Continuum Fluid Dynamics Research Articles

Proven Distributed Memory Parallelization of Particle Methods

We provide a mathematically proven parallelization scheme for particle methods on distributed-memory computer systems. Particle methods are a versatile and widely used class of algorithms for computer simulations and numerical predictions in various applications, ranging from continuum fluid dynamics to discrete granular flows and molecular dynamics simulations. Particle methods naturally lend themselves to implementation on parallel computing systems. So far, however, a mathematical proof of correctness and equivalence to sequential implementations was only available for shared-memory parallelism. Here, we leverage a formal definition of the algorithmic class of particle methods to provide a proven parallelization scheme for distributed-memory computers. We prove that thus parallelized particle methods on distributed-memory computers are formally equivalent to their sequential counterpart for a well-defined class of particle methods, and we provide analytical expressions for the speed-up and scalability bounds of this class of algorithms in function of their parameters. The parallelization scheme analyzed here is the basis of many real-world software designs for parallel particle methods. The present analysis is, therefore, of direct relevance to existing and new parallel implementations of particle methods and places them on solid theoretical grounds, rationalizing best practices and providing useful scalability and speedup bounds for benchmarking.

Exploration of Advanced Fabrication Techniques for Organic Shaped Energy Dissipators in Spillways

This paper focuses on the advanced design and production of concrete energy dissipators which are used for aeration of water on spillways. Traditionally, the concrete energy dissipators assumed simple block shapes which were dictated by limited production capabilities, mainly by the planar formwork and issues related to demolding. The advent of new concrete mix design and flexible construction technologies, such as 3D printing and CNC machines, allowed to consider more optimized organic shapes for increasing the energy dissipation efficiency and reducing the volume of material in our case by 38%. Since the physical laboratory modeling is an integral part of hydraulic research, a prototyping method using small-scale models was developed for design, production, quality control and experimental assessment of concrete energy dissipators of complex shapes. This method helps to expedite the research process when newly designed or modified shapes can be readily produced and tested in the hydraulic test channel for its energy dissipation efficiency and erosion resistance. The digital production, as all geometric information is perfectly digitized, at the same time helps to define the numerical models of the spillways for advanced continuum fluid dynamics analyses.

Lower-thermosphere–ionosphere (LTI) quantities: current status of measuring techniques and models

Abstract. The lower-thermosphere–ionosphere (LTI) system consists of the upper atmosphere and the lower part of the ionosphere and as such comprises a complex system coupled to both the atmosphere below and space above. The atmospheric part of the LTI is dominated by laws of continuum fluid dynamics and chemistry, while the ionosphere is a plasma system controlled by electromagnetic forces driven by the magnetosphere, the solar wind, as well as the wind dynamo. The LTI is hence a domain controlled by many different physical processes. However, systematic in situ measurements within this region are severely lacking, although the LTI is located only 80 to 200 km above the surface of our planet. This paper reviews the current state of the art in measuring the LTI, either in situ or by several different remote-sensing methods. We begin by outlining the open questions within the LTI requiring high-quality in situ measurements, before reviewing directly observable parameters and their most important derivatives. The motivation for this review has arisen from the recent retention of the Daedalus mission as one among three competing mission candidates within the European Space Agency (ESA) Earth Explorer 10 Programme. However, this paper intends to cover the LTI parameters such that it can be used as a background scientific reference for any mission targeting in situ observations of the LTI.

A mean free path approach to the micro/nanochannel gas flows

We investigate the gas flows near to solid surfaces in terms of the local spatial variation in the molecular mean free path (MFP). Molecular dynamics (MD) is the appropriate scientific tool for obtaining molecularly-accurate dynamic information in micro and nano-scale gas flows, and has been used to evaluate the molecular mean free path of gases. In the calibration procedure, the viscosity of a gas in the homogeneous case can be recovered in our MD simulations and reach good agreement with the theoretical prediction and data from NIST. In surface-bounded gas flows, if the collisions between gas molecules and walls are counted, a spatially-varying mean free path is presented, and for the first time we have observed that the distribution of the free paths deviates from the exponential one and spikes appear in their distributions at larger Kn, i.e. in the transition flow regime. Based on elementary kinetic theory, the effective viscosity of the gas derived from the mean free path has been incorporated into the framework of the continuum-fluid dynamics equations, and micro-Couette flows are performed to demonstrate this potential application.

Erratum: “Implementation of three-dimensional physical reflective boundary conditions in mesh-free particle methods for continuum fluid dynamics: Validation tests and case studies” [Phys. Fluids 31, 103606 (2019)

Erratum: “Implementation of three-dimensional physical reflective boundary conditions in mesh-free particle methods for continuum fluid dynamics: Validation tests and case studies” [Phys. Fluids 31, 103606 (2019)

Implementation of three-dimensional physical reflective boundary conditions in mesh-free particle methods for continuum fluid dynamics: Validation tests and case studies

Mesh-free particle methods applied to continuum fluid dynamics still use fictitious, ghost or virtual particles, and/or molecular dynamics concepts in the treatment of the boundaries. The aim of this paper is to present the implementation of the physical reflective boundary conditions (RBC), based on Newton’s restitution law and the foundations of analytical geometry, in the treatment of contours in a three-dimensional (3D) domain. In a previous paper [C. A. D. Fraga Filho, “An algorithmic implementation of physical reflective boundary conditions in particle methods: Collision detection and response,” Phys. Fluids 29, 113602 (2017)], RBC validation tests and simulation results were presented for a two-dimensional (2D) domain. The current work presents the validation of the collision detection and response algorithm employed for the RBC and its application in two cases (hydrostatics and hydrodynamics) in a 3D domain. Following an analysis of the simulation results, the applicability of the RBC to 3D continuum fluid dynamic problems is verified. In the hydrostatics case, a still liquid (Newtonian, incompressible, uniform, and isothermal) inside an immobile reservoir is studied. The fluid flow is modeled using an improved Smoothed Particle Hydrodynamics (SPH) formulation utilizing a modified concept of pressure. The simulation results are excellent, showing complete agreement with the analytical solution and the nonmotion of the particles throughout the simulation time. In the hydrodynamics case, 3D dam break flow modeling is carried out using the standard SPH formulation. Results provided by the RBC and standard SPH modeling are compared with the literature data demonstrating good agreement with the experimental findings.

Tensors.jl — Tensor Computations in Julia

Tensors.jl is a Julia package that provides efficient computations with symmetric and non-symmetric tensors. The focus is on the kind of tensors commonly used in e.g. continuum mechanics and fluid dynamics. Exploiting Julia’s ability to overload Unicode infix operators and using Unicode in identifiers, implemented tensor expressions commonly look very similar to their mathematical writing. This possibly reduces the number of bugs in implementations. Operations on tensors are often compiled into the minimum assembly instructions required, and, when beneficial, SIMD-instructions are used. Computations involving symmetric tensors take symmetry into account to reduce computational cost. Automatic differentiation is supported, which means that most functions written in pure Julia can be efficiently differentiated without having to implement the derivative by hand. The package is useful in applications where efficient tensor operations are required, e.g. in the Finite Element Method. Funding statement: Support for this research was provided by the Swedish Research Council (VR), grant no. 621-2013-3901 and grant no. 2015-05422.

Numerical investigation of the interaction between a shock wave and a particle cloud curtain using a CFD–DEM model

A two-dimensional numerical simulation of the interaction between a shock wave and a particle cloud curtain (PCC) in a shock tube was conducted to develop the numerical method and to understand how the particle layer mitigates the shock wave. In the present study, computational fluid dynamics/the discrete element method in conjunction with drag force and convective heat transfer models were used to separately solve the continuum fluid and particle dynamics. The applicability of the method to the gas flow and particles was validated through comparison with gas–particle shock-tube experiments, in which the PCC was generated by free fall, and particles initially had a gradient of its volume fraction and falling velocity in height. When the incident shock wave interacted with the PCC, it was reflected from and transmitted through the PCC. The transmitted shock wave had a curved front because the initial gradient in the volume fraction of particles locally changed the interaction between the shock wave and the particles. We calculated the effects of the drag force and heat transfer in mitigating the strength of the transmitted shock wave. The propagation of the transmitted and reflected shock waves and the motion of the PCC induced by the gas flow behind the shock wave agreed well with previous experimental data. After the interaction between the gas flow and the PCC, drag force and heat transfer were activated by the gradients in pressure, velocity, and temperature between them, and the gas flow lost momentum and energy, which weakened the transmitted shock wave. At the same time, the PCC gained momentum and energy and was dispersed. The contact forces between two particles affected the local dispersion of the PCC.

Cell Damage Index as Computational Indicator for Blood Cell Activation and Damage.

Shear‐induced hemolysis is a major concern in the design and optimization of blood‐contacting devices. Even with a small amount of mechanical stress, inflammatory reactions can be triggered in the cells. Blood damage is typically estimated using continuum fluid dynamics simulations. In this study, we report a novel cell damage index (CDI) obtained by simulations on the single‐cell level in a lattice Boltzmann fluid flow. The change of the cell surface area gives important information on mechanical stress of individual cells as well as for whole blood. We are using predefined basic channel designs to analyze and compare the newly developed CDI to the conventional blood damage calculations in very weak shear stress scenarios. The CDI can incorporate both volume fraction and channel geometry information into a single quantitative value for the characterization of flow in artificial chambers.

Modeling of heat and mass transfer for dropwise condensation of moist air and the experimental validation

A single droplet model is developed to describe the droplet growth during dropwise condensation of moist air on a cold substrate. The condensation process is divided by the droplet surface into two parts. The first step, i.e. the processes of mass transfer from the surroundings to the droplet surface, is modeled by the Kinetic theory and the laws of continuum fluid dynamics formulated using the two-region concept (Knudsen layer and continuum region) at any droplet size and at any concentration of non-condensable gas (NCG). The second step, i.e. the heat transfer across the droplet, is governed by Fourier’s law of heat conduction. These three regions (the continuum region, the Knudsen layer and the region inside the droplet) are incorporated by the matching both the mass flow rates and the energy flow rates. From these, the droplet growth rate, the nucleation size of droplet, the temperature at the droplet surface and Knudsen layer interface can be evaluated depending on different conditions. For this, a numerical algorithm is developed to reflect the droplet dynamics sufficiently detailed, including nucleation, growth/coalescence, slide-off/fall-off, re-nucleation. This is applied to the simulation of the entire condensation process by putting the growth rate and minimum radius from single droplet model into the growth algorithm. Additionally, dropwise condensation experiments of moist air in different relative humidity (RH) are carried out for validation of the simulation results. Good agreement is obtained which demonstrates that the present droplet growth model for dropwise condensation of moist air is credible. The current model and experiments also indicate that the diffusion resistance of water vapor in air from the free stream toward the droplet surface has a significant influence for the heat transfer performance of dropwise condensation of moist air.

Nonlinear mechanical response of supercooled melts under applied forces

We review recent progress on a microscopic theoretical approach to describe the nonlinear response of glass-forming colloidal dispersions under strong external forcing leading to homogeneous and inhomogeneous flow. Using mode-coupling theory (MCT), constitutive equations for the rheology of viscoelastic shear-thinning fluids are obtained. These are, in suitably simplified form, employed in continuum fluid dynamics, solved by a hybrid-Lattice Boltzmann (LB) algorithm that was developed to deal with long-lasting memory effects. The combined microscopic theoretical and mesoscopic numerical approach captures a number of phenomena far from equilibrium, including the yielding of metastable states, process-dependent mechanical properties, and inhomogeneous pressure-driven channel flow.

MaMiCo: Transient multi-instance molecular-continuum flow simulation on supercomputers

We present extensions of the macro–micro-coupling tool MaMiCo, which was designed to couple continuum fluid dynamics solvers with discrete particle dynamics. To enable local extraction of smooth flow field quantities especially on rather short time scales, sampling over an ensemble of molecular dynamics simulations is introduced. We provide details on these extensions including the transient coupling algorithm, open boundary forcing, and multi-instance sampling. Furthermore, we validate the coupling in Couette flow using different particle simulation software packages and particle models, i.e. molecular dynamics and dissipative particle dynamics. Finally, we demonstrate the parallel scalability of the molecular-continuum simulations by using up to 65 536 compute cores of the supercomputer Shaheen II located at KAUST. New version program summaryProgram Title: MaMiCoProgram Files doi:http://dx.doi.org/10.17632/w7rgdrhb85.1Licensing provisions: BSD 3-clauseProgramming language: C, C++External routines/libraries: For compiling: SCons, MPI (optional)Subprograms used: ESPResSo, LAMMPS, ls1 mardyn, waLBerlaFor installation procedures of the MaMiCo interfaces, see the README files in the respective code directories located in coupling/interface/impl.Journal reference of previous version: P. Neumann, H. Flohr, R. Arora, P. Jarmatz, N. Tchipev, H.-J. Bungartz. MaMiCo: Software design for parallel molecular-continuum flow simulations, Computer Physics Communications 200: 324–335, 2016Does the new version supersede the previous version?: Yes. The functionality of the previous version is completely retained in the new version.Nature of problem: Coupled molecular-continuum simulation for multi-resolution fluid dynamics: parts of the domain are resolved by molecular dynamics or another particle-based solver whereas large parts are covered by a mesh-based CFD solver, e.g. a lattice Boltzmann automaton.Solution method: We couple existing MD and CFD solvers via MaMiCo (macro–micro coupling tool). Data exchange and coupling algorithmics are abstracted and incorporated in MaMiCo. Once an algorithm is set up in MaMiCo, it can be used and extended, even if other solvers are used (as soon as the respective interfaces are implemented/available).Reasons for the new version: We have incorporated a new algorithm to simulate transient molecular-continuum systems and to automatically sample data over multiple MD runs that can be executed simultaneously (on, e.g., a compute cluster). MaMiCo has further been extended by an interface to incorporate boundary forcing to account for open molecular dynamics boundaries. Besides support for coupling with various MD and CFD frameworks, the new version contains a test case that allows to run molecular-continuum Couette flow simulations out-of-the-box. No external tools or simulation codes are required anymore. However, the user is free to switch from the included MD simulation package to LAMMPS.For details on how to run the transient Couette problem, see the file README in the folder coupling/tests, Remark on MaMiCo V1.1.Summary of revisions: Open boundary forcing; Multi-instance MD sampling; support for transient molecular-continuum systemsRestrictions: Currently, only single-centered systems are supported.For access to the LAMMPS-based implementation of DPD boundary forcing, please contact Xin Bian, xin.bian@tum.de.Additional comments: Please see file license_mamico.txt for further details regarding distribution and advertising of this software.

Many-body dissipative particle dynamics modeling of fluid flow in fine-grained nanoporous shales

A many-body dissipative particle dynamics model, namely, MDPD, is applied for simulation of pore-scale, multi-component, multi-phase fluid flows in fine-grained, nanoporous shales. Since this model is able to simultaneously capture the discrete features of fluid molecules in nanometer size pores and continuum fluid dynamics in larger pores, and is relatively easy to parameterize, it has been recognized as being particularly suitable for simulating complex fluid flow in multi-length-scale nanopore networks of shales. A remarkable feature of this work is the integration of a high-resolution FIB-SEM (focused ion beam scanning electron microscopy) digital imaging technique to the MDPD model for providing 3D voxel data that contain the invaluable geometrical and compositional information of shale samples. This is the first time that FIB-SEM is seamlessly linked to a Lagrangian model like MDPD for fluid flow simulation, which offers a robust approach to bridging gaps between the molecular- and continuum-scales, since the relevant spatial and temporal scales are too big for molecular dynamics, and too small for computational fluid dynamics with known constitutive models. Simulations ranging from a number of benchmark problems to a forced two-fluid flow in a Woodford shale sample are presented. Results indicate that this model can be used to deliver reasonable simulations for multi-component, multi-phase fluid flows in arbitrarily complex pore networks in shales.

The Effect of Hydrodynamic Slip on Membrane-Based Salinity-Gradient-Driven Energy Harvesting

The effect of hydrodynamic slip on salinity-gradient-driven power conversion by the process of reverse electrodialysis, in which the free energy of mixing of salt and fresh water across a nanoporous membrane is harnessed to drive an electric current in an external circuit, is investigated theoretically using a continuum fluid dynamics model. A general one-dimensional model is derived that decouples transport inside the membrane pores from the effects of electrical resistance at the pore ends, from which an analytical expression for the power conversion rate is obtained for a perfectly ion-selective membrane as a function of the slip length, surface charge density, membrane thickness, pore radius, and other membrane and electrolyte properties. The theoretical model agrees quantitatively with finite-element numerical calculations and predicts significant enhancements--up to several times--of salinity-gradient power conversion due to hydrodynamic slip for realistic systems.

Neglected transport equations: extended Rankine–Hugoniot conditions and J -integrals for fracture

Transport equations in integral form are well established for analysis in continuum fluid dynamics but less so for solid mechanics. Four classical continuum mechanics transport equations exist, which describe the transport of mass, momentum, energy and entropy and thus describe the behaviour of density, velocity, temperature and disorder, respectively. However, one transport equation absent from the list is particularly pertinent to solid mechanics and that is a transport equation for movement, from which displacement is described. This paper introduces the fifth transport equation along with a transport equation for mechanical energy and explores some of the corollaries resulting from the existence of these equations. The general applicability of transport equations to discontinuous physics is discussed with particular focus on fracture mechanics. It is well established that bulk properties can be determined from transport equations by application of a control volume methodology. A control volume can be selected to be moving, stationary, mass tracking, part of, or enclosing the whole system domain. The flexibility of transport equations arises from their ability to tolerate discontinuities. It is insightful thus to explore the benefits derived from the displacement and mechanical energy transport equations, which are shown to be beneficial for capturing the physics of fracture arising from a displacement discontinuity. Extended forms of the Rankine–Hugoniot conditions for fracture are established along with extended forms of J -integrals.

Sensing Platform for Computational and Experimental Analysis of Blood Cell Mechanical Stress and Activation in Microfluidics

Mechanical damage of blood cells and thus their activation are well known issues in extracorporeal and laboratory bio-fluidics applications. However, standard analysis methods, like hemolysis and inflammatory protein marker measurements, require high sample volumes and are not suitable for microfluidics. To monitor the cell response and quantify the mechanical stimulation during microfluidic perfusion we developed a platform including computational and experimental analysis of the microfluidic system. The theoretical approach includes continuum fluid dynamics of whole blood and simulations of single cells immersed in blood plasma; while the experimental part consists on the real time measurement of intracellular calcium concentration as early marker of cell activation. Our approach can be used to ensure that cell microfluidic applications do not cause non-physiological mechanical stress on blood cells.

Open boundary molecular dynamics

This contribution analyzes several strategies and combination of methodologies to perform molecular dynamic simulations in open systems. Here, the term open indicates that the total system has boundaries where transfer of mass, momentum and energy can take place. This formalism, which we call Open Boundary Molecular Dynamics (OBMD), can act as interface of different schemes, such as Adaptive Resolution Scheme (AdResS) and Hybrid continuum-particle dynamics to link atomistic, coarse-grained (CG) and continuum (Eulerian) fluid dynamics in the general framework of fluctuating Navier-Stokes equations. The core domain of the simulation box is solved using all-atom descriptions. The CG layer introduced using AdResS is located at the outer part of the open box to make feasible the insertion of large molecules into the system. Communications between the molecular system and the outer world are carried out in the outer layers, called buffers. These coupling preserve momentum and mass conservation laws and can thus be linked with Eulerian hydro- dynamic solvers. In its simpler form, OBMD allows, however, to impose a local pressure tensor and a heat flux across the system’s boundaries. For a one component molecular system, the external normal pressure and temperature determine the external chemical potential and thus the independent parameters of a grand-canonical ensemble simulation. Extended ensembles under non-equilibrium stationary states can also be simulated as well as time dependent forcings (e.g. oscillatory rheology). To illustrate the robustness of the combined OBMD-AdResS method, we present simulations of star-polymer melts at equilibrium and in sheared flow.

Improved size distribution control of silicon nanocrystals in a spatially confined remote plasma

This work demonstrates how to improve the size distribution of silicon nanocrystals (Si-NCs) synthesized in a remote plasma, in which the flow dynamics and the particular chemistry initially resulted in the formation of small (2–10 nm) and large (50–120 nm) Si-NCs. Plasma consists of two regions: an axially expanding central plasma beam and a background region around the expansion. Continuum fluid dynamics simulations demonstrate that a significant mass flow occurs from the central beam to the background region. This mass flow can be gradually reduced upon confinement of the central beam, preventing the mass transport to the background region. Transmission electron microscopy and Raman spectroscopy analyses demonstrate that the volume fraction of large Si-NCs decreases from ∼77% to below 45% in parallel with the decrease of mass flow to the background region upon confinement, which indicates that large Si-NCs are synthesized in the background and small Si-NCs are synthesized in the central beam. Spatially resolved ion flux analyses demonstrate that the ions are localized in the central beam despite the mass flow to the background, indicating that the formation of small Si-NCs is governed by ion-assisted growth while the formation of large Si-NCs is governed by radical-neutral-assisted growth in the absence of ions. According to these observations, a better uniformity in the size distribution of Si-NCs can be obtained by creating a more uniform plasma flow and controlling the density of plasma species in the plasma.

Effects of elasticity on the nonlinear collective dynamics of self-propelled particles

Some rodlike self-propelled particles form collective structures because of hydrodynamic interactions characterized by large-scale self-driven flows. Using a continuum fluid dynamics approach, the effects of elasticity on the pseudo-steady state dynamics of the collective patterns are studied. The Oldroyd-B and Jeffery constitutive models are used to represent the suspending fluid as examples of non shear-thinning viscoelastic fluids. A coupling between the fluid and particle dynamics leads to self-driven structures that are shorter and evolve irregularly in comparison with the long periodic correlated structures in Newtonian fluids. Inspired by turbulent drag reduction by polymers, a mechanism has been suggested for how elasticity restricts the formation of the self-driven collective structures. Viscoelasticity forces the system to transition from an “active” state to a “suppressed” state.

Infrasonic attenuation in the upper mesosphere-lower thermosphere: a comparison between Navier-Stokes and Burnett predictions.

This paper presents the results of a pilot study comparing the use of continuum and non-continuum fluid dynamics to predict infrasound attenuation in the rarefied lower thermosphere. The continuum approach is embodied by the Navier-Stokes equations, while the non-continuum method is implemented via the Burnett equations [Proc. London Math. Soc. 39, 385-430 (1935); 40, 382-435 (1936)]. In the Burnett framework, the coupling between stress tensor and heat flux affects the dispersion equation, leading to an attenuation coefficient smaller than its Navier-Stokes counterpart by amounts of order 0.1 dB/km at 0.1 Hz, 10 dB/km at 1 Hz, and 100 dB/km at 10 Hz. It has been observed that many measured thermospheric arrivals are stronger than current predictions based on continuum mechanics. In this context, the consistently smaller Burnett-based absorption is cautiously encouraging.