arXiv subjects

Søren Taverniers

Publications and source records attributed to Søren Taverniers.

7 recordsLinked to original sources

arXiv2024

A finite element method to compute the damping rate and frequency of oscillating fluids inside microfluidic nozzles

The computation of damping rates of an oscillating fluid with a free surface in which viscosity is small and surface tension high is numerically challenging. A typical application requiring such computation is drop-on-demand (DoD) microfluidic devices that eject liquid metal droplets, where accurate knowledge of damping rates for the least-damped oscillation modes following droplet ejection is paramount for assessing jetting stability at higher jetting frequencies. Computational fluid dynamics (CFD) simulations often struggle to accurately predict meniscus damping unless a very fine discretization is adopted, so calculations are computationally expensive. The faster alternative we adopt is to compute damping rates directly from the eigenvalues of the linearized problem. The surface tension term in Stokes or sloshing problems requires approximation of meniscus displacements, which introduces additional complexity in their numerical solution. We consider the combined effects of viscosity and surface tension, approximate the meniscus displacements, and construct a finite element method to compute the fluid's oscillation modes. We prove that the method is free of spurious modes with zero or positive damping rates, and we implement it with Taylor-Hood elements for velocity and pressure, and with continuous piecewise quadratic elements for meniscus displacement. We verify the numerical convergence of the method by reproducing the solution to an analytical benchmark problem and two more complex examples with axisymmetric geometry. We obtain the spatial shape and temporal evolution (angular frequency and damping rate) of the set of least-damped oscillation modes in minutes, compared to days for a CFD simulation. The method's ability to quickly generate accurate estimates of fluid oscillation damping rates makes it suitable for integration into design loops for prototyping microfluidic nozzles.

physics.comp-ph↗

arXiv2023

A multi-physics compiler for generating numerical solvers from differential equations

We develop a tool that enables domain experts to quickly generate numerical solvers for emerging multi-physics phenomena starting from a high-level description based on ordinary/partial differential equations and their initial and boundary conditions over a symbolic spacetime domain. This "multi-physics" compiler aims to bridge the gap between problem formulation and computation, which historically has spanned years or even decades. Specialized numerical solvers in areas such as computational fluid dynamics (CFD) often present a barrier to novice end users not well-versed in the intricacies of their underlying schemes, and requiring surgical modifications when coupling with additional physical components initially not accounted for by the solver. Through the use of an intermediate language that is neutral between classical and exterior calculus, the compiler generates correct-by-construction numerical source code that offers guarantees of immutable physical principles like conservation laws at the discrete level. We present a proof of concept for the multi-physics compiler through some examples involving compilation to OpenFOAM [1]. A specific use case that the compiler is well-suited for involves equation modification approaches, where the aim is to use simple numerical schemes such as central differencing through the additional of artificial terms to the original governing equations of the multi-physics problem [2, 3, 4].

physics.comp-ph↗

arXiv2023

Inverse asymptotic treatment: capturing discontinuities in fluid flows via equation modification

A major challenge in developing accurate and robust numerical solutions to multi-physics problems is to correctly model evolving discontinuities in field quantities, which manifest themselves as interfaces between different phases in multi-phase flows, or as shock and contact discontinuities in compressible flows. When a quick response is required to rapidly emerging challenges, the complexity of bespoke discretization schemes impedes a swift transition from problem formulation to computation, which is exacerbated by the need to compose multiple interacting physics. We introduce "inverse asymptotic treatment" (IAT) as a unified framework for capturing discontinuities in fluid flows that enables building directly computable models based on off-the-shelf numerics. By capturing discontinuities through modifications at the level of the governing equations, IAT can seamlessly handle additional physics and thus enable novice end users to quickly obtain numerical results for various multi-physics scenarios. We outline IAT in the context of phase-field modeling of two-phase incompressible flows, and then demonstrate its generality by showing how localized artificial diffusivity (LAD) methods for single-phase compressible flows can be viewed as instances of IAT. Through the real-world example of a laminar hypersonic compression corner, we illustrate IAT's ability to, within just a few months, generate a directly computable model whose wall metrics predictions for sufficiently small corner angles come close to that of NASA's VULKAN-CFD solver. Finally, we propose a novel LAD approach via "reverse-engineered" PDE modifications, inspired by total variation diminishing (TVD) flux limiters, to eliminate the problem-dependent parameter tuning that plagues traditional LAD. We demonstrate that, when combined with second-order central differencing, it can robustly and accurately model compressible flows.

physics.comp-ph↗

arXiv2022

Accelerating Part-Scale Simulation in Liquid Metal Jet Additive Manufacturing via Operator Learning

Predicting part quality for additive manufacturing (AM) processes requires high-fidelity numerical simulation of partial differential equations (PDEs) governing process multiphysics on a scale of minimum manufacturable features. This makes part-scale predictions computationally demanding, especially when they require many small-scale simulations. We consider drop-on-demand liquid metal jetting (LMJ) as an illustrative example of such computational complexity. A model describing droplet coalescence for LMJ may include coupled incompressible fluid flow, heat transfer, and phase change equations. Numerically solving these equations becomes prohibitively expensive when simulating the build process for a full part consisting of thousands to millions of droplets. Reduced-order models (ROMs) based on neural networks (NN) or k-nearest neighbor (kNN) algorithms have been built to replace the original physics-based solver and are computationally tractable for part-level simulations. However, their quick inference capabilities often come at the expense of accuracy, robustness, and generalizability. We apply an operator learning (OL) approach to learn a mapping between initial and final states of the droplet coalescence process for enabling rapid and accurate part-scale build simulation. Preliminary results suggest that OL requires order-of-magnitude fewer data points than a kNN approach and is generalizable beyond the training set while achieving similar prediction error.

physics.flu-dyn↗

arXiv2021

Mutual Information for Explainable Deep Learning of Multiscale Systems

Timely completion of design cycles for complex systems ranging from consumer electronics to hypersonic vehicles relies on rapid simulation-based prototyping. The latter typically involves high-dimensional spaces of possibly correlated control variables (CVs) and quantities of interest (QoIs) with non-Gaussian and possibly multimodal distributions. We develop a model-agnostic, moment-independent global sensitivity analysis (GSA) that relies on differential mutual information to rank the effects of CVs on QoIs. The data requirements of this information-theoretic approach to GSA are met by replacing computationally intensive components of the physics-based model with a deep neural network surrogate. Subsequently, the GSA is used to explain the network predictions, and the surrogate is deployed to close design loops. Viewed as an uncertainty quantification method for interrogating the surrogate, this framework is compatible with a wide variety of black-box models. We demonstrate that the surrogate-driven mutual information GSA provides useful and distinguishable rankings on two applications of interest in energy storage. Consequently, our information-theoretic GSA provides an "outer loop" for accelerated product design by identifying the most and least sensitive input directions and performing subsequent optimization over appropriately reduced parameter subspaces.

cs.LG↗

arXiv2020

GINNs: Graph-Informed Neural Networks for Multiscale Physics

We introduce the concept of a Graph-Informed Neural Network (GINN), a hybrid approach combining deep learning with probabilistic graphical models (PGMs) that acts as a surrogate for physics-based representations of multiscale and multiphysics systems. GINNs address the twin challenges of removing intrinsic computational bottlenecks in physics-based models and generating large data sets for estimating probability distributions of quantities of interest (QoIs) with a high degree of confidence. Both the selection of the complex physics learned by the NN and its supervised learning/prediction are informed by the PGM, which includes the formulation of structured priors for tunable control variables (CVs) to account for their mutual correlations and ensure physically sound CV and QoI distributions. GINNs accelerate the prediction of QoIs essential for simulation-based decision-making where generating sufficient sample data using physics-based models alone is often prohibitively expensive. Using a real-world application grounded in supercapacitor-based energy storage, we describe the construction of GINNs from a Bayesian network-embedded homogenized model for supercapacitor dynamics, and demonstrate their ability to produce kernel density estimates of relevant non-Gaussian, skewed QoIs with tight confidence intervals.

physics.comp-ph↗

arXiv2019

Estimation of distributions via multilevel Monte Carlo with stratified sampling

We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the cumulative distribution function of a quantity of interest in problems with random input parameters or initial conditions. Our approach combines a standard MLMC method with stratified sampling by replacing standard Monte Carlo at each level with stratified Monte Carlo with proportional allocation. We show that the resulting stratified MLMC algorithm is more efficient than its standard MLMC counterpart, due to the reduction in variance at each level provided by the stratification of the random parameter's domain. A smoothing approximation for the indicator function based on kernel density estimation yields a more efficient algorithm compared to the typically used polynomial smoothing. The difference in computational cost between the smoothing methods depends on the required error tolerance.

math.NA↗