Spurious Flow Research Articles

Application of Large Time Step TVD High Order Scheme to Shallow Water Equations

The numerical modeling of actual river floods faces three challenges related to computational efficiency, accuracy, and proper balancing of terms in the governing equations, all of which are discussed in this paper. Herein, a large time step (LTS) scheme is used to improve efficiency, a high order scheme is used to enhance accuracy, and specific treatment of the bed slope term achieves a well-balanced form of shallow water equations. The LTS scheme, originally proposed by LeVeque in 1998, has led to the development of highly efficient computational solvers of the shallow water equations (SWEs). This paper examines use of a total variation diminishing (TVD) high order scheme in conjunction with LTS. We first applied the scheme to the solution of the homogeneous 1D SWEs and obtained satisfactory results for three cases, even though small oscillations nevertheless occur when the CFL number is very large. The additional source term makes the issue more complicated and can introduce a spurious flow when the term is not correctly handled. Many methods have been developed in traditional differential schemes, but not all are fit for the TVD-LTS scheme; for example, the method of decomposing the source term into simple characteristic waves has proved infeasible. In this paper the TVD-LTS scheme was implemented for the first time for well-balanced SWEs containing bed slope source terms. We found that oscillations were not as suppressed as for the homogeneous SWEs when the TVD-LTS scheme was applied to the three cases of step Riemann problems (SRP) tested for CFL numbers 1 to 10. For free surface flow over a bed hump, the TVD-LTS scheme can only reach CFL number 4 before the solution breaks down.

Incorporating Network Scale River Bathymetry to Improve Characterization of Fluvial Processes in Flood Modeling

AbstractSeveral studies have focused on the importance of river bathymetry (channel geometry) in hydrodynamic routing along individual reaches. However, its effect on other watershed processes such as infiltration and surface water (SW)‐groundwater (GW) interactions has not been explored across large river networks. Surface and sbsurface processes are interdependent, therefore, errors due to inaccurate representation of one watershed process can cascade across other hydraulic or hydrologic processes. This study hypothesizes that accurate bathymetric representation is not only essential for simulating channel hydrodynamics but also affects subsurface processes by impacting SW‐GW interactions. Moreover, quantifying the effect of bathymetry on surface and subsurface hydrological processes across a river network can facilitate an improved understanding of how bathymetric characteristics affect these processes across large spatial domains. The study tests this hypothesis by developing physically based distributed models capable of bidirectional coupling (SW‐GW) with four configurations with progressively reduced levels of bathymetric representation. A comparison of hydrologic and hydrodynamic outputs shows that changes in channel geometry across the four configurations has a considerable effect on infiltration, lateral seepage, and location of water table across the entire river network. For example, when using bathymetry with inaccurate channel conveyance capacity but accurate channel depth, peak lateral seepage rate exhibited 58% error. The results from this study provide insights into the level of bathymetric detail required for accurately simulating flooding‐related physical processes while also highlighting potential issues with ignoring bathymetry across lower order streams such as spurious backwater flow, inaccurate water table elevations, and incorrect inundation extents.

Streamline penetration, velocity error, and consequences of the feedback immersed boundary method

This paper presents a study on streamline penetration, velocity error, and consequences of a fluid–structure interaction (FSI) solver based on the feedback immersed boundary method (IBM). In the FSI solver, the fluid dynamics is solved by the lattice Boltzmann method; the solid structure deformation is solved by the finite difference method and the finite element method for two- and three-dimensional cases, respectively; and the feedback IBM is used to realize the interaction between the fluid and the structure. The IBM is implemented in non-iterative and iterative ways. For the non-iterative version, two types of integration are discussed: without and with velocity prediction step. Five benchmark cases are simulated to study the performance of the three implementations: a uniform flow over a cylinder, flow-induced vibration of a flexible plate attached behind a stationary cylinder in a channel, flow through a two-dimensional asymmetric stenosis, a one-sided collapsible channel, and a three-dimensional collapsible tube. Results show that both the IBM with prediction step, the iterative IBM, and one iteration IBM with proper feedback coefficients can suppress the spurious flow penetration on the solid wall. While the velocity error does not significantly affect the force production and structure deformation for external flows, reducing it significantly improves the prediction of the force distribution and structure deformation for internal flows. In addition, the iterative IBM with smaller feedback coefficient has better numerical stability. This work will provide an important guideline for the correct use of the feedback IBMs.

Godunov-type large time step scheme for shallow water equations with bed-slope source term

This paper presents a Godunov-type large time step (LTS) solver of the non-homogeneous shallow water equations (SWEs). Source terms are decomposed into simple characteristic waves in approximate Riemann solvers (ARS) and exact Riemann solvers (ERS), and information is transferred over multiple cells per time step using the LTS method. Benchmark simulations are presented using different solution algorithms (ARS and ERS with and without entropy fixes) for two rarefactions driven by divergent flow, a pair of bores driven by opposing flows, and a dam break over a shelf-like step. In these cases, spurious flow discontinuities and oscillations can occur for Courant–Friedrichs–Lewy number (CFL) > 1 in the absence of an entropy fix. Implementation of a weak-solution LTS entropy fix improves the results, but shock shifting nevertheless occurs in certain cases. The paper also considers steady, frictionless, transcritical flow over a bed hump. In this final case, the model is run for integer CFL ranging from 1 to 10. For CFL ≤ 3, satisfactory results are obtained (without divergence and oscillation) using ARS without an entropy fix. For larger CFL, the results either diverge or exhibit convergent oscillations downstream of the hydraulic jump. Use of an entropy fix designed for implementation in an LTS scheme improves the results for CFL ≤ 5.

Prediction of gradient‐based similarity functions from the Mellor–Yamada model

AbstractGradient‐based implicit similarity functions are derived theoretically from a few variants of the Mellor–Yamada algebraic turbulence‐closure model under assumptions of local equilibrium conditions in a stably stratified shear flow. The solutions are compared with empirical functions presented by Sorbjan. Good agreement is found in the range of gradient Richardson number extending up to around 0.2. The gradient‐based scaling framework offers better accuracy and reliability than the traditional Monin–Obukhov framework, as it circumvents the problems of small values of fluxes and cross‐correlations. It is also possible to separate the specification of the master length‐scale from the calculation of similarity functions describing second moments and dissipation rate. The related discussion of model performance at higher is included. It is unclear whether the current countermeasures against spurious flow decoupling reflect the observed features of turbulence in the very stable regime, due to the apparent breakdown of the Richardson–Kolmogorov energy cascade, as found by Grachev et al.

An approach for permeable boundary conditions in SPH

Smoothed Particle Hydrodynamics (SPH) has intrinsic advantages over the Finite Volume (FV) method for predicting multiphase flows, since the need for fluid phase interface reconstructions is avoided due to the natural advection of those interfaces based on the Lagrangian description of the control volumes. However, permeable boundary conditions are less straightforward to handle with SPH, even though domain inlets and outlets are needed in most engineering problems. In this work we propose a new framework for permeable boundary conditions for the Weakly Compressible SPH based on ghost particles. The major characteristics of our approach are the application of Navier Stokes Characteristic Boundary Conditions (NSCBC) and a particle mass generation and removal procedure at the boundary. This approach enables the application of non-reflective boundary conditions and redundantizes the need for advecting ghost particles from an external buffer zone to the internal domain. Additionally, the particle mass variation can exactly be balanced with the mass flux defined at the boundary. Furthermore, we are proposing a novel approach to set the ghost particle state based on an extrapolation of the state of particles located in the internal domain and on the domain boundary. We validate the proposed framework for permeable boundaries with one- and two-dimensional test cases. The major findings are as follows. Due to the particle mass generation and removal at the domain boundary, spurious oscillations are introduced due to a non-optimal particle distribution. Those oscillations are reduced in our work to an acceptable level (1×10−5 to 1×10−4 relative to the values of the fluid dynamics variables) using existing stabilization schemes as well as the aforementioned novel methods for setting ghost particle states and particle masses at the permeable boundaries. We observe a very good agreement between the solutions obtained with the presented approach and analytical as well as numerical solutions obtained with the FV method. The proposed approach for setting the ghost particle states is indispensable for achieving a perfect balance between particle mass variation and mass flux across the permeable interface as well as the steady state and the temporal accuracy of the solution. Additionally, the pressure reflectivity at the permeable boundary is found to be in a very good agreement with the theory of the NSCBC method. Furthermore, for a SPH-FV coupled simulation we could demonstrate an excellent agreement compared to the FV method as well as the capability of our approach to handle significant flow unsteadiness and gradients at the permeable coupling interfaces without the introduction of spurious flow behavior.

Achieving high-quality probabilistic predictions from hydrological models calibrated with a wide range of objective functions

Probabilistic predictions of streamflow are important in many environmental modelling applications. These predictions are often constructed using hydrological models combined with residual error models to describe predictive uncertainty. However, many objective functions commonly used to calibrate hydrological models make (implicit) assumptions that do not match the well-known heteroscedasticity and skewness of residual errors. Using a daily-scale hydrological model, we demonstrate that the use of such ‘inconsistent’ objective functions in combination with a commonly used residual error model introduces spurious flow dependencies in the mean of residual errors, which in turn leads to poor-quality probabilistic predictions. We then use residual error diagnostics to develop a simple enhanced error model, where the error mean depends linearly on the (transformed) simulated streamflow. The enhanced error model is compared with a commonly used reference error model that assumes a zero error mean. The empirical case study employs 54 perennial Australian catchments, the hydrological model GR4J, 9 common objective functions and 4 performance metrics (reliability, precision, volumetric bias and errors in the flow duration curve). The enhanced error model overcomes the loss of performance caused by inconsistent objective functions and achieves probabilistic predictions comparable to those obtained using consistent objective functions. These findings hold for all objective functions used in the case study. The enhanced residual error model is expected to facilitate the adoption of probabilistic predictions in the hydrological modelling community. In particular, it can be used to achieve high-quality probabilistic predictions from hydrological models calibrated with a wide range of common objective functions.

Stencil Penalty approach based constraint immersed boundary method

The constraint-based immersed boundary (cIB) method has been shown to be accurate between low and moderate Reynolds number (Re) flows when the immersed body constraint is imposed as a volumetric constraint force. When the IB is modelled as a zero-thickness interface, where it is no longer possible to model a volumetric constraint force, we found that cIB is not able to produce accurate results. The main source of inaccuracies in the cIB method is the distribution of the pressure field around the IB surface. An IB surface results in a jump in the pressure field across the IB. Evaluation of the discrete gradient of pressure close to the IB leads to a pressure gradient that does not satisfy the Neumann boundary condition for pressure at the IB. Furthermore, a non-zero discrete pressure gradient on the IB results in spurious flow at grid points close to the IB. We present a novel numerical formulation which adapts the cIB formulation for ‘zero-thickness’ immersed bodies. To impose the Neumann boundary condition on pressure on the IB more accurately, we introduce an additional body force to the momentum equation. A WENO based stencil penalization technique is used to define the new force term. Due to the more accurate imposition on the Neumann pressure boundary condition on the IB, spurious flow is reduced and the accuracy of no penetration velocity boundary condition on the IB is improved.

Brinkman volume penalization for bathymetry in three-dimensional ocean models

Accurate and stable implementation of bathymetry boundary conditions remains a challenging problem. The dynamics of ocean flow often depend sensitively on satisfying bathymetry boundary conditions and correctly representing their complex geometry. Generalized (e.g. σ) terrain-following coordinates are often used in ocean models, but they require smoothing the bathymetry to reduce pressure gradient errors (Mellor et al., 1994). Geopotential z-coordinates are a common alternative that avoid pressure gradient and numerical diapycnal diffusion errors, but they generate spurious flow due to their “staircase” geometry. We introduce a new Brinkman volume penalization to approximate the no-slip boundary condition and complex geometry of bathymetry in ocean models. This approach corrects the staircase effect of z-coordinates, does not introduce any new stability constraints on the geometry of the bathymetry and is easy to implement in an existing ocean model. The porosity parameter allows modelling subgrid scale details of the geometry. We illustrate the penalization and confirm its accuracy by applying it to three standard test flows: upwelling over a sloping bottom, resting state over a seamount and internal tides over highly peaked bathymetry features. In future work we will explore applying the penalization to more realistic bathymetry configurations, and moving boundaries such as melting/freezing ice shelves.

A robust incompressible Navier-Stokes solver for high density ratio multiphase flows

This paper presents a robust, adaptive numerical scheme for simulating high density ratio and high shear multiphase flows on locally refined staggered Cartesian grids that adapt to the evolving interfaces and track regions of high vorticity. The algorithm combines the interface capturing level set method with a variable-coefficient incompressible Navier-Stokes solver that is demonstrated to stably resolve material contrast ratios of up to six orders of magnitude. The discretization approach ensures second-order pointwise accuracy for both velocity and pressure with several physical boundary treatments, including velocity and traction boundary conditions. The paper includes several test cases that demonstrate the order of accuracy and algorithmic scalability of the flow solver. To ensure the stability of the numerical scheme in the presence of high density and viscosity ratios, we employ a consistent treatment of mass and momentum transport in the conservative form of discrete equations. This consistency is achieved by solving an additional mass balance equation, which we approximate via a strong stability preserving Runga-Kutta time integrator and by employing the same mass flux (obtained from the mass equation) in the discrete momentum equation. The scheme uses higher-order total variation diminishing (TVD) and convection-boundedness criterion (CBC) satisfying limiter to avoid numerical fluctuations in the transported density field. The high-order bounded convective transport is done on a dimension-by-dimension basis, which makes the scheme simple to implement. We also demonstrate through several test cases that the lack of consistent mass and momentum transport in non-conservative formulations, which are commonly used in practice, or the use of non-CBC satisfying limiters can yield very large numerical error and very poor accuracy for convection-dominant high density ratio flows. Our numerical scheme also uses well-balanced surface tension and gravity force discretizations. In the hydrostatic limit, we show that the well-balanced formulation mitigates spurious flow currents and achieves discrete force-balance between the pressure gradient and surface tension or gravity.

Systematic evaluation of the interface description for fluid–structure interaction simulations using the isogeometric mortar-based mapping

Within this study the influence of the interface description for partitioned Fluid–Structure Interaction (FSI) simulations is systematically evaluated. In particular, a Non-Uniform Rational B-Spline (NURBS)-based isogeometric mortar method is elaborated which enables the transfer of fields defined on low-order and isogeometric representations of the interface along which the FSI constraints are defined. Moreover, the concept of the Exact Coupling Layer (ECL) using the proposed isogeometric mortar-based mapping method is presented. It allows for smoothing fields that are transferred between two standard low-order surface discretizations applying the exact interface description in terms of NURBS. This is especially important for highly turbulent flows, where the artificial roughness of the low-order faceted FSI interfaces results in spurious flow fields leading to inaccurate FSI solutions. The approach proposed is subsequently compared to the standard mortar-based mapping method for transferring fields between two low-order surface representations (finite volume method for the fluid and finite element method for the structure) and validated on a simple lid-driven cavity FSI benchmark. Then, the physically motivated 3D example of the turbulent flow around a membranous hemisphere (Wood et al., 2016) is considered. Its behavior is predicted by combining the large-eddy simulation technique with the isogeometric analysis to demonstrate the usefulness of the isogeometric mortar-based mapping method for real-world FSI applications. Additionally, the test case of a bluff body significantly deformed in an eigenmode shape of the aforementioned hemisphere is used. For this purpose, both “standard” low-order finite element discretizations and a smooth IGA-based description of the structural surface are considered. This deformation is transferred to the fluid FSI interface and the influence of the interface description on the fluid flow is analyzed. Finally, the computational costs related to the presented methodology are evaluated. The results suggest that the proposed methodology can effectively improve the overall FSI behavior with minimal effort by considering the exact geometry description based on the Computer-Aided Design (CAD) model of the FSI interface.

Combining multi-scale composite windows with hierarchical smoothing strategy for fingerprint orientation field computation

BackgroundOrientation field (OF) plays a very significant role in automatic fingerprint recognition systems. Many algorithms have been proposed for the estimation of fingerprints’ OF but it is hard to solve the dilemma of correcting spurious ridge structure and avoiding singularity location deviation, especially for poor images. So far, the following drawbacks still need to be solved for OF construction methods for practical application: (1) How to adaptively choose block scales to resolve the contradiction between accuracy and anti-noise, since small scale is beneficial to accuracy but is sensitive to noise, while large scale is more resistant to noise, but the accuracy is deteriorated. (2) How to construct the genuine OF in the areas close-by singular points and to evade singularity location deviation? Current block based methods give spurious OF estimates in the area near singular points because these areas have large curvature thus the detected singular points deviate from the genuine localizations. When these singular points are used as the anchor for referencing minutiae, it makes the average error of matching or recognition even larger. Therefore, it is essentials to construct the genuine OF in the areas close-by singular points and to evade singularity deviation.MethodsTo overcome the above-mentioned limitations, a novel method, combining a weighted multi-scale composite window (WMCM) with a hierarchical smoothing strategy has been proposed for the computation of fingerprint OF. This method mainly contains two procedures: the approximate OF estimation and the hierarchical OF smoothing. In the first procedure, a series of OFs are established under multiple scales of composite windows by using a gradient based method then a coarse OF is estimated using the weight of each scale determined by a squared gradient consistency. In the second procedure, the OF is first quantized into a two-digitized orientation zone and a two-orientation-zone filtering strategy is adapted to the OF blocks based on a filtering mask obtained after eliminating the isolated blocks. In the end a similar three-digitized orientation zone is performed to obtain an accurate and smooth OF. To validate the performance, the proposed method has been applied to OF computation using the FVC2004 databases and three experiments are designed. Experiment 1 aims to validate whether the weighted multi-scale composite window can balance the dilemma of accuracy and robustness more effectively than the previous works do. Experiment 2 is designed to examine whether the hierarchical smoothing method can correct the spurious ridge flow and preserve the genuine localization of singular points. The purpose of experiment 3 is to test the performance of the proposed method on OF reconstruction in low quality fingerprint images. The fingerprint databases FVC 2004 DB1–DB4 are employed in this study.ResultsThe results of experiment I shows that the proposed method is capable to extract the information of OF reliably and it is more robust against singularity localization deviation in comparison with the other three gradient based methods. The results of experiment II indicates that the proposed smoothing method can balance the contradiction in correcting spurious ridge structures and preserving genuine singularity localization. The results of experiment III illustrates that our approach combing WMCW with the hierarchical smoothing method is capable to extract the information of OF ridge reliably and it is more robust against singularity deviation in comparison with the other three gradient based methods. In a word, the experiment results demonstrate that the proposed method can correct spurious ridge structure and meanwhile avoid singularity deviation compared with the previous works.ConclusionsA novel gradient based algorithm has been proposed which is more reliable for the estimation of the ridge information for fingerprint OF and is more accurate in preserving the singularity localization. Compared with the previously proposed gradient based methods, the advantages of the proposed RBSF lie in three aspects. Firstly a weighted multi-scale composite window is put forward to replace the single window used by conventional gradient based methods and to adaptively choose the scales of the blocks. Secondly, a hierarchical smoothing strategy is proposed to enhance the OF by using the two-orientation-zone filtering and the three-orientation-zone filtering, aiming to correct the spurious ridges and preserving the genuine location of singular points. Finally, three experiments are designed to test the proposed algorithm together with other popular gradient based methods on real fingerprint images, which are selected from different categories and all are suffering from obvious noise effects. All the experiment results show that the proposed method is superior with respect to reliable OF construction and avoiding singularity localization deviation.

A study on the unphysical mass transfer of SCMP pseudopotential LBM

In general, a multi-bubble/droplet configuration cannot sustain a steady state using single-component multiphase (SCMP) pseudopotential lattice Boltzmann method (LBM). Our study shows that the unachievable multi-bubble/droplet system is for an unphysical mass transfer, which we call “the big eat the small” – the smaller bubbles/droplets shrink, and eventually disappear while the bigger ones get bigger without a physical coalescence. In our present study, the unphysical mass transfer phenomenon is investigated, and the possible reason is explored. It is found that there is a spurious flow field formed between two bubbles or droplets with different shapes, and such flow field is exactly the transfer of high-density mass. In addition, it is found that the curvatures of the interfaces determine the direction of the spurious flow field, and for the definition of “the big eat the small”, “the big” refers to the interfaces that have larger radii of curvature while “the small” represents the interfaces with smaller radii of curvature. Multi-component multiphase (MCMP) LBM is also tested in this work and it is found to be free of the unphysical mass transfer. Moreover, all the cases show that the most likely reason for the unphysical mass transfer might be the essential attractive interaction forces of the pseudopotential LBM.

On the volume conservation of emulsion drops in boundary integral simulations

Boundary Integral simulations are very common to study the microhydrodynamics of viscous drops and predict the rheology of emulsions. The standard boundary integral formulation for the velocity field at the drop surface is given by surface integrals of singular Green’s functions in space and depends on geometric quantities of the mesh, as the local mean curvature and the unitary exterior normal vector. Typically, the drops deform and rotate under the flow action, which leads to a great distortion of the computational mesh and, therefore, might produce several numerical errors in the surface velocity calculation. In this work, we investigate the numerical errors in the calculation of the surface velocity in boundary integral simulations of a viscous drop in simple shear flows. Assuming that the flow is incompressible, such that the total volume of the drops must remain constant, we use the net flow rate across the drop surface as a measure of the numerical errors in the simulations. For both small and moderate regimes of drop surface deformation, we show that the net mass flow rate across the drop surface is positive, and strongly depends on the drop-to-basis fluid viscosity ratio, capillary number of the flow, and mesh refinement. These results indicate that the volume of the drops increases continuously during the simulations. To remove the spurious mass flow rate from the simulations, we present a mesh convergence study based on an extrapolation procedure to an almost continuous mesh, so that the results become independent of mesh refinement and recover the theoretical prediction of a null net flow rate and constant drop volume in incompressible flows. The extrapolation method proposed here can be straightforwardly implemented to improve the accuracy of BI simulations used to study drop microhydrodynamics and emulsion rheology. As a matter of example, we applied the method to predict the surface deformation of a high-viscosity emulsion drop, and the result is compared in very good agreement with asymptotic theories available in the related literature.

A low-dissipation convection scheme for the stable discretization of turbulent interfacial flow

This paper analyzes a low-dissipation discretization for the resolution of immiscible, incompressible multiphase flow by means of interface-capturing schemes. The discretization is built on a three-dimensional, unstructured finite-volume framework and aims at minimizing the differences in kinetic energy preservation with respect to the continuous governing equations. This property plays a fundamental role in the case of flows presenting significant levels of turbulence. At the same time, the hybrid form of the convective operator proposed in this work incorporates localized low-dispersion characteristics to limit the growth of spurious flow solutions. The low-dissipation discrete framework is presented in detail and, in order to expose the advantages with respect to commonly used methodologies, its conservation properties and accuracy are extensively studied, both theoretically and numerically. Numerical tests are performed by considering a three-dimensional vortex, an exact sinusoidal function, and a spherical drop subjected to surface tension forces in equilibrium and immersed in a swirling velocity field. Finally, the turbulent atomization of a liquid-gas jet is numerically analyzed to further assess the capabilities of the method.

Reducing spurious flow in simulations of electrokinetic phenomena.

Electrokinetic transport phenomena can strongly influence the behaviour of macromolecules and colloidal particles in solution, with applications in, e.g., DNA translocation through nanopores, electro-osmotic flow in nanocapillaries, and electrophoresis of charged macromolecules. Numerical simulations are an important tool to investigate these electrokinetic phenomena, but are often plagued by spurious fluxes and spurious flows that can easily exceed physical fluxes and flows. Here, we present a method that reduces one of these spurious currents, spurious flow, by several orders of magnitude. We demonstrate the effectiveness and generality of our method for both the electrokinetic lattice-Boltzmann and finite-element-method based algorithms by simulating a charged sphere in an electrolyte solution and flow through a nanopore. We also show that previous attempts to suppress these spurious currents introduce other sources of error.

Theory and simulations of water flow through carbon nanotubes: prospects andpitfalls

We study water flow through carbon nanotubes using continuum theory and moleculardynamics simulations. The large slip length in carbon nanotubes greatly enhances thepumping and electrokinetic energy conversion efficiency. In the absence of mobile charges,however, the electro-osmotic flow vanishes. Uncharged nanotubes filled with pure water cantherefore not be used as electric field-driven pumps, contrary to some recentlyventured ideas. This is in agreement with results from a generalized hydrodynamictheory that includes the angular momentum of rotating dipolar molecules. Theelectro-osmotic flow observed in simulations of such carbon nanotubes is caused byan imprudent implementation of the Lennard-Jones cutoff. We also discuss theinfluence of other simulation parameters on the spurious electro-osmotic flow.

On the coupling of wave and three-dimensional circulation models: Choice of theoretical framework, practical implementation and adiabatic tests

Many theoretical approaches and implementations have been proposed for the coupling of the three-dimensional ocean circulation with waves. The theoretical models are reviewed and it is shown that the formulation in terms of the quasi-Eulerian velocity circumvents the essential difficulty of alternative formulations for the Lagrangian mean velocity. Namely, models based on this Lagrangian velocity require an estimation of wave-induced motions to first order in the horizontal gradients of the wave field in order to estimate the vertical flux of wave pseudo-momentum. So far, only three-dimensional wave models have been able to provide these estimates, and all published theories based on the simpler Airy theory are not consistent at the leading order, because they ignore or incorrectly estimate the vertical momentum flux. With an adiabatic example on a sloping bottom it is shown that this inconsistency produces very large spurious velocities. These errors are independent of the slope for the inviscid case, and are still significant when a realistic vertical mixing is applied. A quick diagnostic of the potential accuracy of a theoretical model is the vertical profile of the wave-induced forcing terms: if it is not uniform over depth in adiabatic conditions then it will produce spurious artificial flow patterns in conditions with shoaling waves. Although conceptually more challenging, the quasi-Eulerian velocity theories only introduce minor modifications of the solution procedure for the standard primitive equations: a modification of the surface boundary condition for the mass conservation, the addition of the Stokes drift in the tracer advection equations, and sources of momentum and turbulent kinetic energy with associated surface and bottom fluxes. All the necessary modifications of primitive equation models are given in detail. This implementation is illustrated with the MARS3D model, which passes the test of the adiabatic shoaling waves.

Electrohydraulic Power Conversion in Planar Nanochannels

We explore mechanisms for flow generation in water-filled nanochannels, employing the coupling between translational and rotational momentum. Using a generalized Navier-Stokes equation that includes dipolar polarization and relaxation, we show that static electric fields do not induce fluid flow in the planar geometry, while rotating electric fields efficiently convert electric into hydraulic power on the nanoscale. We also perform extensive molecular dynamics simulations of water in nanochannels and find that erroneous force truncation can give rise to spurious flow effects for static electric fields.

A Quadratic Spline based Interface (QUASI) reconstruction algorithm for accurate tracking of two-phase flows

A new Quadratic Spline based Interface (QUASI) reconstruction algorithm is presented which provides an accurate and continuous representation of the interface in a multiphase domain and facilitates the direct estimation of local interfacial curvature. The fluid interface in each of the mixed cells is represented by piecewise parabolic curves and an initial discontinuous PLIC approximation of the interface is progressively converted into a smooth quadratic spline made of these parabolic curves. The conversion is achieved by a sequence of predictor–corrector operations enforcing function ( C 0) and derivative ( C 1) continuity at the cell boundaries using simple analytical expressions for the continuity requirements. The efficacy and accuracy of the current algorithm has been demonstrated using standard test cases involving reconstruction of known static interface shapes and dynamically evolving interfaces in prescribed flow situations. These benchmark studies illustrate that the present algorithm performs excellently as compared to the other interface reconstruction methods available in literature. Quadratic rate of error reduction with respect to grid size has been observed in all the cases with curved interface shapes; only in situations where the interface geometry is primarily flat, the rate of convergence becomes linear with the mesh size. The flow algorithm implemented in the current work is designed to accurately balance the pressure gradients with the surface tension force at any location. As a consequence, it is able to minimize spurious flow currents arising from imperfect normal stress balance at the interface. This has been demonstrated through the standard test problem of an inviscid droplet placed in a quiescent medium. Finally, the direct curvature estimation ability of the current algorithm is illustrated through the coupled multiphase flow problem of a deformable air bubble rising through a column of water.