An MPI-based implementation of a simplified actuator line model
M. Ventura1, L. Muino1, N. Olaiz3, E. Luján1,2
firstname.lastname@example.org, email@example.com, firstname.lastname@example.org, email@example.com
1. Universidad de Buenos Aires. Argentina
2. Centro de Simulación Computacional para Aplicaciones Tecnológicas. CONICET. Argentina.
3. Laboratorio de Sistemas Complejos. Instituto de Física del Plasma. UBA-CONICET. Argentina.
Mathematical modeling of impeller-generated flows is highly used to simulate many industrial scenarios such as stirred tank bioreactor fluid dynamics. Despite
their ability to mimic realistic problems and save experimental design costs, fluid-structure interaction simulations have drawbacks such as the mathematical
complexity needed for its representation and the time required for large in silico experiments. Here we present a set of combined strategies for improving
planning time consumption at those simulations, consisting in fluid-structure calculus and domain simplification in addition to the application of high
performance computing. This solution implements a two-dimensional simplified actuator line model through an MPI-based parallelized code. This numerical
study provides relevant information about how to efficiently implement a solution for problems with similar characteristics.
MATERIALS AND METHODS
Figure 2 and 3 present the normalized velocity and pressure profiles at time 0.6s, 5.4s and
16.8s, due to the presence of the rotating actuator line over the two-dimensional domain.
Figure 4 shows in silico versus theoretical speedup. Experiments were measured up to 80
cores, distributed by MPI among 20 nodes. Best scenario is presented when the
implemented code scales up to 20 cores achieving, at worst, 87% of the ideal speedup.
When the experiments scales up to 40 cores, a 75% of the ideal speedup is obtained,
again in the worst scenario. Further attempts of scaling the code, up to 80 cores, present
50% of the optimal speedup. As can be appreciated, this results present relevant
information as a basis for recommendation of the number of processors necessary to
optimise analogous problems. These kind of combined numerical improvements could
have a significant impact on planning methodologies aimed at enhance the effectiveness
of several industrial sectors.
 L. Barba. 12 steps to Navier Stokes.
 G. Marshall. Solución numérica de ecuaciones diferenciales.
 P. S. Pacheco. Parallel programming with MPI.
In silico experiments represent valuable tools for investigate complex systems
such as bioreactors and the influence that vessels, impellers, baffles, and
operating conditions have on the mixing efficiency and the power that is
required to drive those impellers. In this context fluid-structure mathematical
complexity, associated with such simulations, address computational
performance issues for accomplishing large in silico experimentation.
Regarding this matters, actuator lines are good representative of actual
impellers and allow save computational costs, replacing those blades for
equivalent thrust forces over the impeller line. In cases where the study
involves high flat blades, a bidimensional domain approach can also notably
reduce the amount of calculations. Additionally, due to the required mesh
density of those problems, computer parallelism techniques suppose
significant improvements of computational performance. The present study
provides a finite difference solution of Navier-Stokes equations for
incompressible flows, in a bidimensional domain, where blades were
approximated by an actuator line and the code was parallelized through the
distributed memory technology MPI. The obtained results present good
agreement with literature.
XIX GIAMBIAGI WINTER SCHOOL - 2017
Computational fluid dynamics and applications
where (u,v) is the 2D-velocity field. p is the pressure. ν and ρ are the
kinematic viscosity and fluid density, respectively. The represented liquid is
water. Impellers were modeled using a simplified actuator line approach. Fu
and Fv represent the rotating actuator lines effect. The equations were
solved numerically through standard finite difference method, a stable
discretization can be found in . A uniform mesh of 32.400 (180 x 180)
nodes was needed for the in silico experiment. The used time step was 1
ms, and the total simulated time, 1s. The code was parallelized by the
distributed memory technology MPI . Computational domain was divided
by horizontal bands, giving the same amount of rows to each worker core
and exchanging only the first and last row of each band between processes
with the objective of minimizing data exchange during the simulation. The
program runs over a cluster of 20 computers, equipped with an Intel Core
i5-3550, 3.30 GHz and 8GB of memory. Networking was done using a
standard ethernet connection. Model implementation was verified against
cavity flow and channel flow known benchmarks .
Figure 4 - Speedup curve
RESULTS AND DISCUSSION
This simplified theoretical model, consists in characterize the fluid dynamic
of high flat impellers over a plane, as can be seen in the scheme presented
in Figure 1. Navier-Stokes equations for incompressible fluids [1,2] were
used to represent this phenomena:
We would like to thank Eng. G. Navarro Díaz, Dr. A. Otero and Lic. M. L. Mayol for their
comments and suggestions.
Figure 1 -
Figure 3 - Pressure over time. Scale bar: 1m
Figure 2 - Velocity over time. Scale bar: 1m