In this work, we propose an efficient solution of the inverse Stefan problem by multi-fidelity Bayesian optimization. We construct a multi-fidelity Gaussian process surrogate model by combining many low-fidelity estimates of a solidification problem with only a few high-fidelity measurements. To solve the inverse problem, we employ the Gaussian process model in a Bayesian optimization approach based on a multi-fidelity knowledge gradient acquisition function. To account for the specific structure of the target function, we reformulate it as a composite function and thus significantly improve the stability of the optimization procedure. Target values can be switched easily, and previously obtained samples and surrogate models can be reused. The proposed method iteratively improves the recommended solution of the inverse problem. Explicitly adding recommended points of previous iterations to the solution procedure enhances the convergence properties of the algorithm.We demonstrate the applicability of the algorithm by solving the inverse problem for a planar solidification front in a singlefidelity setting. Process parameters are identified for targeted crystal-growth velocities during directional dendritic solidification. The relation between these velocities and process parameters, such as undercooling, thermal diffusivity, capillarity, and capillary anisotropy, defines the thermo-mechanical properties of the solidified part in metal-based additive manufacturing. Material design is based on the corresponding inverse problem. Cost-efficiency of solving the inverse problem is improved by introducing a fidelity hierarchy based on coarse-grid approximations of high-fidelity numerical simulations. The open-source simulation framework ALPACA for multiphase flows allows to generate data at all fidelities. We demonstrate the superior convergence properties of the presented multi-fidelity approach by comparison with an approach solely based on high-fidelity measurements of the tip velocity.(c) 2023 Elsevier B.V. All rights reserved.

In this work, we propose a novel framework coupling state-of-the-art multi-fidelity Gaussian Process modeling techniques with input-space warping for a cost-efficient construction of a stochastic surrogate model. During model generation, we achieve high computational efficiency by combining a large number of cheap estimates (low-fidelity model) with only a few, computationally expensive, high-fidelity measurements. We base the fidelity hierarchy on coarse-grid approximations of high-fidelity numerical simulations and show its successful application within the proposed framework. Utilizing coarse-grid approximations for multi-fidelity modeling is attractive for many practical applications, since it often allows for multi-fidelity data generation with a single simulator. As benchmark, we apply this framework to generate a surrogate model for crystal growth velocities in directional dendritic solidification. The derivation of a relation between this tip velocity and process parameters, such as undercooling, thermal diffusivity, capillarity, and capillary anisotropy, has been in the focus of research for decades due to its important role on microstructure evolution during solidification. It defines the thermo-mechanical properties of the solidified part and influences its behavior in subsequent manufacturing steps.As data generator, we use the open-source simulation framework ALPACA, applying a conservative sharp-interface level-set model. We assess the accuracy of the multi-fidelity tip velocity model by using cross-validation techniques. Compared to single-fidelity models purely based on high-fidelity data, our approach improves prediction accuracy significantly but only requires a little cost overhead for data generation. The stochastic nature of the resulting surrogate model allows for quantifying the uncertainty associated with predictions. This motivates the application of the model in Bayesian-optimization algorithms for inverse problems. Also, it may serve as input for microstructure simulations which rely on accurate relations between local solidification velocities and process parameters such as undercooling to predict grain-scale crystalline structures and which need material-dependent model calibration.

We present a novel storage-and-access approach for Lagrangian particles in a multiresolution local-timestepping framework for multiphase flow simulations. The proposed method applies a block-particle mapping strategy for efficient access of all particles on a specific refinement level while traversing through the multiresolution tree. This allows for extending the local timestepping algorithm with its refinement level-dependent timestep sizes to the evolution of particles, which results in significant speed-up in comparison to standard timestepping. For multi-scale multiphase flow simulations, the particle model is combined with a level-set based multiphase model on a Cartesian grid. To maintain robustness of fluid-state interpolation for particles near the level set-based fluid-fluid interface, WENO-based interpolation is applied which includes both real- and ghost-fluid cells. This enforces the sharp interface property also for interpolated fluid states, and suppresses spurious oscillations in the event of discontinuities. We validate the particle model with a one-dimensional simulation of a single particle in an air-helium shock tube for one-way coupling, and with two-dimensional simulations of a particle injected in a quiescent domain for the feedback force. Simulations of two-dimensional aerodynamic fragmentation in shear-induced entrainment and Rayleigh-Taylor piercing regimes use Lagrangian particles as sub-grid scale representation of small droplets post-breakup. Finally, three-dimensional massively-parallel simulations of single- and triple-bubble collapse near a wall coated with free-floating particles are presented. The particle cleaning radius of the single-bubble setup agrees reasonably well with experimental reference data. These simulations consider 10(6) particles and an Eulerian grid with effectively 10(12) finite-volume cells at compression rates of more than 90% for the particulate phase. This underlines the advantageous effect of embedding the particles in the multiresolution tree with its spatial and temporal adaptivity, which is necessary for performing such large scale simulations efficiently. (C) 2021 Elsevier B.V. All rights reserved.

Machine Learning (ML) and Digital Twins (DT) are at the heart of today’s different industries, ranging from advanced manufacturing to biomedical systems to resilient ecosystems, civil infrastructures, smart cities, and healthcare. They have become indispensable for solving complex problems in science, engineering, and technology development. The purpose of the MMLDT-CSET 2021 conference is to facilitate the transition of ML and DT from fundamental research to mainstream fields and technologies through advanced data science, mechanistic methods, and computational technologies. This 3-day conference features technical tracks of emerging ML-DT fields and applications, special public lectures, short courses, and demonstrations. The conference will be held in a hybrid format, featuring both on-site and virtual sessions.

The solidification of an undercooled liquid is physically unstable. The dominating instability modes are affected by both the evolving temperature field in the solid and liquid phases, and characteristics of the phase interface such as the curvature and the propagation velocity. To capture the instability mode, therefore both the temperature field and the interface have to be represented accurately in a numerical model of the phase-change process. In this work, we develop conservative interface exchange terms for a sharp-interface formulation of liquid-solid phase transition. Conservation at the interface is maintained by explicit formulation of interface fluxes into both solid and liquid phases. We propose a semi-implicit level-set formulation to evolve the phase interface. A new formulation for the interface surface in a cut cell is derived, which includes the Stefan condition. We achieve low numerical dissipation by an explicit third-order Runge-Kutta scheme for time discretization, and a novel WENO-like (Weighted Essentially Non-Oscillatory) interface-gradient reconstruction. This distinguishes our level-set based sharp-interface model from previous level-set based approaches, which rely on finite-difference based interface treatment, and thus do not ensure discrete conservation at the interface. The flux terms in our approach take into account surface-tension and kinetic effects on the interface temperature (Gibbs-Thomson relation). The Stefan condition provides a relation between interface fluxes of mass and energy, and the interface-propagation velocity. Computational efficiency is maintained by a multiresolution approach for local mesh adaptation, and an adaptive local time-stepping scheme. We present one- and two-dimensional simulation results for the growth of a planar solidification front and a single parabolic dendrite affected by surface tension. The results agree well with experimental and analytical reference data, showing that the model is capable to capture both stable (planar) and unstable (dendritic-like) growth processes in the heat-diffusion dominated regime. The convergence order for successively finer meshes in the one-dimensional case is one for the interface location and the temperature field, outperforming previously reported level-set based approaches. We present numerical data of a growing crystal with four-fold symmetry. Our results indicate that the artificial dissipation of the underlying numerical scheme affects its capability to reproduce consistently physical tip-splitting instabilities. The proposed low-dissipation scheme is able to resolve such instabilities. Finally, we demonstrate the capability of the method to simulate multiple growing crystals with anisotropic surface-tension and kinetic effects. (C) 2020 The Authors. Published by Elsevier Ltd.

In this work, we study the interface deformation during the early-stages of breakup of a water column in an ambient flow field by high-resolution numerical simulation. The compressible Navier-Stokes equations govern the motion of the two fluids, and capillary forces and viscous effects are considered. We model the multiphase flow with a level-set based sharp-interface method with conservative interface interaction. The governing equations are discretized with a finite-volume approach with low-dissipation flux reconstruction at cell faces based on a fifth-order WENO scheme, and a third-order Runge-Kutta TVD explicit time integration scheme. We validate our numerical simulations by comparison with experimental reference data. We achieve an accurate prediction of wave dynamics and interface deformation of the liquid column. Both flattening of the cylinder (first stage) and shearing of the sheet at the droplet equator (second stage) are reproduced. We show that a distinct pressure-wave pattern forms in the supersonic flow region near the cylinder equator after shock passage. These waves interact with the phase interface, resulting in local interface disturbances that coincide with the onset of the second stage. Resolving these waves is essential for the prediction of the hat-like structure at the upstream face of the cylinder during the second stage of the breakup, which so far only has been observed in experimental visualizations of this particular breakup mode. Our results support the connection of the sheet-stripping mechanism with the local formation of recirculation zones. Extending previous work, our high-resolution results indicate that recirculation zones appear at multiple locations along the interface, and are directly linked to the growth of water sheet-forming interface disturbances. (C) 2020 The Authors. Published by Elsevier Ltd.

•Full time-step size adaptivity for local-time stepping schemes.•Improved stability for flow problems with steep wave-speed gradients.•No limitations on the number of refinement levels.•No limitations on the order of the spatial reconstruction scheme.

We present twoand three-dimensional numerical simulation results of a shock-induced droplet breakup. We study the breakup mechanism for two different Weber numbers. Reynolds and Ohnesorge numbers are kept constant. We apply a conservative interface-interaction model to compute the exchange of momentum and energy between the two immiscible fluids water and air. The fluids are separated by a sharp interface (level set). A block-structured multiresolution scheme is used to adapt the mesh to the evolving flow field. We verify our simulation setup using a twodimensional shock-induced breakup with a high Weber number, which is compared to experimental and numerical data. Simulation results show that the flattening of the droplet, which is the first stage of the droplet breakup, is independent of the Weber number. Once interfacial instabilities appear at the water-air interface, surface-tension effects play a dominant role in determining the second stage of the breakup. For small surface-tension forces, the droplet breakup occurs in the shear-induced entrainment (SIE) regime. Shear instabilities grow near the droplet equator, and form the sheet which is characteristic for this regime. For large surface-tension forces, the droplet breakup occurs in the Rayleigh-Taylor piercing (RTP) regime. Surface tension forces suppress the growth of the sheet, and lead instead to a smooth water-air interface. At later stages, the onset of the characteristic bag shape is observed. INTRODUCTION Aerodynamic fragmentation, i.e. the breakup of an initially spherical drop into smaller droplets, is a matter of interest for a wide range of technological applications and environmental phenomena, for example in internal liquid fuel combustion engines or for the splatter of rain drops on supersonic aircrafts. The underlying fluid mechanical instability mechanism that dominates the breakup process depends on the ratio of aerodynamic forces, viscous forces, and surface tension. Five main breakup modes are classically distinguished: vibrational, bag, multimode, shear stripping, and catastrophic (Guildenbecher et al., 2009). Dai & Faeth (2001) proposed that the multimode breakup is a transi∗jakob.kaiser@tum.de †stefan.adami@tum.de ‡nikolaus.adams@tum.de tional mode from bag to sheet thinning, which occurs either as bag/plume breakup or plume/sheet-thinning. A reclassification of these breakup regimes was suggested by Theofanous (2011), motivated by the physical mechanisms which dominate the different breakup regimes: RayleighTaylor piercing (RTP) and shear-induced entrainment (SIE). For lower ratios of aerodynamic forces to surface tension and viscous forces, RTP is the relevant instability mode for breakup (bag). With increasing aerodynamic forces, SIE becomes dominating (shear stripping). The multimode breakup occurs at the transition between these two mechanisms. The exact interplay between these two instability mechanisms remains, however, an open question. Due to the inherent difficulties of analyzing droplet breakup experimentally especially small spatial and temporal scales and increasing computational capabilities, direct numerical simulation emerges as possible choice for detailed investigations. Many studies so far have been limited to two dimensions (2D) or assume axisymmetry (Aalburg et al., 2003, e.g.). Khosla et al. (2006) were among the first to perform fully three-dimensional simulations. Their investigations focused on the low Webernumber range. Meng & Colonius (2018) performed a detailed fully three-dimensional simulation of drop breakup in the SIE regime, using a non-adaptive cylindrical grid to solve the compressible Euler equations and the volume-offluid (VOF) approach for interface capturing. First threedimensional results in the RTP regime have recently been published by Yang et al. (2017), assuming incompressible fluid flow. In this work, we investigate drop breakup dynamics in the RTP and SIE regimes. Based on our previous work (Kaiser et al., 2017), twoand three-dimensional simulations of a water droplet in air flow are conducted for different Weber numbers. We approximate the compressible Navier-Stokes equations with a finite-volume approach. A fifth-order WENO scheme for flux reconstruction at cell faces ensures high-order representation of small flow scales, while overall computational efficiency is improved by our wavelet-based block-structured multiresolution scheme with adaptive local time-stepping. This allows for adapting our mesh to the changing flow field, including instantaneous time-step size adaptation. The phase interface is described by a level-set function, and explicit interface exchange terms are formulated to model the interface interaction. After validating the multi-phase model, we compare

We present two- and three-dimensional numerical results of the shock-induced breakup of a liquid droplet in air. We apply a conservative interface interaction model for sharp-interface representation and a block-based multi-resolution scheme to adaptively refine our mesh. Numerical modeling effects, such as the flux reconstruction scheme and the use of a scale separation model, that treats non-resolved interface segments, are investigated. Similarly as a previous study (Meng, 2016), we identify two dominant mechanisms of droplet breakup at certain Mach numbers - flattening of the droplet and sheet stripping - occurring simultaneously and influencing each other in our simulations. Three-dimensional simulations show the flattening mechanism and the mushroom-like deformation of the droplet. They also explain the occurrence of a recirculation zone in the droplet wake. The two-dimensional simulations already exhibit the sheet stripping mechanism, which occurs during and after droplet flattening. Small sheets emerge from both the upstream and the downstream side of the 2D droplet, while the main sheet develops at the droplet equator.

We present fully three-dimensional numerical simulation results of shock-induced bubble collapse near a water-gelatin interface. We study how the incoming pulse form and its amplitude affect the dynamics of bubble collapse and the subsequent gelatin penetration. Three immiscible fluids (water, air, and gelatin) are considered, separated by a sharp interface (level set). A conservative interface-interaction model determines the exchange of momentum and energy. A block-structured multiresolution scheme is used to adapt the mesh to the evolving flow field. Validation simulations (free-field bubble collapse, bubble collapse near a rigid wall) show that our numerical setup accurately predicts bubble collapse dynamics and post-collapse wave dynamics. Two-dimensional simulations assuming cylindrical symmetry reveal a quasi self-similar collapse behavior of the bubble for each wave form. The gelatin-penetration dynamics are self-similar, too, and occur in three stages. The onset of the gelatin penetration is governed by the post-shock momentum after the bubble collapse. This is followed by a fast penetration upon the impact of the water hammer. The penetration rate slows down once interfacial instabilities grow at the water-gelatin interface. Our three dimensional simulation results confirm the two-dimensional cylindrically-symmetric results of a single-bubble collapse. The collapse of two equi-sized bubbles results in a change of direction of the emitted water hammers. For our setup, the water hammers are deflected in the direction of the second bubble, and therefore impinge on the gelatin interface obliquely. The actual direction depends on the initial bubble separation distance and the stand-off distance from the interface, and will be further investigated in future work. © 2019 International Symposium on Turbulence and Shear Flow Phenomena, TSFP. All rights reserved.