The main lines of my on-going research are listed below. For further
details you can check my
Most of the numerical simulations have been carried out with the in-house STG-code (for Soria Trias Gorobets, main
developers of the code).
Regularization modeling & Large-Eddy
Although formally derived from different principles, regularization and
LES equations share many features and objectives. Both approaches aim
to reduce the dynamical complexity of the original Navier-Stokes
equations resulting into a new set of PDE that are more amenable to be
numerically solved on a coarse mesh. The regularization methods
basically alter the convective terms to reduce the production of small
scales of motion. The first outstanding approach in this
direction goes back to Leray. Other regularization models
also been proposed and tested in the last decade. Although the
underlying idea remains the same, the list of properties from
Navier-Stokes equations that are exactly preserved differs.
Here, we propose to preserve the symmetries and conservation properties
of the original convective term. Doing so, the production of smaller
and smaller scales of motion is restrained in an unconditionally stable
manner. Then, the only additional ingredient is a self-adjoint linear
filter  whose local filter length is determined from the requirement
that vortex-stretching must be stopped at the scale set by the grid .
The on-going research focuses on the development of new regularization
models  while exploring their connections with LES models.
On the other hand, a simple approach to discretize the viscous terms
with spatially varying eddy-viscosity has been presented in .
The numerical approximation of this term may be quite cumbersome
especially for high-order staggered formulations. To circumvent this
problem, an alternative form of the viscous term has been derived. From
a numerical point-of-view, the most remarkable property of this new
form is that it can be straightforwardly implemented by simply re-using
operators that are already available in any code. Moreover, for
constant viscosity, formulations become identical to the original
formulation in a natural manner.
Presentation to European Turbulence Conference (ETC14), September 2013, Lyon (pdf).
Presentation to "Connections Between Regularized and Large-Eddy Simulation Methods for Turbulence" workshop at BIRS, May 2012, Banff, Alberta (Canada) (pdf)
Presentation to European Turbulence Conference (ETC13), September 2011,
Presentation to Parallel CFD conference, May 2011, Barcelona (pdf).
Natural convection flows
Buoyancy-driven flows in enclosed cavities have been the subject of
numerous experimental and numerical studies in the last decades.
Despite the great effort devoted there are still many questions that
remain open. Firstly, significant discrepancies are still observed
between numerical and experimental studies. They are strongly connected
with the role of the transitional thermal boundary layer: numerical
results provide strong evidences that the flow structure
capture well unless the transition point at the vertical boundary is
correctly located . At relatively high Rayleigh numbers, LES models have
consistently failed on accurately predicting the transition of the
vertical boundary layer for an air-filled differentially heated cavity
(DHC) of aspect ratio 5 and Ra=4.5e10. Actually, for this
configuration, recent DNS results have revealed that the transition of
the vertical boundary layer occurs at more downstream positions than
those observed in the experiments . The above-mentioned
symmetry-preserving regularization models have shown their ability to
capture well the general pattern of the flow even for very
coarse meshes. On the other hand, the heat transfer scaling at (very)
high Rayleigh number is also one of the fundamental questions on
natural convection that remains open. Most recent developments on
regularization modeling may also help to elucidate this issue in a near
Presentation to 7th International Conference on Computational
Heat and Mass Transfer (ICCHMT), July 2011, Istambul (pdf).
gallery of DNSs of natural convection flows
Forced convection flows
Most advanced numerical techniques will be used to perform direct
simulations of several forced convection flows. These simulations give
new insights into the physics of turbulence and provide indispensable
data for the further progress of turbulence modeling. Examples of
thereof are (i) a turbulent flow around a wall-mounted cube in a
channel flow at Re_tau = 590 (Re = 7235, based on the cube height and
the bulk velocity) and (ii) a turbulent plane impinging jet at Re=20000
(based on the bulk inlet velocity and the nozzle width) and aspect
ratio 4 . Regarding the latter configuration significant discrepancies
have been observed respect to the experimental works presented in the
literature. They are mainly attributed to the effect of the outflow
boundary conditions usually located at x/B = ±10 ∼ 15, whereas the main
recirculating region extends clearly to more downstream locations.
Time-averaged DNS results have revealed that the main recirculating
flow cannot be captured well unless the outflow is placed at least at
40B from the jet centreline approximately. This suggests that previous
experimental data may not be adequate to study the flow configuration
far from the jet.
Presentation to Parallel CFD conference (PCFD09), May 2009, San
of DNSs of forced convection flows
Numerical methods for CFD
The incompressible Navier-Stokes equations form an excellent
mathematical model of turbulent flows. Unfortunately, attempts at
performing direct numerical simulations (DNS) with the available
computational resources and numerical methods are limited to relatively
low-Reynolds-numbers. Regarding the numerical algorithms, cost
reductions can be achieved by one or more of the following: (1)
decreasing the number of grid points using more accurate numerical
schemes, (2) reducing the computational cost per iteration, or (3)
using larger time steps, all without affecting the quality of the
numerical solution. With regard to the time-integration schemes an
efficient self-adaptive strategy for the explicit time integration of
the Navier-Stokes equations has been recently proposed . It is based on
a one-parameter second-order-explicit scheme. First, the eigenvalues of
our dynamical system are bounded by means of an almost inexpensive
method. Second, the linear stability domain of the time-integration
method is adapted in order to maximize the time-step. To do so, the
control parameter is automatically tuned. The method works
independently of the underlying spatial mesh and therefore is suitable
for both structured and unstructured codes. Compared with the standard
CFL-based approach CPU cost reductions of up to 2.9
and 4.3 (unstructured) have been measured.
issue the on-going research focuses on the development of
fully-conservative schemes for unstructured meshes and the appropriate
cure for the well-known checkerboard problem for collocated
formulations . Namely, the crucial symmetry properties of the underlying differential operators are exactly preserved, i.e.,
the convective operator is approximated by a skew-symmetric matrix and
the diffusive operator by a symmetric, positive-definite matrix.
Moreover, a novel approach to eliminate the checkerboard spurious modes
without introducing any non-physical dissipation is proposed. To do so,
a fully-conservative regularization of the convective term is used. The
supraconvergence of the method is numerically showed and the treatment
of boundary conditions is discussed. Finally, the new discretization
method is successfully tested for a buoyancy-driven turbulent flow in a
differentially heated cavity.
Parallel Poisson solvers and HPC
The progress in DNS is closely related with the efficient use of modern
high performance computing (HPC) systems that offer a rapidly growing
computing power. Since the irruption of multi-core architectures, this
trend is mainly based on increasing both the number of nodes and the
number of cores per node. However, the number of cores tends to grow
faster than the memory size and the network bandwidth. These tendencies
bring new problems that must be solved in order to exploit efficiently
the new computing potential. In this context, the Poisson equation,
which arises from the incompressibility constraint and has to be solved
at least once per time step, is usually the most time-consuming and
difficult-to-parallelize part of the DNS algorithm. The Poisson used in
our code is restricted to problems with one uniform periodic direction.
It is a combination of a block preconditioned Conjugate Gradient (PCG)
method and a Fast Fourier Transform (FFT) . The Fourier diagonalization
decomposes the original system into a set of mutually independent 2D
systems that are solved by means of the PCG algorithm. The most
ill-conditioned systems correspond to the lowest frequencies in the
spectral space. In this case, to avoid a slow convergence, the PCG
solver is replaced by a Direct Schur complement Decomposition (DSD)
The initial version of the Poisson solver was conceived for single-core
processors and therefore, the distributed memory model with
message-passing interface (MPI) was used. The irruption of multi-core
architectures motivated the use of a two-level hybrid MPI + OpenMP
parallelization with the shared memory model on the second level .
Numerical experiments show that, within its range of efficient
scalability, the previous MPI-only parallelization is slightly
outperformed by the MPI + OpenMP approach. But more importantly, the
hybrid parallelization has allowed to significantly extend the range of
efficient scalability. Here, the solver has been successfully tested up
to 12800 CPU cores for meshes with up to 1e9 grid points. However,
estimations based on the presented results show that this range can be
potentially stretched up until 200,000 cores approximately.
Following the current trends in HPC, the use of computing accelerators
(GPUs in particular) is being implemented by means of the hardware
independent OpenCL standard . It has been chosen due to the fact that it
is supported by all of the main hardware vendors, including NVidia,
Intel, AMD, IBM. For further information you can visit the webpage
of my friend and colleague Dr.Andrey Gorobets.
Presentation to Parallel CFD conference (PCFD11), May 2011, Barcelona (pdf).