arXiv subjects

Nikolaus A. Adams

Publications and source records attributed to Nikolaus A. Adams.

50 records · Page 3Linked to original sources

arXiv2020

A low-dissipation shock-capturing framework with flexible nonlinear dissipation control

In this work, a framework to construct arbitrarily high-order low-dissipation shock-capturing schemes with flexible and controllable nonlinear dissipation for convection-dominated problems is proposed. While a set of candidate stencils of incremental width is constructed, each one is indicated as smooth or nonsmooth by the ENO-like stencil selection procedure proposed in the targeted essentially non-oscillatory (TENO) scheme [Fu et al., Journal of Computational Physics 305 (2016): 333-359]. Rather than being discarded directly as with TENO schemes, the nonsmooth candidates are filtered by an extra nonlinear limiter, such as a monotonicity-preserving (MP) limiter or a total variation diminishing (TVD) limiter. Consequently, high-order reconstruction is achieved by assembling candidate fluxes with optimal linear weights since they are either smooth reconstructions or filtered ones which feature good non-oscillation property. A weight renormalization procedure as with the standard TENO paradigm is not necessary. This new framework concatenates the concepts of TENO, WENO and other nonlinear limiters for shock-capturing, and provides a new insight to designing low-dissipation nonlinear schemes. Through the adaptation of nonlinear limiters, nonlinear dissipation in the newly proposed framework can be controlled separately without affecting the performance in smooth regions. Based on the proposed framework, a family of new six- and eight-point nonlinear schemes with controllable dissipation is proposed. A set of critical benchmark cases involving strong discontinuities and broadband fluctuations is simulated. Numerical results reveal that the proposed new schemes capture discontinuities sharply and resolve the high-wavenumber fluctuations with low dissipation, while maintaining the desired accuracy order in smooth regions.

math.NA↗

arXiv2020

Investigation of condensation shocks and re-entrant jet dynamics in a cavitating nozzle flow by Large-Eddy Simulation

Cloud cavitation is related to an intrinsic instability where clouds are shed periodically. The shedding process is initiated either by the motion of a liquid re-entrant jet or a condensation shock. Cloud cavitation in nozzles interacts with the flow field in the nozzle, the mass flow and the spray break-up, and causes erosion damage. For nozzle geometries cloud shedding and the associated processes have not yet been studied in detail. In this paper, we investigate the process of cloud cavitation shedding, the re-entrant jet and condensation shocks in a scaled-up generic step nozzle with injection into gas using implicit Large-Eddy Simulations (LES). For modeling of the cavitating liquid we employ a barotropic equilibrium cavitation model, embedded in a homogeneous multi-component mixture model. Full compressibility of all components is taken into account to resolve the effects of collapsing vapor structures. We carry out simulations of two operating points exhibiting different cavitation regimes. The time-resolved, three-dimensional simulation results cover several shedding cycles and provide deeper insight into the flow field. Our results show that at lower cavitation numbers, shedding is initiated by condensation shocks, which has not yet been reported for nozzle flows with a constant cross-section. We analyze the cavitation dynamics and the shedding cycles of both operating points. Based on our observations we propose modifications to established schematics of the cloud shedding process. Additionally, we analyze the near-wall upstream flow in and underneath the vapor sheet and possible driving mechanism behind the formation of the re-entrant jet.

physics.flu-dyn↗

arXiv2019

Near-surface dynamics of a gas bubble collapsing above a crevice

The impact of a collapsing gas bubble above rigid, notched walls is considered. Such surface crevices and imperfections often function as bubble nucleation sites, and thus have a direct relation to cavitation-induced erosion and damage structures. A generic configuration is investigated numerically using a second-order-accurate compressible multi-component flow solver in a two-dimensional axisymmetric coordinate system. Results show that the crevice geometry has a significant effect on the collapse dynamics, jet formation, subsequent wave dynamics, and interactions. The wall-pressure distribution associated with erosion potential is a direct consequence of development and intensity of these flow phenomena.

physics.flu-dyn↗

arXiv2019

Sparse Identification of Truncation Errors

This work presents a data-driven approach to the identification of spatial and temporal truncation errors for linear and nonlinear discretization schemes of Partial Differential Equations (PDEs). Motivated by the central role of truncation errors, for example in the creation of implicit Large Eddy schemes, we introduce the Sparse Identification of Truncation Errors (SITE) framework to automatically identify the terms of the modified differential equation from simulation data. We build on recent advances in the field of data-driven discovery and control of complex systems and combine it with classical work on modified differential equation analysis of Warming, Hyett, Lerat and Peyret. We augment a sparse regression-rooted approach with appropriate preconditioning routines to aid in the identification of the individual modified differential equation terms. The construction of such a custom algorithm pipeline allows attenuating of multicollinearity effects as well as automatic tuning of the sparse regression hyperparameters using the Bayesian information criterion (BIC). As proof of concept, we constrain the analysis to finite difference schemes and leave other numerical schemes open for future inquiry. Test cases include the linear advection equation with a forward-time, backward-space discretization, the Burgers' equation with a MacCormack predictor-corrector scheme and the Korteweg-de Vries equation with a Zabusky and Kruska discretization scheme. Based on variation studies, we derive guidelines for the selection of discretization parameters, preconditioning approaches and sparse regression algorithms. The results showcase highly accurate predictions underlining the promise of SITE for the analysis and optimization of discretization schemes, where analytic derivation of modified differential equations is infeasible.

math.NA↗

arXiv2019

Investigation of dissipative particle dynamics with colored noise

We investigate the behavior of dissipative particle dynamics (DPD) with time-correlated random noise. A new stochastic force for DPD is proposed which consists of a random force whose noise has an algebraic correlation proportional to 1/t and is generated by the so called Kangaroo process. We stress the benefits of a time correlated noise in stochastic systems. We show that the system exhibits significantly different properties from classical DPD, driven by Wiener noise. While the probability distribution function of the velocity is Gaussian, the acceleration develops a bi-modal character. Although the fluctuation dissipation theorem may not strictly hold, we demonstrate that the system reaches equilibrium states with fluctuation-dissipation balance. We believe that our explorative research on the DPD model may stimulate the application of modified DPD to unconventional problems beyond molecular modeling.

cond-mat.stat-mech↗

arXiv2018

Lattice Boltzmann model with self-tuning equation of state for coupled thermo-hydrodynamic flows

A novel lattice Boltzmann (LB) model with self-tuning equation of state (EOS) is developed in this work for simulating coupled thermo-hydrodynamic flows. The velocity field is solved by the recently developed multiple-relaxation-time (MRT) LB equation for density distribution function (DF), by which a self-tuning EOS can be recovered. As to the temperature field, a novel MRT LB equation for total energy DF is directly developed at the discrete level. By introducing a density-DF-related term into this LB equation and devising the equilibrium moment function for total energy DF, the viscous dissipation and compression work are consistently considered, and by modifying the collision matrix, the targeted energy conservation equation is recovered without deviation term. The full coupling of thermo-hydrodynamic effects is achieved via the self-tuning EOS and the viscous dissipation and compression work. The present LB model is developed on the basis of the standard lattice, and various EOSs can be adopted in real applications. Moreover, both the Prandtl number and specific heat ratio can be arbitrarily adjusted. Furthermore, boundary condition treatment is also proposed on the basis of the judicious decomposition of DF into its equilibrium, force (source), and nonequilibrium parts. The local conservation of mass, momentum, and energy can be strictly satisfied at the boundary node. Numerical simulations of thermal Poiseuille and Couette flows are carried out with three different EOSs, and the numerical results are in good agreement with the analytical solutions. Then, natural convection in a square cavity with a large temperature difference is simulated for the Rayleigh number from $10^3$ up to $10^8$. Good agreement between the present and previous numerical results is observed, which further validates the present LB model for coupled thermo-hydrodynamic flows.

physics.comp-ph↗

arXiv2018

Lattice Boltzmann model with self-tuning equation of state for multiphase flows

A novel lattice Boltzmann (LB) model for multiphase flows is developed that complies with the thermodynamic foundations of kinetic theory. By directly devising the collision term for LB equation at the discrete level, a self-tuning equation of state is achieved, which can be interpreted as the incorporation of short-range molecular interaction. A pairwise interaction force is introduced to mimic the long-range molecular interaction, which is responsible for interfacial dynamics. The derived pressure tensor is naturally consistent with thermodynamic theory, and surface tension and interface thickness can be independently prescribed.

physics.comp-ph↗

arXiv2018

A species-clustered ODE solver for large-scale chemical kinetics using detailed mechanisms

In this study, a species-clustered ordinary differential equations (ODE) solver for chemical kinetics with large detailed mechanisms based on operator-splitting is presented. The ODE system is split into clusters of species by using graph partition methods which has been intensively studied in areas of model reduction, parameterization and coarse-graining, etc. , such as diffusion maps based on the concept of Markov random walk. Definition of the weight (similarity) matrix is application-driven and according to chemical kinetics. Each cluster of species is then integrated by VODE, an implicit solver which is intractable and costly for large systems of many species and reactions. Expected speedup in computational efficiency is observed by numerical experiments on three zero-dimensional (0D) auto-ignition problems, considering the detailed hydrocarbon/air combustion mechanisms in varying scales, from 53 species with 325 reactions of methane to 2115 species with 8157 reactions of n-hexadecane.

physics.comp-ph↗

arXiv2018

A Lagrangian Inertial Centroidal Voronoi Particle method for dynamic load balancing in particle-based simulations

In this paper we develop a Lagrangian Inertial Centroidal Voronoi Particle (LICVP) method to extend the original CVP method \cite{fu2017physics} to dynamic load balancing in particle-based simulations. Two new concepts are proposed to address the additional problems encountered in repartitioning the system. First, a background velocity is introduced to transport Voronoi particle according to the local fluid field, which facilitates data reuse and lower data redistribution cost during rebalancing. Second, in order to handle problems with skew-aligned computational load and large void space, we develop an inertial-based partitioning strategy, where the inertial matrix is utilized to characterize the load distribution, and to confine the motion of Voronoi particles dynamically adapting to the physical simulation. Intensive numerical tests in fluid dynamics simulations reveal that the underlying LICVP method improves the incremental property remarkably without sacrifices on other objectives, i.e. the inter-processor communication is optimized simultaneously, and the repartitioning procedure is highly efficient.

physics.comp-ph↗

arXiv2018

A Split Random Time Stepping Method for Stiff and Non-stiff Chemically Reacting Flows

In this paper, a new fractional step method is proposed for simulating stiff and nonstiff chemically reacting flows. In stiff cases, a well-known spurious numerical phenomenon, i.e. the incorrect propagation speed of discontinuities, may be produced by general fractional step methods due to the under-resolved discretization in both space and time. The previous random projection method has been successfully applied for stiff detonation capturing in under-resolved conditions. Not to randomly project the intermediate state into two presumed equilibrium states (completely burnt or unburnt) as in the random projection method, the present study is to randomly choose the time-dependent advance or stop of a reaction process. Each one-way reaction has been decoupled from the multi-reaction kinetics using operator splitting and the local smeared temperature due to numerical dissipation of shock-capturing schemes is compared with a random one within two limited temperatures corresponding to the advance and its inverse states, respectively, to control the random reaction. The random activation or deactivation in the reaction step is thus promising to correct the deterministic accumulative error of the propagation of discontinuities. Extensive numerical experiments, including model problems and realistic reacting flows in one and two dimensions, demonstrate this expectation as well as the effectiveness and robustness of the method. Meanwhile, for nonstiff problems when spatial and temporal resolutions are fine, the proposed random method recovers the results as general fractional step methods, owing to the increasing possibility of activation with diminishing randomness by adding a shift term.

physics.comp-ph↗

arXiv2018

A network partition method for solving large-scale complex nonlinear processes

A numerical framework based on network partition and operator splitting is developed to solve nonlinear differential equations of large-scale dynamic processes encountered in physics, chemistry and biology. Under the assumption that those dynamic processes can be characterized by sparse networks, we minimize the number of splitting for constructing subproblems by network partition. Then the numerical simulation of the original system is simplified by solving a small number of subproblems, with each containing uncorrelated elementary processes. In this way, numerical difficulties of conventional methods encountered in large-scale systems such as numerical instability, negative solutions, and convergence issue are avoided. In addition, parallel simulations for each subproblem can be achieved, which is beneficial for large-scale systems. Examples with complex underlying nonlinear processes, including chemical reactions and reaction-diffusion on networks, demonstrate that this method generates convergent solution in a efficient and robust way.

physics.comp-ph↗

arXiv2017

Experimental and Numerical Investigation of Phase Separation due to Multi-Component Mixing at High-Pressure Conditions

Experiments and numerical simulations were carried out in order to contribute to a better understanding and prediction of high-pressure injection into a gaseous environment. Specifically, the focus was put on the phase separation processes of an initially supercritical fluid due to the interaction with its surrounding. N-hexane was injected into a chamber filled with pure nitrogen at 5 MPa and 293 K and three different test cases were selected such that they cover regimes in which the thermodynamic non-idealities, in particular the effects that stem from the potential phase separation, are significant. Simultaneous shadowgraphy and elastic light scattering experiments were conducted to capture both the flow structure as well as the phase separation. In addition, large-eddy simulations with a vapor-liquid equilibrium model were performed. Both experimental and numerical results show phase formation for the cases, where the a-priori calculation predicts two-phase flow. Moreover, qualitative characteristics of the formation process agree well between experiments and numerical simulations and the transition behaviour from a dense-gas to a spray-like jet was captured by both.

physics.flu-dyn↗

arXiv2017

High-resolution transport of regional level sets for evolving complex interface networks

In this paper we describe a high-resolution transport formulation of the regional level-set approach for an improved prediction of the evolution of complex interface networks. The novelty of this method is twofold: (i) construction of local level sets and reconstruction of a global regional level sets, (ii) locally transporting the interface network by employing high-order spatial discretization schemes for improved representation of complex topologies. Various numerical test cases of multi-region flow problems, including triple-point advection, single vortex flow, mean curvature flow, normal driven flow and dry foam dynamics, show that the method is accurate and suitable for a wide range of complex interface-network evolutions. Its overall computational cost is comparable to the Semi-Lagrangian regional level-set method while the prediction accuracy is significantly improved. The approach thus offers a \textbf{viable} alternative to previous interface-network level-set method.

math.NA↗

arXiv2015

A cut-cell finite volume - finite element coupling approach for fluid-structure interaction in compressible flow

We present a loosely coupled approach for the solution of fluid-structure interaction problems between a compressible flow and a deformable structure. The method is based on staggered Dirichlet-Neumann partitioning. The interface motion in the Eulerian frame is accounted for by a conservative cut-cell Immersed Boundary method. The present approach enables sub-cell resolution by considering individual cut-elements within a single fluid cell, which guarantees an accurate representation of the time-varying solid interface. The cut-cell procedure inevitably leads to non-matching interfaces, demanding for a special treatment. A Mortar method is chosen in order to obtain a conservative and consistent load transfer. We validate our method by investigating two-dimensional test cases comprising a shock-loaded rigid cylinder and a deformable panel. Moreover, the aeroelastic instability of a thin plate structure is studied with a focus on the prediction of flutter onset. Finally, we propose a three-dimensional fluid-structure interaction test case of a flexible inflated thin shell interacting with a shock wave involving large and complex structural deformations.

math.NA↗