Srdjan Simunovic

Modeling the coupling of reaction kinetics and hydrodynamics in a collapsing cavity

We introduce a model of cavitation based on the multiphase Lattice Boltzmann method (LBM) that allows for coupling between the hydrodynamics of a collapsing cavity and supported solute chemical species. We demonstrate that this model can also be coupled to deterministic or stochastic chemical reactions. In a two-species model of chemical reactions (with a major and a minor species), the major difference observed between the deterministic and stochastic reactions takes the form of random fluctuations in concentration of the minor species. We demonstrate that advection associated with the hydrodynamics of a collapsing cavity leads to highly inhomogeneous concentration of solutes. In turn these inhomogeneities in concentration may lead to significant increase in concentration-dependent reaction rates and can result in a local enhancement in the production of minor species.

Time-parallel multiscale/multiphysics framework

We introduce the time-parallel compound wavelet matrix method (tpCWM) for modeling the temporal evolution of multiscale and multiphysics systems. The method couples time parallel (TP) and CWM methods operating at different spatial and temporal scales. We demonstrate the efficiency of our approach on two examples: a chemical reaction kinetic system and a non-linear predator-prey system. Our results indicate that the tpCWM technique is capable of accelerating time-to-solution by 2-3-orders of magnitude and is amenable to efficient parallel implementation.

An efficient algorithm for simulating fracture using large fuse networks

The high computational cost involved in modelling of the progressive fracture simulations using large discrete lattice networks stems from the requirement to solve a new large set of linear equations every time a new lattice bond is broken. To address this problem, we propose an algorithm that combines the multiple-rank sparse Cholesky downdating algorithm with the rank-p inverse updating algorithm based on the Sherman–Morrison–Woodbury formula for the simulation of progressive fracture in disordered quasi-brittle materials using discrete lattice networks. Using the present algorithm, the computational complexity of solving the new set of linear equations after breaking a bond reduces to the same order as that of a simple backsolve (forward elimination and backward substitution) using the already LU factored matrix. That is, the computational cost is O(nnz(L)), where nnz(L) denotes the number of non-zeros of the Cholesky factorization L of the stiffness matrix A. This algorithm using the direct sparse solver is faster than the Fourier accelerated preconditioned conjugate gradient (PCG) iterative solvers, and eliminates the critical slowing down associated with the iterative solvers that is especially severe close to the critical points. Numerical results using random resistor networks substantiate the efficiency of the present algorithm.

Multiscale modeling and characterization for performance and safety of lithium-ion batteries

Lithium-ion batteries are highly complex electrochemical systems whose performance and safety are governed by coupled nonlinear electrochemical-electrical-thermal-mechanical processes over a range of spatiotemporal scales. Gaining an understanding of the role of these processes as well as development of predictive capabilities for design of better performing batteries requires synergy between theory, modeling, and simulation, and fundamental experimental work to support the models. This paper presents the overview of the work performed by the authors aligned with both experimental and computational efforts. In this paper, we describe a new, open source computational environment for battery simulations with an initial focus on lithium-ion systems but designed to support a variety of model types and formulations. This system has been used to create a three-dimensional cell and battery pack models that explicitly simulate all the battery components (current collectors, electrodes, and separator). The models are used to predict battery performance under normal operations and to study thermal and mechanical safety aspects under adverse conditions. This paper also provides an overview of the experimental techniques to obtain crucial validation data to benchmark the simulations at various scales for performance as well as abuse. We detail some initial validation using characterization experiments such as infrared and neutron imaging and micro-Raman mapping. In addition, we identify opportunities for future integration of theory, modeling, and experiments.

Spatiotemporal Compound Wavelet Matrix Framework for Multiscale/Multiphysics Reactor Simulation: Case Study of a Heterogeneous Reaction/Diffusion System

We present a mathematical method for efficiently compounding information from different models of species diffusion from a chemically reactive boundary. The proposed method is intended to serve as a key component of a multiscale/multiphysics framework for heterogeneous chemically reacting processes. An essential feature of the method is the merging of wavelet representations of the different models and their corresponding time and length scales. Up-and-down-scaling of the information between the scales is accomplished by application of a compounding wavelet operator, which is assembled by establishing limited overlap in scales between the models. We show that the computational efficiency gain and potential error associated with the method depend on the extent of scale overlap and wavelet filtering used. We demonstrate the method for an example problem involving a two-dimensional chemically reactive boundary and first order reactions involving two species.

Parareal in Time for Fast Power System Dynamic Simulations

Recent advancements in high-performance parallel computing platforms and parallel algorithms have significantly enhanced the opportunities for real-time power system protection and control. This paper investigates application of Parareal in time algorithm for fast dynamic simulations. Parareal algorithm belongs to the class of temporal decomposition methods which divide the time interval into sub-intervals and solve them concurrently. Time-parallel algorithms face the difficulty of providing correct initial conditions for all the sub-intervals which impact the convergence rates. Parareal overcomes this difficulty by using an approximate trajectory. It has become popular in recent years for long transient simulations (e.g., molecular dynamics, fusion, reacting flows). This paper presents an approach for reliable implementation of Parareal with detailed models of power systems including saturation. Windowing approach is proposed for improving the convergence. Parareal is compared with the Newton-based time-parallel method. Effectiveness of the algorithm is analyzed by parallel emulation using extensive case studies on 10-generator 39-bus system and 327-generator 2383-bus system for various disturbances. Parareal with simulation windows of 1 s have shown convergence in 1 to 3 iterations for majority of the simulated cases, irrespective of the size of the system and nature of the disturbance. All the cases tested have converged with the proposed implementation.

An efficient block-circulant preconditioner for simulating fracture using large fuse networks

Critical slowing down associated with the iterative solvers close to the critical point often hinders large-scale numerical simulation of fracture using discrete lattice networks. This paper presents a block-circulant preconditioner for iterative solvers for the simulation of progressive fracture in disordered, quasi-brittle materials using large discrete lattice networks. The average computational cost of the present algorithm per iteration is O(rslog s) +  delops, where the stiffness matrix A is partitioned into r × r blocks such that each block is an s × s matrix, and delops represents the operational count associated with solving a block-diagonal matrix with r × r dense matrix blocks. This algorithm using the block-circulant preconditioner is faster than the Fourier accelerated preconditioned conjugate gradient algorithm, and alleviates the critical slowing down that is especially severe close to the critical point. Numerical results using random resistor networks substantiate the efficiency of the present algorithm.

Scaling of fracture strength in disordered quasi-brittle materials

AbstractThis paper presents two main results. The first result indicates that in materials with broadly distributed microscopic heterogeneities, the fracture strength distribution corresponding to the peak load of the material response does not follow the commonly used Weibull and (modified) Gumbel distributions. Instead, a lognormal distribution describes more adequately the fracture strengths corresponding to the peak load of the response. Lognormal distribution arises naturally as a consequence of multiplicative nature of large number of random distributions representing the stress scale factors necessary to break the subsequent “primary” bond (by definition, an increase in applied stress is required to break a “primary” bond) leading up to the peak load. Numerical simulations based on two-dimensional triangular and diamond lattice topologies with increasing system sizes substantiate that a lognormal distribution represents an excellent fit for the fracture strength distribution at the peak load. The second significant result of the present study is that, in materials with broadly distributed microscopic heterogeneities, the mean fracturestrength of the lattice system behaves as

Safer Batteries through Coupled Multiscale Modeling

\mu _f = \tfrac{{\mu _{_f }^* }} {{(LogL)^\psi }} + \tfrac{c} {L}