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Two-dimensional unsteady flows in complex geometries that are characterized by simple (low-dimensional) dynamical behavior are considered. Detailed spectral element simulations are performed, and the proper orthogonal decomposition or POD (also called method of empirical eigenfunctions) is applied to the resulting data for two examples: the flow in a periodically grooved channel and the wake of an isolated circular cylinder. Low-dimensional dynamical models for these systems are obtained using the empirically derived global eigenfunctions in the spectrally discretized Navier–Stokes equations. The short- and long-term accuracy of the models is studied through simulation, continuation, and bifurcation analysis. Their ability to mimic the full simulations for Reynolds numbers (Re) beyond the values used for eigenfunction extraction is evaluated. In the case of the grooved channel, where the primary horizontal wave number of the flow is imposed from the channel periodicity and so remains unchanged with Re, the models extrapolate reasonably well over a range of Re values. In the case of the cylinder wake, however, due to the significant spatial wave number changes of the flow with the Re, the models are only valid in a small neighborhood of the decompositional Reynolds number.

Multi-fidelity modelling enables accurate inference of quantities of interest by synergistically combining realizations of low-cost/low-fidelity models with a small set of high-fidelity observations. This is particularly effective when the low- and high-fidelity models exhibit strong correlations, and can lead to significant computational gains over approaches that solely rely on high-fidelity models. However, in many cases of practical interest, low-fidelity models can only be well correlated to their high-fidelity counterparts for a specific range of input parameters, and potentially return wrong trends and erroneous predictions if probed outside of their validity regime. Here we put forth a probabilistic framework based on Gaussian process regression and nonlinear autoregressive schemes that is capable of learning complex nonlinear and space-dependent cross-correlations between models of variable fidelity, and can effectively safeguard against low-fidelity models that provide wrong trends. This introduces a new class of multi-fidelity information fusion algorithms that provide a fundamental extension to the existing linear autoregressive methodologies, while still maintaining the same algorithmic complexity and overall computational cost. The performance of the proposed methods is tested in several benchmark problems involving both synthetic and real multi-fidelity datasets from computational fluid dynamics simulations.

The viscosity of blood has long been used as an indicator in the understanding and treatment of disease, and the advent of modern viscometers allows its measurement with ever-improving clinical convenience. However, these advances have not been matched by theoretical developments that can yield a quantitative understanding of blood's microrheology and its possible connection to relevant biomolecules (e.g., fibrinogen). Using coarse-grained molecular dynamics and two different red blood cell models, we accurately predict the dependence of blood viscosity on shear rate and hematocrit. We explicitly represent cell-cell interactions and identify the types and sizes of reversible rouleaux structures that yield a tremendous increase of blood viscosity at low shear rates. We also present the first quantitative estimates of the magnitude of adhesive forces between red cells. In addition, our simulations support the hypothesis, previously deduced from experiments, of yield stress as an indicator of cell aggregation. This non-Newtonian behavior is analyzed and related to the suspension's microstructure, deformation, and dynamics of single red blood cells. The most complex cell dynamics occurs in the intermediate shear rate regime, where individual cells experience severe deformation and transient folded conformations. The generality of these cell models together with single-cell measurements points to the future prediction of blood-viscosity anomalies and the corresponding microstructures associated with various diseases (e.g., malaria, AIDS, and diabetes mellitus). The models can easily be adapted to tune the properties of a much wider class of complex fluids including capsule and vesicle suspensions.blood rheology | blood modeling | shear thinning | aggregation force | dissipative particle dynamics R heological and material properties of cell, capsule, and vesicle suspensions have many applications in medicine, biology, engineering, and materials science. One of the main examples of such suspensions is blood, which consists of RBCs, predominant by volume, and a small fraction of other cells and proteins suspended in the plasma. Understanding blood flow and its relation to cellular properties and interactions may lead to advances in biomedical applications (e.g., drug delivery, blood substitutes). Moreover, a change in blood rheological and flow properties is often associated with hematological diseases or disorders (e.g., sickle-cell anemia, malaria), and therefore the viscosity of blood has long been used as an indicator in the understanding and treatment of disease.Modern rheometry techniques and instruments yield reliable measurements of macroscopic properties of cell suspensions with ever-improving convenience-for example, the bulk properties of blood measured in various laboratories (1-6). Virtually all bloodviscosity measurements are necessarily in vitro, and before newly drawn blood is introduced into a viscometer it must at least be stabilized with an anticoagulant, which is then called "whole blood." Under flow...

Red blood cells (RBCs) can be cleared from circulation when alterations in their size, shape, and deformability are detected. This function is modulated by the spleen-specific structure of the interendothelial slit (IES). Here, we present a unique physiological framework for development of prognostic markers in RBC diseases by quantifying biophysical limits for RBCs to pass through the IES, using computational simulations based on dissipative particle dynamics. The results show that the spleen selects RBCs for continued circulation based on their geometry, consistent with prior in vivo observations. A companion analysis provides critical bounds relating surface area and volume for healthy RBCs beyond which the RBCs fail the “physical fitness test” to pass through the IES, supporting independent experiments. Our results suggest that the spleen plays an important role in determining distributions of size and shape of healthy RBCs. Because mechanical retention of infected RBC impacts malaria pathogenesis, we studied key biophysical parameters for RBCs infected with Plasmodium falciparum as they cross the IES. In agreement with experimental results, surface area loss of an infected RBC is found to be a more important determinant of splenic retention than its membrane stiffness. The simulations provide insights into the effects of pressure gradient across the IES on RBC retention. By providing quantitative biophysical limits for RBCs to pass through the IES, the narrowest circulatory bottleneck in the spleen, our results offer a broad approach for developing quantitative markers for diseases such as hereditary spherocytosis, thalassemia, and malaria.

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