# Research

## Topics of Interest

- Turbulence
- Direct Numerical Simulation and Large-Eddy Simulation
- Subgrid modeling: dynamic procedure, multiscale modeling,...
- Quality of DNS and LES: accuracy and error control
- Numerical techniques for DNS and LES.

## Ph.D. Dissertation

My Ph.D. dissertation on the Development of a Dynamic Finite Difference Method for Large-Eddy Simulation can be found here.

## Dynamic Finite Difference schemes for Large-Eddy Simulation

Motivation:

In the past decades,
the necessity for
numerical quality in Direct Numerical Simulations (DNS) and especially
Large-Eddy Simulations (LES) of turbulent flows, has been recognized by
many researchers. In a properly resolved Direct Numerical Simulation,
the smallest resolved scales are located far into the dissipation
range. Since these scales have only a very small energy-content in
comparison with the largest resolved scales in the flow, they are often
considered to have a negligible influence on the mean flow statistics.
In a Large-Eddy Simulation, however, where only the most important
large scale structures are resolved, the smallest resolved scales are
part of the inertial subrange such that they contain relatively more
energy than those in the dissipation range. Hence, the smallest
resolved scales in Large-Eddy Simulation are not negligible and have a
significant influence on the evolution of the LES-flow. The accuracy
with which these small scales are described is therefore expected to be
important. In order to reduce the computational costs, it is highly
desirable in LES to resolve as much scales as possible on a given
computational grid. In order to accomplish this, the numerical method
requires sufficient accuracy for all scales. This ensure that the
magnitudes of the discretization errors remain smaller than the
magnitude of the modeled unresolved scales of motion. However, if the
accuracy of the numerical method cannot be guaranteed, the amount of
resolved small-scale structures must be reduced in order to control the
discretization errors. Hence, in order to resolve the same amount of
scales as before, a much finer computational grid is required. This is
often prohibitively expensive for most three-dimensional LES
computations of industrial applications.

Scope:

The
current research focuses on the development of a family of Dynamic Finite
Difference approximations, which succeed in minimizing the
instantaneous global discretization error on the solution during the
calculation. This strategy allows to obtain always a (nearly)
optimal numerical method that corresponds to the flow properties
related to the spectral content, at that time. The approach implies
that the intrinsic characteristics of the developed Dynamic Finite
Difference method vary during the simulation in such a way that the
global numerical error is always minimized.

The newly developed Dynamic Finite Difference Approximations have been successfully applied to Large-Eddy Simulation of the Taylor-Green Vortex flow at Re=1500. An illustration of the Taylor-Green Vortex flow at Re=3000 is given in the movie below.

Results on the good numerical performance of the dynamic finite difference schemes can be found in my Ph.D. dissertation, or in my papers.

Illustration:

Direct Numerical Simulation (384

The newly developed Dynamic Finite Difference Approximations have been successfully applied to Large-Eddy Simulation of the Taylor-Green Vortex flow at Re=1500. An illustration of the Taylor-Green Vortex flow at Re=3000 is given in the movie below.

Results on the good numerical performance of the dynamic finite difference schemes can be found in my Ph.D. dissertation, or in my papers.

Illustration:

Direct Numerical Simulation (384

^{3}) of the Taylor-Green Vortex flow at Reynolds number Re=3000