Olivier Desjardins

A dissipation-free, sharp-interface discretization strategy is presented for the accurate simulation of complex compressible multiphase flows, such as shock-droplet interaction. The approach employs a hybrid scheme where either a centered or WENO3 discretization in the bulk phases, time-integrated with a fourth-order Runge–Kutta method, is coupled at phasic interfaces to a semi-Lagrangian geometric volume-of-fluid method that transports discontinuous phasic quantities with second-order accuracy. The hybridization is both spatial and temporal, and it preserves the dissipation-free property across interfaces. Localized dissipation is introduced only where temporal errors become significant, improving robustness in challenging configurations. By minimizing numerical dissipation, the solver reveals the need for subgrid-scale models for under-resolved turbulence, shocks, and breakup—providing a platform for their development and evaluation. Simulations of shock impact on a liquid droplet at high Reynolds and Weber numbers demonstrate accuracy and robustness in multiphase environments relevant to hypersonic flows.

High-speed droplet aerobreakup has been the focus of numerous experimental and numerical investigations due to its application in hypersonic aircraft development. This paper presents a preliminary mesh convergence study for fully 3D droplet aerobreakup simulations behind a steady normal shock of Mach numbers 5.12 and 3.03 using the open-source multiphase compressible flow solver from the NGA2 CFD framework (https://github.com/desjardi/NGA2). Primary droplet mass and displacement from simulation data is compared to previously published experimental and numerical results as well as previously developed empirical models. This work starts preliminary verification activities and provides the foundation for future work using the NGA2 solver to study the droplet aerobreakup problem.

Despite the high mortality rates associated with thromboembolic diseases, computational modeling of the physics of thromboembolism remains underdeveloped in the literature due to the inadequacy of classical finite element methods to accommodate the growth, large deformation, and fracture of blood clots, especially under the influence of fluid dynamic forces. Accordingly, we present a meshless numerical framework, employing peridynamics (PD) that readily captures the constitutive response, damage progression, and eventual failure of a blood clot. The PD framework was validated against three benchmark test cases: tensile loading of a plate with a hole, torsional loading of a column, and tensile loading of thin structural plates both with and without notches. Comparative quantitative and qualitative analysis demonstrated excellent agreement with finite element solutions generated using the commercial software ANSYS. The validated framework was then used to calibrate the peridynamic parameters to accurately reproduce the mechanical response, the cohesive bulk fracture of blood clots under tensile loading, and the debonding of blood clots from artificial surfaces, including titanium (Ti), polyurethane (PU), and polytetrafluoroethylene (PTFE). Force-displacement curves obtained using these calibrated parameters demonstrated a strong correlation with experimental data.

Multiphase flows are ubiquitous in both nature and engineering. Over the past two to three decades, substantial progress has been made in developing numerical methods for simulating these complex flows. Yet, significant challenges persist in accurately capturing intricate interfacial dynamics and the multi-scale interactions inherent to multiphase systems. This review focuses on several key numerical approaches that have proven particularly relevant from both practical and theoretical perspectives. In particular, we discuss Volume-Of-Fluid techniques, level set methods, diffuse interface models, and front tracking methods, along with immersed boundary strategies designed for particle-laden flows. We also examine multi-fluid Eulerian frameworks, population balance models for reactive processes, and sub-grid scale techniques for handling unresolved dynamics. Furthermore, emerging hybrid strategies that integrate conventional numerical methods with data-driven machine learning techniques are highlighted as promising directions. In conclusion, while current methodologies offer valuable insights into multiphase flow behavior, continued interdisciplinary efforts are essential to enhance predictive accuracy, computational efficiency, and the overall applicability of these simulations to real-world challenges.

Predicting droplet size distribution in liquid atomization processes from numerical simulations is an objective of critical importance to the aerospace industry. Because classical Eulerian interface capturing methods such as Volume of Fluid (VOF) suffer from spurious numerical break-up when interfacial scales approach the mesh size, they tend to generate wildly inaccurate droplet size distributions, even on very refined meshes. In recent work, we introduced a VOF reconstruction technique that allows for two phase interfaces to coexist within a grid cell, providing the novel capability to represent and transport sub-grid scale liquid and gas films without numerical break-up. In this work, we use this framework to simulate a realistic simplex atomizer, demonstrating the ability of this approach to capture the thin liquid film that characterizes the liquid hollow cone. In addition, we provide encouraging preliminary comparison of droplet size distribution against experimental measurements.

Direct numerical simulations of single and multiphase planar shear layers are performed using NGA2's compressible multiphase flow solver. The effects of compressibility are first observed in the single-phase limit by comparing the momentum thickness growth rate across a range of convective Mach numbers and validating the results with literature. The turbulent kinetic energy budget for the quasi-incompressible case is used to further validate the results. The shear layer flow is then modified to consider compressible mixing between a low-speed liquid layer and high-speed gas layer, which allows for the combined effects of gas compressibility, density ratio, and surface tension to be investigated. In this study, we focus on the evolution of the multiphase shear layer for a range of gas Mach numbers. Increasing the gas Mach number is shown to dampen not only the gas momentum thickness growth rate, but also the volume fraction thickness growth rate. A qualitative analysis of the interface reveals a similar initial evolution of interfacial structures but a greater number of interface features like droplets and ligaments for the low gas Mach number case at later times. Examining the density gradients of the high gas Mach number case reveals a mixture of oblique shocks upstream of waves and ligaments and small density fluctuations around droplets.

The interaction between turbulence and surface tension is studied numerically using the one-dimensional-turbulence (ODT) model. ODT is a stochastic model simulating turbulent flow evolution along a notional one-dimensional line of sight by applying instantaneous maps that represent the effects of individual turbulent eddies on property fields. It provides affordable high resolution of interface creation and property gradients within each phase, which are key for capturing the local behavior as well as overall trends, and has been shown to reproduce the main features of an experimentally determined regime diagram for primary jet breakup. Here ODT is used to investigate the interaction of turbulence with an initially planar interface. The notional flat interface is inserted into a periodic box of decaying homogeneous isotropic turbulence, simulated for a variety of turbulent Reynolds and Weber numbers. Unity density and viscosity ratios serve to focus solely on the interaction between fluid inertia and the surface-tension force. Statistical measures of interface surface density and spatial structure along the direction normal to the initial surface are compared to corresponding direct-numerical-simulation (DNS) data. Allowing the origin of the lateral coordinate system to follow the location of the median interface element improves the agreement between ODT and DNS, reflecting the absence of lateral nonvortical displacements in ODT. Beyond the DNS-accessible regime, ODT is shown to obey the predicted parameter dependencies of the Kolmogorov critical scale in both the inertial and dissipative turbulent-cascade subranges. Notably, the probability density function of local fluctuations of the critical scale is found to collapse to a universal curve across both subranges. Published by the American Physical Society 2024

Abstract Context: Low-density lipoprotein cholesterol (LDL-c) plays a key role in the development and progression of atherosclerotic cardiovascular disease (ASCVD). Despite the availability of effective lipid-lowering treatments, patients who have experienced an acute coronary syndrome (ACS) continue to face a high risk of recurrent cardiovascular events and mortality. Achieving the recommended LDL-c target of <0.55 g/L in secondary cardiovascular prevention remains a significant challenge, with fewer than 30% of patients reaching this goal. Aim To investigate the factors influencing LDL-c control after ACS and the effectiveness of intensive teleconsultation monitoring to control LDL-c, even in sub-groups where control is poorest. Methods This bi-centric prospective cohort study conducted between december 2019 and december 2021 compared a group that received standard follow-up after an ACS with an interventional group that received regular follow-up by teleconsultation in addition of usual care to optimize lipid-lowering treatment. A subgroup analysis was carried out to examine the effect of teleconsultation in subpopulations known to be significantly associated with better or worse LDL-c control in the usual care group or described in the literature. Results 1602 patients met the inclusion criteria for our study (814 in the usual care group and 788 in the teleconsultation group). Baseline characteristics were similar between groups. In the usual care group, factors influencing lipid control included gender, diabetes, cardiology consultation, distance to the nearest cardiologist, social deprivation and initial LDL-C levels. Teleconsultation significantly improved LDL-C target attainment compared to usual care (74.7% vs. 26.6%, p<0.001 with multivariate analysis OR 5.06 [4.21 ; 6.07]), particularly benefiting geographically and socially disadvantaged patients. Conclusion Teleconsultation significantly improves lipid control in acute coronary syndrome patients compared to usual care. This universal intervention, particularly beneficial for geographically and socially disadvantaged patients, highlights the potential of telemedicine in enhancing cardiovascular management.analysis in usual care groupTeleconsultation effect in sub-groups

A novel interface reconstruction strategy for volume of fluid (VOF) methods is introduced that represents the liquid-gas interface as two planes that co-exist within a single computational cell. In comparison to the piecewise linear interface calculation (PLIC), this new algorithm greatly improves the accuracy of the reconstruction, in particular when dealing with thin structures such as films. The placement of the two planes requires the solution of a non-linear optimization problem in six dimensions, which has the potential to be overly expensive. An efficient solution to this optimization problem is presented here that exploits two key ideas: an algorithm for extracting multiple plane orientations from transported surface data, and an efficient and mass-conserving distance-finding algorithm that accounts for two planes with arbitrary orientation. Additionally, a simple and robust strategy is presented to accurately represent the surface tension forces produced at the interface of subgrid-thickness films. The performance of this new VOF reconstruction is demonstrated on several test cases that illustrate the capability to handle arbitrarily thin films.

Coaxial atomization is an established atomization strategy for many stationary combustion systems. While modeling spray formation in coaxial atomization is challenging due to the existence of a wide range of length and time scales, typical models introduce a substantial uncertainty for Euler–Lagrange simulations of the actual application, e.g., a spray flame. To reduce uncertainties, a recently proposed multiscale approach is adopted for simulations of realistic applications in this work. The multiscale approach uses three one-way coupled simulation domains that cover the internal nozzle flow, the interfacial flow of the near-field, and the dispersed flow of the far-field. The capabilities of the approach are explored by applying it to a standardized non-reacting experiment from the flame spray pyrolysis research community. In order to assess the relevance for application simulations, results are discussed in the context of mixture formation. The results are compared against shadowgraphy images of the near-field and measured droplet statistics in the far-field. It is found that the multiscale approach is capable of providing similarly accurate droplet statistics as experiments or models derived from them. In addition, it is found that the breakup dynamics in the near-field introduce substantial mixture fraction fluctuations. These fluctuations are only included because of the deterministic coupling of the multiscale approach and are typically neglected in conventional approaches. • Multiscale simulations for a real coaxial atomizer are performed. • The capability of the multiscale approach is explored using experimental measurements. • The relevance of spray formation modeling limitations is highlighted. • The importance of the breakup dynamic for the mixture formation is demonstrated.

The mesh-dependency of the breakup of liquid films, including their breakup length scales and resulting drop size distributions, has long been an obstacle inhibiting the computational modeling of large-scale spray systems. With the aim of overcoming this barrier, this work presents a framework for the prediction and modeling of subgrid-thickness liquid film formation and breakup within two-phase simulations using the volume of fluid method. A two-plane interface reconstruction is used to capture the development of liquid films as their thickness decreases below the mesh size. The breakup of the film is predicted with a semi-analytical model that incorporates the film geometry captured through the two-plane reconstruction. The framework is validated against experiments of the bag breakup of a liquid drop at $\text{We}=13.8$ through the comparison of the resulting drop size and velocity distributions. The generated distributions show good agreement with experimental results for drop resolutions as low as 25.6 cells across the initial diameter. The presented framework enables these drop breakup simulations to be performed at a computational cost three orders of magnitude lower than the cost of simulations utilizing adaptive mesh refinement.

The accurate reconstruction of immiscible fluid-fluid interfaces from the volume fraction field is a critical component of geometric Volume of Fluid (VOF) methods. A common strategy is the Piecewise Linear Interface Calculation (PLIC), which fits a plane in each mixed-phase computational cell. However, recent work goes beyond PLIC by using two planes or even a paraboloid. To select such planes or paraboloids, complex optimization algorithms as well as carefully crafted heuristics are necessary. Yet, the potential exists for a well-trained machine learning model to efficiently provide broadly applicable solutions to the interface reconstruction problem at lower costs. In this work, the viability of a machine learning approach is demonstrated in the context of a single plane reconstruction. A feed-forward deep neural network is used to predict the normal vector of a PLIC plane given volume fraction and phasic barycenter data in a $3\times3\times3$ stencil. The PLIC plane is then translated in its cell to ensure exact volume conservation. Our proposed neural network PLIC reconstruction (PLIC-Net) is equivariant to reflections about the Cartesian planes. Training data is analytically generated with $\mathcal{O}(10^6)$ randomized paraboloid surfaces, which allows for sampling a wide range of interface shapes. PLIC-Net is tested in multiphase flow simulations where it is compared to standard (E)LVIRA reconstruction algorithms, and the impact of training data statistics on PLIC-Net's performance is also explored. It is found that PLIC-Net greatly limits the formation of spurious planes and generates cleaner numerical break-up of the interface. Additionally, the computational cost of PLIC-Net is lower than that of (E)LVIRA. These results establish that machine learning is a viable approach to VOF interface reconstruction and is superior to current reconstruction algorithms for some cases.

The mesh-dependency of the breakup of liquid films, including their breakup length scales and resulting drop size distributions, has long been an obstacle inhibiting the computational modeling of large-scale spray systems. With the aim of overcoming this barrier, this work presents a framework for the prediction and modeling of subgrid-thickness liquid film formation and breakup within two-phase simulations using the volume of fluid method. A two-plane interface reconstruction is used to capture the development of liquid films as their thickness decreases below the mesh size. The breakup of the film is predicted with a semi-analytical model that incorporates the film geometry captured through the two-plane reconstruction. The framework is validated against experiments of the bag breakup of a liquid drop at $\text{We}=13.8$ through the comparison of the resulting drop size and velocity distributions. The generated distributions show good agreement with experimental results for drop resolutions as low as 25.6 cells across the initial diameter. The presented framework enables these drop breakup simulations to be performed at a computational cost three orders of magnitude lower than the cost of simulations utilizing adaptive mesh refinement.

The interaction between turbulence and surface tension is studied numerically using the one-dimensional-turbulence (ODT) model. ODT is a stochastic model simulating turbulent flow evolution along a notional one-dimensional line of sight by applying instantaneous maps that represent the effects of individual turbulent eddies on property fields. It provides affordable high resolution of interface creation and property gradients within each phase, which are key for capturing the local behavior as well as overall trends, and has been shown to reproduce the main features of an experimentally determined regime diagram for primary jet breakup. Here, ODT is used to investigate the interaction of turbulence with an initially planar interface. The notional flat interface is inserted into a periodic box of decaying homogeneous isotropic turbulence, simulated for a variety of turbulent Reynolds and Weber numbers. Unity density and viscosity ratios serve to focus solely on the interaction between fluid inertia and the surface-tension force. Statistical measures of interface surface density and spatial structure along the direction normal to the initial surface are compared to corresponding direct-numerical-simulation (DNS) data. Allowing the origin of the lateral coordinate system to follow the location of the median interface element improves the agreement between ODT and DNS, reflecting the absence of lateral non-vortical displacements in ODT. Beyond the DNS-accessible regime, ODT is shown to obey the predicted parameter dependencies of the Kolmogorov critical scale in both the inertial and dissipative turbulent-cascade sub-ranges. Notably, the probability density function of local fluctuations of the critical scale is found to collapse to a universal curve across both sub-ranges.

A novel interface reconstruction strategy for volume of fluid (VOF) methods is introduced that represents the liquid-gas interface as two planes that co-exist within a single computational cell. In comparison to the piecewise linear interface calculation (PLIC), this new algorithm greatly improves the accuracy of the reconstruction, in particular when dealing with thin structures such as films. The placement of the two planes requires the solution of a non-linear optimization problem in six dimensions, which has the potential to be overly expensive. An efficient solution to this optimization problem is presented here that exploits two key ideas: an algorithm for extracting multiple plane orientations from transported surface data, and an efficient and mass-conserving distance-finding algorithm that accounts for two planes with arbitrary orientation. Additionally, a simple and robust strategy is presented to accurately represent the surface tension forces produced at the interface of subgrid-thickness films. The performance of this new VOF reconstruction is demonstrated on several test cases that illustrate the capability to handle arbitrarily thin films.

This paper evaluates and compares the accuracy and robustness of curvature estimation methods for three-dimensional interfaces represented implicitly by discrete volume fractions on a Cartesian mesh. The height function (HF) method is compared to three paraboloid fitting methods: fitting to the piecewise linear interface reconstruction centroids (PC), fitting to the piecewise linear interface reconstruction volumetrically (PV), and volumetrically fitting (VF) the paraboloid directly to the volume fraction field. The numerical studies presented in this work find that while the curvature error from the VF method converges with second-order accuracy as with the HF method for static interfaces represented by exact volume fractions, the PV method best balances low curvature errors with low computational cost for dynamic interfaces when the interface reconstruction and advection are coupled to a two-phase Navier-Stokes solver.

Over the past decades, the volume-of-fluid (VOF) method has been the method of choice for simulating atomization processes, owing to its unique ability to discretely conserve mass. Current state-of-the-art VOF methods, however, rely on the piecewise-linear interface calculation (PLIC) to represent the interface used when calculating advection fluxes. This renders the estimated curvature of the transported interface zeroth-order accurate at best, adversely impacting the simulation of surface-tension-driven flows. In the past few years, there have been several attempts at using piecewise-parabolic interface approximations instead of piecewise-linear ones for computing advection fluxes, albeit all limited to two-dimensional cases or not inherently mass conservative. In this contribution, we present our most recent work on three-dimensional piecewise-parabolic interface reconstruction and apply it in the context of the VOF method. As a result of increasing the order of the interface representation, the reconstruction of the interface and the estimation of its curvature now become a single step instead of two separate ones. The performance of this new approach is assessed both in terms of accuracy and stability and compared to the classical PLIC-VOF approach on a range of canonical test-cases and cases of surface-tension-driven instabilities.

In liquid-fueled combustion systems, optimization of the fuel atomization process is critical to reducing fuel consumption and lowering pollutant emissions. Accurate and efficient computational modeling of liquid atomization can open the door to spray optimization, however it presents a significant challenge to modelers due to the extremely complex flow field and wide range of length and time scales involved. In this work, a multi-scale and multi-domain simulation strategy is used to model end-to-end the turbulent spray produced by a swirled two-fluid coaxial atomizer, a device that utilize a high-speed swirled gas stream to destabilize a co-flowing low-speed liquid, widely used in systems such as fuel injectors. Our computational method relies on sub-grid scale modeling; in particular, we will introduce a thin structure break-up model to account for topology changes, converting thin liquid structures into spherical Lagrangian particles. With such simulations, the impact of swirl on the break-up process can be analyzed by varying the swirl ratio, and we aim to quantitatively validate our simulations against experiments at identical operating conditions, including drop size statistics.

We provide closed-form expressions for the first moments (i.e., the volume and volume-weighted centroid) of a polyhedron clipped by a paraboloid, that is, of a polyhedron intersected with the subset of the three-dimensional real space located on one side of a paraboloid. These closed-form expressions are derived following successive applications of the divergence theorem and the judicious parametrization of the intersection of the polyhedron’s faces with the paraboloid. Here, we provide means for identifying ambiguous discrete intersection topologies, and propose a corrective procedure for preventing their occurence. Finally, we put our proposed closed-form expressions and numerical approach to the test with millions of random and manually engineered polyhedron/paraboloid intersection configurations. The results of these tests show that we are able to provide robust machine-accurate estimates of the first moments at a computational cost that is within one order of magnitude of that of state-of-the-art half-space clipping algorithms.

This paper evaluates and compares the accuracy and robustness of curvature estimation methods for three-dimensional interfaces represented implicitly by discrete volume fractions on a Cartesian mesh. The height function (HF) method is compared to three paraboloid fitting methods: fitting to the piecewise linear interface reconstruction centroids (PC), fitting to the piecewise linear interface reconstruction volumetrically (PV), and volumetrically fitting (VF) the paraboloid directly to the volume fraction field. The numerical studies presented in this work find that while the curvature error from the VF method converges with second-order accuracy as with the HF method for static interfaces represented by exact volume fractions, the PV method best balances low curvature errors with low computational cost for dynamic interfaces when the interface reconstruction and advection are coupled to a two-phase Navier-Stokes solver.