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Many mechanical engineering applications call for multiscale computational modeling and simulation. However, solving for complex multiscale systems remains computationally onerous due to the high dimensionality of the solution space. Recently, machine learning (ML) has emerged as a promising solution that can either serve as a surrogate for, accelerate or augment traditional numerical methods. Pioneering work has demonstrated that ML provides solutions to governing systems of equations with comparable accuracy to those obtained using direct numerical methods, but with significantly faster computational speed. These high-speed, high-fidelity estimations can facilitate the solving of complex multiscale systems by providing a better initial solution to traditional solvers. This paper provides a perspective on the opportunities and challenges of using ML for complex multiscale modeling and simulation. We first outline the current state-of-the-art ML approaches for simulating multiscale systems and highlight some of the landmark developments. Next, we discuss current challenges for ML in multiscale computational modeling, such as the data and discretization dependence, interpretability, and data sharing and collaborative platform development. Finally, we suggest several potential research directions for the future.

Abstract: A major drawback in the operation of mechanical heart valve prostheses is thrombus formation in the near valve region. Detailed flow analysis in this region during the valve closure phase is of interest in understanding the relationship between shear stress and platelet activation. A fixed-grid Cartesian mesh flow solver is used to simulate the blood flow through a bi-leaflet mechanical valve employing a two-dimensional geometry of the leaflet with a pivot point representing the hinge region. A local mesh refinement algorithm allows efficient and fast flow computations with mesh adaptation based on the gradients of the flow field in the leaflet-housing gap at the instant of valve closure. Leaflet motion is calculated dynamically based on the fluid forces acting on it employing a fluid-structure interaction algorithm. Platelets are modeled and tracked as point particles by a Lagrangian particle tracking method which incorporates the hemodynamic forces on the particles. A platelet activation model is included to predict regions which are prone to platelet activation. Closure time of the leaflet is validated against experimental studies. Results show that the orientation of the jet flow through the gap between the housing and the leaflet causes the boundary layer from the valve housing to be drawn in by the shear layer separating from the leaflet. The interaction between the separating shear layers is seen to cause a region of intensely rotating flow with high shear stress and high residence time of particles leading to high likelihood of platelet activation in that region.

New hydrocarbon fuels with high-energy density content can substantially advance high-thrust, high-temperature, and reduced-size combustion technology. The present work investigates the phase change dynamics of the PCU alkene dirtier, a newly synthesized high-energy density hydrocarbon fuel, in turbulent reacting flows. The shape, location, and velocity of the propellant-gas interface is treated explicitly. A Lagrangian moving grid technique in conjunction with an established body-fitted field equation solver is developed. Owing to the complex flow structure and uneven heat flux distribution along the propellant surface, the interface experiences nonuniform regression between the front and the rear ends. Consistent with experimental observations, the thermal characteristics near the solid-gas interface vary in space and time. The present computational capacity can advance our understanding of phase change, thermal decomposition, and subsequent mixing and burning dynamics of the energetic fuel.

A methodology is presented to simulate the growth and interaction of unstable fronts. Such fronts are found to be important in instabilities arising in several natural and industrial processes, such as solidification, spray dynamics, and bubble growth. The numerical simulation of such phenomena is challenging on account of the highly distorted moping boundary at which, often, curvature-dependent boundary conditions need be applied in each phase. Herein is presented a numerical technique to capture highly distorted interfaces. The interface is represented employing marker particles. Joining successive markers with circular arcs yields values of curvatures and normals on the interface. The markers are followed over an underlying Cartesian grid and new marker particles are generated at each time step by an intersection procedure. The issue of mergers of interfaces is also attacked and the use of cells permits the simulation of merger-breakup processes. Thus, the method presented here, unlike previous marker particle-based schemes, tan handle particle depletion / accumulation and merger / breakup issues with good accuracy. Results are presented, employing velocity functions modeled to mimic the actual instability phenomena, to demonstrate the accuracy and capability of the scheme developed.

We report on measures to improve the robustness and performance of a three-dimensional pressure-based multiblock algorithm. In particular, we demonstrate the implementation of the treatment at block interfaces for arbitrary orientations of the blocks and investigate the effects of applying different boundary conditions on the pressure-correction equation at block boundaries. It is shown that the pressure corrections in different blocks need to be strongly coupled in order to achieve better convergence. The performance of the algorithm is also shown to be significantly affected by the way in which the multiblock solution scheme is organized for the individual equations, which are solved sequentially. The method developed is then applied to two practical flow problems involving turbulent and rotational effects in complex geometries.

Moving-boundary problems arise in numerous important physical phenomena, and often form complex shapes during their evolution. The ability to track the interface in such cases in two dimensions is well established. However, modifying the grid representing the interface as it evolves in three-dimensional space introduces additional issues. In the current work, three-dimensional interfaces are represented by adaptive unstructured grids. The grids are restructured and refined based on the shape and size of the triangular elements in the grid that forms the interfaces. As the interface deforms, points are automatically added to ensure that the accuracy of interface representation remains consistent. Results are presented to show how complex interface features, including surface curvatures and normals, can be captured by modifying an existing method that uses an approximation to the Dupin indicatrix.

Validation exercises for computational models of materials under impact must contend with sparse experimental data as well as with uncertainties due to microstructural stochasticity and variabilities in thermomechanical properties of the material. This paper develops statistical methods for determining confidence levels for verification and validation of computational models subject to aleatoric and epistemic uncertainties and sparse stochastic experimental datasets. To demonstrate the method, the classical problem of Taylor impact of a copper bar is simulated. Ensembles of simulations are performed to cover the range of variabilities in the material properties of copper, specifically the nominal yield strength A, the hardening constant B, and the hardening exponent n in a Johnson–Cook material model. To quantify uncertainties in the simulation models, we construct probability density functions (PDFs) of the ratios of the quantities of interest, viz., the final bar diameter Df to the original diameter D0 and the final length Lf to the original length L0. The uncertainties in the experimental data are quantified by constructing target output distributions for these QoIs (Df/D0 and Lf/L0) from the sparse experimental results reported in literature. The simulation output and the experimental output distributions are compared to compute two metrics, viz., the median of the model prediction error and the model confidence at user-specified error level. It is shown that the median is lower and the model confidence is higher for Lf/L0 compared to Df/D0, implying that the simulation models predict the final length of the bar more accurately than the diameter. The calculated confidence levels are shown to be consistent with expectations from the physics of the impact problem and the assumptions in the computational model. Thus, this paper develops and demonstrates physically meaningful metrics for validating simulation models using limited stochastic experimental datasets. The tools and techniques developed in this work can be used for validating a wide range of computational models operating under input uncertainties and sparse experimental datasets.

The fluid dynamics during valve closure resulting in high shear flows and large residence times of particles has been implicated in platelet activation and thrombus formation in mechanical heart valves. Our previous studies with bileaflet valves have shown that large shear stresses induced in the gap between the leaflet edge and valve housing results in relatively high platelet activation levels, whereas flow between the leaflets results in shed vortices not conducive to platelet damage. In this study we compare the result of closing dynamics of a tilting disk valve with that of a bileaflet valve. The two-dimensional fluid-structure interaction analysis of a tilting disk valve closure mechanics is performed with a fixed grid Cartesian mesh flow solver with local mesh refinement, and a Lagrangian particle dynamic analysis for computation of potential for platelet activation. Throughout the simulation the flow remains in the laminar regime, and the flow through the gap width is marked by the development of a shear layer, which separates from the leaflet downstream of the valve. Zones of recirculation are observed in the gap between the leaflet edge and valve housing on the major orifice region of the tilting disk valve and are seen to be migrating toward the minor orifice region. Jet flow is observed at the minor orifice region and a vortex is formed, which sheds in the direction of fluid motion, as observed in experiments using PIV measurements. The activation parameter computed for the tilting disk valve at the time of closure was found to be 2.7 times greater than that of the bileaflet mechanical valve and was found to be in the vicinity of the minor orifice region, mainly due to the migration of vortical structures from the major to the minor orifice region during the leaflet rebound of the closing phase.