Stochastic framework for modeling the linear apparent behavior of complex materials:Application to random porous materials with interphases

This paper is concerned with the modeling of randomness in multiscale analysis of heterogeneous materials. More specifically, a framework dedicated to the stochastic modeling of random properties is first introduced. A probabilistic model for matrix-valued second-order random fields with symmetry propertries, recently proposed in the literature, is further reviewed. Algorithms adapted to the Monte Carlo simulation of the proposed representation are also provided. The derivations and calibration procedure are finally exemplified through the modeling of the apparent properties associated with an elastic porous microstructure containing stochastic interphases.

Derivation of FFT numerical bounds of the effective properties ofcomposites and polycristals

In this paper,we provide exact fast Fourier transform(FFT)-based numerical bounds for the elastic prop-erties of composites having arbitrary microstructures.Two bounds,an upper and a lower,are derivedby considering usual variational principles based on the strain and the stress potentials.The bounds arecomputed by solving the Lippmann-Schwinger equation together with the shape coefficients which al-low an exact description of the microstructure of the composite.These coefficients are the exact Fouriertransform of the characteristic functions of the phases.In this study,the geometry of the microstructureis approximated by polygonals(two-dimensional,2D objects)and by polyhedrons(three-dimensional,3Dobjects)for which exact expressions of the shape coefficients are available.Various applications are pre-sented in the paper showing the relevance of the approach.In the first benchmark example,we considerthe case of a composite with fibers.The effective elastic coefficients ares derived and compared,consider-ing the exact shape coefficient of the circular inclusion and its approximation with a polygonal.Next,thehomogenized elastic coefficients are derived for a composite reinforced by 2D flower-shaped inclusionsand with 3D toroidal-shaped inclusions.Finally,the method is applied to polycristals considering Voronoitessellations for which the description with polygonals and polyhedrons becomes exact.The comparisonwith the original FFT method of Moulinec and Suquet is provided in order to show the relevance of thesenumerical bounds.

The Algebraic Immersed Interface and Boundary Method for Elliptic Equations with Jump Conditions

A new simple fictitious domain method, the algebraic immersed interface and boundary (AIIB) method, is presented for elliptic equations with immersed interface conditions. This method allows jump conditions on immersed interfaces to be discretized with a good accuracy on a compact stencil. Auxiliary unknowns are created at existing grid locations to increase the degrees of freedom of the initial problem. These auxiliary unknowns allow imposing various constraints to the system on interfaces of complex shapes. For instance, the method is able to deal with immersed interfaces for elliptic equations with jump conditions on the solution or discontinuous coefficients with a second order of spatial accuracy. As the AIIB method acts on an algebraic level and only changes the problem matrix, no particular attention to the initial discretization is required. The method can be easily implemented in any structured grid code and can deal with immersed boundary problems too. Several validation problems are presented to demonstrate the interest and accuracy of the method.

Modeling the Interaction between a Thermal Flow and a Liquid: Review and Future Eulerian-Lagrangian Approaches

Suspension Plasma Spraying is a complex process in which several physical mechanisms play a part. So the modeling and understanding of the interaction between a high-velocity and thermal flow and a liquid precursor phase is of major importance concerning the control and characterization of the process. The liquid droplet size distribution has a high influence on the kinetic properties of the as-sprayed nanometer particles before impacting on a target substrate. An overview of existing models is provided dealing with the penetration of the liquid phase into the thermal flame and the resulting fragmentation and vaporization of this phase before impact. The physical characteristics of the flow as well as existing Lagrangian and Eulerian modeling strategies are briefly discussed while paying attention to the physical parameters characterized and measured by numerical simulation. The potential of the various models and also their limits are intended to be highlighted. Future coupled Eulerian-Lagrangian modeling strategies are also proposed for a global and more exhaustive representation of the injection, fragmentation and dispersion part of the two-phase gas-liquid flow before particle impact on the substrate.

A Kinematics Scalar Projection Method (KSP) for Incompressible Flows with Variable Density

A new scalar projection method presented for simulating incompressible flows with variable density is proposed. It reverses conventional projection algorithm by computing first the irrotational component of the velocity and then the pressure. The first phase of the projection is purely kinematics. The predicted velocity field is subjected to a discrete Hodge-Helmholtz decomposition. The second phase of upgrade of pressure from the density uses Stokes’ theorem to explicitly compute the pressure. If all or part of the boundary conditions is then fixed on the divergence free physical field, the system required to be solved for the scalar potential of velocity becomes a Poisson equation with constant coefficients fitted with Dirichlet conditions.

Numerical Investigation and Optimization of a Flat Plate Solar Collector Operating with Cu/CuO/Al_(2)O_(3)–Water Nanofluids

Nanofluids are a potential alternative to significantly improving the performance of heat transfer applications. In this work, a numerical analysis to examine the eff ect of dispersing copper(Cu), copper oxide(CuO), and aluminum(Al2O3) nanoparticles in pure water on the performance of a flat plate solar collector(FPSC) and a numerical model was proposed. The influence of the nanofluid type on the thermal efficiency was critically investigated and discussed. The eff ect of the mass flow rate on the performance was also analyzed and discussed. Based on correlations of the thermophysical properties of nanofluids, a sensitivity analysis was used to analyze the impact of the nanoparticles on the base fluid. The results indicate that the performance of the FPSC with Cu/water nanofluid was better than that of FPSCs using CuO/water or Al2O3/water nanofluids. When the mass flow rate of the nanofluids was 8.0 L/min, the efficiency of the FPSC was much greater than those at the flow rates of 5.0 L/min and 2.0 L/min. Mean enhancements in thermal efficiency of 4.44%, 4.27%, and 4.21% were observed when 2.0 L/min was applied using Cu/water, Cu O/water, and Al2O3/water nanofluids, respectively. Improvements in thermal efficiency of 2.76%, 2.53%, and 2.47% occurred when 8.0 L/min was applied.

Improvement of the Viscous Penalty Method for Particle-Resolved Simulations

A numerical study of the parameters controlling the viscous penalty method is investigated to better set up Particle-Resolved Direct Numerical Simulations (PR-DNS) of particulate flows. Based on this analysis, improvements of the methods are proposed in order to reach an almost second order convergence in space. The viscous penalty method is validated in Stokes regime by simulating a uniform flow past a fixed isolated cylinder. Moreover, it is also utilized in moderate Reynolds number regime for a uniform flow past a square configuration of cylinder and compared in terms of friction factor to the well-known Ergun correlation.

High-Order Two-Scale Asymptotic Paradigm for the Elastodynamic Homogenization of Periodic Composites

The classical two-scale asymptotic paradigm provides macroscopic and microscopic analyses for the elastodynamic homogenization of periodic composites based on the spatial or/and temporal variable,which offers an approximate framework for the asymptotic homogenization analysis of the motion equation.However,in this framework,the growing complexity of the homogenization formulation gradually becomes an obstacle as the asymptotic order increases.In such a context,a compact,fast,and accurate asymptotic paradigm is developed.This work reviews the high-order spatial two-scale asymptotic paradigm with the effective displacement field representation and optimizes the implementation by symmetrizing the tensor to be determined.Remarkably,the modified implementation gets rid of the excessive memory consumption required for computing the high-order tensor,which is demonstrated by representative one-and two-dimensional cases.The numerical results show that(1)the contrast of the material parameters between media in composites directly affects the convergence rate of the asymptotic results for the homogenization of periodic composites,(2)the convergence error of the asymptotic results mainly comes from the truncation error of the modified asymptotic homogenized motion equation,and(3)the excessive norm of the normalized wavenumber vector in the two-dimensional inclusion case may lead to a non-convergence of the asymptotic results.

Patient-specific modeling of left ventricle mechanics

We present a computational framework for the study of cardiac motion.The bio-mechanical model captures the passive and active properties of the cardiac tissue as well as the fiber architecture.We focus on the analysis of deformations of a beating left ventricle(LV),comparing numerical simulations with real data acquired by echocardiography.The goal is to determine the clinical relevance of the LV strains pattern and to investigate the relationships between that pattern and the arrangement of myocardial fibers.The proposed framework could in principle be used for a wide range of clinical applications.