Daniele Cerroni

A penalty-projection algorithm for a monolithic fluid-structure interaction solver

In this paper we propose a new iterative penalty-projection algorithm for a monolithic fluid-structure interaction solver. Projection methods, that split the computation of the velocity from the pressure, are very popular in fluid dynamics since the boundary errors generated by the projection method are localized mainly near the boundary layers where the incorrect pressure boundary conditions are imposed. However, when solid regions are taken into account, the pressure projected field cannot satisfy fully coupled boundary constraints imposed on external solid surfaces such as stress-free conditions, and, due to the rigidity of the medium, the boundary errors propagate deeply in the interior. In order to reduce the projection errors we propose a one-step penalty-projection method in the fluid domain and an iterative penalty-projection method in the solid region. This technique decouples the pressure-velocity degrees of freedom and, as a consequence, the computational cost. In order to verify the accuracy and robustness of the proposed method we compare the results between this splitting velocity-pressure algorithm and the coupled one. These numerical results show stability and robustness of the proposed algorithm with a strong reduction of the computational effort. A new penalty-projection algorithm for a monolithic FSI solver is proposed.Projection method error is localized where pressure boundary conditions are imposed.A one-step penalty together with an iterative projection algorithm is used.This technique reduces the problem degrees of freedom and the computational cost.Numerical results show stability and reduction of cpu effort for large problems.

CFD and Neutron codes coupling on a computational platform

In this work we investigate the thermal-hydraulics behavior of a PWR nuclear reactor core, evaluating the power generation distribution taking into account the local temperature field. The temperature field, evaluated using a self-developed CFD module, is exchanged with a neutron code, DONJON-DRAGON, which updates the macroscopic cross sections and evaluates the new neutron flux. From the updated neutron flux the new peak factor is evaluated and the new temperature field is computed. The exchange of data between the two codes is obtained thanks to their inclusion into the computational platform SALOME, an open-source tools developed by the collaborative project NURESAFE. The numerical libraries MEDmem, included into the SALOME platform, are used in this work, for the projection of computational fields from one problem to another. The two problems are driven by a common supervisor that can access to the computational fields of both systems, in every time step, the temperature field, is extracted from the CFD problem and set into the neutron problem. After this iteration the new power peak factor is projected back into the CFD problem and the new time step can be computed. Several computational examples, where both neutron and thermal-hydraulics quantities are parametrized, are finally reported in this work.

A preliminary investigation of the growth of an aneurysm with a multiscale monolithic Fluid-Structure interaction solver

In this work we investigate the potentialities of multi-scale engineering techniques to approach complex problems related to biomedical and biological fields. In particular we study the interaction between blood and blood vessel focusing on the presence of an aneurysm. The study of each component of the cardiovascular system is very difficult due to the fact that the movement of the fluid and solid is determined by the rest of system through dynamical boundary conditions. The use of multi-scale techniques allows us to investigate the effect of the whole loop on the aneurysm dynamic. A three-dimensional fluid-structure interaction model for the aneurysm is developed and coupled to a mono-dimensional one for the remaining part of the cardiovascular system, where a point zero-dimensional model for the heart is provided. In this manner it is possible to achieve rigorous and quantitative investigations of the cardiovascular disease without loosing the system dynamic. In order to study this biomedical problem we use a monolithic fluid-structure interaction (FSI) model where the fluid and solid equations are solved together. The use of a monolithic solver allows us to handle the convergence issues caused by large deformations. By using this monolithic approach different solid and fluid regions are treated as a single continuum and the interface conditions are automatically taken into account. In this way the iterative process characteristic of the commonly used segregated approach, it is not needed any more.

Preliminary Monolithic Fluid Structure Interaction Model for Ventricle Contraction

In this work we test the performance of different algorithms for the solution of a monolithic Fluid Structure Interaction (FSI) problem with a simplified ventricle model with the purpose to reduce the computational time. We study this challenging FSI problem by solving the fully coupled and the projection algorithm with a different number of penalty correction steps. The proposed FSI penalty projection algorithm is a modification of the Chorin method for fluids based on a predictor and a corrector step. The performance of the modified algorithm is tested by comparing the results obtained with the standard coupled algorithm with the ones obtained with the modified penalty projection scheme.

A projection method for coupling two-phase VOF and fluid structure interaction simulations

Abstract The study of Multiphase Fluid Structure Interaction (MFSI) is becoming of great interest in many engineering applications. In this work we propose a new algorithm for coupling a FSI problem to a multiphase interface advection problem. An unstructured computational grid and a Cartesian mesh are used for the FSI and the VOF problem, respectively. The coupling between these two different grids is obtained by interpolating the velocity field into the Cartesian grid through a projection operator that can take into account the natural movement of the FSI domain. The piecewise color function is interpolated back on the unstructured grid with a Galerkin interpolation to obtain a point-wise function which allows the direct computation of the surface tension forces.

Adjoint optimal control problems for the RANS system

Adjoint optimal control in computational fluid dynamics has become increasingly popular recently because of its use in several engineering and research studies. However the optimal control of turbulent flows without the use of Direct Numerical Simulation is still an open problem and various methods have been proposed based on different approaches. In this work we study optimal control problems for a turbulent flow modeled with a Reynolds-Averaged Navier-Stokes system. The adjoint system is obtained through the use of a Lagrangian multiplier method by setting as objective of the control a velocity matching profile or an increase or decrease in the turbulent kinetic energy. The optimality system is solved with an in-house finite element code and numerical results are reported in order to show the validity of this approach.

Fluid structure interaction solver coupled with volume of fluid method for two-phase flow simulations

In this work we propose to study the behavior of a solid elastic object that interacts with a multiphase flow. Fluid structure interaction and multiphase problems are of great interest in engineering and science because of many potential applications. The study of this interaction by coupling a fluid structure interaction (FSI) solver with a multiphase problem could open a large range of possibilities in the investigation of realistic problems. We use a FSI solver based on a monolithic approach, while the two-phase interface advection and reconstruction is computed in the framework of a Volume of Fluid method which is one of the more popular algorithms for two-phase flow problems. The coupling between the FSI and VOF algorithm is efficiently handled with the use of MEDMEM libraries implemented in the computational platform Salome. The numerical results of a dam break problem over a deformable solid are reported in order to show the robustness and stability of this numerical approach.

COUPLING OF FLUID STUCTURE INTRACTION SOLVER WITH A VOF METHOD FOR MULTIPHASE STRUCTURE INTERACTION

In this work we propose a preliminary model to study the deformation of solid structures induced by the interaction with a two-phase flow. The study of Fluid Structure Interaction and multiphase problems is of great interest because of many potential applications ranging from the biomedical field to the pressure tank design. We use a monolithic approach for the FSI problem while a Volume Of Fluid method (VOF) is considered for the reconstruction and the advection of the multiphase interface. An unstructured, time dependent computational grid and a fine Cartesian mesh are used for the FSI and the VOF problem, respectively. The interaction between the two different grids is obtained by projecting the velocity and the displacement field into the Cartesian grid and the color function into the unstructured mesh. This projection is performed with the MEDmem libraries included in the Salome platform. Concerning the VOF method, for an accurate reconstruction of the interface a huge number of computational elements are required and a multilevel algorithm coupled to an efficient compression-expansion technique is developed to reduce computational costs and memory requirements. After the mathematical description of the problems we test the proposed algorithm with different cases where the solid domain undergoes to both small and large deformation.

ADJOINT OPTIMAL CONTROL PROBLEMS FOR FLUID-STRUCTURE INTERACTION SYSTEMS

In the last years adjoint optimal control has been increasingly used for design and simulations in several research fields. Applications to Computational Fluid Dynamics problems dedicated to the study of transient-diffusion equations, shape optimization problems, fluid-solid conjugate heat transfer and turbulent flows can be found in literature. The study of FluidStructure Interaction problems gained popularity recently because of many interesting applications in engineering and biomedical fields. In this paper we study adjoint optimal control problems for Fluid-Structure Interaction systems in order to improve the advantages of using FSI simulations when designing engineering devices where fluid-dynamical interactions between a fluid and a solid play a significant role. We assess distributed optimal control problems with the purpose to control the fluid behavior by moving the solid region to obtain a desired fluid velocity in specific parts of the domain. The adjoint equations of the FSI monolithic system are derived and the optimality system solved for some simple cases with an in-house finite element code with mesh-moving capabilities for the study of large displacements in the solid. The approach presented in this work is general and can be used to assess different objectives and types of control in future works.

NUMERICAL VALIDATION OF A FOUR PARAMETER LOGARITHMIC TURBULENCE MODEL

Computational Fluid Dynamics codes are used in many industrial applications in order to evaluate interesting physical quantities, such as the heat transfer in turbulent flows. Commercial CFD codes use only turbulence models with an imposed constant turbulent Prandtl number Prt, which can give accurate results only for simulations when a strong similarity between the velocity field and the temperature field can be assumed. For fluids with a low Prandtl number, as for heavy liquid metals, a constant turbulent Prandtl number leads to an overestimation of the heat transfer, so experimental results and Direct Numerical Simulation cannot be reproduced. In this work we propose a new k-Ω-kθ-Ωθ turbulence model as an improvement of the k-ω-kθ-ωθ turbulence model, already validated by the authors, where Ω and Ωθ are calculated as the natural logarithm of the variables ω and ωθ. With this reformulation of the previous turbulence model we obtain some important advantages in numerical stability and robustness of the code. Results for the simulations of fully developed turbulent flows in two and three dimensional geometries are reported and compared with experimental correlations and DNS data, when available.