The behavior of blood flow containing gyrotactic microorganisms propelled through a capillary with permeable and stretching medium in the presence of a magnetic field was studied numerically. The governing partial differential equations were modified into ordinary differential equations by using similarity transformation variables. The emerging equations computed numerically with the help of Successive Taylor series linearization method (STSLM). The influence of unsteadiness parameter, Hartman number, permeability parameter, radiation parameter, Prandtl number, Brownian motion parameter, thermophoresis parameter, Schmidt number, bio-convection Schmidt number, and bioconvection Peclet number on the velocity, temperature, concentration, motile microorganisms profiles and also the skin friction coefficient, Nusselt number, Sherwood number and local density number of motile microorganisms were drawn graphically to study the physical importance of the present problem.

We present an unsteady analysis using the Seamless-Domain Method (SDM), which is a multiscale modeling technique. The SDM has previously been applied to steady-state problems to demonstrate that complicated behavior in a heterogeneous structure can be represented with relatively few points. In this article, an unsteady analysis is carried out using SDM in the space–time domain. This domain is assumed to be composed of repeating units called "space– time unit cells," which are discretized by coarse-grained points (CPs). The first step is a local analysis of the space–time domain consisting of multiple unit cells, which derives the space–time interpolation functions. The next step is a global analysis to obtain the variable distribution in the entire global domain using the interpolation functions. This two-scale analysis with respect to both space and time is computationally efficient, resulting in highly accurate solutions at low computational cost. A method that improves the computational accuracy by searching the optimum set of "reference CPs" given in the interpolation is also presented. We consider an example problem of two-dimensional thermal diffusion in a heterogeneous structure, and compute the solution using unsteady SDM and a conventional finite-difference method. The solutions are compared in terms of computational accuracy and time.

Descriptions of complex multiscaled physical systems often involve many physical processes interacting through a multitude of scales. In many cases, the primary interest lies in predicting behavior of the system at the macroscale (i.e., engineering scale) where continuum, physics-based, models such as partial differential equations provide high-fidelity descriptions. However, in multiscale systems, the behavior of continuum models can depend strongly on microscale properties and effects, which are often included in the macroscale model as a parameter field obtained by some upscaling process from a microscale model. Generally, a number of choices have to be made in choosing an upscaling procedure and the resulting representation of the parameter. These choices have a strong impact on both the fidelity and the computational efficiency of the model. Thus, choosing a good parameter representation and upscaling procedure becomes part of the uncertainty quantification and prediction problem for a multiscale model. We consider the use of output data from the macroscale model to formulate and solve a stochastic inverse problem to determine probability information about the upscaled parameter field. In particular, we extend a measure-theoretic inverse problem frame-work and non-intrusive sample-based algorithm to determine the choices of parameter representation and upscaling procedure that are most probable given uncertain data from the macroscale model.We illustrate the methodology in the context of shallow water flow and sub-surface flow.

A two-scale modeling framework for sintering processes has been presented. Formulation of the micromechanical model of sintering developed in the discrete element method and basic relationships in the macroscopic model of sintering have been briefly reviewed. The methodology to determine macroscopic quantities–stress, strains, and constitutive viscous properties-from the discrete element simulations has been presented. This methodology has been applied to modeling of NiAl sintering. First, the discrete element model (DEM) has been calibrated by fitting the numerical densification curve to the experimental data. The DEM model with calibrated parameters has been used in simulations specially conceived to give macroscopic viscous moduli of the sintered material. Using the averaging procedures macroscopic stresses and strains have been calculated. Strain rates have been obtained differentiating the strain curves with respect to time. Finally, the viscous constitutive properties of the sintered material have been determined. The dependence of the shear and volumetric viscous moduli on the relative density (or equivalently) on the porosity has been obtained. It has been found that the numerical simulations predict a similar dependence as that assumed in the phenomenological macroscopic models. Thus, the validity of the micro-macro relationships obtained from the discrete element simulations of powder sintering has been confirmed. The proposed methodology allows us to use the discrete element model in the framework of multiscale modeling of sintering.

In this paper, a test for connections between models via parameter sets is developed. A set of parameters from the flow rule of a crystal plasticity model for bcc Fe is identified for connecting top-down and bottom-up information. The top-down calibration is performed using experimental measurements of single-crystal yield strength at multiple temperatures and crystallographic orientations, where a likelihood function in parameter space is informed using second-order regression surrogate modeling. A bottom-up calibration of the same model uses the parameter estimates from atomistic simulations to inform penalty functions. A constrained likelihood function incorporates the top-down and bottom-up information in one calibration of parameters. Decision making within hierarchical multiscale modeling is approached. The benefit to calibration precision brought by incorporating additional data from bottom up is considered against the uncertainty in the requisite multiscale connection. This trade-off is formulated into an empirical test of connections. Hypothetical decision making is demonstrated between multiple alternative bottom-up estimates.

The particle filter is used to couple a coarse-grained (CG) deterministic solution for a reacting flow with a fine-grained (FG) stochastic solution. The proposed method investigates the feasibility of implementing a multiscale approach for turbulent reacting flows based on large-eddy simulation (LES) coupled with a low-dimensional fine-grained stochastic solution for the subfilter scales reaction and transport. In this study, a model for the turbulent transport in the FG solution is implemented using the linear-eddy model (LEM), which combines a deterministic implementation for reaction, diffusion, and large-scale transport with a stochastic implementation for fine-scale transport. The solution for the continuity and momentum (the Burgers' equation) equations are implemented in 1D. The filtered densities obtained through the FG and the CG solutions are combined using the particle filter to obtain an updated density for the coarse solution that combines the effects of heat release (from the FG solution) and flow dynamics (from the CG solution). The results demonstrate that the particle filter may be a viable tool to couple deterministic CG solutions and stochastic FG solutions in reacting flow applications.

International audience