness and
new physical results of such a formulation. In this fashion, an elegant formulation of the Dirac
equation in terms of biquaternions was found. After this...

## Questions

Question (1)

For as long (or rather, short) as I've been in the fields of turbulence research and computational fluid dynamics, I've been told that the Reynolds-averaged Navier-Stokes (RANS) approach of modeling and simulating turbulent flows is based on ensemble or time averaging of the Navier-Stokes equations. Here, the Reynolds stresses have to be modeled to close the resulting equations before they can be solved.

On the other hand, large-eddy simulations (LES) are (formally) based on (spatially) filtering the Navier-Stokes equations. In this case, the subgrid-scale or subfilter-scale stresses have to be modeled. In a commonly used approach to large-eddy simulations, the theoretical approach/description of filtering is just that: a theoretical formality that is not used in practice. A practical large-eddy simulation then consists in solving the Navier-Stokes equations on a grid that is too coarse to resolve all scales up to the Kolmogorov scale, but fine enough to still resolve the large scales. An extra forcing term (the subgrid-scale model) is added to model all the missing physics (for example, the dissipation of kinetic energy).

I wonder now how actual RANS simulations are performed, especially given the existence of hybrid RANS/LES methods? Does time or ensemble averaging ever play a role in an actual practical RANS simulation? I could imagine that time averaging implicitly plays a role if practical RANS simulations are like iterative methods that try to obtain a steady-state solution of the Navier-Stokes equations on a coarse grid. But then I don't understand how switching between RANS and LES modes, like in hybrid RANS/LES is possible. Or is the time/ensemble averaging of RANS just part of the theoretical description that is not used in practice, as is the case with filtering in the practical approach to LES I describe above? Is a practical RANS simulation then 'just' a very-coarse-grid simulation of the Navier-Stokes equations? (In which, for example, eddy viscosity or Reynolds stress models just serve as extra forcing terms to capture any missing physics?)

## Projects

Projects (3)

Rotating turbulent flows are ubiquitous in geophysics, astrophysics and engineering. Consider, for example, flows in the oceans, in the atmosphere or in turbomachinery. Understanding and being able to predict the behavior of such flows is of great importance for many applications. However, despite the increased fundamental understanding, predicting rotating turbulent flows remains a challenge. This is mainly because such flows often contain a large range of scales of motion, which cannot be resolved using direct numerical simulations. With the aim to improve the numerical prediction of incompressible rotating turbulent flows, we, therefore, turn to large-eddy simulation.
In large-eddy simulation, the large scales of motion in a flow are explicitly computed, whereas the effects of the small-scale motions are modeled using subgrid-scale models. Eddy viscosity models are commonly used subgrid-scale models. These subgrid-scale models prescribe the net dissipation of kinetic energy caused by small-scale turbulent motions. Although eddy viscosity models are effective in many cases, they have an important drawback. They model turbulence as an essentially dissipative process. Given the importance of energy transfer in rotating turbulent flows, it seems unlikely that eddy viscosity models are always suitable for large-eddy simulations of such flows.
In this project, we, therefore, propose a new subgrid-scale model for large-eddy simulations of incompressible rotating turbulent flows. This subgrid-scale model consists of a dissipative eddy viscosity term as well as a nondissipative term that is nonlinear in the rate-of-strain and rate-of-rotation tensors. We study and validate this subgrid-scale model using detailed direct numerical and large-eddy simulations of two canonical rotating turbulent flows, namely, rotating decaying turbulence and spanwise-rotating plane-channel flow. We also provide a comparison with the commonly used dynamic Smagorinsky model, the scaled anisotropic minimum-dissipation model and the vortex-stretching-based eddy viscosity model.

The Navier–Stokes equations form a very accurate mathematical model for turbulent flows. The behavior of most turbulent flows can, however, not (yet) directly be predicted using these equations, because the current computational power does not suffice to resolve all physically relevant scales of motion in such flows. We, therefore, turn to large-eddy simulation to predict the large-scale behavior of incompressible turbulent flows. In large-eddy simulation, the large scales of motion in a flow are explicitly computed, whereas effects of small-scale motions have to be modeled. Here, the question is: how to model these effects? Moreover, one can wonder: what defines a well-designed subgrid-scale model?
In this project, we aim to answer these questions by following a systematic approach, based on the idea that subgrid-scale models should respect the fundamental physical and mathematical properties of the Navier–Stokes equations and the turbulent stresses. We thereby obtain a framework of constraints for the construction of physics-based subgrid-scale models. We apply this framework to a general class of subgrid-scale models based on the local velocity gradient. We also analyze the properties of a number of existing models from this class. Finally, we illustrate how new physics-based subgrid-scale models with desired built-in properties can be created.

The present work focus on the calculation of the subgrid characteristic length, a key element for any eddy-viscosity model. Namely, a new approach based on the Taylor series expansion of the subgrid stress (SGS) tensor in the computational space is proposed. Its simplicity and mathematical properties suggest that it can be a robust definition of the subgrid characteristic length that minimizes the effect of mesh anisotropies on the performance of LES models.