An exact peak capturing and essentially oscillation-free (EPCOF) algorithm, consisting of advection-dispersion decoupling, backward method of characteristics, forward node tracking, and adaptive local grid refinement, is developed to solve transport equations. This algorithm repr...
Analytical solution for the advection-dispersion transport equation in layered media
Technology Transfer Automated Retrieval System (TEKTRAN)
The advection-dispersion transport equation with first-order decay was solved analytically for multi-layered media using the classic integral transform technique (CITT). The solution procedure used an associated non-self-adjoint advection-diffusion eigenvalue problem that had the same form and coef...
Lin, Guang; Tartakovsky, Alexandre M.
2010-04-01
In this study, we solve the three-dimensional stochastic Darcy's equation and stochastic advection-diffusion-dispersion equation using a probabilistic collocation method (PCM) on sparse grids. Karhunen-Lo\\`{e}ve (KL) decomposition is employed to represent the three-dimensional log hydraulic conductivity $Y=\\ln K_s$. The numerical examples which demonstrate the convergence of PCM are presented. It appears that the faster convergence rate in the variance can be obtained by using the Jacobi-chaos representing the truncated Gaussian distributions than using the Hermite-chaos for the Gaussian distribution. The effect of dispersion coefficient on the mean and standard deviation of the hydraulic head and solute concentration is investigated. Additionally, we also study how the statistical properties of the hydraulic head and solute concentration vary while using different types of random distributions and different standard deviations of random hydraulic conductivity.
Technology Transfer Automated Retrieval System (TEKTRAN)
Analytical solutions of the advection-dispersion equation and related models are indispensable for predicting or analyzing contaminant transport processes in streams and rivers, as well as in other surface water bodies. Many useful analytical solutions originated in disciplines other than surface-w...
A novel method for analytically solving a radial advection-dispersion equation
NASA Astrophysics Data System (ADS)
Lai, Keng-Hsin; Liu, Chen-Wuing; Liang, Ching-Ping; Chen, Jui-Sheng; Sie, Bing-Ruei
2016-11-01
An analytical solution for solute transport in a radial flow field has a variety of practical applications in the study of the transport in push-pull/divergent/convergent flow tracer tests, aquifer remediation by pumping and aquifer storage and recovery. However, an analytical solution for radial advective-dispersive transport has been proven very difficult to develop and relatively few in subsurface hydrology have made efforts to do so, because variable coefficients in the governing partial differential equations. Most of the solutions for radial advective-dispersive transport presented in the literature have generally been solved semi-analytically with the final concentration values being obtained with the help of a numerical Laplace inversion. This study presents a novel solution strategy for analytically solving the radial advective-dispersive transport problem. A Laplace transform with respect to the time variable and a generalized integral transform technique with respect to the spatial variable are first performed to convert the transient governing partial differential equations into an algebraic equation. Subsequently, the algebraic equation is solved using simple algebraic manipulations, easily yielding the solution in the transformed domain. The solution in the original domain is ultimately obtained by successive applications of the Laplace and corresponding generalized integral transform inversions. A convergent flow tracer test is used to demonstrate the robustness of the proposed method for deriving an exact analytical solution to the radial advective-dispersive transport problem. The developed analytical solution is verified against a semi-analytical solution taken from the literature. The results show perfect agreement between our exact analytical solution and the semi-analytical solution. The solution method presented in this study can be applied to create more comprehensive analytical models for a great variety of radial advective-dispersive
İbiş, Birol
2014-01-01
This paper aims to obtain the approximate solution of time-fractional advection-dispersion equation (FADE) involving Jumarie's modification of Riemann-Liouville derivative by the fractional variational iteration method (FVIM). FVIM provides an analytical approximate solution in the form of a convergent series. Some examples are given and the results indicate that the FVIM is of high accuracy, more efficient, and more convenient for solving time FADEs. PMID:24578662
Technology Transfer Automated Retrieval System (TEKTRAN)
Analytical solutions of the advection-dispersion solute transport equation remain useful for a large number of applications in science and engineering. In this paper we extend the Duhamel theorem, originally established for diffusion type problems, to the case of advective-dispersive transport subj...
Least-Squares Spectral Method for the solution of a fractional advection-dispersion equation
NASA Astrophysics Data System (ADS)
Carella, Alfredo Raúl; Dorao, Carlos Alberto
2013-01-01
Fractional derivatives provide a general approach for modeling transport phenomena occurring in diverse fields. This article describes a Least Squares Spectral Method for solving advection-dispersion equations using Caputo or Riemann-Liouville fractional derivatives. A Gauss-Lobatto-Jacobi quadrature is implemented to approximate the singularities in the integrands arising from the fractional derivative definition. Exponential convergence rate of the operator is verified when increasing the order of the approximation. Solutions are calculated for fractional-time and fractional-space differential equations. Comparisons with finite difference schemes are included. A significant reduction in storage space is achieved by lowering the resolution requirements in the time coordinate.
NASA Astrophysics Data System (ADS)
Pérez Guerrero, J. S.; Skaggs, T. H.
2010-08-01
SummaryMathematical models describing contaminant transport in heterogeneous porous media are often formulated as an advection-dispersion transport equation with distance-dependent transport coefficients. In this work, a general analytical solution is presented for the linear, one-dimensional advection-dispersion equation with distance-dependent coefficients. An integrating factor is employed to obtain a transport equation that has a self-adjoint differential operator, and a solution is found using the generalized integral transform technique (GITT). It is demonstrated that an analytical expression for the integrating factor exists for several transport equation formulations of practical importance in groundwater transport modeling. Unlike nearly all solutions available in the literature, the current solution is developed for a finite spatial domain. As an illustration, solutions for the particular case of a linearly increasing dispersivity are developed in detail and results are compared with solutions from the literature. Among other applications, the current analytical solution will be particularly useful for testing or benchmarking numerical transport codes because of the incorporation of a finite spatial domain.
Space-fractional advection-dispersion equations by the Kansa method
NASA Astrophysics Data System (ADS)
Pang, Guofei; Chen, Wen; Fu, Zhuojia
2015-07-01
The paper makes the first attempt at applying the Kansa method, a radial basis function meshless collocation method, to the space-fractional advection-dispersion equations, which have recently been observed to accurately describe solute transport in a variety of field and lab experiments characterized by occasional large jumps with fewer parameters than the classical models of integer-order derivative. However, because of non-local property of integro-differential operator of space-fractional derivative, numerical solution of these novel models is very challenging and little has been reported in literature. It is stressed that local approximation techniques such as the finite element and finite difference methods lose their sparse discretization matrix due to this non-local property. Thus, the global methods appear to have certain advantages in numerical simulation of these non-local models because of their high accuracy and smaller size resultant matrix equation. Compared with the finite difference method, popular in the solution of fractional equations, the Kansa method is a recent meshless global technique and is promising for high-dimensional irregular domain problems. In this study, the resultant matrix of the Kansa method is accurately calculated by the Gauss-Jacobi quadrature rule. Numerical results show that the Kansa method is highly accurate and computationally efficient for space-fractional advection-dispersion problems.
Solution of the advection-dispersion equation: Continuous load of finite duration
Runkel, R.L.
1996-01-01
Field studies of solute fate and transport in streams and rivers often involve an. experimental release of solutes at an upstream boundary for a finite period of time. A review of several standard references on surface-water-quality modeling indicates that the analytical solution to the constant-parameter advection-dispersion equation for this type of boundary condition has been generally overlooked. Here an exact analytical solution that considers a continuous load of unite duration is compared to an approximate analytical solution presented elsewhere. Results indicate that the exact analytical solution should be used for verification of numerical solutions and other solute-transport problems wherein a high level of accuracy is required. ?? ASCE.
Knopman, Debra S.; Voss, Clifford I.
1987-01-01
The spatial and temporal variability of sensitivities has a significant impact on parameter estimation and sampling design for studies of solute transport in porous media. Physical insight into the behavior of sensitivities is offered through an analysis of analytically derived sensitivities for the one-dimensional form of the advection-dispersion equation. When parameters are estimated in regression models of one-dimensional transport, the spatial and temporal variability in sensitivities influences variance and covariance of parameter estimates. Several principles account for the observed influence of sensitivities on parameter uncertainty. (1) Information about a physical parameter may be most accurately gained at points in space and time. (2) As the distance of observation points from the upstream boundary increases, maximum sensitivity to velocity during passage of the solute front increases. (3) The frequency of sampling must be 'in phase' with the S shape of the dispersion sensitivity curve to yield the most information on dispersion. (4) The sensitivity to the dispersion coefficient is usually at least an order of magnitude less than the sensitivity to velocity. (5) The assumed probability distribution of random error in observations of solute concentration determines the form of the sensitivities. (6) If variance in random error in observations is large, trends in sensitivities of observation points may be obscured by noise. (7) Designs that minimize the variance of one parameter may not necessarily minimize the variance of other parameters.
Embry, Irucka; Roland, Victor; Agbaje, Oluropo; ...
2013-01-01
A new residence-time distribution (RTD) function has been developed and applied to quantitative dye studies as an alternative to the traditional advection-dispersion equation (AdDE). The new method is based on a jointly combined four-parameter gamma probability density function (PDF). The gamma residence-time distribution (RTD) function and its first and second moments are derived from the individual two-parameter gamma distributions of randomly distributed variables, tracer travel distance, and linear velocity, which are based on their relationship with time. The gamma RTD function was used on a steady-state, nonideal system modeled as a plug-flow reactor (PFR) in the laboratory to validate themore » effectiveness of the model. The normalized forms of the gamma RTD and the advection-dispersion equation RTD were compared with the normalized tracer RTD. The normalized gamma RTD had a lower mean-absolute deviation (MAD) (0.16) than the normalized form of the advection-dispersion equation (0.26) when compared to the normalized tracer RTD. The gamma RTD function is tied back to the actual physical site due to its randomly distributed variables. The results validate using the gamma RTD as a suitable alternative to the advection-dispersion equation for quantitative tracer studies of non-ideal flow systems.« less
Healy, R.W.; Russell, T.F.
1993-01-01
Test results demonstrate that the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) outperforms standard finite-difference methods for solute transport problems that are dominated by advection. FVELLAM systematically conserves mass globally with all types of boundary conditions. Integrated finite differences, instead of finite elements, are used to approximate the governing equation. This approach, in conjunction with a forward tracking scheme, greatly facilitates mass conservation. The mass storage integral is numerically evaluated at the current time level, and quadrature points are then tracked forward in time to the next level. Forward tracking permits straightforward treatment of inflow boundaries, thus avoiding the inherent problem in backtracking of characteristic lines intersecting inflow boundaries. FVELLAM extends previous results by obtaining mass conservation locally on Lagrangian space-time elements. -from Authors
Kurikami, Hiroshi; Malins, Alex; Takeishi, Minoru; Saito, Kimiaki; Iijima, Kazuki
2017-02-17
Radiocesium is an important environmental contaminant in fallout from nuclear reactor accidents and atomic weapons testing. A modified Diffusion-Sorption-Fixation (mDSF) model, based on the advection-dispersion equation, is proposed to describe the vertical migration of radiocesium in soils following fallout. The model introduces kinetics for the reversible binding of radiocesium. We test the model by comparing its results to depth profiles measured in Fukushima Prefecture, Japan, since 2011. The results from the mDSF model are a better fit to the measurement data (as quantified by R(2)) than results from a simple diffusion model and the original DSF model. The introduction of reversible sorption kinetics means that the exponential-shape depth distribution can be reproduced immediately following fallout. The initial relaxation mass depth of the distribution is determined by the diffusion length, which depends on the distribution coefficient, sorption rate and dispersion coefficient. The mDSF model captures the long tails of the radiocesium distribution at large depths, which are caused by different rates for kinetic sorption and desorption. The mDSF model indicates that depth distributions displaying a peak in activity below the surface are possible for soils with high organic matter content at the surface. The mDSF equations thus offers a physical basis for various types of radiocesium depth profiles observed in contaminated environments.
Parker, Jack C; Kim, Ungtae
2015-11-01
The mono-continuum advection-dispersion equation (mADE) is commonly regarded as unsuitable for application to media that exhibit rapid breakthrough and extended tailing associated with diffusion between high and low permeability regions. This paper demonstrates that the mADE can be successfully used to model such conditions if certain issues are addressed. First, since hydrodynamic dispersion, unlike molecular diffusion, cannot occur upstream of the contaminant source, models must be formulated to prevent "back-dispersion." Second, large variations in aquifer permeability will result in differences between volume-weighted average concentration (resident concentration) and flow-weighted average concentration (flux concentration). Water samples taken from wells may be regarded as flux concentrations, while soil samples may be analyzed to determine resident concentrations. While the mADE is usually derived in terms of resident concentration, it is known that a mADE of the same mathematical form may be written in terms of flux concentration. However, when solving the latter, the mathematical transformation of a flux boundary condition applied to the resident mADE becomes a concentration type boundary condition for the flux mADE. Initial conditions must also be consistent with the form of the mADE that is to be solved. Thus, careful attention must be given to the type of concentration data that is available, whether resident or flux concentrations are to be simulated, and to boundary and initial conditions. We present 3-D analytical solutions for resident and flux concentrations, discuss methods of solving numerical models to obtain resident and flux concentrations, and compare results for hypothetical problems. We also present an upscaling method for computing "effective" dispersivities and other mADE model parameters in terms of physically meaningful parameters in a diffusion-limited mobile-immobile model. Application of the latter to previously published studies of
Lattice Boltzmann method for the fractional advection-diffusion equation.
Zhou, J G; Haygarth, P M; Withers, P J A; Macleod, C J A; Falloon, P D; Beven, K J; Ockenden, M C; Forber, K J; Hollaway, M J; Evans, R; Collins, A L; Hiscock, K M; Wearing, C; Kahana, R; Villamizar Velez, M L
2016-04-01
Mass transport, such as movement of phosphorus in soils and solutes in rivers, is a natural phenomenon and its study plays an important role in science and engineering. It is found that there are numerous practical diffusion phenomena that do not obey the classical advection-diffusion equation (ADE). Such diffusion is called abnormal or superdiffusion, and it is well described using a fractional advection-diffusion equation (FADE). The FADE finds a wide range of applications in various areas with great potential for studying complex mass transport in real hydrological systems. However, solution to the FADE is difficult, and the existing numerical methods are complicated and inefficient. In this study, a fresh lattice Boltzmann method is developed for solving the fractional advection-diffusion equation (LabFADE). The FADE is transformed into an equation similar to an advection-diffusion equation and solved using the lattice Boltzmann method. The LabFADE has all the advantages of the conventional lattice Boltzmann method and avoids a complex solution procedure, unlike other existing numerical methods. The method has been validated through simulations of several benchmark tests: a point-source diffusion, a boundary-value problem of steady diffusion, and an initial-boundary-value problem of unsteady diffusion with the coexistence of source and sink terms. In addition, by including the effects of the skewness β, the fractional order α, and the single relaxation time τ, the accuracy and convergence of the method have been assessed. The numerical predictions are compared with the analytical solutions, and they indicate that the method is second-order accurate. The method presented will allow the FADE to be more widely applied to complex mass transport problems in science and engineering.
Lattice Boltzmann method for the fractional advection-diffusion equation
NASA Astrophysics Data System (ADS)
Zhou, J. G.; Haygarth, P. M.; Withers, P. J. A.; Macleod, C. J. A.; Falloon, P. D.; Beven, K. J.; Ockenden, M. C.; Forber, K. J.; Hollaway, M. J.; Evans, R.; Collins, A. L.; Hiscock, K. M.; Wearing, C.; Kahana, R.; Villamizar Velez, M. L.
2016-04-01
Mass transport, such as movement of phosphorus in soils and solutes in rivers, is a natural phenomenon and its study plays an important role in science and engineering. It is found that there are numerous practical diffusion phenomena that do not obey the classical advection-diffusion equation (ADE). Such diffusion is called abnormal or superdiffusion, and it is well described using a fractional advection-diffusion equation (FADE). The FADE finds a wide range of applications in various areas with great potential for studying complex mass transport in real hydrological systems. However, solution to the FADE is difficult, and the existing numerical methods are complicated and inefficient. In this study, a fresh lattice Boltzmann method is developed for solving the fractional advection-diffusion equation (LabFADE). The FADE is transformed into an equation similar to an advection-diffusion equation and solved using the lattice Boltzmann method. The LabFADE has all the advantages of the conventional lattice Boltzmann method and avoids a complex solution procedure, unlike other existing numerical methods. The method has been validated through simulations of several benchmark tests: a point-source diffusion, a boundary-value problem of steady diffusion, and an initial-boundary-value problem of unsteady diffusion with the coexistence of source and sink terms. In addition, by including the effects of the skewness β , the fractional order α , and the single relaxation time τ , the accuracy and convergence of the method have been assessed. The numerical predictions are compared with the analytical solutions, and they indicate that the method is second-order accurate. The method presented will allow the FADE to be more widely applied to complex mass transport problems in science and engineering.
The LEM exponential integrator for advection-diffusion-reaction equations
NASA Astrophysics Data System (ADS)
Caliari, Marco; Vianello, Marco; Bergamaschi, Luca
2007-12-01
We implement a second-order exponential integrator for semidiscretized advection-diffusion-reaction equations, obtained by coupling exponential-like Euler and Midpoint integrators, and computing the relevant matrix exponentials by polynomial interpolation at Leja points. Numerical tests on 2D models discretized in space by finite differences or finite elements, show that the Leja-Euler-Midpoint (LEM) exponential integrator can be up to 5 times faster than a classical second-order implicit solver.
Solving the advection-diffusion equations in biological contexts using the cellular Potts model
NASA Astrophysics Data System (ADS)
Dan, Debasis; Mueller, Chris; Chen, Kun; Glazier, James A.
2005-10-01
The cellular Potts model (CPM) is a robust, cell-level methodology for simulation of biological tissues and morphogenesis. Both tissue physiology and morphogenesis depend on diffusion of chemical morphogens in the extra-cellular fluid or matrix (ECM). Standard diffusion solvers applied to the cellular potts model use finite difference methods on the underlying CPM lattice. However, these methods produce a diffusing field tied to the underlying lattice, which is inaccurate in many biological situations in which cell or ECM movement causes advection rapid compared to diffusion. Finite difference schemes suffer numerical instabilities solving the resulting advection-diffusion equations. To circumvent these problems we simulate advection diffusion within the framework of the CPM using off-lattice finite-difference methods. We define a set of generalized fluid particles which detach advection and diffusion from the lattice. Diffusion occurs between neighboring fluid particles by local averaging rules which approximate the Laplacian. Directed spin flips in the CPM handle the advective movement of the fluid particles. A constraint on relative velocities in the fluid explicitly accounts for fluid viscosity. We use the CPM to solve various diffusion examples including multiple instantaneous sources, continuous sources, moving sources, and different boundary geometries and conditions to validate our approximation against analytical and established numerical solutions. We also verify the CPM results for Poiseuille flow and Taylor-Aris dispersion.
2014-04-01
downstream boundary (when needed) is obtained by extrapolation, taking into account the hyperbolic character of the equation . By separating the...for Developing Reduced Order Models of Reaction-Advection Equations 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT...advection scalar equation is used as a representative equation to investigate the overall approach. Both linear and nonlinear model equations are
Lewis, F.M.; Voss, C.I.; Rubin, Jacob
1986-01-01
A model was developed that can simulate the effect of certain chemical and sorption reactions simultaneously among solutes involved in advective-dispersive transport through porous media. The model is based on a methodology that utilizes physical-chemical relationships in the development of the basic solute mass-balance equations; however, the form of these equations allows their solution to be obtained by methods that do not depend on the chemical processes. The chemical environment is governed by the condition of local chemical equilibrium, and may be defined either by the linear sorption of a single species and two soluble complexation reactions which also involve that species, or binary ion exchange and one complexation reaction involving a common ion. Partial differential equations that describe solute mass balance entirely in the liquid phase are developed for each tenad (a chemical entity whose total mass is independent of the reaction process) in terms of their total dissolved concentration. These equations are solved numerically in two dimensions through the modification of an existing groundwater flow/transport computer code. (Author 's abstract)
An operator splitting algorithm for the three-dimensional advection-diffusion equation
NASA Astrophysics Data System (ADS)
Khan, Liaqat Ali; Liu, Philip L.-F.
1998-09-01
Operator splitting algorithms are frequently used for solving the advection-diffusion equation, especially to deal with advection dominated transport problems. In this paper an operator splitting algorithm for the three-dimensional advection-diffusion equation is presented. The algorithm represents a second-order-accurate adaptation of the Holly and Preissmann scheme for three-dimensional problems. The governing equation is split into an advection equation and a diffusion equation, and they are solved by a backward method of characteristics and a finite element method, respectively. The Hermite interpolation function is used for interpolation of concentration in the advection step. The spatial gradients of concentration in the Hermite interpolation are obtained by solving equations for concentration gradients in the advection step. To make the composite algorithm efficient, only three equations for first-order concentration derivatives are solved in the diffusion step of computation. The higher-order spatial concentration gradients, necessary to advance the solution in a computational cycle, are obtained by numerical differentiations based on the available information. The simulation characteristics and accuracy of the proposed algorithm are demonstrated by several advection dominated transport problems.
NASA Astrophysics Data System (ADS)
Liu, Q.; Liu, F.; Turner, I.; Anh, V.
2007-03-01
In this paper we present a random walk model for approximating a Lévy-Feller advection-dispersion process, governed by the Lévy-Feller advection-dispersion differential equation (LFADE). We show that the random walk model converges to LFADE by use of a properly scaled transition to vanishing space and time steps. We propose an explicit finite difference approximation (EFDA) for LFADE, resulting from the Grünwald-Letnikov discretization of fractional derivatives. As a result of the interpretation of the random walk model, the stability and convergence of EFDA for LFADE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.
Wave-equation dispersion inversion
NASA Astrophysics Data System (ADS)
Li, Jing; Feng, Zongcai; Schuster, Gerard
2017-03-01
We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by vertical-component geophones. Similar to wave-equation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phase-velocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2-D or 3-D S-wave velocity models. This procedure, denoted as wave-equation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycle-skipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves.
NASA Astrophysics Data System (ADS)
Sanskrityayn, Abhishek; Kumar, Naveen
2016-12-01
Some analytical solutions of one-dimensional advection-diffusion equation (ADE) with variable dispersion coefficient and velocity are obtained using Green's function method (GFM). The variability attributes to the heterogeneity of hydro-geological media like river bed or aquifer in more general ways than that in the previous works. Dispersion coefficient is considered temporally dependent, while velocity is considered spatially and temporally dependent. The spatial dependence is considered to be linear and temporal dependence is considered to be of linear, exponential and asymptotic. The spatio-temporal dependence of velocity is considered in three ways. Results of previous works are also derived validating the results of the present work. To use GFM, a moving coordinate transformation is developed through which this ADE is reduced into a form, whose analytical solution is already known. Analytical solutions are obtained for the pollutant's mass dispersion from an instantaneous point source as well as from a continuous point source in a heterogeneous medium. The effect of such dependence on the mass transport is explained through the illustrations of the analytical solutions.
NASA Astrophysics Data System (ADS)
Lowry, Thomas; Li, Shu-Guang
2005-02-01
Difficulty in solving the transient advection-diffusion equation (ADE) stems from the relationship between the advection derivatives and the time derivative. For a solution method to be viable, it must account for this relationship by being accurate in both space and time. This research presents a unique method for solving the time-dependent ADE that does not discretize the derivative terms but rather solves the equation analytically in the space-time domain. The method is computationally efficient and numerically accurate and addresses the common limitations of numerical dispersion and spurious oscillations that can be prevalent in other solution methods. The method is based on the improved finite analytic (IFA) solution method [Lowry TS, Li S-G. A characteristic based finite analytic method for solving the two-dimensional steady-state advection-diffusion equation. Water Resour Res 38 (7), 10.1029/2001WR000518] in space coupled with a Laplace transformation in time. In this way, the method has no Courant condition and maintains accuracy in space and time, performing well even at high Peclet numbers. The method is compared to a hybrid method of characteristics, a random walk particle tracking method, and an Eulerian-Lagrangian Localized Adjoint Method using various degrees of flow-field heterogeneity across multiple Peclet numbers. Results show the IFALT method to be computationally more efficient while producing similar or better accuracy than the other methods.
Barajas-Solano, David A.; Tartakovsky, A. M.
2016-10-13
We present a hybrid scheme for the coupling of macro and microscale continuum models for reactive contaminant transport in fractured and porous media. The transport model considered is the advection-dispersion equation, subject to linear heterogeneous reactive boundary conditions. The Multiscale Finite Volume method (MsFV) is employed to define an approximation to the microscale concentration field defined in terms of macroscopic or \\emph{global} degrees of freedom, together with local interpolator and corrector functions capturing microscopic spatial variability. The macroscopic mass balance relations for the MsFV global degrees of freedom are coupled with the macroscopic model, resulting in a global problem for the simultaneous time-stepping of all macroscopic degrees of freedom throughout the domain. In order to perform the hybrid coupling, the micro and macroscale models are applied over overlapping subdomains of the simulation domain, with the overlap denoted as the handshake subdomain $\\Omega^{hs}$, over which continuity of concentration and transport fluxes between models is enforced. Continuity of concentration is enforced by posing a restriction relation between models over $\\Omega^{hs}$. Continuity of fluxes is enforced by prolongating the macroscopic model fluxes across the boundary of $\\Omega^{hs}$ to microscopic resolution. The microscopic interpolator and corrector functions are solutions to local microscopic advection-diffusion problems decoupled from the global degrees of freedom and from each other by virtue of the MsFV decoupling ansatz. The error introduced by the decoupling ansatz is reduced iteratively by the preconditioned GMRES algorithm, with the hybrid MsFV operator serving as the preconditioner.
An enriched finite element method to fractional advection-diffusion equation
NASA Astrophysics Data System (ADS)
Luan, Shengzhi; Lian, Yanping; Ying, Yuping; Tang, Shaoqiang; Wagner, Gregory J.; Liu, Wing Kam
2017-03-01
In this paper, an enriched finite element method with fractional basis [ 1,x^{α }] for spatial fractional partial differential equations is proposed to obtain more stable and accurate numerical solutions. For pure fractional diffusion equation without advection, the enriched Galerkin finite element method formulation is demonstrated to simulate the exact solution successfully without any numerical oscillation, which is advantageous compared to the traditional Galerkin finite element method with integer basis [ 1,x] . For fractional advection-diffusion equation, the oscillatory behavior becomes complex due to the introduction of the advection term which can be characterized by a fractional element Peclet number. For the purpose of addressing the more complex numerical oscillation, an enriched Petrov-Galerkin finite element method is developed by using a dimensionless fractional stabilization parameter, which is formulated through a minimization of the residual of the nodal solution. The effectiveness and accuracy of the enriched finite element method are demonstrated by a series of numerical examples of fractional diffusion equation and fractional advection-diffusion equation, including both one-dimensional and two-dimensional, steady-state and time-dependent cases.
A global spectral element model for poisson equations and advective flow over a sphere
NASA Astrophysics Data System (ADS)
Mei, Huan; Wang, Faming; Zeng, Zhong; Qiu, Zhouhua; Yin, Linmao; Li, Liang
2016-03-01
A global spherical Fourier-Legendre spectral element method is proposed to solve Poisson equations and advective flow over a sphere. In the meridional direction, Legendre polynomials are used and the region is divided into several elements. In order to avoid coordinate singularities at the north and south poles in the meridional direction, Legendre-Gauss-Radau points are chosen at the elements involving the two poles. Fourier polynomials are applied in the zonal direction for its periodicity, with only one element. Then, the partial differential equations are solved on the longitude-latitude meshes without coordinate transformation between spherical and Cartesian coordinates. For verification of the proposed method, a few Poisson equations and advective flows are tested. Firstly, the method is found to be valid for test cases with smooth solution. The results of the Poisson equations demonstrate that the present method exhibits high accuracy and exponential convergence. Highprecision solutions are also obtained with near negligible numerical diffusion during the time evolution for advective flow with smooth shape. Secondly, the results of advective flow with non-smooth shape and deformational flow are also shown to be reasonable and effective. As a result, the present method is proved to be capable of solving flow through different types of elements, and thereby a desirable method with reliability and high accuracy for solving partial differential equations over a sphere.
NASA Astrophysics Data System (ADS)
Bernabé, Y.; Wang, Y.; Qi, T.; Li, M.
2016-02-01
The main purpose of this work is to investigate the relationship between passive advection-dispersion and permeability in porous materials presumed to be statistically homogeneous at scales larger than the pore scale but smaller than the reservoir scale. We simulated fluid flow through pipe network realizations with different pipe radius distributions and different levels of connectivity. The flow simulations used periodic boundary conditions, allowing monitoring of the advective motion of solute particles in a large periodic array of identical network realizations. In order to simulate dispersion, we assumed that the solute particles obeyed Taylor dispersion in individual pipes. When a particle entered a pipe, a residence time consistent with local Taylor dispersion was randomly assigned to it. When exiting the pipe, the particle randomly proceeded into one of the pipes connected to the original one according to probabilities proportional to the outgoing volumetric flow in each pipe. For each simulation we tracked the motion of at least 6000 solute particles. The mean fluid velocity was 10-3 ms-1, and the distance traveled was on the order of 10 m. Macroscopic dispersion was quantified using the method of moments. Despite differences arising from using different types of lattices (simple cubic, body-centered cubic, and face-centered cubic), a number of general observations were made. Longitudinal dispersion was at least 1 order of magnitude greater than transverse dispersion, and both strongly increased with decreasing pore connectivity and/or pore size variability. In conditions of variable hydraulic radius and fixed pore connectivity and pore size variability, the simulated dispersivities increased as power laws of the hydraulic radius and, consequently, of permeability, in agreement with previously published experimental results. Based on these observations, we were able to resolve some of the complexity of the relationship between dispersivity and permeability.
Noise Prevents Infinite Stretching of the Passive Field in a Stochastic Vector Advection Equation
NASA Astrophysics Data System (ADS)
Flandoli, Franco; Maurelli, Mario; Neklyudov, Mikhail
2014-09-01
A linear stochastic vector advection equation is considered; the equation may model a passive magnetic field in a random fluid. When the driving velocity field is rough but deterministic, in particular just Hölder continuous and bounded, one can construct examples of infinite stretching of the passive field, arising from smooth initial conditions. The purpose of the paper is to prove that infinite stretching is prevented if the driving velocity field contains in addition a white noise component.
It is well known that the fate and transport of contaminants in the subsurface are controlled by complex processes including advection, dispersion-diffusion, and chemical reactions. However, the interplay between the physical transport processes and chemical reactions, and their...
Comparison of Nonlinear and Linear Stabilization Schemes for Advection-Diffusion Equations
NASA Astrophysics Data System (ADS)
Grove, R. R.; Heister, T.
2015-12-01
Accurately solving advection-diffusion equations that appear in the finite element discretization of a mantle convection simulation is an important computational issue to the computational geoscience community. This is because it allows for users studying mantle convection to create reliable simulations for something as small and simple as a 2D simulation on their personal laptop to something as complex as a massively parallel 3D simulation on their university supercomputer. Standard finite element discretizations of advection-diffusion equations introduce unphysical oscillations around steep gradients. Therefore, stabilization must be added to the discrete formulation to obtain correct solutions. Using the open source scientific library ASPECT, the SUPG and Entropy Viscosity schemes are compared using stationary and non-stationary test equations. Differences in maximum overshoot and undershoot, smear, and convergence orders are compared to see if improvements can be made to the existing numerical method existing in ASPECT.
Reactive-Diffusive-Advective Traveling Waves in a Family of Degenerate Nonlinear Equations.
Sánchez-Garduño, Faustino; Pérez-Velázquez, Judith
This paper deals with the analysis of existence of traveling wave solutions (TWS) for a diffusion-degenerate (at D(0) = 0) and advection-degenerate (at h'(0) = 0) reaction-diffusion-advection (RDA) equation. Diffusion is a strictly increasing function and the reaction term generalizes the kinetic part of the Fisher-KPP equation. We consider different forms of the convection term h(u): (1) h'(u) is constant k, (2) h'(u) = ku with k > 0, and (3) it is a quite general form which guarantees the degeneracy in the advective term. In Case 1, we prove that the task can be reduced to that for the corresponding equation, where k = 0, and then previous results reported from the authors can be extended. For the other two cases, we use both analytical and numerical tools. The analysis we carried out is based on the restatement of searching TWS for the full RDA equation into a two-dimensional dynamical problem. This consists of searching for the conditions on the parameter values for which there exist heteroclinic trajectories of the ordinary differential equations (ODE) system in the traveling wave coordinates. Throughout the paper we obtain the dynamics by using tools coming from qualitative theory of ODE.
Reactive-Diffusive-Advective Traveling Waves in a Family of Degenerate Nonlinear Equations
Sánchez-Garduño, Faustino
2016-01-01
This paper deals with the analysis of existence of traveling wave solutions (TWS) for a diffusion-degenerate (at D(0) = 0) and advection-degenerate (at h′(0) = 0) reaction-diffusion-advection (RDA) equation. Diffusion is a strictly increasing function and the reaction term generalizes the kinetic part of the Fisher-KPP equation. We consider different forms of the convection term h(u): (1) h′(u) is constant k, (2) h′(u) = ku with k > 0, and (3) it is a quite general form which guarantees the degeneracy in the advective term. In Case 1, we prove that the task can be reduced to that for the corresponding equation, where k = 0, and then previous results reported from the authors can be extended. For the other two cases, we use both analytical and numerical tools. The analysis we carried out is based on the restatement of searching TWS for the full RDA equation into a two-dimensional dynamical problem. This consists of searching for the conditions on the parameter values for which there exist heteroclinic trajectories of the ordinary differential equations (ODE) system in the traveling wave coordinates. Throughout the paper we obtain the dynamics by using tools coming from qualitative theory of ODE. PMID:27689131
NASA Astrophysics Data System (ADS)
Cartwright, Ian
Advection-dispersion fluid flow models implicitly assume that the infiltrating fluid flows through an already fluid-saturated medium. However, whether rocks contain a fluid depends on their reaction history, and whether any initial fluid escapes. The behaviour of different rocks may be illustrated using hypothetical marble compositions. Marbles with diverse chemistries (e.g. calcite + dolomite + quartz) are relatively reactive, and will generally produce a fluid during heating. By contrast, marbles with more restricted chemistries (e.g. calcite + quartz or calcite-only) may not. If the rock is not fluid bearing when fluid infiltration commences, mineralogical reactions may produce a reaction-enhanced permeability in calcite + dolomite + quartz or calcite + quartz, but not in calcite-only marbles. The permeability production controls the pattern of mineralogical, isotopic, and geochemical resetting during fluid flow. Tracers retarded behind the mineralogical fronts will probably be reset as predicted by the advection-dispersion models; however, tracers that are expected to be reset ahead of the mineralogical fronts cannot progress beyond the permeability generating reaction. In the case of very unreactive lithologies (e.g. pure calcite marbles, cherts, and quartzites), the first reaction to affect the rocks may be a metasomatic one ahead of which there is little pervasive resetting of any tracer. Centimetre-scale layering may lead to the formation of self-perpetuating fluid channels in rocks that are not fluid saturated due to the juxtaposition of reactants. Such layered rocks may show patterns of mineralogical resetting that are not predicted by advection-dispersion models. Patterns of mineralogical and isotopic resetting in marbles from a number of terrains, for example: Chillagoe, Marulan South, Reynolds Range (Australia); Adirondack Mountains, Old Woman Mountains, Notch Peak (USA); and Stephen Cross Quarry (Canada) vary as predicted by these models.
NASA Astrophysics Data System (ADS)
Paparella, F.; Oliveri, F.
2009-04-01
The interplay of advection, reaction and diffusion terms in ADR equations is a rather difficult one to be modeled numerically. The kind of spurious oscillations that is usually harmless for non-reacting scalars is often amplified without bounds by reaction terms. Furthermore, in most biogeochimical applications, such as mesoscale or global-scale plankton modeling, the diffusive fluxes may be smaller than the numerical ones. Inspired by the particle-mesh methods used by cosmologists, we propose to discretize on a grid only the diffusive term of the equation, and solve the advection-reaction terms as ordinary differential equations along the characteristic lines. Diffusion happens by letting the concentration field carried by each particle to relax towards the diffusive field known on the grid, without redistributing the particles. This method, in the limit of vanishing diffusivity and for a fixed mesh size, recovers the advection-reaction solution with no numerical diffusion. We show some example numerical solutions of the ADR equations stemming from a simple predator-prey model.
Lichtner, P.C.; Helgeson, H.C.
1986-06-20
A general formulation of multi-phase fluid flow coupled to chemical reactions was developed based on a continuum description of porous media. A preliminary version of the computer code MCCTM was constructed which implemented the general equations for a single phase fluid. The computer code MCCTM incorporates mass transport by advection-diffusion/dispersion in a one-dimensional porous medium coupled to reversible and irreversible, homogeneous and heterogeneous chemical reactions. These reactions include aqueous complexing, oxidation/reduction reactions, ion exchange, and hydrolysis reactions of stoichiometric minerals. The code MCCTM uses a fully implicit finite difference algorithm. The code was tested against analytical calculations. Applications of the code included investigation of the propagation of sharp chemical reaction fronts, metasomatic alteration of microcline at elevated temperatures and pressures, and ion-exchange in a porous column. Finally numerical calculations describing fluid flow in crystalline rock in the presence of a temperature gradient were compared with experimental results for quartzite.
Dynamic typology of hydrothermal systems: competing effects of advection, dispersion and reactivity
NASA Astrophysics Data System (ADS)
Dolejs, David
2016-04-01
Genetic interpretation hydrothermal systems relies on recognition of (i) hydrothermal fluid source, (ii) fluid migration pathways, and (iii) deposition site identified by hydrothermal alteration and/or mineralization. Frequently, only the last object is of interest or accessible to direct observation, but constraints on the fluid source (volume) and pathways can be obtained from evaluation of the time-integrated fluid flux during hydrothermal event. Successful interpretation of the petrological record, that is, progress of alteration reactions, relies on identification of individual contributions arising from solute advection (to the deposition site), its lateral dispersion, and reaction efficiency. Although these terms are all applicable in a mass-conservation relationship within the framework of the transport theory, they are rarely considered simultaneously and their relative magnitudes evaluated. These phenomena operate on variable length and time scales, and may in turn provide insight into the system dynamics such as flow, diffusion and reaction rates, or continuous vs. episodic behavior of hydrothermal events. In addition, here we demonstrate that they also affect estimate of the net fluid flux, frequently by several orders of magnitude. The extent of alteration and mineralization reactions between the hydrothermal fluid and the host environment is determined by: (i) temperature, pressure or any other gradients across the mineralization site, (ii) magnitude of disequilibrium at inflow to the mineralization site, which is related to physico-chemical gradient between the fluid source and the mineralization site, and (iii) chemical redistribution (dispersion) within the mineralization site. We introduce quantitative mass-transport descriptors - Péclet and Damköhler II numbers - to introduce division into dispersion-dominated, advection-dominated and reaction-constrained systems. Dispersive systems are characterized by lateral solute redistribution, driven by
Boso, F; Broyda, S V; Tartakovsky, D M
2014-06-08
We derive deterministic cumulative distribution function (CDF) equations that govern the evolution of CDFs of state variables whose dynamics are described by the first-order hyperbolic conservation laws with uncertain coefficients that parametrize the advective flux and reactive terms. The CDF equations are subjected to uniquely specified boundary conditions in the phase space, thus obviating one of the major challenges encountered by more commonly used probability density function equations. The computational burden of solving CDF equations is insensitive to the magnitude of the correlation lengths of random input parameters. This is in contrast to both Monte Carlo simulations (MCSs) and direct numerical algorithms, whose computational cost increases as correlation lengths of the input parameters decrease. The CDF equations are, however, not exact because they require a closure approximation. To verify the accuracy and robustness of the large-eddy-diffusivity closure, we conduct a set of numerical experiments which compare the CDFs computed with the CDF equations with those obtained via MCSs. This comparison demonstrates that the CDF equations remain accurate over a wide range of statistical properties of the two input parameters, such as their correlation lengths and variance of the coefficient that parametrizes the advective flux.
Quantification of numerical diffusivity due to TVD schemes in the advection equation
NASA Astrophysics Data System (ADS)
Bidadi, Shreyas; Rani, Sarma L.
2014-03-01
In this study, the numerical diffusivity νnum inherent to the Roe-MUSCL scheme has been quantified for the scalar advection equation. The Roe-MUSCL scheme employed is a combination of: (1) the standard extension of the original Roe's formulation to the advection equation, and (2) van Leer's Monotone Upwind Scheme for Conservation Laws (MUSCL) technique that applies a linear variable reconstruction in a cell along with a scaled limiter function. An explicit expression is derived for the numerical diffusivity in terms of the limiter function, the distance between the cell centers on either side of a face, and the face-normal velocity. The numerical diffusivity formulation shows that a scaled limiter function is more appropriate for MUSCL in order to consistently recover the central-differenced flux at the maximum value of the limiter. The significance of the scaling factor is revealed when the Roe-MUSCL scheme, originally developed for 1-D scenarios, is applied to 2-D scalar advection problems. It is seen that without the scaling factor, the MUSCL scheme may not necessarily be monotonic in multi-dimensional scenarios. Numerical diffusivities of the minmod, superbee, van Leer and Barth-Jesperson TVD limiters were quantified for four problems: 1-D advection of a step function profile, and 2-D advection of step, sinusoidal, and double-step profiles. For all the cases, it is shown that the superbee scheme provides the lowest numerical diffusivity that is also most confined to the vicinity of the discontinuity. The minmod scheme is the most diffusive, as well as active in regions away from high gradients. As expected, the grid resolution study demonstrates that the magnitude and the spatial extent of the numerical diffusivity decrease with increasing resolution.
New Solution of Diffusion-Advection Equation for Cosmic-Ray Transport Using Ultradistributions
NASA Astrophysics Data System (ADS)
Rocca, M. C.; Plastino, A. R.; Plastino, A.; Ferri, G. L.; de Paoli, A.
2015-11-01
In this paper we exactly solve the diffusion-advection equation (DAE) for cosmic-ray transport. For such a purpose we use the Theory of Ultradistributions of J. Sebastiao e Silva, to give a general solution for the DAE. From the ensuing solution, we obtain several approximations as limiting cases of various situations of physical and astrophysical interest. One of them involves Solar cosmic-rays' diffusion.
Cox, T.J.; Runkel, R.L.
2008-01-01
Past applications of one-dimensional advection, dispersion, and transient storage zone models have almost exclusively relied on a central differencing, Eulerian numerical approximation to the nonconservative form of the fundamental equation. However, there are scenarios where this approach generates unacceptable error. A new numerical scheme for this type of modeling is presented here that is based on tracking Lagrangian control volumes across a fixed (Eulerian) grid. Numerical tests are used to provide a direct comparison of the new scheme versus nonconservative Eulerian numerical methods, in terms of both accuracy and mass conservation. Key characteristics of systems for which the Lagrangian scheme performs better than the Eulerian scheme include: nonuniform flow fields, steep gradient plume fronts, and pulse and steady point source loadings in advection-dominated systems. A new analytical derivation is presented that provides insight into the loss of mass conservation in the nonconservative Eulerian scheme. This derivation shows that loss of mass conservation in the vicinity of spatial flow changes is directly proportional to the lateral inflow rate and the change in stream concentration due to the inflow. While the nonconservative Eulerian scheme has clearly worked well for past published applications, it is important for users to be aware of the scheme's limitations. ?? 2008 ASCE.
Huang, Y.H.; Saiers, J.E.; Harvey, J.W.; Noe, G.B.; Mylon, S.
2008-01-01
The movement of particulate matter within wetland surface waters affects nutrient cycling, contaminant mobility, and the evolution of the wetland landscape. Despite the importance of particle transport in influencing wetland form and function, there are few data sets that illuminate, in a quantitative way, the transport behavior of particulate matter within surface waters containing emergent vegetation. We report observations from experiments on the transport of 1 ??m latex microspheres at a wetland field site located in Water Conservation Area 3A of the Florida Everglades. The experiments involved line source injections of particles inside two 4.8-m-long surface water flumes constructed within a transition zone between an Eleocharis slough and Cladium jamaicense ridge and within a Cladium jamaicense ridge. We compared the measurements of particle transport to calculations of two-dimensional advection-dispersion model that accounted for a linear increase in water velocities with elevation above the ground surface. The results of this analysis revealed that particle spreading by longitudinal and vertical dispersion was substantially greater in the ridge than within the transition zone and that particle capture by aquatic vegetation lowered surface water particle concentrations and, at least for the timescale of our experiments, could be represented as an irreversible, first-order kinetics process. We found generally good agreement between our field-based estimates of particle dispersion and water velocity and estimates determined from published theory, suggesting that the advective-dispersive transport of particulate matter within complex wetland environments can be approximated on the basis of measurable properties of the flow and aquatic vegetation. Copyright 2008 by the American Geophysical Union.
Reformulations for general advection-diffusion-reaction equations and locally implicit ADER schemes
NASA Astrophysics Data System (ADS)
Montecinos, Gino I.; Toro, Eleuterio F.
2014-10-01
Following Cattaneo's original idea, in this article we first present two relaxation formulations for time-dependent, non-linear systems of advection-diffusion-reaction equations. Such formulations yield time-dependent non-linear hyperbolic balance laws with stiff source terms. Then we present a locally implicit version of the ADER method to solve these stiff systems to high accuracy. The new ingredient of the numerical methodology is a locally implicit solution of the generalised Riemann problem. We illustrate the formulations and the resulting numerical approach by solving the compressible Navier-Stokes equations.
Pointwise interactions of finite element modeling of advection-diffusion equations
Yeh, G.T.
1984-07-01
Pointwise iteration techniques including successive under-relaxation (SUR), Gauss-Seidel (G-S), and successive over-relaxation (SOR) schemes, are applied to advection-diffusion equations to derive the matrix equation with finite element methods. These schemes are tested using two simple examples for which analytical solutions are available so that numerical results can be checked to ensure code consistency. Numerical experiments indicate that the iteration schemes, if convergent, produce almost identical solutions as those obtained by the direct elimination scheme. For diffusion dominant transport, all three iteration schemes generate convergent computations. However, for advection-diffusion equally dominant or advection dominant transport, only SUR and G-S schemes yield convergent calculations, the SOR scheme leads to divergent computations. Pointwise iteration schemes offer substantial savings in central process unit (CPU) memory over the direct elimination scheme, even for the small, two-dimensional verification example, without complicating the programming efforts and, in the meantime, keeps the CPU time comparable. A realistic, hypothetical problem is used to demonstrate the applicability and versatility of pointwise iterations and direct elimination schemes. The saving in CPU memory using the pointwise iterations is more than tenfold that using the direct elimination solution for this hypothetical problem. The saving in CPU time is even better, more than 40 fold.
NASA Astrophysics Data System (ADS)
Jiang, Tian; Zhang, Yong-Tao
2016-04-01
Implicit integration factor (IIF) methods were developed in the literature for solving time-dependent stiff partial differential equations (PDEs). Recently, IIF methods were combined with weighted essentially non-oscillatory (WENO) schemes in Jiang and Zhang (2013) [19] to efficiently solve stiff nonlinear advection-diffusion-reaction equations. The methods can be designed for arbitrary order of accuracy. The stiffness of the system is resolved well and the methods are stable by using time step sizes which are just determined by the non-stiff hyperbolic part of the system. To efficiently calculate large matrix exponentials, Krylov subspace approximation is directly applied to the implicit integration factor (IIF) methods. So far, the IIF methods developed in the literature are multistep methods. In this paper, we develop Krylov single-step IIF-WENO methods for solving stiff advection-diffusion-reaction equations. The methods are designed carefully to avoid generating positive exponentials in the matrix exponentials, which is necessary for the stability of the schemes. We analyze the stability and truncation errors of the single-step IIF schemes. Numerical examples of both scalar equations and systems are shown to demonstrate the accuracy, efficiency and robustness of the new methods.
Barth, Andrea Lang, Annika
2012-12-15
In this paper, the strong approximation of a stochastic partial differential equation, whose differential operator is of advection-diffusion type and which is driven by a multiplicative, infinite dimensional, cadlag, square integrable martingale, is presented. A finite dimensional projection of the infinite dimensional equation, for example a Galerkin projection, with nonequidistant time stepping is used. Error estimates for the discretized equation are derived in L{sup 2} and almost sure senses. Besides space and time discretizations, noise approximations are also provided, where the Milstein double stochastic integral is approximated in such a way that the overall complexity is not increased compared to an Euler-Maruyama approximation. Finally, simulations complete the paper.
NASA Astrophysics Data System (ADS)
Jiang, Tian; Zhang, Yong-Tao
2013-11-01
Implicit integration factor (IIF) methods are originally a class of efficient “exactly linear part” time discretization methods for solving time-dependent partial differential equations (PDEs) with linear high order terms and stiff lower order nonlinear terms. For complex systems (e.g. advection-diffusion-reaction (ADR) systems), the highest order derivative term can be nonlinear, and nonlinear nonstiff terms and nonlinear stiff terms are often mixed together. High order weighted essentially non-oscillatory (WENO) methods are often used to discretize the hyperbolic part in ADR systems. There are two open problems on IIF methods for solving ADR systems: (1) how to obtain higher than the second order global time discretization accuracy; (2) how to design IIF methods for solving fully nonlinear PDEs, i.e., the highest order terms are nonlinear. In this paper, we solve these two problems by developing new Krylov IIF-WENO methods to deal with both semilinear and fully nonlinear advection-diffusion-reaction equations. The methods can be designed for arbitrary order of accuracy. The stiffness of the system is resolved well and the methods are stable by using time step sizes which are just determined by the nonstiff hyperbolic part of the system. Large time step size computations are obtained. We analyze the stability and truncation errors of the schemes. Numerical examples of both scalar equations and systems in two and three spatial dimensions are shown to demonstrate the accuracy, efficiency and robustness of the methods.
Variational Integration for Ideal MHD with Built-in Advection Equations
Zhou, Yao; Qin, Hong; Burby, J. W.; Bhattacharjee, A.
2014-08-05
Newcomb's Lagrangian for ideal MHD in Lagrangian labeling is discretized using discrete exterior calculus. Variational integrators for ideal MHD are derived thereafter. Besides being symplectic and momentum preserving, the schemes inherit built-in advection equations from Newcomb's formulation, and therefore avoid solving them and the accompanying error and dissipation. We implement the method in 2D and show that numerical reconnection does not take place when singular current sheets are present. We then apply it to studying the dynamics of the ideal coalescence instability with multiple islands. The relaxed equilibrium state with embedded current sheets is obtained numerically.
Multigrid techniques for the solution of the passive scalar advection-diffusion equation
NASA Technical Reports Server (NTRS)
Phillips, R. E.; Schmidt, F. W.
1985-01-01
The solution of elliptic passive scalar advection-diffusion equations is required in the analysis of many turbulent flow and convective heat transfer problems. The accuracy of the solution may be affected by the presence of regions containing large gradients of the dependent variables. The multigrid concept of local grid refinement is a method for improving the accuracy of the calculations in these problems. In combination with the multilevel acceleration techniques, an accurate and efficient computational procedure is developed. In addition, a robust implementation of the QUICK finite-difference scheme is described. Calculations of a test problem are presented to quantitatively demonstrate the advantages of the multilevel-multigrid method.
Preconditioned iterative methods for space-time fractional advection-diffusion equations
NASA Astrophysics Data System (ADS)
Zhao, Zhi; Jin, Xiao-Qing; Lin, Matthew M.
2016-08-01
In this paper, we propose practical numerical methods for solving a class of initial-boundary value problems of space-time fractional advection-diffusion equations. First, we propose an implicit method based on two-sided Grünwald formulae and discuss its stability and consistency. Then, we develop the preconditioned generalized minimal residual (preconditioned GMRES) method and preconditioned conjugate gradient normal residual (preconditioned CGNR) method with easily constructed preconditioners. Importantly, because resulting systems are Toeplitz-like, fast Fourier transform can be applied to significantly reduce the computational cost. We perform numerical experiments to demonstrate the efficiency of our preconditioners, even in cases with variable coefficients.
Design and analysis of ADER-type schemes for model advection-diffusion-reaction equations
NASA Astrophysics Data System (ADS)
Busto, S.; Toro, E. F.; Vázquez-Cendón, M. E.
2016-12-01
We construct, analyze and assess various schemes of second order of accuracy in space and time for model advection-diffusion-reaction differential equations. The constructed schemes are meant to be of practical use in solving industrial problems and are derived following two related approaches, namely ADER and MUSCL-Hancock. Detailed analysis of linear stability and local truncation error are carried out. In addition, the schemes are implemented and assessed for various test problems. Empirical convergence rate studies confirm the theoretically expected accuracy in both space and time.
Variational integration for ideal magnetohydrodynamics with built-in advection equations
Zhou, Yao; Burby, J. W.; Bhattacharjee, A.; Qin, Hong
2014-10-15
Newcomb's Lagrangian for ideal magnetohydrodynamics (MHD) in Lagrangian labeling is discretized using discrete exterior calculus. Variational integrators for ideal MHD are derived thereafter. Besides being symplectic and momentum-preserving, the schemes inherit built-in advection equations from Newcomb's formulation, and therefore avoid solving them and the accompanying error and dissipation. We implement the method in 2D and show that numerical reconnection does not take place when singular current sheets are present. We then apply it to studying the dynamics of the ideal coalescence instability with multiple islands. The relaxed equilibrium state with embedded current sheets is obtained numerically.
Application of a Particle Method to the Advection-Diffusion-Reaction Equation
NASA Astrophysics Data System (ADS)
Paster, A.; Bolster, D.; Benson, D. A.
2012-12-01
A reaction between two chemical species can only happen if molecules collide and react. Thus, the mixing of a system can become a limiting factor in the onset of reaction. Solving for reaction rate in a well-mixed system is typically a straightforward task. However, when incomplete mixing kicks in, obtaining a solution becomes more challenging. Since reaction can only happen in regions where both reactants co-exist, the incomplete mixing may slow down the reaction rate, when compared to a well-mixed system. The effect of incomplete mixing upon reaction is a highly important aspect of various processes in natural and engineered systems, ranging from mineral precipitation in geological formations to groundwater remediation in aquifers. We study a relatively simple system with a bi-molecular irreversible kinetic reaction A+B → Ø where the underlying transport of reactants is governed by an advection-diffusion equation, and the initial concentrations are given in terms of an average and a perturbation. Such a system does not have an analytical solution to date, even for the zero advection case. We model the system by a Monte Carlo particle tracking method, where particles represent some reactant mass. In this method, diffusion is modeled by a random walk of the particles, and reaction is modeled by annihilation of particles. The probability of the annihilation is proportional to the reaction rate constant and the probability density associated with particle co-location. We study the numerical method in depth, characterizing typical numerical errors and time step restrictions. In particular, we show that the numerical method converges to the advection-diffusion-reaction equation at the limit Δt →0. We also rigorously derive the relationship between the initial number of particles in the system and the initial concentrations perturbations represented by that number. We then use the particle simulations of zero-advection system to demonstrate the well
Xu, Bruce S; Lollar, Barbara Sherwood; Passeport, Elodie; Sleep, Brent E
2016-04-15
Aqueous phase diffusion-related isotope fractionation (DRIF) for carbon isotopes was investigated for common groundwater contaminants in systems in which transport could be considered to be one-dimensional. This paper focuses not only on theoretically observable DRIF effects in these systems but introduces the important concept of constraining "observable" DRIF based on constraints imposed by the scale of measurements in the field, and on standard limits of detection and analytical uncertainty. Specifically, constraints for the detection of DRIF were determined in terms of the diffusive fractionation factor, the initial concentration of contaminants (C0), the method detection limit (MDL) for isotopic analysis, the transport time, and the ratio of the longitudinal mechanical dispersion coefficient to effective molecular diffusion coefficient (Dmech/Deff). The results allow a determination of field conditions under which DRIF may be an important factor in the use of stable carbon isotope measurements for evaluation of contaminant transport and transformation for one-dimensional advective-dispersive transport. This study demonstrates that for diffusion-dominated transport of BTEX, MTBE, and chlorinated ethenes, DRIF effects are only detectable for the smaller molar mass compounds such as vinyl chloride for C0/MDL ratios of 50 or higher. Much larger C0/MDL ratios, corresponding to higher source concentrations or lower detection limits, are necessary for DRIF to be detectable for the higher molar mass compounds. The distance over which DRIF is observable for VC is small (less than 1m) for a relatively young diffusive plume (<100years), and DRIF will not easily be detected by using the conventional sampling approach with "typical" well spacing (at least several meters). With contaminant transport by advection, mechanical dispersion, and molecular diffusion this study suggests that in field sites where Dmech/Deff is larger than 10, DRIF effects will likely not be
NASA Astrophysics Data System (ADS)
Ginzburg, Irina
2017-01-01
The effect of the heterogeneity in the soil structure or the nonuniformity of the velocity field on the modeled resident time distribution (RTD) and breakthrough curves is quantified by their moments. While the first moment provides the effective velocity, the second moment is related to the longitudinal dispersion coefficient (kT) in the developed Taylor regime; the third and fourth moments are characterized by their normalized values skewness (Sk) and kurtosis (Ku), respectively. The purpose of this investigation is to examine the role of the truncation corrections of the numerical scheme in kT, Sk, and Ku because of their interference with the second moment, in the form of the numerical dispersion, and in the higher-order moments, by their definition. Our symbolic procedure is based on the recently proposed extended method of moments (EMM). Originally, the EMM restores any-order physical moments of the RTD or averaged distributions assuming that the solute concentration obeys the advection-diffusion equation in multidimensional steady-state velocity field, in streamwise-periodic heterogeneous structure. In our work, the EMM is generalized to the fourth-order-accurate apparent mass-conservation equation in two- and three-dimensional duct flows. The method looks for the solution of the transport equation as the product of a long harmonic wave and a spatially periodic oscillating component; the moments of the given numerical scheme are derived from a chain of the steady-state fourth-order equations at a single cell. This mathematical technique is exemplified for the truncation terms of the two-relaxation-time lattice Boltzmann scheme, using plug and parabolic flow in straight channel and cylindrical capillary with the d2Q9 and d3Q15 discrete velocity sets as simple but illustrative examples. The derived symbolic dependencies can be readily extended for advection by another, Newtonian or non-Newtonian, flow profile in any-shape open-tabular conduits. It is
Ginzburg, Irina
2017-01-01
The effect of the heterogeneity in the soil structure or the nonuniformity of the velocity field on the modeled resident time distribution (RTD) and breakthrough curves is quantified by their moments. While the first moment provides the effective velocity, the second moment is related to the longitudinal dispersion coefficient (k_{T}) in the developed Taylor regime; the third and fourth moments are characterized by their normalized values skewness (Sk) and kurtosis (Ku), respectively. The purpose of this investigation is to examine the role of the truncation corrections of the numerical scheme in k_{T}, Sk, and Ku because of their interference with the second moment, in the form of the numerical dispersion, and in the higher-order moments, by their definition. Our symbolic procedure is based on the recently proposed extended method of moments (EMM). Originally, the EMM restores any-order physical moments of the RTD or averaged distributions assuming that the solute concentration obeys the advection-diffusion equation in multidimensional steady-state velocity field, in streamwise-periodic heterogeneous structure. In our work, the EMM is generalized to the fourth-order-accurate apparent mass-conservation equation in two- and three-dimensional duct flows. The method looks for the solution of the transport equation as the product of a long harmonic wave and a spatially periodic oscillating component; the moments of the given numerical scheme are derived from a chain of the steady-state fourth-order equations at a single cell. This mathematical technique is exemplified for the truncation terms of the two-relaxation-time lattice Boltzmann scheme, using plug and parabolic flow in straight channel and cylindrical capillary with the d2Q9 and d3Q15 discrete velocity sets as simple but illustrative examples. The derived symbolic dependencies can be readily extended for advection by another, Newtonian or non-Newtonian, flow profile in any-shape open-tabular conduits. It is
Kordilla, Jannes; Pan, Wenxiao; Tartakovsky, Alexandre
2014-12-14
We propose a novel smoothed particle hydrodynamics (SPH) discretization of the fully coupled Landau-Lifshitz-Navier-Stokes (LLNS) and stochastic advection-diffusion equations. The accuracy of the SPH solution of the LLNS equations is demonstrated by comparing the scaling of velocity variance and the self-diffusion coefficient with kinetic temperature and particle mass obtained from the SPH simulations and analytical solutions. The spatial covariance of pressure and velocity fluctuations is found to be in a good agreement with theoretical models. To validate the accuracy of the SPH method for coupled LLNS and advection-diffusion equations, we simulate the interface between two miscible fluids. We study formation of the so-called "giant fluctuations" of the front between light and heavy fluids with and without gravity, where the light fluid lies on the top of the heavy fluid. We find that the power spectra of the simulated concentration field are in good agreement with the experiments and analytical solutions. In the absence of gravity, the power spectra decay as the power -4 of the wavenumber-except for small wavenumbers that diverge from this power law behavior due to the effect of finite domain size. Gravity suppresses the fluctuations, resulting in much weaker dependence of the power spectra on the wavenumber. Finally, the model is used to study the effect of thermal fluctuation on the Rayleigh-Taylor instability, an unstable dynamics of the front between a heavy fluid overlaying a light fluid. The front dynamics is shown to agree well with the analytical solutions.
Kordilla, Jannes; Pan, Wenxiao Tartakovsky, Alexandre
2014-12-14
We propose a novel smoothed particle hydrodynamics (SPH) discretization of the fully coupled Landau-Lifshitz-Navier-Stokes (LLNS) and stochastic advection-diffusion equations. The accuracy of the SPH solution of the LLNS equations is demonstrated by comparing the scaling of velocity variance and the self-diffusion coefficient with kinetic temperature and particle mass obtained from the SPH simulations and analytical solutions. The spatial covariance of pressure and velocity fluctuations is found to be in a good agreement with theoretical models. To validate the accuracy of the SPH method for coupled LLNS and advection-diffusion equations, we simulate the interface between two miscible fluids. We study formation of the so-called “giant fluctuations” of the front between light and heavy fluids with and without gravity, where the light fluid lies on the top of the heavy fluid. We find that the power spectra of the simulated concentration field are in good agreement with the experiments and analytical solutions. In the absence of gravity, the power spectra decay as the power −4 of the wavenumber—except for small wavenumbers that diverge from this power law behavior due to the effect of finite domain size. Gravity suppresses the fluctuations, resulting in much weaker dependence of the power spectra on the wavenumber. Finally, the model is used to study the effect of thermal fluctuation on the Rayleigh-Taylor instability, an unstable dynamics of the front between a heavy fluid overlaying a light fluid. The front dynamics is shown to agree well with the analytical solutions.
Kordilla, Jannes; Pan, Wenxiao; Tartakovsky, Alexandre M.
2014-12-14
We propose a novel Smoothed Particle Hydrodynamics (SPH) discretization of the fully-coupled Landau-Lifshitz-Navier-Stokes (LLNS) and advection-diffusion equations. The accuracy of the SPH solution of the LLNS equations is demonstrated by comparing the scaling of velocity variance and self-diffusion coefficient with kinetic temperature and particle mass obtained from the SPH simulations and analytical solutions. The spatial covariance of pressure and velocity fluctuations are found to be in a good agreement with theoretical models. To validate the accuracy of the SPH method for the coupled LLNS and advection-diffusion equations, we simulate the interface between two miscible fluids. We study the formation of the so-called giant fluctuations of the front between light and heavy fluids with and without gravity, where the light fluid lays on the top of the heavy fluid. We find that the power spectra of the simulated concentration field is in good agreement with the experiments and analytical solutions. In the absence of gravity the the power spectra decays as the power -4 of the wave number except for small wave numbers which diverge from this power law behavior due to the effect of finite domain size. Gravity suppresses the fluctuations resulting in the much weaker dependence of the power spectra on the wave number. Finally the model is used to study the effect of thermal fluctuation on the Rayleigh-Taylor instability, an unstable dynamics of the front between a heavy fluid overlying a light fluid. The front dynamics is shown to agree well with the analytical solutions.
Preconditioned time-difference methods for advection-diffusion-reaction equations
Aro, C.; Rodrigue, G.; Wolitzer, D.
1994-12-31
Explicit time differencing methods for solving differential equations are advantageous in that they are easy to implement on a computer and are intrinsically very parallel. The disadvantage of explicit methods is the severe restrictions placed on stepsize due to stability. Stability bounds for explicit time differencing methods on advection-diffusion-reaction problems are generally quite severe and implicit methods are used instead. The linear systems arising from these implicit methods are large and sparse so that iterative methods must be used to solve them. In this paper the authors develop a methodology for increasing the stability bounds of standard explicit finite differencing methods by combining explicit methods, implicit methods, and iterative methods in a novel way to generate new time-difference schemes, called preconditioned time-difference methods.
Analytical solutions of a fractional diffusion-advection equation for solar cosmic-ray transport
Litvinenko, Yuri E.; Effenberger, Frederic
2014-12-01
Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we analytically solve a one-dimensional fractional diffusion-advection equation for the particle density. We derive an exact Fourier transform solution, simplify it in a weak diffusion approximation, and compare the new solution with previously available analytical results and with a semi-numerical solution based on a Fourier series expansion. We apply the results to the problem of describing the transport of energetic particles, accelerated at a traveling heliospheric shock. Our analysis shows that significant errors may result from assuming an infinite initial distance between the shock and the observer. We argue that the shock travel time should be a parameter of a realistic superdiffusive transport model.
Analytical Solutions of a Fractional Diffusion-advection Equation for Solar Cosmic-Ray Transport
NASA Astrophysics Data System (ADS)
Litvinenko, Yuri E.; Effenberger, Frederic
2014-12-01
Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we analytically solve a one-dimensional fractional diffusion-advection equation for the particle density. We derive an exact Fourier transform solution, simplify it in a weak diffusion approximation, and compare the new solution with previously available analytical results and with a semi-numerical solution based on a Fourier series expansion. We apply the results to the problem of describing the transport of energetic particles, accelerated at a traveling heliospheric shock. Our analysis shows that significant errors may result from assuming an infinite initial distance between the shock and the observer. We argue that the shock travel time should be a parameter of a realistic superdiffusive transport model.
Mixing-Driven Equilibrium Reactions in Multidimensional Fractional Advection Dispersion Systems
Bolster, Diogo; Benson, David A; Meerschaert, MM; Baeumer, Boris
2013-01-01
We study instantaneous, mixing-driven, bimolecular equilibrium reactions in a system where transport is governed by a multidimensional space fractional dispersion equation. The superdiffusive, nonlocal nature of the system causes the location and magnitude of reactions that take place to change significantly from a classical Fickian diffusion model. In particular, regions where reaction rates would be zero for the Fickian case become regions where the maximum reaction rate occurs when anomalous dispersion operates. We also study a global metric of mixing in the system, the scalar dissipation rate and compute its asymptotic scaling rates analytically. The scalar dissipation rate scales asymptotically as t−(d+α)/α, where d is the number of spatial dimensions and α is the fractional derivative exponent. PMID:24223468
NASA Astrophysics Data System (ADS)
Costa, C. P.; Vilhena, M. T.; Moreira, D. M.; Tirabassi, T.
We present a three-dimensional solution of the steady-state advection-diffusion equation considering a vertically inhomogeneous planetary boundary layer (PBL). We reach this goal applying the generalized integral transform technique (GITT), a hybrid method that had solved a wide class of direct and inverse problems mainly in the area of heat transfer and fluid mechanics. The transformed problem is solved by the advection-diffusion multilayer model (ADMM) method, a semi-analytical solution based on a discretization of the PBL in sub-layers where the advection-diffusion equation is solved by the Laplace transform technique. Numerical simulations are presented and the performances of the solution are compared against field experiments data.
NASA Astrophysics Data System (ADS)
Bhrawy, A. H.; Baleanu, D.
2013-10-01
An efficient Legendre-Gauss-Lobatto collocation (L-GL-C) method is applied to solve the space-fractional advection diffusion equation with nonhomogeneous initial-boundary conditions. The Legendre-Gauss-Lobatto points are used as collocation nodes for spatial fractional derivatives as well as the Caputo fractional derivative. This approach is reducing the problem to the solution of a system of ordinary differential equations in time which can be solved by using any standard numerical techniques. The proposed numerical solutions when compared with the exact solutions reveal that the obtained solution produces highly accurate results. The results show that the proposed method has high accuracy and is efficient for solving the space-fractional advection diffusion equation.
AN EULERIAN-LAGRANGIAN LOCALIZED ADJOINT METHOD FOR THE ADVECTION-DIFFUSION EQUATION
Many numerical methods use characteristic analysis to accommodate the advective component of transport. Such characteristic methods include Eulerian-Lagrangian methods (ELM), modified method of characteristics (MMOC), and operator splitting methods. A generalization of characteri...
1992-01-01
formulations for the advection- diffusion equation with time-dependent domains 0. Pironneau Universite Paris 6. Analyse Numerique . T 55-65/5. 4 place...solution of the advection- dissipation equation, Correspondence to: Dr. 0. Pironneau, Universit6 Paris 6, Analyse Numerique . T 55-65/5, 4 place...for Partial Differential Equations (Cambridize Univ. Press. Cambridge. 1989). 1121 TE. Tezduvar. .I. Behr and J. Liou. A new strategy for finite
NASA Astrophysics Data System (ADS)
Gharehbaghi, Amin
2016-10-01
In this paper, a numerical solution of one-dimensional time-dependent advection-diffusion equation with variable coefficients in semi-infinite domain is presented by using the differential quadrature method. Both the explicit and implicit approaches are provided. Totally, two solute dispersion problems are employed to simulate various conditions. The inhomogeneity of the domain is supplied by the spatially dependent flow. The problem domains are modeled with Chebyshev-Gauss-Lobatto grid points. In order to examine the accuracy and the efficiency of the suggested explicit and implicit approaches, analytical solutions, which are presented in the literature, are employed. In addition, the results of the above-mentioned method are compared with outcomes of the finite difference method. The results show that both of the explicit and implicit forms of the differential quadrature method are efficient, robust and reliable. But between these two forms, numerical predictions of implicit form are more accurate than explicit form.
NASA Technical Reports Server (NTRS)
Hung, R. J.; Liaw, G. S.
1980-01-01
The effects of multi-disperse distribution of the aerosol population are presented. Single component and multi-component aerosol species on the condensation/nucleation processes which affect the reduction in visibility are described. The aerosol population with a high particle concentration provided more favorable conditions for the formation of a denser fog than the aerosol population with a greater particle size distribution when the value of the mass concentration of the aerosols was kept constant. The results were used as numerical predictions of fog formation. Two dimensional observations in horizontal and vertical coordinates, together with time-dependent measurements were needed as initial values for the following physical parameters: (1)wind profiles; (2) temperature profiles; (3) humidity profiles; (4) mass concentration of aerosol particles; (5) particle size distribution of aerosols; and (6) chemical composition of aerosols. Formation and dissipation of advection fog, thus, can be forecasted numerically by introducing initial values obtained from the observations.
Stochastic differential equations and turbulent dispersion
NASA Technical Reports Server (NTRS)
Durbin, P. A.
1983-01-01
Aspects of the theory of continuous stochastic processes that seem to contribute to an understanding of turbulent dispersion are introduced and the theory and philosophy of modelling turbulent transport is emphasized. Examples of eddy diffusion examined include shear dispersion, the surface layer, and channel flow. Modeling dispersion with finite-time scale is considered including the Langevin model for homogeneous turbulence, dispersion in nonhomogeneous turbulence, and the asymptotic behavior of the Langevin model for nonhomogeneous turbulence.
NASA Astrophysics Data System (ADS)
Ahmad, Nawaz; Wörman, Anders; Sanchez-Vila, Xavier; Bottacin-Busolin, Andrea
2016-12-01
CO2 that is injected into a geological storage reservoir can leak in dissolved form because of brine displacement from the reservoir, which is caused by large-scale groundwater motion. Simulations of the reactive transport of leaking CO2aq along a conducting fracture in a clay-rich caprock are conducted to analyze the effect of various physical and geochemical processes. Whilst several modeling transport studies along rock fractures have considered diffusion as the only transport process in the surrounding rock matrix (diffusive transport), this study analyzes the combined role of advection and dispersion in the rock matrix in addition to diffusion (advection-dominated transport) on the migration of CO2aq along a leakage pathway and its conversion in geochemical reactions. A sensitivity analysis is performed to quantify the effect of fluid velocity and dispersivity. Variations in the porosity and permeability of the medium are found in response to calcite dissolution and precipitation along the leakage pathway. We observe that advection and dispersion in the rock matrix play a significant role in the overall transport process. For the parameters that were used in this study, advection-dominated transport increased the leakage of CO2aq from the reservoir by nearly 305%, caused faster transport and increased the mass conversion of CO2aq in geochemical reactions along the transport pathway by approximately 12.20% compared to diffusive transport.
Power-law spatial dispersion from fractional Liouville equation
Tarasov, Vasily E.
2013-10-15
A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the absolute permittivity on the wave vector. The fractional differential equations for electrostatic potential in the media with power-law spatial dispersion are derived. The particular solutions of these equations for the electric potential of point charge in this media are considered.
Alcaraz, Mar; García-Gil, Alejandro; Vázquez-Suñé, Enric; Velasco, Violeta
2016-02-01
Borehole Heat Exchangers (BHEs) are increasingly being used to exploit shallow geothermal energy. This paper presents a new methodology to provide a response to the need for a regional quantification of the geothermal potential that can be extracted by BHEs and the associated environmental impacts. A set of analytical solutions facilitates accurate calculation of the heat exchange of BHEs with the ground and its environmental impacts. For the first time, advection and dispersion heat transport mechanisms and the temporal evolution from the start of operation of the BHE are taken into account in the regional estimation of shallow geothermal resources. This methodology is integrated in a GIS environment, which facilitates the management of input and output data at a regional scale. An example of the methodology's application is presented for Barcelona, in Spain. As a result of the application, it is possible to show the strengths and improvements of this methodology in the development of potential maps of low temperature geothermal energy as well as maps of environmental impacts. The minimum and maximum energy potential values for the study site are 50 and 1800 W/m(2) for a drilled depth of 100 m, proportionally to Darcy velocity. Regarding to thermal impacts, the higher the groundwater velocity and the energy potential, the higher the size of the thermal plume after 6 months of exploitation, whose length ranges from 10 to 27 m long. A sensitivity analysis was carried out in the calculation of heat exchange rate and its impacts for different scenarios and for a wide range of Darcy velocities. The results of this analysis lead to the conclusion that the consideration of dispersion effects and temporal evolution of the exploitation prevent significant differences up to a factor 2.5 in the heat exchange rate accuracy and up to several orders of magnitude in the impacts generated.
A dynamical equation for the distribution of a scalar advected by turbulence
NASA Astrophysics Data System (ADS)
Venaille, Antoine; Sommeria, Joel
2007-02-01
A phenomenological model for the dissipation of scalar fluctuations due to the straining by the fluid motion is proposed in this Brief Communication. An explicit equation is obtained for the time evolution of the probability distribution function of a coarse-grained scalar concentration. The model relies on a self-convolution process. We first present this model in the Batchelor regime and then extend empirically our result to the turbulent case. This approach is finally compared with other models.
Ho, David T; Schlosser, Peter; Caplow, Theodore
2002-08-01
Physical processes such as advection, dispersion, and air-water gas exchange play important roles in determining the movement and change in concentration of contaminants discharged into rivers. In the following, we report results from a large-scale SF6 tracer release experiment conducted in the tidal Hudson Riverto examine longitudinal dispersion and net advection. SF6 was injected into the Hudson River near Newburgh, NY, and surveyed for 13 days using a new, fully automated, high-resolution SF6 sampling and analysis system. Net down river advection of the water body originally tagged with SF6 was slow, averaging mean displacement rates of about 0.5 +/- 0.2 km d(-1). In contrast, spreading of the tracer was driven by tidal movement, causing rapid mixing of the water up and down river. By examining the change in the second moment of the tracer distribution with time, we determined the mean longitudinal dispersion coefficient to be 70.1 +/- 4.3 m2 s(-1). Temporal evolution of the SF6 inventory indicates an average gas transfer velocity over the period of the experiment of 6.5 +/- 0.5 cm h(-1) (1.56 +/- 0.12 m d(-1)). Vertical profiles show that mixing into the bottom layers of the river, in places reaching more than 53 m, seemed to be rapid.
Erratum: A Comparison of Closures for Stochastic Advection-Diffusion Equations
Jarman, Kenneth D.; Tartakovsky, Alexandre M.
2015-01-01
This note corrects an error in the authors' article [SIAM/ASA J. Uncertain. Quantif., 1 (2013), pp. 319 347] in which the cited work [Neuman, Water Resour. Res., 29(3) (1993), pp. 633 645] was incorrectly represented and attributed. Concentration covariance equations presented in our article as new were in fact previously derived in the latter work. In the original abstract, the phrase " . . .we propose a closed-form approximation to two-point covariance as a measure of uncertainty. . ." should be replaced by the phrase " . . .we study a closed-form approximation to two-point covariance, previously derived in [Neuman 1993], as a measure of uncertainty." The primary results in our article--the analytical and numerical comparison of existing closure methods for specific example problems are not changed by this correction.
Wang, Wei; Shu, Chi-Wang; Yee, H.C.; Sjögreen, Björn
2012-01-01
A new high order finite-difference method utilizing the idea of Harten ENO subcell resolution method is proposed for chemical reactive flows and combustion. In reaction problems, when the reaction time scale is very small, e.g., orders of magnitude smaller than the fluid dynamics time scales, the governing equations will become very stiff. Wrong propagation speed of discontinuity may occur due to the underresolved numerical solution in both space and time. The present proposed method is a modified fractional step method which solves the convection step and reaction step separately. In the convection step, any high order shock-capturing method can be used. In the reaction step, an ODE solver is applied but with the computed flow variables in the shock region modified by the Harten subcell resolution idea. For numerical experiments, a fifth-order finite-difference WENO scheme and its anti-diffusion WENO variant are considered. A wide range of 1D and 2D scalar and Euler system test cases are investigated. Studies indicate that for the considered test cases, the new method maintains high order accuracy in space for smooth flows, and for stiff source terms with discontinuities, it can capture the correct propagation speed of discontinuities in very coarse meshes with reasonable CFL numbers.
Drift-free kinetic equations for turbulent dispersion.
Bragg, A; Swailes, D C; Skartlien, R
2012-11-01
The dispersion of passive scalars and inertial particles in a turbulent flow can be described in terms of probability density functions (PDFs) defining the statistical distribution of relevant scalar or particle variables. The construction of transport equations governing the evolution of such PDFs has been the subject of numerous studies, and various authors have presented formulations for this type of equation, usually referred to as a kinetic equation. In the literature it is often stated, and widely assumed, that these PDF kinetic equation formulations are equivalent. In this paper it is shown that this is not the case, and the significance of differences among the various forms is considered. In particular, consideration is given to which form of equation is most appropriate for modeling dispersion in inhomogeneous turbulence and most consistent with the underlying particle equation of motion. In this regard the PDF equations for inertial particles are considered in the limit of zero particle Stokes number and assessed against the fully mixed (zero-drift) condition for fluid points. A long-standing question regarding the validity of kinetic equations in the fluid-point limit is answered; it is demonstrated formally that one version of the kinetic equation (derived using the Furutsu-Novikov method) provides a model that satisfies this zero-drift condition exactly in both homogeneous and inhomogeneous systems. In contrast, other forms of the kinetic equation do not satisfy this limit or apply only in a limited regime.
Guyonvarch, Estelle; Ramin, Elham; Kulahci, Murat; Plósz, Benedek Gy
2015-10-15
The present study aims at using statistically designed computational fluid dynamics (CFD) simulations as numerical experiments for the identification of one-dimensional (1-D) advection-dispersion models - computationally light tools, used e.g., as sub-models in systems analysis. The objective is to develop a new 1-D framework, referred to as interpreted CFD (iCFD) models, in which statistical meta-models are used to calculate the pseudo-dispersion coefficient (D) as a function of design and flow boundary conditions. The method - presented in a straightforward and transparent way - is illustrated using the example of a circular secondary settling tank (SST). First, the significant design and flow factors are screened out by applying the statistical method of two-level fractional factorial design of experiments. Second, based on the number of significant factors identified through the factor screening study and system understanding, 50 different sets of design and flow conditions are selected using Latin Hypercube Sampling (LHS). The boundary condition sets are imposed on a 2-D axi-symmetrical CFD simulation model of the SST. In the framework, to degenerate the 2-D model structure, CFD model outputs are approximated by the 1-D model through the calibration of three different model structures for D. Correlation equations for the D parameter then are identified as a function of the selected design and flow boundary conditions (meta-models), and their accuracy is evaluated against D values estimated in each numerical experiment. The evaluation and validation of the iCFD model structure is carried out using scenario simulation results obtained with parameters sampled from the corners of the LHS experimental region. For the studied SST, additional iCFD model development was carried out in terms of (i) assessing different density current sub-models; (ii) implementation of a combined flocculation, hindered, transient and compression settling velocity function; and (iii
Merritt, M.L.
1993-01-01
The simulation of the transport of injected freshwater in a thin brackish aquifer, overlain and underlain by confining layers containing more saline water, is shown to be influenced by the choice of the finite-difference approximation method, the algorithm for representing vertical advective and dispersive fluxes, and the values assigned to parametric coefficients that specify the degree of vertical dispersion and molecular diffusion that occurs. Computed potable water recovery efficiencies will differ depending upon the choice of algorithm and approximation method, as will dispersion coefficients estimated based on the calibration of simulations to match measured data. A comparison of centered and backward finite-difference approximation methods shows that substantially different transition zones between injected and native waters are depicted by the different methods, and computed recovery efficiencies vary greatly. Standard and experimental algorithms and a variety of values for molecular diffusivity, transverse dispersivity, and vertical scaling factor were compared in simulations of freshwater storage in a thin brackish aquifer. Computed recovery efficiencies vary considerably, and appreciable differences are observed in the distribution of injected freshwater in the various cases tested. The results demonstrate both a qualitatively different description of transport using the experimental algorithms and the interrelated influences of molecular diffusion and transverse dispersion on simulated recovery efficiency. When simulating natural aquifer flow in cross-section, flushing of the aquifer occurred for all tested coefficient choices using both standard and experimental algorithms. ?? 1993.
Fisher equation for anisotropic diffusion: simulating South American human dispersals.
Martino, Luis A; Osella, Ana; Dorso, Claudio; Lanata, José L
2007-09-01
The Fisher equation is commonly used to model population dynamics. This equation allows describing reaction-diffusion processes, considering both population growth and diffusion mechanism. Some results have been reported about modeling human dispersion, always assuming isotropic diffusion. Nevertheless, it is well-known that dispersion depends not only on the characteristics of the habitats where individuals are but also on the properties of the places where they intend to move, then isotropic approaches cannot adequately reproduce the evolution of the wave of advance of populations. Solutions to a Fisher equation are difficult to obtain for complex geometries, moreover, when anisotropy has to be considered and so few studies have been conducted in this direction. With this scope in mind, we present in this paper a solution for a Fisher equation, introducing anisotropy. We apply a finite difference method using the Crank-Nicholson approximation and analyze the results as a function of the characteristic parameters. Finally, this methodology is applied to model South American human dispersal.
Dispersion relation equation preserving FDTD method for nonlinear cubic Schrödinger equation
NASA Astrophysics Data System (ADS)
Sheu, Tony W. H.; Le Lin
2015-10-01
In this study we aim to solve the cubic nonlinear Schrödinger (CNLS) equation by the method of fractional steps. Over a time step from tn to tn+1, the linear part of the Schrödinger equation is solved firstly through four time integration steps. In this part of the simulation, the explicit symplectic scheme of fourth order accuracy is adopted to approximate the time derivative term. The second-order spatial derivative term in the linear Schrödinger equation is approximated by centered scheme. The resulting symplectic and space centered difference scheme renders an optimized numerical dispersion relation equation. In the second part of the simulation, the solution of the nonlinear equation is computed exactly thanks to the embedded invariant nature within each time increment. The proposed semi-discretized difference scheme underlying the modified equation analysis of second kind and the method of dispersion error minimization has been assessed in terms of the spatial modified wavenumber or the temporal angular frequency resolution. Several problems have been solved to show that application of this new finite difference scheme for the calculation of one- and two-dimensional Schrödinger equations can deemed conserve Hamiltonian quantities and preserve dispersion relation equation (DRE).
Langevin equation model of dispersion in the convective boundary layer
Nasstrom, J S
1998-08-01
This dissertation presents the development and evaluation of a Lagrangian stochastic model of vertical dispersion of trace material in the convective boundary layer (CBL). This model is based on a Langevin equation of motion for a fluid particle, and assumes the fluid vertical velocity probability distribution is skewed and spatially homogeneous. This approach can account for the effect of large-scale, long-lived turbulent structures and skewed vertical velocity distributions found in the CBL. The form of the Langevin equation used has a linear (in velocity) deterministic acceleration and a skewed randomacceleration. For the case of homogeneous fluid velocity statistics, this ""linear-skewed" Langevin equation can be integrated explicitly, resulting in a relatively efficient numerical simulation method. It is shown that this approach is more efficient than an alternative using a "nonlinear-Gaussian" Langevin equation (with a nonlinear deterministic acceleration and a Gaussian random acceleration) assuming homogeneous turbulence, and much more efficient than alternative approaches using Langevin equation models assuming inhomogeneous turbulence. "Reflection" boundary conditions for selecting a new velocity for a particle that encounters a boundary at the top or bottom of the CBL were investigated. These include one method using the standard assumption that the magnitudes of the particle incident and reflected velocities are positively correlated, and two alternatives in which the magnitudes of these velocities are negatively correlated and uncorrelated. The constraint that spatial and velocity distributions of a well-mixed tracer must be the same as those of the fluid, was used to develop the Langevin equation models and the reflection boundary conditions. The two Langevin equation models and three reflection methods were successfully tested using cases for which exact, analytic statistical properties of particle velocity and position are known, including well
Sharp, R.W. Jr.; Barton, R.T.
1981-01-21
A continuous rezoning procedure has been implemented in the computational cycle of a version of the HEMP two-dimensional, Lagrange, fluid dynamics code. The rezoning problem is divided into two steps. The first step requires the solving of ordinary Lagrange equations of motion; the second step consists of adding equipotential grid relaxation along with an advective remapping scheme.
NASA Astrophysics Data System (ADS)
Vukadinovic, J.; Dedits, E.; Poje, A. C.; Schäfer, T.
2015-08-01
We consider the two-dimensional advection-diffusion equation (ADE) on a bounded domain subject to Dirichlet or von Neumann boundary conditions involving a Liouville integrable Hamiltonian. Transformation to action-angle coordinates permits averaging in time and angle, resulting in an equation that allows for separation of variables. The Fourier transform in the angle coordinate transforms the equation into an effective diffusive equation and a countable family of non-self-adjoint Schrödinger equations. For the corresponding Liouville-Sturm problem, we apply complex-plane WKB methods to study the spectrum in the semi-classical limit for vanishing diffusivity. The spectral limit graph is found to consist of analytic curves (branches) related to Stokes graphs forming a tree-structure. Eigenvalues in the neighborhood of branches emanating from the imaginary axis are subject to various sublinear power laws with respect to diffusivity, leading to convection-enhanced rates of dissipation of the corresponding modes. The solution of the ADE converges in the limit of vanishing diffusivity to the solution of the effective diffusion equation on convective time scales that are sublinear with respect to the diffusive time scales.
Wagner, Brian J.; Gorelick, Steven M.
1986-01-01
A simulation nonlinear multiple-regression methodology for estimating parameters that characterize the transport of contaminants is developed and demonstrated. Finite difference containment transport simulation is combined with a nonlinear weighted least squares multiple-regression procedure. The technique provides optimal parameter estimates and gives statistics for assessing the reliability of these estimates under certain general assumptions about the distributions of the random measurement errors. Monte Carlo analysis is used to estimate parameter reliability for a hypothetical homogeneous soil column for which concentration data contain large random measurement errors. The value of data collected spatially versus data collected temporally was investigated for estimation of velocity, dispersion coefficient, effective porosity, first-order decay rate, and zero-order production. The use of spatial data gave estimates that were 2-3 times more reliable than estimates based on temporal data for all parameters except velocity. (Estimated author abstract) Refs.
Long time behavior of some nonlinear dispersive equations
NASA Astrophysics Data System (ADS)
Deng, Yu
This thesis is divided into two parts. The first part consists of Chapters 2 and 3, in which we study the random data theory for the Benjamin-Ono equation on the periodic domain. In Chapter 2 we shall prove the invariance of the Gibbs measure associated to the Hamiltonian E1 of the equation, which was constructed in [49]. Despite the fact that the support of the Gibbs measure contains very rough functions that are not even in L2, we have successfully established the global dynamics by combining probabilistic arguments, Xs,b type estimates and the hidden structure of the equation. In Chapter 3, which is joint work with N. Tzvetkov and N. Visciglia, we extend this invariance result to the weighted Gaussian measures associated with the higher order conservation laws E2 and E3, thus completing the collection of invariant measures (except for the white noise), given the result of [51]. The second part concerns the global behavior of solutions to quasilinear dispersive systems in Rd with suitably small data. In Chapter 4 we shall prove global existence and scattering for small data solutions to systems of quasilinear Klein-Gordon equations with arbitrary speed and mass in 3 D, which extends the results in [20] and [32]. Moreover, the methods introduced here are quite general, and can be applied in a number of different situations. In Chapter 5, we briefly discuss how these methods, together with other techniques, are used in recent joint work with A. Ionescu and B. Pausader to study the 2D Euler-Maxwell system.
Harmonic admittance and dispersion equations--the theorem.
Plessky, Viktor P; Biryukov, Sergey V; Koskela, Julius
2002-04-01
The harmonic admittance is known as a powerful tool for analyzing the excitation and propagation of surface acoustic waves (SAWs) in periodic electrode arrays. In particular, the dispersion relationships for open- and short-circuited systems are indicated, respectively, by the zeros and poles of the harmonic admittance. Here, we show that a strict reverse relationship also exists: the harmonic admittance of a periodic system of electrodes may always be expressed as the ratio of two determinants, which have been specifically constructed to describe the eigen-modes of the open- and short-circuited systems. There is no need to solve these equations to find the admittance. The existence of a connection between the excitation and propagation problems was recognized within the coupling-of-modes theory by Chen and Haus and was recently used to model surface transverse waves by Koskela et al., but a rigorous mathematical proof was only found later by Biryukov. Here, we reproduce this theorem in detail, give some examples of calculations based on this theorem, and compare the results with measured admittance curves.
Whitham modulation equations, coalescing characteristics, and dispersive Boussinesq dynamics
NASA Astrophysics Data System (ADS)
Ratliff, Daniel J.; Bridges, Thomas J.
2016-10-01
Whitham modulation theory with degeneracy in wave action is considered. The case where all components of the wave action conservation law, when evaluated on a family of periodic travelling waves, have vanishing derivative with respect to wavenumber is considered. It is shown that Whitham modulation equations morph, on a slower time scale, into the two way Boussinesq equation. Both the 1 + 1 and 2 + 1 cases are considered. The resulting Boussinesq equation arises in a universal form, in that the coefficients are determined from the abstract properties of the Lagrangian and do not depend on particular equations. One curious by-product of the analysis is that the theory can be used to confirm that the two-way Boussinesq equation is not a valid model in shallow water hydrodynamics. Modulation of nonlinear travelling waves of the complex Klein-Gordon equation is used to illustrate the theory.
On a hierarchy of nonlinearly dispersive generalized Korteweg - de Vries evolution equations
Christov, Ivan C.
2015-08-20
We propose a hierarchy of nonlinearly dispersive generalized Korteweg–de Vries (KdV) evolution equations based on a modification of the Lagrangian density whose induced action functional the KdV equation extremizes. Two recent nonlinear evolution equations describing wave propagation in certain generalized continua with an inherent material length scale are members of the proposed hierarchy. Like KdV, the equations from the proposed hierarchy possess Hamiltonian structure. Unlike KdV, the solutions to these equations can be compact (i.e., they vanish outside of some open interval) and, in addition, peaked. Implicit solutions for these peaked, compact traveling waves (“peakompactons”) are presented.
The zero dispersion limit for the Korteweg-deVries KdV equation
Lax, Peter D.; Levermore, C. David
1979-01-01
We use the inverse scattering method to determine the weak limit of solutions of the Korteweg-deVries equation as dispersion tends to zero. The limit, valid for all time, is characterized in terms of a quadratic programming problem which can be solved with the aid of function theoretic methods. For large t, the solutions satisfy Whitham's averaged equations at some times and the equations found by Flaschka et al. at other times. PMID:16592690
Toda, Kiyoshi; Furuse, Hisamoto
2006-12-01
A viscosity equation for concentrated solutions or suspensions is derived as an extension of Einstein's hydrodynamic viscosity theory for dilute dispersions of spherical particles. The derivation of the equation is based on the calculation of dissipation of mechanical energy into heat in the dispersion, subtracting the energy dissipation in the portion of solutes or particles. The viscosity equation derived thus was well fitted to the viscosity-concentration relationship of the concentrated aqueous solutions of glucose and sucrose. For the suspensions of bakers' yeast, the concentration dependency of viscosity was expressed well with some modification for the flow pattern around suspended particles. It is suggested that these viscosity equations can be widely applied to both diluted and concentrated dispersions of various solutes and particles.
NASA Astrophysics Data System (ADS)
Mudunuru, M. K.; Nakshatrala, K. B.
2016-01-01
We present a robust computational framework for advective-diffusive-reactive systems that satisfies maximum principles, the non-negative constraint, and element-wise species balance property. The proposed methodology is valid on general computational grids, can handle heterogeneous anisotropic media, and provides accurate numerical solutions even for very high Péclet numbers. The significant contribution of this paper is to incorporate advection (which makes the spatial part of the differential operator non-self-adjoint) into the non-negative computational framework, and overcome numerical challenges associated with advection. We employ low-order mixed finite element formulations based on least-squares formalism, and enforce explicit constraints on the discrete problem to meet the desired properties. The resulting constrained discrete problem belongs to convex quadratic programming for which a unique solution exists. Maximum principles and the non-negative constraint give rise to bound constraints while element-wise species balance gives rise to equality constraints. The resulting convex quadratic programming problems are solved using an interior-point algorithm. Several numerical results pertaining to advection-dominated problems are presented to illustrate the robustness, convergence, and the overall performance of the proposed computational framework.
A new dispersion-relation preserving method for integrating the classical Boussinesq equation
NASA Astrophysics Data System (ADS)
Jang, T. S.
2017-02-01
In this paper, a dispersion-relation preserving method is proposed for nonlinear dispersive waves, starting from the oldest weakly nonlinear dispersive wave mathematical model in shallow water waves, i.e., the classical Boussinesq equation. It is a semi-analytic procedure, however, which preserves, as a distinctive feature, the dispersion-relation imbedded in the model equation without adding (unwelcome) numerical effects, i.e., the proposed method has the same dispersion-relation as the original classical Boussinesq equation. This remarkable (dispersion-relation) preserving property is proved mathematically for small wave motion in present study. The property is also numerically examined by observing both the local wave number and the local frequency of a slowly varying water-wave group. The dispersion-relation preserving method proposed here is powerful as well for observing nonlinear wave phenomena such as solitary waves and their collision. In fact, the main features of nonlinear wave characteristics are clearly seen through not only a single propagating solitary wave but counter-propagating (head-on) solitary wave collisions. They are compared with known (exact) nonlinear solutions, the results of which represent a major improvement over existing solution formulations in the literature.
Conservative modified Serre-Green-Naghdi equations with improved dispersion characteristics
NASA Astrophysics Data System (ADS)
Clamond, Didier; Dutykh, Denys; Mitsotakis, Dimitrios
2017-04-01
For surface gravity waves propagating in shallow water, we propose a variant of the fully nonlinear Serre-Green-Naghdi equations involving a free parameter that can be chosen to improve the dispersion properties. The novelty here consists in the fact that the new model conserves the energy, contrary to other modified Serre's equations found in the literature. Numerical comparisons with the Euler equations show that the new model is substantially more accurate than the classical Serre equations, especially for long time simulations and for large amplitudes.
Drum dispersion equation for Littrow-type prism spectrometers.
Sidran, M; Stalzer, H J; Hauptman, M H
1966-07-01
A simple analytic procedure has been developed for calibrating the wavelength drum of a Littrow-type prism spectrometer. Only three measured drum readings are required to specify the drum calibration over a broad wavelength range (uv to ir) with an accuracy of the order of the instrumental accuracy. This procedure can be applied to different prism materials for which measurements of refractive index have been performed. It is based on an approximate expression, derived from geometrical optics, relating the drum reading D(lambda) to the calculated refractive index n(lambda): D= A - B(a(2) - n(2))((1/2)). The index n(lambda) is calculated from the appropriate parametric equation. The temperature for the n(lambda) values need not be exactly that of the prism temperature during measurements. This expression was investigated for wavelengths in the range 0.3 micro to 2.25 micro using a sodium chloride prism. Computed drum positions D agreed with measured drum positions to within experimental error. Unknown wavelengths were computed from their measured drum positions to within the accuracy of the measurements.
Comparison of equations for the EDTD solution in anisotropic and dispersive media
Burke, G.J.; Steich, D.J.
1997-01-01
The recursive-convolution solution for anisotropic and dispersive media was seen to yield accurate results for reflection from ferrite slabs up to a frequency limit set by the sampling interval. Depending on the application, the results shown might be considered usable up to about 300 GHz, which corresponds to about 13 cells per wavelength. Results at still higher frequencies might be usable when a time delay or frequency shift due to dispersion can be tolerated. Several different forms of the update equations were considered which can result from different approximations in reducing the continuous equations to discrete form.
Modeling Solution of Nonlinear Dispersive Partial Differential Equations using the Marker Method
Jerome L.V. Lewandowski
2005-01-25
A new method for the solution of nonlinear dispersive partial differential equations is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details.
Dispersive shock waves in the Kadomtsev-Petviashvili and two dimensional Benjamin-Ono equations
NASA Astrophysics Data System (ADS)
Ablowitz, Mark J.; Demirci, Ali; Ma, Yi-Ping
2016-10-01
Dispersive shock waves (DSWs) in the Kadomtsev-Petviashvili (KP) equation and two dimensional Benjamin-Ono (2DBO) equation are considered using step like initial data along a parabolic front. Employing a parabolic similarity reduction exactly reduces the study of such DSWs in two space one time (2 + 1) dimensions to finding DSW solutions of (1 + 1) dimensional equations. With this ansatz, the KP and 2DBO equations can be exactly reduced to the cylindrical Korteweg-de Vries (cKdV) and cylindrical Benjamin-Ono (cBO) equations, respectively. Whitham modulation equations which describe DSW evolution in the cKdV and cBO equations are derived and Riemann type variables are introduced. DSWs obtained from the numerical solutions of the corresponding Whitham systems and direct numerical simulations of the cKdV and cBO equations are compared with very good agreement obtained. In turn, DSWs obtained from direct numerical simulations of the KP and 2DBO equations are compared with the cKdV and cBO equations, again with good agreement. It is concluded that the (2 + 1) DSW behavior along self similar parabolic fronts can be effectively described by the DSW solutions of the reduced (1 + 1) dimensional equations.
Monger, Gregg R.; Duncan, Candice Morrison; Brusseau, Mark L.
2015-01-01
A gas-phase tracer test (GTT) was conducted at a landfill in Tucson, AZ, to help elucidate the impact of landfill gas generation on the transport and fate of chlorinated aliphatic volatile organic contaminants (VOCs). Sulfur hexafluoride (SF6) was used as the non-reactive gas tracer. Gas samples were collected from a multiport monitoring well located 15.2 m from the injection well, and analyzed for SF6, CH4, CO2, and VOCs. The travel times determined for SF6 from the tracer test are approximately two to ten times smaller than estimated travel times that incorporate transport by only gas-phase diffusion. In addition, significant concentrations of CH4 and CO2 were measured, indicating production of landfill gas. Based on these results, it is hypothesized that the enhanced rates of transport observed for SF6 are caused by advective transport associated with landfill gas generation. The rates of transport varied vertically, which is attributed to multiple factors including spatial variability of water content, refuse mass, refuse permeability, and gas generation. PMID:26380532
Monger, Gregg R; Duncan, Candice Morrison; Brusseau, Mark L
2014-12-01
A gas-phase tracer test (GTT) was conducted at a landfill in Tucson, AZ, to help elucidate the impact of landfill gas generation on the transport and fate of chlorinated aliphatic volatile organic contaminants (VOCs). Sulfur hexafluoride (SF6) was used as the non-reactive gas tracer. Gas samples were collected from a multiport monitoring well located 15.2 m from the injection well, and analyzed for SF6, CH4, CO2, and VOCs. The travel times determined for SF6 from the tracer test are approximately two to ten times smaller than estimated travel times that incorporate transport by only gas-phase diffusion. In addition, significant concentrations of CH4 and CO2 were measured, indicating production of landfill gas. Based on these results, it is hypothesized that the enhanced rates of transport observed for SF6 are caused by advective transport associated with landfill gas generation. The rates of transport varied vertically, which is attributed to multiple factors including spatial variability of water content, refuse mass, refuse permeability, and gas generation.
Eulerian-Lagrangian solution of the convection-dispersion equation in natural co-ordinates.
Cheng, R.T.; Casulli, V.; Milford, S.N.
1984-01-01
The vast majority of numerical investigations of transport phenomena use an Eulerian formulation for the convenience that the computational grids are fixed in space. An Eulerian-Lagrangian method (ELM) of solution for the convection-dispersion equation is discussed and analyzed. The ELM uses the Lagrangian concept in an Eulerian computational grid system.-from Authors
Dispersion equation and eigenvalues for quantum wells using spectral parameter power series
Castillo-Perez, Raul; Oviedo-Galdeano, Hector; Rabinovich, Vladimir S.
2011-04-15
We derive a dispersion equation for determining eigenvalues of inhomogeneous quantum wells in terms of spectral parameter power series and apply it for the numerical treatment of eigenvalue problems. The method is algorithmically simple and can be easily implemented using available routines of such environments for scientific computing as MATLAB.
Dispersion Interactions between Rare Gas Atoms: Testing the London Equation Using ab Initio Methods
ERIC Educational Resources Information Center
Halpern, Arthur M.
2011-01-01
A computational chemistry experiment is described in which students can use advanced ab initio quantum mechanical methods to test the ability of the London equation to account quantitatively for the attractive (dispersion) interactions between rare gas atoms. Using readily available electronic structure applications, students can calculate the…
Symmetries of the TDNLS equations for weakly nonlinear dispersive MHD waves
NASA Technical Reports Server (NTRS)
Webb, G. M.; Brio, M.; Zank, G. P.
1995-01-01
In this paper we consider the symmetries and conservation laws for the TDNLS equations derived by Hada (1993) and Brio, Hunter and Johnson, to describe the propagation of weakly nonlinear dispersive MHD waves in beta approximately 1 plasmas. The equations describe the interaction of the Alfven and magnetoacoustic modes near the triple umbilic, where the fast magnetosonic, slow magnetosonic and Alfven speeds coincide and a(g)(exp 2) = V(A)(exp 2) where a(g) is the gas sound speed and V(A) is the Alfven speed. We discuss Lagrangian and Hamiltonian formulations, and similarity solutions for the equations.
Wave-packet formation at the zero-dispersion point in the Gardner-Ostrovsky equation
NASA Astrophysics Data System (ADS)
Whitfield, A. J.; Johnson, E. R.
2015-05-01
The long-time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual emergence of a coherent, steadily propagating, nonlinear wave packet. There is currently no entirely satisfactory explanation as to why these wave packets form. Here the initial value problem is considered within the context of the Gardner-Ostrovsky, or rotation-modified extended Korteweg-de Vries, equation. The linear Gardner-Ostrovsky equation has maximum group velocity at a critical wave number, often called the zero-dispersion point. It is found here that a nonlinear splitting of the wave-number spectrum at the zero-dispersion point, where energy is shifted into the modulationally unstable regime of the Gardner-Ostrovsky equation, is responsible for the wave-packet formation. Numerical comparisons of the decay of a solitary wave in the Gardner-Ostrovsky equation and a derived nonlinear Schrödinger equation at the zero-dispersion point are used to confirm the spectral splitting.
Wave-packet formation at the zero-dispersion point in the Gardner-Ostrovsky equation.
Whitfield, A J; Johnson, E R
2015-05-01
The long-time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual emergence of a coherent, steadily propagating, nonlinear wave packet. There is currently no entirely satisfactory explanation as to why these wave packets form. Here the initial value problem is considered within the context of the Gardner-Ostrovsky, or rotation-modified extended Korteweg-de Vries, equation. The linear Gardner-Ostrovsky equation has maximum group velocity at a critical wave number, often called the zero-dispersion point. It is found here that a nonlinear splitting of the wave-number spectrum at the zero-dispersion point, where energy is shifted into the modulationally unstable regime of the Gardner-Ostrovsky equation, is responsible for the wave-packet formation. Numerical comparisons of the decay of a solitary wave in the Gardner-Ostrovsky equation and a derived nonlinear Schrödinger equation at the zero-dispersion point are used to confirm the spectral splitting.
On the Klein-Gordon equation using the dispersion relation of Doubly Special Relativity
NASA Astrophysics Data System (ADS)
Felipe, Yese J.
2017-01-01
The theory of Doubly Special Relativity or Deformed Special Relativity (DSR), proposes that there is a maximum energy scale and a minimum length scale that is invariant for all observers. These maximum energy and minimum length correspond to the Planck energy and the Planck length, respectively. As a consequence, the dispersion relation is modified to be E2 =p2c2 +m2c4 + λE3 + ... Previous work has been done to express Quantum Mechanics using the dispersion relation of DSR. Solutions of the free particle, the harmonic oscillator, and the Hydrogen atom have been obtained from the DSR Schrodinger equation. We explore how the DSR Klein-Gordon equation can be consistently approximated in the non-relativistic limit in order to derive the DSR Schrodinger equation.
Pathways for Advective Transport
2001-01-19
the approach is given and an application to the Gulf of Mexico is described where the analysis precisely identifies the boundaries of coherent vortical structures as well as pathways for advective transport.
NASA Astrophysics Data System (ADS)
Annamalai, Subramanian; Balachandar, S.; Sridharan, P.; Jackson, T. L.
2017-02-01
An analytical expression describing the unsteady pressure evolution of the dispersed phase driven by variations in the carrier phase is presented. In this article, the term "dispersed phase" represents rigid particles, droplets, or bubbles. Letting both the dispersed and continuous phases be inhomogeneous, unsteady, and compressible, the developed pressure equation describes the particle response and its eventual equilibration with that of the carrier fluid. The study involves impingement of a plane traveling wave of a given frequency and subsequent volume-averaged particle pressure calculation due to a single wave. The ambient or continuous fluid's pressure and density-weighted normal velocity are identified as the source terms governing the particle pressure. Analogous to the generalized Faxén theorem, which is applicable to the particle equation of motion, the pressure expression is also written in terms of the surface average of time-varying incoming flow properties. The surface average allows the current formulation to be generalized for any complex incident flow, including situations where the particle size is comparable to that of the incoming flow. Further, the particle pressure is also found to depend on the dispersed-to-continuous fluid density ratio and speed of sound ratio in addition to dynamic viscosities of both fluids. The model is applied to predict the unsteady pressure variation inside an aluminum particle subjected to normal shock waves. The results are compared against numerical simulations and found to be in good agreement. Furthermore, it is shown that, although the analysis is conducted in the limit of negligible flow Reynolds and Mach numbers, it can be used to compute the density and volume of the dispersed phase to reasonable accuracy. Finally, analogous to the pressure evolution expression, an equation describing the time-dependent particle radius is deduced and is shown to reduce to the Rayleigh-Plesset equation in the linear limit.
NASA Astrophysics Data System (ADS)
Kim, Bong-Sik
Three dimensional (3D) Navier-Stokes-alpha equations are considered for uniformly rotating geophysical fluid flows (large Coriolis parameter f = 2O). The Navier-Stokes-alpha equations are a nonlinear dispersive regularization of usual Navier-Stokes equations obtained by Lagrangian averaging. The focus is on the existence and global regularity of solutions of the 3D rotating Navier-Stokes-alpha equations and the uniform convergence of these solutions to those of the original 3D rotating Navier-Stokes equations for large Coriolis parameters f as alpha → 0. Methods are based on fast singular oscillating limits and results are obtained for periodic boundary conditions for all domain aspect ratios, including the case of three wave resonances which yields nonlinear "2½-dimensional" limit resonant equations for f → 0. The existence and global regularity of solutions of limit resonant equations is established, uniformly in alpha. Bootstrapping from global regularity of the limit equations, the existence of a regular solution of the full 3D rotating Navier-Stokes-alpha equations for large f for an infinite time is established. Then, the uniform convergence of a regular solution of the 3D rotating Navier-Stokes-alpha equations (alpha ≠ 0) to the one of the original 3D rotating NavierStokes equations (alpha = 0) for f large but fixed as alpha → 0 follows; this implies "shadowing" of trajectories of the limit dynamical systems by those of the perturbed alpha-dynamical systems. All the estimates are uniform in alpha, in contrast with previous estimates in the literature which blow up as alpha → 0. Finally, the existence of global attractors as well as exponential attractors is established for large f and the estimates are uniform in alpha.
NASA Astrophysics Data System (ADS)
Lee, C. T.; Lee, C. C.
2015-04-01
This paper introduces a systematic approach to investigate a higher order nonlinear dispersive wave equation for modeling different wave modes. We present both the conventional KdV-type soliton and anomaly type solitons for the equation. We also show the conservation laws and Hamiltonian structures for the equation. Our results suggest that the underlying equation has more interacting soliton phenomena than one would have known for the classical KdV and Boussinesq equation.
1982-07-01
MODELSLDS#-1 7. AUTHOR(*)11.CNRCOGRNNUB(* H.T. Banks and P. Kareiva AFOSR-81-0198 93 PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT...parameters that predicted several consecutive recapture distributions. Because insects are ectotherms and are very sensitive to weather, their moveet...regression equations describing the density distribution of dispersing organisms , Nature, vol. 286, 53-55, 1980. tb 4J / • t
Dispersion reducing methods for edge discretizations of the electric vector wave equation
NASA Astrophysics Data System (ADS)
Bokil, V. A.; Gibson, N. L.; Gyrya, V.; McGregor, D. A.
2015-04-01
We present a novel strategy for minimizing the numerical dispersion error in edge discretizations of the time-domain electric vector wave equation on square meshes based on the mimetic finite difference (MFD) method. We compare this strategy, called M-adaptation, to two other discretizations, also based on square meshes. One is the lowest order Nédélec edge element discretization. The other is a modified quadrature approach (GY-adaptation) proposed by Guddati and Yue for the acoustic wave equation in two dimensions. All three discrete methods use the same edge-based degrees of freedom, while the temporal discretization is performed using the standard explicit Leapfrog scheme. To obtain efficient and explicit time stepping methods, the three schemes are further mass lumped. We perform a dispersion and stability analysis for the presented schemes and compare all three methods in terms of their stability regions and phase error. Our results indicate that the method produced by GY-adaptation and the Nédélec method are both second order accurate for numerical dispersion, but differ in the order of their numerical anisotropy (fourth order, versus second order, respectively). The result of M-adaptation is a discretization that is fourth order accurate for numerical dispersion as well as numerical anisotropy. Numerical simulations are provided that illustrate the theoretical results.
Van der Waals equation of state revisited: importance of the dispersion correction.
de Visser, Sam P
2011-04-28
One of the most basic equations of state describing nonideal gases and liquids is the van der Waals equation of state, and as a consequence, it is generally taught in most first year undergraduate chemistry courses. In this work, we show that the constants a and b in the van der Waals equation of state are linearly proportional to the polarizability volume of the molecules in a gas or liquid. Using this information, a new thermodynamic one-parameter equation of state is derived that contains experimentally measurable variables and physics constants only. This is the first equation of state apart from the Ideal Gas Law that contains experimentally measurable variables and physics constants only, and as such, it may be a very useful and practical equation for the description of dilute gases and liquids. The modified van der Waals equation of state describes pV as the sum of repulsive and attractive intermolecular interaction energies that are represented by an exponential repulsion function between the electron clouds of the molecules and a London dispersion component, respectively. The newly derived equation of state is tested against experimental data for several gas and liquid examples, and the agreement is satisfactory. The description of the equation of state as a one-parameter function also has implications on other thermodynamic functions, such as critical parameters, virial coefficients, and isothermal compressibilities. Using our modified van der Waals equation of state, we show that all of these properties are a function of the molecular polarizability volume. Correlations of experimental data confirm the derived proportionalities.
NASA Astrophysics Data System (ADS)
Bekki, Naoaki; Shintani, Seine A.
2015-12-01
We consider the Rayleigh-Lamb-type equation for propagating pulsive waves excited by aortic-valve closure at end-systole in the human heart wall. We theoretically investigate the transcendental dispersion equation of pulsive waves for the asymmetrical zero-order mode of the Lamb wave. We analytically find a simple dispersion equation with a universal constant for a small Lamb wavenumber. We show that the simple dispersion equation can qualitatively explain the myocardial noninvasive measurements in vivo of pulsive waves in the human heart wall. We can also consistently estimate the viscoelastic constant of the myocardium in the human heart wall using the simple dispersion equation for a small Lamb wavenumber instead of using a complex nonlinear optimization.
Local-in-Space Criteria for Blowup in Shallow Water and Dispersive Rod Equations
NASA Astrophysics Data System (ADS)
Brandolese, Lorenzo
2014-08-01
We unify a few of the best known results on wave breaking for the Camassa-Holm equation (by R. Camassa, A. Constantin, J. Escher, L. Holm, J. Hyman and others) in a single theorem: a sufficient condition for the breakdown is that is strictly negative in at least one point . Such blowup criterion looks more natural than the previous ones, as the condition on the initial data is purely local in the space variable. Our method relies on the introduction of two families of Lyapunov functions. Contrary to McKean's necessary and sufficient condition for blowup, our approach applies to other equations that are not integrable: we illustrate this fact by establishing new local-in-space blowup criteria for an equation modeling nonlinear dispersive waves in elastic rods.
Construction of the wave operator for non-linear dispersive equations
NASA Astrophysics Data System (ADS)
Tsuruta, Kai Erik
In this thesis, we will study non-linear dispersive equations. The primary focus will be on the construction of the positive-time wave operator for such equations. The positive-time wave operator problem arises in the study of the asymptotics of a partial differential equation. It is a map from a space of initial data X into itself, and is loosely defined as follows: Suppose that for a solution ψlin to the dispersive equation with no non-linearity and initial data ψ +, there exists a unique solution ψ to the non-linear equation with initial data ψ0 such that ψ behaves as ψ lin as t → infinity. Then the wave operator is the map W+ that takes ψ + to ψ0. By its definition, W+ is injective. An important additional question is whether or not the map is also surjective. If so, then every non-linear solution emanating from X behaves, in some sense, linearly as it evolves (this is known as asymptotic completeness). Thus, there is some justification for treating these solutions as their much simpler linear counterparts. The main results presented in this thesis revolve around the construction of the wave operator(s) at critical non-linearities. We will study the "semi-relativistic" Schrodinger equation as well as the Klein-Gordon-Schrodinger system on R2 . In both cases, we will impose fairly general quadratic non-linearities for which conservation laws cannot be relied upon. These non-linearities fall below the scaling required to employ such tools as the Strichartz estimates. We instead adapt the "first iteration method" of Jang, Li, and Zhang to our setting which depends crucially on the critical decay of the non-linear interaction of the linear evolution. To see the critical decay in our problem, careful analysis is needed to treat the regime where one has spatial and/or time resonance.
Formation of wave packets in the Ostrovsky equation for both normal and anomalous dispersion
Grimshaw, Roger; Stepanyants, Yury; Alias, Azwani
2016-01-01
It is well known that the Ostrovsky equation with normal dispersion does not support steady solitary waves. An initial Korteweg–de Vries solitary wave decays adiabatically through the radiation of long waves and is eventually replaced by an envelope solitary wave whose carrier wave and envelope move with different velocities (phase and group velocities correspondingly). Here, we examine the same initial condition for the Ostrovsky equation with anomalous dispersion, when the wave frequency increases with wavenumber in the limit of very short waves. The essential difference is that now there exists a steady solitary wave solution (Ostrovsky soliton), which in the small-amplitude limit can be described asymptotically through the solitary wave solution of a nonlinear Schrödinger equation, based at that wavenumber where the phase and group velocities coincide. Long-time numerical simulations show that the emergence of this steady envelope solitary wave is a very robust feature. The initial Korteweg–de Vries solitary wave transforms rapidly to this envelope solitary wave in a seemingly non-adiabatic manner. The amplitude of the Ostrovsky soliton strongly correlates with the initial Korteweg–de Vries solitary wave. PMID:26997887
Tracer dispersion simulation in low wind speed conditions with a new 2D Langevin equation system
NASA Astrophysics Data System (ADS)
Anfossi, D.; Alessandrini, S.; Trini Castelli, S.; Ferrero, E.; Oettl, D.; Degrazia, G.
The simulation of atmospheric dispersion in low wind speed conditions (LW) is still recognised as a challenge for modellers. Recently, a new system of two coupled Langevin equations that explicitly accounts for meandering has been proposed. It is based on the study of turbulence and dispersion properties in LW. The new system was implemented in the Lagrangian stochastic particle models LAMBDA and GRAL. In this paper we present simulations with this new approach applying it to the tracer experiments carried out in LW by Idaho National Engineering Laboratory (INEL, USA) in 1974 and by the Graz University of Technology and CNR-Torino near Graz in 2003. To assess the improvement obtained with the present model with respect to previous models not taking into account the meandering effect, the simulations for the INEL experiments were also performed with the old version of LAMBDA. The results of the comparisons clearly indicate that the new approach improves the simulation results.
The scattering transform for the Benjamin-Ono equation in the small-dispersion limit
NASA Astrophysics Data System (ADS)
Miller, Peter D.; Wetzel, Alfredo N.
2016-10-01
Using exact formulae for the scattering data of the Benjamin-Ono equation valid for general rational potentials recently obtained in Miller and Wetzel [17], we rigorously analyze the scattering data in the small-dispersion limit. In particular, we deduce precise asymptotic formulae for the reflection coefficient, the location of the eigenvalues and their density, and the asymptotic dependence of the phase constant (associated with each eigenvalue) on the eigenvalue itself. Our results give direct confirmation of conjectures in the literature that have been partly justified by means of inverse scattering, and they also provide new details not previously reported in the literature.
GENERAL: Periodic folded waves for a (2+1)-dimensional modified dispersive water wave equation
NASA Astrophysics Data System (ADS)
Huang, Wen-Hua
2009-08-01
A general solution, including three arbitrary functions, is obtained for a (2+1)-dimensional modified dispersive water-wave (MDWW) equation by means of the WTC truncation method. Introducing proper multiple valued functions and Jacobi elliptic functions in the seed solution, special types of periodic folded waves are derived. In the long wave limit these periodic folded wave patterns may degenerate into single localized folded solitary wave excitations. The interactions of the periodic folded waves and the degenerated single folded solitary waves are investigated graphically and found to be completely elastic.
Dispersion estimates for one-dimensional Schrödinger and Klein-Gordon equations revisited
NASA Astrophysics Data System (ADS)
Egorova, I. E.; Kopylova, E. A.; Marchenko, V. A.; Teschl, G.
2016-06-01
It is shown that for a one-dimensional Schrödinger operator with a potential whose first moment is integrable the elements of the scattering matrix are in the unital Wiener algebra of functions with integrable Fourier transforms. This is then used to derive dispersion estimates for solutions of the associated Schrödinger and Klein-Gordon equations. In particular, the additional decay conditions are removed in the case where a resonance is present at the edge of the continuous spectrum. Bibliography: 29 titles.
Classical non-Markovian Boltzmann equation
Alexanian, Moorad
2014-08-01
The modeling of particle transport involves anomalous diffusion, (x²(t) ) ∝ t{sup α} with α ≠ 1, with subdiffusive transport corresponding to 0 < α < 1 and superdiffusive transport to α > 1. These anomalies give rise to fractional advection-dispersion equations with memory in space and time. The usual Boltzmann equation, with only isolated binary collisions, is Markovian and, in particular, the contributions of the three-particle distribution function are neglected. We show that the inclusion of higher-order distribution functions give rise to an exact, non-Markovian Boltzmann equation with resulting transport equations for mass, momentum, and kinetic energy with memory in both time and space. The two- and the three-particle distribution functions are considered under the assumption that the two- and the three-particle correlation functions are translationally invariant that allows us to obtain advection-dispersion equations for modeling transport in terms of spatial and temporal fractional derivatives.
Classical non-Markovian Boltzmann equation
NASA Astrophysics Data System (ADS)
Alexanian, Moorad
2014-08-01
The modeling of particle transport involves anomalous diffusion, ⟨x2(t) ⟩ ∝ tα with α ≠ 1, with subdiffusive transport corresponding to 0 < α < 1 and superdiffusive transport to α > 1. These anomalies give rise to fractional advection-dispersion equations with memory in space and time. The usual Boltzmann equation, with only isolated binary collisions, is Markovian and, in particular, the contributions of the three-particle distribution function are neglected. We show that the inclusion of higher-order distribution functions give rise to an exact, non-Markovian Boltzmann equation with resulting transport equations for mass, momentum, and kinetic energy with memory in both time and space. The two- and the three-particle distribution functions are considered under the assumption that the two- and the three-particle correlation functions are translationally invariant that allows us to obtain advection-dispersion equations for modeling transport in terms of spatial and temporal fractional derivatives.
Modelling drug degradation in a spray dried polymer dispersion using a modified Arrhenius equation.
Patterson, Adele; Ferreira, Ana P; Banks, Elizabeth; Skeene, Kirsty; Clarke, Graham; Nicholson, Sarah; Rawlinson-Malone, Clare
2015-01-15
The Pharmaceutical industry is increasingly utilizing amorphous technologies to overcome solubility challenges. A common approach is the use of drug in polymer dispersions to prevent recrystallization of the amorphous drug. Understanding the factors affecting chemical and physical degradation of the drug within these complex systems, e.g., temperature and relative humidity, is an important step in the selection of a lead formulation, and development of appropriate packaging/storage control strategies. The Arrhenius equation has been used as the basis of a number of models to predict the chemical stability of formulated product. In this work, we investigate the increase in chemical degradation seen for one particular spray dried dispersion formulation using hydroxypropyl methylcellulose acetate succinate (HPMC-AS). Samples, prepared using polymers with different substitution levels, were placed on storage for 6 months under a range of different temperature and relative humidity conditions and the degradant level monitored using high-performance liquid chromatography (HPLC). While the data clearly illustrates the impact of temperature and relative humidity on the degradant levels detected, it also highlighted that these terms do not account for all the variability in the data. An extension of the Arrhenius equation to include a term for the polymer chemistry, specifically the degree of succinoyl substitution on the polymer backbone, was shown to improve the fit of the model to the data.
Anomalous scaling of a scalar field advected by turbulence
Kraichnan, R.H.
1995-12-31
Recent work leading to deduction of anomalous scaling exponents for the inertial range of an advected passive field from the equations of motion is reviewed. Implications for other turbulence problems are discussed.
Hydrodynamic dispersion within porous biofilms
NASA Astrophysics Data System (ADS)
Davit, Y.; Byrne, H.; Osborne, J.; Pitt-Francis, J.; Gavaghan, D.; Quintard, M.
2013-01-01
Many microorganisms live within surface-associated consortia, termed biofilms, that can form intricate porous structures interspersed with a network of fluid channels. In such systems, transport phenomena, including flow and advection, regulate various aspects of cell behavior by controlling nutrient supply, evacuation of waste products, and permeation of antimicrobial agents. This study presents multiscale analysis of solute transport in these porous biofilms. We start our analysis with a channel-scale description of mass transport and use the method of volume averaging to derive a set of homogenized equations at the biofilm-scale in the case where the width of the channels is significantly smaller than the thickness of the biofilm. We show that solute transport may be described via two coupled partial differential equations or telegrapher's equations for the averaged concentrations. These models are particularly relevant for chemicals, such as some antimicrobial agents, that penetrate cell clusters very slowly. In most cases, especially for nutrients, solute penetration is faster, and transport can be described via an advection-dispersion equation. In this simpler case, the effective diffusion is characterized by a second-order tensor whose components depend on (1) the topology of the channels' network; (2) the solute's diffusion coefficients in the fluid and the cell clusters; (3) hydrodynamic dispersion effects; and (4) an additional dispersion term intrinsic to the two-phase configuration. Although solute transport in biofilms is commonly thought to be diffusion dominated, this analysis shows that hydrodynamic dispersion effects may significantly contribute to transport.
NASA Astrophysics Data System (ADS)
Erdoğan, M. Burak; Green, William R.
2016-12-01
We investigate dispersive estimates for the two dimensional Dirac equation with a potential. In particular, we show that the Dirac evolution satisfies a t -1 decay rate as an operator from the Hardy space H 1 to BMO, the space of functions of bounded mean oscillation. This estimate, along with the L 2 conservation law allows one to deduce a family of Strichartz estimates. We classify the structure of threshold obstructions as being composed of s-wave resonances, p-wave resonances and eigenfunctions. We show that, as in the case of the Schrödinger evolution, the presence of a threshold s-wave resonance does not destroy the t -1 decay rate. As a consequence of our analysis we obtain a limiting absorption principle in the neighborhood of the threshold, and show that there are only finitely many eigenvalues in the spectral gap.
Population persistence under advection-diffusion in river networks.
Ramirez, Jorge M
2012-11-01
An integro-differential equation on a tree graph is used to model the time evolution and spatial distribution of a population of organisms in a river network. Individual organisms become mobile at a constant rate, and disperse according to an advection-diffusion process with coefficients that are constant on the edges of the graph. Appropriate boundary conditions are imposed at the outlet and upstream nodes of the river network. The local rates of population growth/decay and that by which the organisms become mobile, are assumed constant in time and space. Imminent extinction of the population is understood as the situation whereby the zero solution to the integro-differential equation is stable. Lower and upper bounds for the eigenvalues of the dispersion operator, and related Sturm-Liouville problems are found. The analysis yields sufficient conditions for imminent extinction and/or persistence in terms of the values of water velocity, channel length, cross-sectional area and diffusivity throughout the river network.
NASA Astrophysics Data System (ADS)
Monobe, Harunori; Wu, Chang-Hong
2016-12-01
In this paper, we investigate a reaction-diffusion-advection equation with a free boundary which models the spreading of an invasive species in one-dimensional heterogeneous environments. We assume that the species has a tendency to move upward along the resource gradient in addition to random dispersal, and the spreading mechanism of species is determined by a Stefan-type condition. Investigating the sign of the principal eigenvalue of the associated linearized eigenvalue problem, under certain conditions we obtain the sharp criteria for spreading and vanishing via system parameters. Also, we establish the long-time behavior of the solution and the asymptotic spreading speed. Finally, some biological implications are discussed.
NASA Technical Reports Server (NTRS)
Lenardic, A.; Kaula, W. M.
1993-01-01
Effective numerical treatment of multicomponent viscous flow problems involving the advection of sharp interfaces between materials of differing physical properties requires correction techniques to prevent spurious diffusion and dispersion. We develop a particular algorithm, based on modern shock-capture techniques, employing a two-step nonlinear method. The first step involves the global application of a high-order upwind scheme to a hyperbolic advection equation used to model the distribution of distinct material components in a flow field. The second step is corrective and involves the application of a global filter designed to remove dispersion errors that result from the advection of discontinuities (e.g., material interfaces) by high-order, minimally dissipative schemes. The filter introduces no additional diffusion error. Nonuniform viscosity across a material interface is allowed for by the implementation of a compositionally weighted-inverse interface viscosity scheme. The combined method approaches the optimal accuracy of modern shock-capture techniques with a minimal increase in computational time and memory. A key advantage of this method is its simplicity to incorporate into preexisting codes be they finite difference, element, or volume of two or three dimensions.
Wu, Junru; Layman, Christopher; Liu, Jun
2004-02-01
A fundamental mathematical framework for applications of Doublet Mechanics to ultrasound propagation in a discrete material is introduced. A multiscale wave equation, dispersion relation for longitudinal waves, and shear waves are derived. The van Hove singularities and corresponding highest frequency limits for the Mth-order wave equations of longitudinal and shear waves are determined for a widely used microbundle structure. Doublet Mechanics is applied to soft tissue and low-density polyethylene. The experimental dispersion data for soft tissue and low-density polyethylene are compared with results predicted by Doublet Mechanics and an attenuation model based on a Kramers-Kronig relation in classical continuum mechanics.
NASA Astrophysics Data System (ADS)
Wu, Junru; Layman, Christopher; Liu, Jun
2004-02-01
A fundamental mathematical framework for applications of Doublet Mechanics to ultrasound propagation in a discrete material is introduced. A multiscale wave equation, dispersion relation for longitudinal waves, and shear waves are derived. The van Hove singularities and corresponding highest frequency limits for the Mth-order wave equations of longitudinal and shear waves are determined for a widely used microbundle structure. Doublet Mechanics is applied to soft tissue and low-density polyethylene. The experimental dispersion data for soft tissue and low-density polyethylene are compared with results predicted by Doublet Mechanics and an attenuation model based on a Kramers-Kronig relation in classical continuum mechanics.
Clobert, J.; Danchin, E.; Dhondt, A.A.; Nichols, J.D.
2001-01-01
The ability of species to migrate and disperse is a trait that has interested ecologists for many years. Now that so many species and ecosystems face major environmental threats from habitat fragmentation and global climate change, the ability of species to adapt to these changes by dispersing, migrating, or moving between patches of habitat can be crucial to ensuring their survival. This book provides a timely and wide-ranging overview of the study of dispersal and incorporates much of the latest research. The causes, mechanisms, and consequences of dispersal at the individual, population, species and community levels are considered. The potential of new techniques and models for studying dispersal, drawn from molecular biology and demography, is also explored. Perspectives and insights are offered from the fields of evolution, conservation biology and genetics. Throughout the book, theoretical approaches are combined with empirical data, and care has been taken to include examples from as wide a range of species as possible.
NASA Astrophysics Data System (ADS)
Tariq, Kalim Ul-Haq; Seadawy, A. R.
The Boussinesq equation with dual dispersion and modified Korteweg-de Vries-Kadomtsev-Petviashvili equations describe weakly dispersive and small amplitude waves propagating in a quasi three-dimensional media. In this article, we study the analytical Bright-Dark solitary wave solutions for (3 + 1)-dimensional Breaking soliton equation, Boussinesq equation with dual dispersion and modified Korteweg-de Vries-Kadomtsev-Petviashvili equation have been extracted. These results hold numerous travelling wave solutions that are of key importance in elucidating some physical circumstance. The technique can also be functional to other sorts of nonlinear evolution equations in contemporary areas of research.
NASA Technical Reports Server (NTRS)
Wang, Xiao-Yen; Chow, Chuen-Yen; Chang, Sin-Chung
1999-01-01
Test problems are used to examine the performance of several one-dimensional numerical schemes based on the space-time conservation and solution element (CE/SE) method. Investigated in this paper are the CE/SE schemes constructed previously for solving the linear unsteady advection-diffusion equation and the schemes derived here for solving the nonlinear viscous and inviscid Burgers equations. In comparison with the numerical solutions obtained using several traditional finite-difference schemes with similar accuracy, the CE/SE solutions display much lower numerical dissipation and dispersion errors.
LAYER DEPENDENT ADVECTION IN CMAQ
The advection methods used in CMAQ require that the Courant-Friedrichs-Lewy (CFL) condition be satisfied for numerical stability and accuracy. In CMAQ prior to version 4.3, the ADVSTEP algorithm established CFL-safe synchronization and advection timesteps that were uniform throu...
Predoi, Mihai Valentin
2014-09-01
The dispersion curves for hollow multilayered cylinders are prerequisites in any practical guided waves application on such structures. The equations for homogeneous isotropic materials have been established more than 120 years ago. The difficulties in finding numerical solutions to analytic expressions remain considerable, especially if the materials are orthotropic visco-elastic as in the composites used for pipes in the last decades. Among other numerical techniques, the semi-analytical finite elements method has proven its capability of solving this problem. Two possibilities exist to model a finite elements eigenvalue problem: a two-dimensional cross-section model of the pipe or a radial segment model, intersecting the layers between the inner and the outer radius of the pipe. The last possibility is here adopted and distinct differential problems are deduced for longitudinal L(0,n), torsional T(0,n) and flexural F(m,n) modes. Eigenvalue problems are deduced for the three modes classes, offering explicit forms of each coefficient for the matrices used in an available general purpose finite elements code. Comparisons with existing solutions for pipes filled with non-linear viscoelastic fluid or visco-elastic coatings as well as for a fully orthotropic hollow cylinder are all proving the reliability and ease of use of this method.
Non-dispersive carrier transport in molecularly doped polymers and the convection-diffusion equation
NASA Astrophysics Data System (ADS)
Tyutnev, A. P.; Parris, P. E.; Saenko, V. S.
2015-08-01
We reinvestigate the applicability of the concept of trap-free carrier transport in molecularly doped polymers and the possibility of realistically describing time-of-flight (TOF) current transients in these materials using the classical convection-diffusion equation (CDE). The problem is treated as rigorously as possible using boundary conditions appropriate to conventional time of flight experiments. Two types of pulsed carrier generation are considered. In addition to the traditional case of surface excitation, we also consider the case where carrier generation is spatially uniform. In our analysis, the front electrode is treated as a reflecting boundary, while the counter electrode is assumed to act either as a neutral contact (not disturbing the current flow) or as an absorbing boundary at which the carrier concentration vanishes. As expected, at low fields transient currents exhibit unusual behavior, as diffusion currents overwhelm drift currents to such an extent that it becomes impossible to determine transit times (and hence, carrier mobilities). At high fields, computed transients are more like those typically observed, with well-defined plateaus and sharp transit times. Careful analysis, however, reveals that the non-dispersive picture, and predictions of the CDE contradict both experiment and existing disorder-based theories in important ways, and that the CDE should be applied rather cautiously, and even then only for engineering purposes.
NASA Astrophysics Data System (ADS)
Yu, Fajun; Li, Li
2015-07-01
A high-order dispersive cubic-quintic Gross-Pitaevskii (HDCQGP) equation (a generalized variable coefficients nonlinear Schrödinger equation with the third and fourth-order and the cubic-quintic nonlinear terms) is considered, and is transformed into a standard cubic-quintic nonlinear Schrödinger equation (NLSE). By using the generalized tanh-function method, we study exact solutions of the HDCQGP equation with time-modulated potential and nonlinearity. In particular, based on the similarity transformation, we report several families of non-autonomous wave solutions of the HDCQGP equation with snaking behaviors and different amplitude surfaces. At last, we consider the numerical simulation of two solitons collision for the NLSE with different parameters. These results may raise the possibility of relative experiments and potential applications.
Theory of advection-driven long range biotic transport
Technology Transfer Automated Retrieval System (TEKTRAN)
We propose a simple mechanistic model to examine the effects of advective flow on the spread of fungal diseases spread by wind-blown spores. The model is defined by a set of two coupled non-linear partial differential equations for spore densities. One equation describes the long-distance advectiv...
NASA Astrophysics Data System (ADS)
Ma, Xiao; Yang, Dinghui
2017-03-01
The finite-difference method, which is an important numerical tool for solving seismic wave equations, is widely applied in wavefield simulation, wave-equation-based migration and inversion. As the seismic wave phase plays a critical role in forward simulation and inversion, it should be preserved during wavefield simulation. In this paper, we propose a type of phase-preserving stereomodelling method, which is simultaneously symplectic and low numerical dispersive. First, we propose three new time-marching schemes for solving wave equations that are optimal symplectic partitioned Runge-Kutta schemes with minimized phase errors. Relevant simulations on a harmonic oscillator show that even after 200,000 temporal iterations, our schemes can still avoid the phase drifting issue that appears in other symplectic schemes. We use these symplectic schemes as time integrators, and a numerically low dispersive operator called the stereomodelling discrete operator as a spatial discretization approach to solve seismic wave equations. Theoretical analysis on the stability conditions shows that the new methods are more stable than previous methods. We also investigate the numerical dispersion relations of the methods proposed in this study. To further investigate phase accuracy, we compare the numerical solutions generated by the proposed methods with analytic solutions. Several numerical experiments indicate that our proposed methods are efficient for various models and perform well with perfectly matched layer boundary conditions.
NASA Astrophysics Data System (ADS)
Soto-Crespo, J. M.; Akhmediev, N. N.; Afanasjev, V. V.; Wabnitz, S.
1997-04-01
Time-localized solitary wave solutions of the one-dimensional complex Ginzburg-Landau equation (CGLE) are analyzed for the case of normal group-velocity dispersion. Exact soliton solutions are found for both the cubic and the quintic CGLE. The stability of these solutions is investigated numerically. The regions in the parameter space in which stable pulselike solutions of the quintic CGLE exist are numerically determined. These regions contain subspaces where analytical solutions may be found. An investigation of the role of group-velocity dispersion changes in magnitude and sign on the spectral and temporal characteristics of the stable pulse solutions is also carried out.
Anisotropic Turbulent Advection of a Passive Vector Field: Effects of the Finite Correlation Time
NASA Astrophysics Data System (ADS)
Antonov, N. V.; Gulitskiy, N. M.
2016-02-01
The turbulent passive advection under the environment (velocity) field with finite correlation time is studied. Inertial-range asymptotic behavior of a vector (e.g., magnetic) field, passively advected by a strongly anisotropic turbulent flow, is investigated by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity field is Gaussian, with finite correlation time and prescribed pair correlation function. The inertial-range behavior of the model is described by two regimes (the limits of vanishing or infinite correlation time) that correspond to nontrivial fixed points of the RG equations and depend on the relation between the exponents in the energy energy spectrum ɛ ∝ k⊥1-ξ and the dispersion law ω ∝ k⊥2-η . The corresponding anomalous exponents are associated with the critical dimensions of tensor composite operators built solely of the passive vector field itself. In contrast to the well-known isotropic Kraichnan model, where various correlation functions exhibit anomalous scaling behavior with infinite sets of anomalous exponents, here the dependence on the integral turbulence scale L has a logarithmic behavior: instead of power-like corrections to ordinary scaling, determined by naive (canonical) dimensions, the anomalies manifest themselves as polynomials of logarithms of L. Due to the presence of the anisotropy in the model, all multiloop diagrams are equal to zero, thus this result is exact.
High Order Semi-Lagrangian Advection Scheme
NASA Astrophysics Data System (ADS)
Malaga, Carlos; Mandujano, Francisco; Becerra, Julian
2014-11-01
In most fluid phenomena, advection plays an important roll. A numerical scheme capable of making quantitative predictions and simulations must compute correctly the advection terms appearing in the equations governing fluid flow. Here we present a high order forward semi-Lagrangian numerical scheme specifically tailored to compute material derivatives. The scheme relies on the geometrical interpretation of material derivatives to compute the time evolution of fields on grids that deform with the material fluid domain, an interpolating procedure of arbitrary order that preserves the moments of the interpolated distributions, and a nonlinear mapping strategy to perform interpolations between undeformed and deformed grids. Additionally, a discontinuity criterion was implemented to deal with discontinuous fields and shocks. Tests of pure advection, shock formation and nonlinear phenomena are presented to show performance and convergence of the scheme. The high computational cost is considerably reduced when implemented on massively parallel architectures found in graphic cards. The authors acknowledge funding from Fondo Sectorial CONACYT-SENER Grant Number 42536 (DGAJ-SPI-34-170412-217).
NASA Astrophysics Data System (ADS)
Baskonus, Haci Mehmet; Bulut, Hasan
2015-10-01
In this study, we have studied to obtain some new analytical solutions to the (1 + 1)-dimensional nonlinear Dispersive Modified Benjamin-Bona-Mahony equation by using modified exp-function method. We have submitted the general structure of modified exp-function method. We have founded some new analytical solutions such as hyperbolic and rational function solutions. Afterward, we have plotted 2D and 3D surfaces of analytical solutions obtained in this study by using computer programming wolfram Mathematica 9.
Andrea Prosperetti
2006-03-24
The report briefly describes the activities carried out in the course of the project. A first line of research was the development of systematic closure relations for averaged equations for disperse multiphase flow. A second line was the development of efficient numerical methods for the simulation of Navier-Stokes flows with many suspended particles. The report also lists the 21 journal articles in which this work is more fully decsribed.
NASA Astrophysics Data System (ADS)
Klein, C.; Peter, R.
2015-06-01
We present a detailed numerical study of solutions to general Korteweg-de Vries equations with critical and supercritical nonlinearity, both in the context of dispersive shocks and blow-up. We study the stability of solitons and show that they are unstable against being radiated away and blow-up. In the L2 critical case, the blow-up mechanism by Martel, Merle and Raphaël can be numerically identified. In the limit of small dispersion, it is shown that a dispersive shock always appears before an eventual blow-up. In the latter case, always the first soliton to appear will blow up. It is shown that the same type of blow-up as for the perturbations of the soliton can be observed which indicates that the theory by Martel, Merle and Raphaël is also applicable to initial data with a mass much larger than the soliton mass. We study the scaling of the blow-up time t∗ in dependence of the small dispersion parameter ɛ and find an exponential dependence t∗(ɛ) and that there is a minimal blow-up time t0∗ greater than the critical time of the corresponding Hopf solution for ɛ → 0. To study the cases with blow-up in detail, we apply the first dynamic rescaling for generalized Korteweg-de Vries equations. This allows to identify the type of the singularity.
Analysis of the small dispersion limit of a non-integrable generalized Korteweg-de Vries equation
NASA Astrophysics Data System (ADS)
Zakeri, Gholam-Ali; Yomba, Emmanuel
2013-08-01
A generalized non-integrable Korteweg-de Vries (KdV) equation is investigated for the qualitative behavior of its solutions with a small dispersion limit. We obtained two reduced ordinary differential equations using a similarity analysis and discussed the solutions of generalized KdV (gKdV) by employing singular perturbation and asymptotic methods. We found a new closed form solution and provided various approximate solutions. We have shown that for sech-type initial value data the cumulative primitive function of the gKdV solution converges point-wise as the coefficient of the dispersive term goes to zero. Our numerical experiments provide strong evidence that for each fixed time, the solutions of gKdV are bounded by well-defined envelopes as the coefficient of the dispersion term goes to zero. We have shown that for a higher order of nonlinearity, the soliton becomes shaper, with a larger amplitude, but remains bounded. Comparatively, for a smaller coefficient of the dispersion term, its base gets smaller and the soliton becomes narrower, but the amplitude of the soliton remains the same.
Striated populations in disordered environments with advection
NASA Astrophysics Data System (ADS)
Chotibut, Thiparat; Nelson, David R.; Succi, Sauro
2017-01-01
Growth in static and controlled environments such as a Petri dish can be used to study the spatial population dynamics of microorganisms. However, natural populations such as marine microbes experience fluid advection and often grow up in heterogeneous environments. We investigate a generalized Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation describing single species population subject to a constant flow field and quenched random spatially inhomogeneous growth rates with a fertile overall growth condition. We analytically and numerically demonstrate that the non-equilibrium steady-state population density develops a flow-driven striation pattern. The striations are highly asymmetric with a longitudinal correlation length that diverges linearly with the flow speed and a transverse correlation length that approaches a finite velocity-independent value. Linear response theory is developed to study the statistics of the steady states. Theoretical predictions show excellent agreement with the numerical steady states of the generalized FKPP equation obtained from Lattice Boltzmann simulations. These findings suggest that, although the growth disorder can be spatially uncorrelated, correlated population structures with striations emerge naturally at sufficiently strong advection.
NASA Astrophysics Data System (ADS)
Jacques, Diederik; Šimůnek, Jirka; Timmerman, Anthony; Feyen, Jan
2002-03-01
In this paper, the applicability of Richards' equation for water flow and the convection-dispersion equation for solute transport is evaluated to model field-scale flow and transport under natural boundary conditions by using detailed experimental data and inverse optimization. The data consisted of depth-averaged time series of water content, pressure head and resident solute concentration data measured several times a day during 384 d. In a first approach, effective parameters are estimated using the time series for one depth and assuming a homogeneous soil profile. In a second approach, all time series were used simultaneously to estimate the parameters of a multi-layered soil profile. Water flow was described by the Richards' equation and solute transport either by the equilibrium convection-dispersion (CDE) or the physical non-equilibrium convection-dispersion (MIM) equation. To represent the dynamics of the water content and pressure head data, the multi-layered soil profile approach gave better results. Fitted soil hydraulic parameters were comparable with parameters obtained with other methods on the same soil. At larger depths, both the CDE- and MIM-models gave acceptable descriptions of the observed breakthrough data, although the MIM performed somewhat better in the tailing part. Both models underestimated significantly the fast breakthrough. To describe the breakthrough curves at the first depth, only the MIM with a mixing layer close to the soil surface gave acceptable results. Starting from an initial value problem with solutes homogeneously distributed over the mobile and immobile water phase was preferable compared to the incorporation of a small layer with only mobile water near the soil surface.
Advection around ventilated U-shaped burrows: A model study
NASA Astrophysics Data System (ADS)
Brand, Andreas; Lewandowski, JöRg; Hamann, Enrico; Nützmann, Gunnar
2013-05-01
Advective transport in the porous matrix of sediments surrounding burrows formed by fauna such as Chironomus plumosus has been generally neglected. A positron emission tomography study recently revealed that the pumping activity of the midge larvae can indeed induce fluid flow in the sediment. We present a numerical model study which explores the conditions at which advective transport in the sediment becomes relevant. A 0.15 m deep U-shaped burrow with a diameter of 0.002 m within the sediment was represented in a 3-D domain. Fluid flow in the burrow was calculated using the Navier-Stokes equation for incompressible laminar flow in the burrow, and flow in the sediment was described by Darcy's law. Nonreactive and reactive transport scenarios were simulated considering diffusion and advection. The pumping activity of the model larva results in considerable advective flow in the sediment at reasonable high permeabilities with flow velocities of up to 7.0 × 10-6 m s-1 close to the larva for a permeability of 3 × 10-12 m2. At permeabilities below 7 × 10-13 m2 advection is negligible compared to diffusion. Reactive transport simulations using first-order kinetics for oxygen revealed that advective flux into the sediment downstream of the pumping larva enhances sedimentary uptake, while the advective flux into the burrow upstream of the larvae inhibits diffusive sedimentary uptake. Despite the fact that both effects cancel each other with respect to total solute uptake, the advection-induced asymmetry in concentration distribution can lead to a heterogeneous solute and redox distribution in the sediment relevant to complex reaction networks.
NASA Astrophysics Data System (ADS)
Seadawy, Aly R.
2017-01-01
The propagation of three-dimensional nonlinear irrotational flow of an inviscid and incompressible fluid of the long waves in dispersive shallow-water approximation is analyzed. The problem formulation of the long waves in dispersive shallow-water approximation lead to fifth-order Kadomtsev-Petviashvili (KP) dynamical equation by applying the reductive perturbation theory. By using an extended auxiliary equation method, the solitary travelling-wave solutions of the two-dimensional nonlinear fifth-order KP dynamical equation are derived. An analytical as well as a numerical solution of the two-dimensional nonlinear KP equation are obtained and analyzed with the effects of external pressure flow.
NASA Astrophysics Data System (ADS)
Szybisz, Leszek
1990-06-01
The self-consistency of solutions obtained from a recently proposed numerical relaxation method of solving the Euler-Lagrange equations for the ground state of inhomogeneous Bose systems at zero temperature is investigated. For this kind of system at least three different dispersion relations can be formulated, all of them providing information about the same eigenstates. The quality of our optimization scheme is studied by analyzing the convergence of the low-lying eigenvalues and eigenfunctions of these dispersion relations. Numerical results for the spectrum and spatial shape of elementary excitations of a thin film of liquid 4He supported by an external potential are reported. The optimal lowest-lying eigenvalues are compared with estimations based on simple theoretical approaches and with calculations performed by other authors.
Classification of dispersion equations for homogeneous, dielectric-magnetic, uniaxial materials.
Depine, Ricardo A; Inchaussandague, Marina E; Lakhtakia, Akhlesh
2006-04-01
The geometric representation at a fixed frequency of the wave vector (or dispersion) surface omega(k) for lossless, homogeneous, dielectric-magnetic uniaxial materials is explored for the case when the elements of the relative permittivity and permeability tensors of the material can have any sign. Electromagnetic plane waves propagating inside the material can exhibit dispersion surfaces in the form of ellipsoids of revolution, hyperboloids of one sheet, or hyperboloids of two sheets. Furthermore, depending on the relative orientation of the optic axis, the intersections of these surfaces with fixed planes of propagation can be circles, ellipses, hyperbolas, or straight lines. The understanding obtained is used to study the reflection and refraction of electromagnetic plane waves due to a planar interface with an isotropic medium.
Waves, advection, and cloud patterns on Venus
NASA Technical Reports Server (NTRS)
Schinder, Paul J.; Gierasch, Peter J.; Leroy, Stephen S.; Smith, Michael D.
1990-01-01
The stable layers adjacent to the nearly neutral layer within the Venus clouds are found to be capable of supporting vertically trapped, horizontally propagating waves with horizontal wavelengths of about 10 km and speeds of a few meters per second relative to the mean wind in the neutral layer. These waves may possibly be excited by turbulence within the neutral layer. Here, the properties of the waves, and the patterns which they might produce within the visible clouds if excited near the subsolar point are examined. The patterns can be in agreement with many features in images. The waves are capable of transferring momentum latitudinally to help maintain the general atmospheric spin, but at present we are not able to evaluate wave amplitudes. We also examine an alternative possibility that the cloud patterns are produced by advection and shearing by the mean zonal and meridional flow of blobs formed near the equator. It is concluded that advection and shearing by the mean flow is the most likely explanation for the general pattern of small scale striations.
Parallel algorithms for semi-lagrangian advection
NASA Astrophysics Data System (ADS)
Malevsky, A. V.; Thomas, S. J.
1997-08-01
Numerical time step limitations associated with the explicit treatment of advection-dominated problems in computational fluid dynamics are often relaxed by employing Eulerian-Lagrangian methods. These are also known as semi-Lagrangian methods in the atmospheric sciences. Such methods involve backward time integration of a characteristic equation to find the departure point of a fluid particle arriving at a Eulerian grid point. The value of the advected field at the departure point is obtained by interpolation. Both the trajectory integration and repeated interpolation influence accuracy. We compare the accuracy and performance of interpolation schemes based on piecewise cubic polynomials and cubic B-splines in the context of a distributed memory, parallel computing environment. The computational cost and interprocessor communication requirements for both methods are reported. Spline interpolation has better conservation properties but requires the solution of a global linear system, initially appearing to hinder a distributed memory implementation. The proposed parallel algorithm for multidimensional spline interpolation has almost the same communication overhead as local piecewise polynomial interpolation. We also compare various techniques for tracking trajectories given different values for the Courant number. Large Courant numbers require a high-order ODE solver involving multiple interpolations of the velocity field.
Dark solitons in the Lugiato-Lefever equation with normal dispersion
NASA Astrophysics Data System (ADS)
Parra-Rivas, P.; Knobloch, E.; Gomila, D.; Gelens, L.
2016-06-01
The regions of existence and stability of dark solitons in the Lugiato-Lefever model with normal chromatic dispersion are described. These localized states are shown to be organized in a bifurcation structure known as collapsed snaking implying the presence of a region in parameter space with a finite multiplicity of dark solitons. For some parameter values dynamical instabilities are responsible for the appearance of oscillations and temporal chaos. The importance of the results for understanding frequency comb generation in microresonators is emphasized.
Charalampidis, E G; Kevrekidis, P G; Frantzeskakis, D J; Malomed, B A
2016-08-01
We consider a two-component, two-dimensional nonlinear Schrödinger system with unequal dispersion coefficients and self-defocusing nonlinearities, chiefly with equal strengths of the self- and cross-interactions. In this setting, a natural waveform with a nonvanishing background in one component is a vortex, which induces an effective potential well in the second component, via the nonlinear coupling of the two components. We show that the potential well may support not only the fundamental bound state, but also multiring excited radial state complexes for suitable ranges of values of the dispersion coefficient of the second component. We systematically explore the existence, stability, and nonlinear dynamics of these states. The complexes involving the excited radial states are weakly unstable, with a growth rate depending on the dispersion of the second component. Their evolution leads to transformation of the multiring complexes into stable vortex-bright solitons ones with the fundamental state in the second component. The excited states may be stabilized by a harmonic-oscillator trapping potential, as well as by unequal strengths of the self- and cross-repulsive nonlinearities.
Feng, Xin; Ye, Xingyou; Park, Jun-Bom; Lu, Wenli; Morott, Joe; Beissner, Brad; Lian, Zhuoyang John; Pinto, Elanor; Bi, Vivian; Porter, Stu; Durig, Tom; Majumdar, Soumyajit; Repka, Michael A
2015-01-01
The recrystallization of an amorphous drug in a solid dispersion system could lead to a loss in the drug solubility and bioavailability. The primary objective of the current research was to use an improved kinetic model to evaluate the recrystallization kinetics of amorphous structures and to further understand the factors influencing the physical stability of amorphous solid dispersions. Amorphous solid dispersions of fenofibrate with different molecular weights of hydroxypropylcellulose, HPC (Klucel™ LF, EF, ELF) were prepared utilizing hot-melt extrusion technology. Differential scanning calorimetry was utilized to quantitatively analyze the extent of recrystallization in the samples stored at different temperatures and relative humidity (RH) conditions. The experimental data were fitted into the improved kinetics model of a modified Avrami equation to calculate the recrystallization rate constants. Klucel LF, the largest molecular weight among the HPCs used, demonstrated the greatest inhibition of fenofibrate recrystallization. Additionally, the recrystallization rate (k) decreased with increasing polymer content, however exponentially increased with higher temperature. Also k increased linearly rather than exponentially over the range of RH studied.
Mathematical analysis of electromigration dispersion fronts
NASA Astrophysics Data System (ADS)
Christov, Ivan C.
2016-11-01
It is of interest to understand traveling electromigration wave phenomena, such as isotachophoretic boundaries, because of their applications in electrophoretic separation methods. To this end, we construct exact solutions to an unusual nonlinear advection-diffusion equation arising in the study of Taylor-Aris (also known as shear) dispersion due to electroosmotic flow during electromigration in a capillary. An exact reduction to a Darboux equation is found under a traveling-wave anzats. The equilibria of this ordinary differential equation are analyzed, showing that their stability is determined solely by the (dimensionless) wave speed without regard to any (dimensionless) physical parameters. Integral curves, connecting the appropriate equilibria of the Darboux equation that governs traveling waves, are constructed, which in turn are shown to be asymmetric kink solutions (i.e., non-Taylor shocks). Furthermore, it is shown that the governing Darboux equation exhibits bistability, which leads to two coexisting non-negative kink solutions for (dimensionless) wave speeds greater than unity.
Arditi, Roger; Lobry, Claude; Sari, Tewfik
2015-12-01
The standard model for the dynamics of a fragmented density-dependent population is built from several local logistic models coupled by migrations. First introduced in the 1970s and used in innumerable articles, this standard model applied to a two-patch situation has never been completely analysed. Here, we complete this analysis and we delineate the conditions under which fragmentation associated to dispersal is either beneficial or detrimental to total population abundance. Therefore, this is a contribution to the SLOSS question. Importantly, we also show that, depending on the underlying mechanism, there is no unique way to generalize the logistic model to a patchy situation. In many cases, the standard model is not the correct generalization. We analyse several alternative models and compare their predictions. Finally, we emphasize the shortcomings of the logistic model when written in the r-K parameterization and we explain why Verhulst's original polynomial expression is to be preferred.
Numerical simulation for treatment of dispersive shallow water waves with Rosenau-KdV equation
NASA Astrophysics Data System (ADS)
Ak, Turgut; Battal Gazi Karakoc, S.; Triki, Houria
2016-10-01
In this paper, numerical solutions for the Rosenau-Korteweg-de Vries equation are studied by using the subdomain method based on the sextic B-spline basis functions. Numerical results for five test problems including the motion of single solitary wave, interaction of two and three well-separated solitary waves of different amplitudes, evolution of solitons with Gaussian and undular bore initial conditions are obtained. Stability and a priori error estimate of the scheme are discussed. A comparison of the values of the obtained invariants and error norms for single solitary wave with earlier results is also made. The results show that the present method is efficient and reliable.
NASA Astrophysics Data System (ADS)
Meza-Fajardo, Kristel C.; Lai, Carlo G.
2007-12-01
The theory of linear viscoelasticity is the simplest constitutive model that can be adopted to accurately predict the small-strain mechanical response of materials exhibiting the ability to both store and dissipate strain energy. An important result implied by this theory is the relationship existing between material attenuation and the velocity of propagation of a mechanical disturbance. The functional dependence of these important parameters is represented by the Kramers-Kronig (KK) equations, also known as dispersion equations, which are nothing but a statement of the necessary and sufficient conditions to satisfy physical causality. This paper illustrates the derivation of exact solutions of the KK equations to provide explicit relations between frequency-dependent phase velocity and material damping ratio (or equivalently, quality factor). The assumptions that form the basis of the derivation are not beyond those established by the standard theory of viscoelasticity for a viscoelastic solid. The explicit expression for phase velocity as a function of damping ratio was derived by means of the theory of linear singular integral equations, and in particular by the solution of the associated Homogeneous Riemann Boundary Value Problem. It is shown that the same solution may be obtained also by using the implications of physical causality on the Fourier Transform. On the other hand, the explicit solution for damping ratio as a function of phase velocity was found through the components of the complex wavenumber. The exact solutions make it possible to obtain frequency-dependent material damping ratio solely from phase velocity measurements, and conversely. Hence, these relations provide an innovative and inexpensive tool to determine the small-strain dynamic properties of geomaterials. It is shown that the obtained rigorous solutions are in good agreement with well-known solutions based on simplifying assumptions that have been developed in the fields of seismology
NASA Astrophysics Data System (ADS)
Zhang, Guo-Bao; Ma, Ruyun
2014-10-01
This paper is concerned with the traveling wave solutions and the spreading speeds for a nonlocal dispersal equation with convolution-type crossing-monostable nonlinearity, which is motivated by an age-structured population model with time delay. We first prove the existence of traveling wave solution with critical wave speed c = c*. By introducing two auxiliary monotone birth functions and using a fluctuation method, we further show that the number c = c* is also the spreading speed of the corresponding initial value problem with compact support. Then, the nonexistence of traveling wave solutions for c < c* is established. Finally, by means of the (technical) weighted energy method, we prove that the traveling wave with large speed is exponentially stable, when the initial perturbation around the wave is relatively small in a weighted norm.
NASA Astrophysics Data System (ADS)
Trogdon, Thomas; Deconinck, Bernard
2014-01-01
All solutions of the Korteweg-de Vries equation that are bounded on the real line are physically relevant, depending on the application area of interest. Usually, both analytical and numerical approaches consider solution profiles that are either spatially localized or (quasi-)periodic. In this paper, we discuss a class of solutions that is a nonlinear superposition of these two cases: their asymptotic state for large |x| is (quasi-)periodic, but they may contain solitons, with or without dispersive tails. Such scenarios might occur in the case of localized perturbations of previously present sea swell, for instance. Such solutions have been discussed from an analytical point of view only recently. We numerically demonstrate different features of these solutions.
Effects of demographic stochasticity on population persistence in advective media.
Kolpas, Allison; Nisbet, Roger M
2010-07-01
Many populations live and disperse in advective media. A fundamental question, known as the "drift paradox" in stream ecology, is how a closed population can survive when it is constantly being transported downstream by the flow. Recent population-level models have focused on the role of diffusive movement in balancing the effects of advection, predicting critical conditions for persistence. Here, we formulate an individual-based stochastic analog of the model described in (Lutscher et al., SIAM Rev. 47(4):749-772, 2005) to quantify the effects of demographic stochasticity on persistence. Population dynamics are modeled as a logistic growth process and dispersal as a position-jump process on a finite domain divided into patches. When there is no correlation in the interpatch movement of residents, stochasticity simply smooths the persistence-extinction boundary. However, when individuals disperse in "packets" from one patch to another and the flow field is memoryless on the timescale of packet transport, the probability of persistence is greatly enhanced. The latter transport mechanism may be characteristic of larval dispersal in the coastal ocean or wind-dispersed seed pods.
Ainsworth, Mark
2004-03-15
The dispersive behaviour of high-order Nédélec element approximation of the time harmonic Maxwell equations at a prescribed temporal frequency omega on tensor-product meshes of size h is analysed. A simple argument is presented, showing that the discrete dispersion relation may be expressed in terms of that for the approximation of the scalar Helmholtz equation in one dimension. An explicit form for the one-dimensional dispersion relation is given, valid for arbitrary order of approximation. Explicit expressions for the leading term in the error in the regimes where omega h is small, showing that the dispersion relation is accurate to order 2p for a pth-order method; and in the high-wavenumber limit where 1< omega h, showing that in this case the error reduces at a super-exponential rate once the order of approximation exceeds a certain threshold, which is given explicitly.
NASA Astrophysics Data System (ADS)
Chen, Jui-Sheng; Ni, Chuen-Fa; Liang, Ching-Ping; Chiang, Chen-Chung
2008-11-01
SummaryA hyperbolic asymptotic function, which characterizes that the dispersivity initially increases with travel distance and eventually reaches an asymptotic value at long travel distance, is adopted and incorporated into the general advection-dispersion equation for describing scale-dependent solute transport in porous media in this study. An analytical technique for solving advection-dispersion equation with hyperbolic asymptotic distance-dependent dispersivity is presented. The analytical solution is derived by applying the extended power series method coupling with the Laplace transform. The developed analytical solution is compared with the corresponding numerical solution to evaluate its accuracy. Results demonstrate that the breakthrough curves at different locations obtained from the derived power series solution agree closely with those from the numerical solution. Moreover, breakthrough curves obtained from the hyperbolic asymptotic dispersivity model are compared with those obtained from the constant dispersivity model to scrutinize the relationship of the transport parameters derived by Mishra and Parker [Mishra, S., Parker, J.C., 1990. Analysis of solute transport with a hyperbolic scale dependent dispersion model. Hydrol. Proc. 4(1), 45-47]. The result reveals that the relationship postulated by Mishra and Parker [Mishra, S., Parker, J.C., 1990. Analysis of solute transport with a hyperbolic scale dependent dispersion model. Hydrol. Proc. 4(1), 45-47] is only valid under conditions with small dimensionless asymptotic dispersivity ( aa) and large dimensionless characteristic half length ( b).
High-resolution two dimensional advective transport
Smith, P.E.; Larock, B.E.
1989-01-01
The paper describes a two-dimensional high-resolution scheme for advective transport that is based on a Eulerian-Lagrangian method with a flux limiter. The scheme is applied to the problem of pure-advection of a rotated Gaussian hill and shown to preserve the monotonicity property of the governing conservation law.
Evolution and advection of solar mesogranulation
NASA Technical Reports Server (NTRS)
Muller, Richard; Auffret, Herve; Roudier, Thierry; Vigneau, Jean; Simon, George W.; Frank, Zoe; Shine, Richard A.; Title, Alan M.
1992-01-01
A three-hour sequence of observations at the Pic du Midi observatory has been obtained which shows the evolution of solar mesogranules from appearance to disappearance with unprecedented clarity. It is seen that the supergranules, which are known to advect the granules with their convective motion, also advect the mesogranules to their boundaries. This process controls the evolution and disappearance of mesogranules.
NASA Astrophysics Data System (ADS)
Li, Jin Hua; Chan, Hiu Ning; Chiang, Kin Seng; Chow, Kwok Wing
2015-11-01
Breathers and rogue waves of special coupled nonlinear Schrödinger systems (the Manakov equations) are studied analytically. These systems model the orthogonal polarization modes in an optical fiber with randomly varying birefringence. Studies earlier in the literature had shown that rogue waves can occur in these Manakov systems with dispersion and nonlinearity of opposite signs, and that the criterion for the existence of rogue waves correlates closely with the onset of modulation instability. In the present work the Hirota bilinear transform is employed to calculate the breathers (pulsating modes), and rogue waves are obtained as a long wave limit of such breathers. In terms of wave profiles, a 'black' rogue wave (intensity dropping to zero) and the transition to a four-petal configuration are elucidated analytically. Sufficiently strong modulation instabilities of the background may overwhelm or mask the development of the rogue waves, and such thresholds are correlated to actual physical properties of optical fibers. Numerical simulations on the evolution of breathers are performed to verify the prediction of the analytical formulations.
NASA Astrophysics Data System (ADS)
Deng, Guo; Biondini, Gino; Trillo, Stefano
2016-10-01
We study the small dispersion limit of the Korteweg-de Vries (KdV) equation with periodic boundary conditions and we apply the results to the Zabusky-Kruskal experiment. In particular, we employ a WKB approximation for the solution of the scattering problem for the KdV equation [i.e., the time-independent Schrödinger equation] to obtain an asymptotic expression for the trace of the monodromy matrix and thereby of the spectrum of the problem. We then perform a detailed analysis of the structure of said spectrum (i.e., band widths, gap widths and relative band widths) as a function of the dispersion smallness parameter ɛ. We then formulate explicit approximations for the number of solitons and corresponding soliton amplitudes as a function of ɛ. Finally, by performing an appropriate rescaling, we compare our results to those in the famous Zabusky and Kruskal's paper, showing very good agreement with the numerical results.
Advection-Induced Spectrotemporal Defects in a Free-Electron Laser
Bielawski, S.; Szwaj, C.; Bruni, C.; Garzella, D.; Orlandi, G.L.; Couprie, M.E.
2005-07-15
We evidence numerically and experimentally that advection can induce spectrotemporal defects in a system presenting a localized structure. Those defects in the spectrum are associated with the breakings induced by the drift of the localized solution. The results are based on simulations and experiments performed on the super-ACO free-electron laser. However, we show that this instability can be generalized using a real Ginzburg-Landau equation with (i) advection and (ii) a finite-size supercritical region.
NASA Technical Reports Server (NTRS)
Mazaheri, Alireza; Ricchiuto, Mario; Nishikawa, Hiroaki
2016-01-01
In this paper, we introduce a new hyperbolic first-order system for general dispersive partial differential equations (PDEs). We then extend the proposed system to general advection-diffusion-dispersion PDEs. We apply the fourth-order RD scheme of Ref. 1 to the proposed hyperbolic system, and solve time-dependent dispersive equations, including the classical two-soliton KdV and a dispersive shock case. We demonstrate that the predicted results, including the gradient and Hessian (second derivative), are in a very good agreement with the exact solutions. We then show that the RD scheme applied to the proposed system accurately captures dispersive shocks without numerical oscillations. We also verify that the solution, gradient and Hessian are predicted with equal order of accuracy.
A subordinated advection model for uniform bed load transport from local to regional scales
NASA Astrophysics Data System (ADS)
Zhang, Yong; Martin, Raleigh L.; Chen, Dong; Baeumer, Boris; Sun, Hongguang; Chen, Li
2014-12-01
Sediment tracers moving as bed load can exhibit anomalous dispersion behavior deviating from Fickian diffusion. The presence of heavy-tailed resting time distributions and thin-tailed step length distributions motivate adoption of fractional-derivative models (FDMs) to describe sediment dispersion, but these models require many parameters that are difficult to quantify. Here we propose a considerably simplified FDM for anomalous transport of uniformly sized grains along straight channels, the subordinated advection equation (SAE), which is based on the concept of time subordination. Unlike previous FDM models with time index γ between 0 and 1, our SAE model adopts a value of γ between 1 and 2. This γ describes random velocities deviating significantly from the mean velocity and models both long resting periods and relatively fast displacements. We show that the model quantifies the dynamics of four bed load transport experiments recorded in the literature. In addition to γ, SAE model parameters—velocity and capacity coefficient—are related to the mean and variance of particle velocities, respectively. Successful application of the SAE model also implies a universal probability density for the heavy-tailed waiting time distribution (with finite mean) and a relatively lighter tailed step length distribution for uniform bed load transport from local to regional scales.
Potravkin, N N; Perezhogin, I A; Makarov, V A
2012-11-01
We propose an alternative method of integration of Maxwell equations. This method is the generalization of a finite-difference time-domain method with an auxiliary differential equation for the case of a linear optical medium with a frequency dispersion and an arbitrary source of spatial dispersion. We apply this method to the problem of the propagation of short plane-wave linearly polarized light pulses in such a medium. It is shown that some features of their propagation are completely different from those that are generally recognized for the linear optical activity phenomenon. For example, in some cases an initially linearly polarized light pulse becomes elliptically polarized during the propagation. This effect is more prominent in the front part of the pulse.
Evolution and Advection of Solar Mesogranulation
1992-03-01
unprecedented clarity. We see that the supergranules, which are known to carry along (advect) the granules with their convective motion, also advect...I Solar mesogranulation, Solar observations, Solar super- 2 granulation 16. PRICE COCE 1i7. SECJ-3T LSiIATO 8 EUITY CLASSIFICA ION 19. SECURITY CLAS...mo~iesý sho~ed that granules are adl~ectedl b• Richard Muller*, Hers& Auffret*, Thierry Roudiert, the larger-scale consectie flowss. and thu, could
A Quasi-Conservative Adaptive Semi-Lagrangian Advection-Diffusion Scheme
NASA Astrophysics Data System (ADS)
Behrens, Joern
2014-05-01
Many processes in atmospheric or oceanic tracer transport are conveniently represented by advection-diffusion type equations. Depending on the magnitudes of both components, the mathematical representation and consequently the discretization is a non-trivial problem. We will focus on advection-dominated situations and will introduce a semi-Lagrangian scheme with adaptive mesh refinement for high local resolution. This scheme is well suited for pollutant transport from point sources, or transport processes featuring fine filamentation with corresponding local concentration maxima. In order to achieve stability, accuracy and conservation, we combine an adaptive mesh refinement quasi-conservative semi-Lagrangian scheme, based on an integral formulation of the underlying advective conservation law (Behrens, 2006), with an advection diffusion scheme as described by Spiegelman and Katz (2006). The resulting scheme proves to be conservative and stable, while maintaining high computational efficiency and accuracy.
NASA Astrophysics Data System (ADS)
Manikandan, K.; Senthilvelan, M.
2016-07-01
We construct spatiotemporal localized envelope solutions of a (3 + 1)-dimensional nonlinear Schrödinger equation with varying coefficients such as dispersion, nonlinearity and gain parameters through similarity transformation technique. The obtained localized rational solutions can serve as prototypes of rogue waves in different branches of science. We investigate the characteristics of constructed localized solutions in detail when it propagates through six different dispersion profiles, namely, constant, linear, Gaussian, hyperbolic, logarithm, and exponential. We also obtain expressions for the hump and valleys of rogue wave intensity profiles for these six dispersion profiles and study the trajectory of it in each case. Further, we analyze how the intensity of another localized solution, namely, breather, changes when it propagates through the aforementioned six dispersion profiles. Our studies reveal that these localized solutions co-exist with the collapsing solutions which are already found in the (3 + 1)-dimensional nonlinear Schrödinger equation. The obtained results will help to understand the corresponding localized wave phenomena in related fields.
Kumar, Shiva; Shao, Jing; Liang, Xiaojun
2014-12-29
In the presence of pre-dispersion, an exact solution of nonlinear Schrödinger equation (NLSE) is derived for impulse input. The phase factor of the exact solution is obtained in a closed form using the exponential integral. The nonlinear interaction among periodically placed impulses launched at the input is investigated, and the condition under which these pulses do not exchange energy is examined. It is found that if the complex weights of the impulses at the input have a secant-hyperbolic envelope and a proper chirp factor, they will propagate over long distances without exchanging energy. To describe their interaction, a discrete version of NLSE is derived. The derived equation is a form of discrete self-trapping (DST) equation, which is found to admit fundamental and higher order soliton solutions in the presence of high pre-dispersion. Nonlinear eigenmodes derived here may be useful for description of signal propagation and nonlinear interaction in highly pre-dispersion fiber-optic systems.
NASA Astrophysics Data System (ADS)
Bodin, Jacques
2015-03-01
In this study, new multi-dimensional time-domain random walk (TDRW) algorithms are derived from approximate one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) analytical solutions of the advection-dispersion equation and from exact 1-D, 2-D, and 3-D analytical solutions of the pure-diffusion equation. These algorithms enable the calculation of both the time required for a particle to travel a specified distance in a homogeneous medium and the mass recovery at the observation point, which may be incomplete due to 2-D or 3-D transverse dispersion or diffusion. The method is extended to heterogeneous media, represented as a piecewise collection of homogeneous media. The particle motion is then decomposed along a series of intermediate checkpoints located on the medium interface boundaries. The accuracy of the multi-dimensional TDRW method is verified against (i) exact analytical solutions of solute transport in homogeneous media and (ii) finite-difference simulations in a synthetic 2-D heterogeneous medium of simple geometry. The results demonstrate that the method is ideally suited to purely diffusive transport and to advection-dispersion transport problems dominated by advection. Conversely, the method is not recommended for highly dispersive transport problems because the accuracy of the advection-dispersion TDRW algorithms degrades rapidly for a low Péclet number, consistent with the accuracy limit of the approximate analytical solutions. The proposed approach provides a unified methodology for deriving multi-dimensional time-domain particle equations and may be applicable to other mathematical transport models, provided that appropriate analytical solutions are available.
Shear dispersion in a capillary tube with a porous wall.
Dejam, Morteza; Hassanzadeh, Hassan; Chen, Zhangxin
2016-01-01
An analytical expression is presented for the shear dispersion during solute transport in a coupled system comprised of a capillary tube and a porous medium. The dispersion coefficient is derived in a capillary tube with a porous wall by considering an accurate boundary condition, which is the continuity of concentration and mass flux, at the interface between the capillary tube and porous medium. A comparison of the obtained results with that in a non-coupled system identifies three regimes including: diffusion-dominated, transition, and advection-dominated. The results reveal that it is essential to include the exchange of solute between the capillary tube and porous medium in development of the shear dispersion coefficient for the last two regimes. The resulting equivalent transport equation revealed that due to mass transfer between the capillary tube and the porous medium, the dispersion coefficient is decreased while the effective velocity in the capillary tube increases. However, a larger effective advection term leads to faster breakthrough of a solute and enhances mass delivery to the porous medium as compared with the classical double-porosity model with a non-coupled dispersion coefficient. The obtained results also indicate that the finite porous medium gives faster breakthrough of a solute as compared with the infinite one. These results find applications in solute transport in porous capillaries and membranes.
Space-fractional advection-diffusion and reflective boundary condition.
Krepysheva, Natalia; Di Pietro, Liliana; Néel, Marie-Christine
2006-02-01
Anomalous diffusive transport arises in a large diversity of disordered media. Stochastic formulations in terms of continuous time random walks (CTRWs) with transition probability densities showing space- and/or time-diverging moments were developed to account for anomalous behaviors. A broad class of CTRWs was shown to correspond, on the macroscopic scale, to advection-diffusion equations involving derivatives of noninteger order. In particular, CTRWs with Lévy distribution of jumps and finite mean waiting time lead to a space-fractional equation that accounts for superdiffusion and involves a nonlocal integral-differential operator. Within this framework, we analyze the evolution of particles performing symmetric Lévy flights with respect to a fluid moving at uniform speed . The particles are restricted to a semi-infinite domain limited by a reflective barrier. We show that the introduction of the boundary condition induces a modification in the kernel of the nonlocal operator. Thus, the macroscopic space-fractional advection-diffusion equation obtained is different from that in an infinite medium.
Vortex emission accompanies the advection of optical localized structures.
Haudin, F; Rojas, R G; Bortolozzo, U; Clerc, M G; Residori, S
2011-02-11
We show that the advection of optical localized structures is accompanied by the emission of vortices, with phase singularities appearing in the wake of the drifting structure. Localized structures are obtained in a light-valve experiment and made to drift by a mirror tilt in the feedback loop. Pairs of oppositely charged vortices are detected for small drifts, whereas for large drifts a vortex array develops. Observations are supported by numerical simulations and linear stability analysis of the system equations and are expected to be generic for a large class of translated optical patterns.
A convexity preserving scheme for conservative advection transport
NASA Astrophysics Data System (ADS)
Xiao, Feng; Peng, Xindong
2004-08-01
A simple and practical scheme for advection transport equation is presented. The scheme, namely piecewise rational method (PRM), is a variant of the existing piecewise parabolic method (PPM) of Colella and Woodward (1984). Instead of the parabolic function, a rational function is used for the reconstruction. Making use of the convexity preserving nature of the rational function enables us to obtain oscillation-less numerical solutions, but avoids the adjustments of the cell-interface values to enforce the monotonicity in PPM. The PRM is very simple and computationally efficient. Our numerical results show that PRM is competitive to the PPM in many aspects, such as numerical accuracy and shape-preserving property.
High-Order Non-Reflecting Boundary Conditions for the Linearized Euler Equations
2008-09-01
Bérenger [11] for the 2-D Maxwell equations. This absorbing layer method surrounds the computational domain with a dispersive medium, defined in such a...no advection or forcing terms. After demon - strating the validity of this prototypical implementation in Section B, we proceed to incorporate the...may improve these results [55], but for the purpose of this dissertation, it is sufficient to demon - strate how to use the auxiliary variable NRBC
Chen, Yong; Yan, Zhenya
2016-03-22
Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields.
Chen, Yong; Yan, Zhenya
2016-01-01
Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields. PMID:27002543
NASA Astrophysics Data System (ADS)
Gogoi, R.; Kalita, L.; Devi, N.
2010-02-01
Much interest was shown towards the studies on nonlinear stability in the late sixties. Plasma instabilities play an important role in plasma dynamics. More attention has been given towards stability analysis after recognizing that they are one of the principal obstacles in the way of a successful resolution of the problem of controlled thermonuclear fusion. Nonlinearity and dispersion are the two important characteristics of plasma instabilities. Instabilities and nonlinearity are the two important and interrelated terms. In our present work, the continuity and momentum equations for both ions and electrons together with the Poisson equation are considered as cold plasma model. Then we have adopted the modified reductive perturbation technique (MRPT) from Demiray [1] to derive the higher order equation of the Nonlinear Schrödinger equation (NLSE). In this work, detailed mathematical expressions and calculations are done to investigate the changing character of the modulation of ion acoustic plasma wave through our derived equation. Thus we have extended the application of MRPT to derive the higher order equation. Both progressive wave solutions as well as steady state solutions are derived and they are plotted for different plasma parameters to observe dark/bright solitons. Interesting structures are found to exist for different plasma parameters.
Surfzone alongshore advective accelerations: observations and modeling
NASA Astrophysics Data System (ADS)
Hansen, J.; Raubenheimer, B.; Elgar, S.
2014-12-01
The sources, magnitudes, and impacts of non-linear advective accelerations on alongshore surfzone currents are investigated with observations and a numerical model. Previous numerical modeling results have indicated that advective accelerations are an important contribution to the alongshore force balance, and are required to understand spatial variations in alongshore currents (which may result in spatially variable morphological change). However, most prior observational studies have neglected advective accelerations in the alongshore force balance. Using a numerical model (Delft3D) to predict optimal sensor locations, a dense array of 26 colocated current meters and pressure sensors was deployed between the shoreline and 3-m water depth over a 200 by 115 m region near Duck, NC in fall 2013. The array included 7 cross- and 3 alongshore transects. Here, observational and numerical estimates of the dominant forcing terms in the alongshore balance (pressure and radiation-stress gradients) and the advective acceleration terms will be compared with each other. In addition, the numerical model will be used to examine the force balance, including sources of velocity gradients, at a higher spatial resolution than possible with the instrument array. Preliminary numerical results indicate that at O(10-100 m) alongshore scales, bathymetric variations and the ensuing alongshore variations in the wave field and subsequent forcing are the dominant sources of the modeled velocity gradients and advective accelerations. Additional simulations and analysis of the observations will be presented. Funded by NSF and ASDR&E.
Adaptive Computations for Partial Differential Equations Governing Advective Fluid Flows
1990-12-27
finite element methods have been studied in [30,34,42,45]. Mixed methods have been coupled with other techniques in multicomponent and multiphase...D. Guerillot and 0. Guillon, eds.), Editors Technip, Paris, 1990, 157-163. 81. M.S. Espedal, R.E. Ewing, and T.F. Russell, Mixed methods , operator...May 1988, 85-91. B. ACCEPTED 84. M.S. Espedal, R.E. Ewing, T.F. Russell, and 0. Saevareid, Reservoir simula- tion using mixed methods , a modified
First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems
NASA Technical Reports Server (NTRS)
Mazaheri, Alireza; Nishikawa, Hiroaki
2014-01-01
A time-dependent extension of the first-order hyperbolic system method for advection-diffusion problems is introduced. Diffusive/viscous terms are written and discretized as a hyperbolic system, which recovers the original equation in the steady state. The resulting scheme offers advantages over traditional schemes: a dramatic simplification in the discretization, high-order accuracy in the solution gradients, and orders-of-magnitude convergence acceleration. The hyperbolic advection-diffusion system is discretized by the second-order upwind residual-distribution scheme in a unified manner, and the system of implicit-residual-equations is solved by Newton's method over every physical time step. The numerical results are presented for linear and nonlinear advection-diffusion problems, demonstrating solutions and gradients produced to the same order of accuracy, with rapid convergence over each physical time step, typically less than five Newton iterations.
An approximate calculation of advective gas-phase transport of 14C at Yucca Mountain, Nevada
NASA Astrophysics Data System (ADS)
Knapp, R. B.
1990-01-01
A quasilinear partial differential equation, which describes gas-phase transport of a 14C kinematic wave through a porous medium, is derived, its sensitivity to system variables is analyzed and it is applied to one possible release scenarion at the porposed Yucca Mountain, Nevada high-level radioactive waste repository. Advection, isotope exchange between CO 2 in a flowing gas phase and HCO 3- in a static aqueous phase, and radioactive decay are incorporated. The governing equation is solved analytically by the method of characteristics. The mass fraction of 14C in the gas phase,X 14g, is controlled by radioactive decay. The relatively long half-line of 14C, about 5720 years, and the relatively shallow proposed burial depth of the radioactive waste, about 350m, requires significant retardation of the 14C wave velocity for significant reduction in X 14g. 14C wave velocity is most sensitive to temperature and pH which control the distribution of total carbon between gas and liquid phase; the greater the partitioning of carbon into the liquid phase, the greater the retardation of the 14C wave velocity and the greater the ultimate reduction in X 14g from initial conditions. Partitioning of total carbon into the liquid phase is greatest at low temperatures, < 100° C, and high pH values, > 8. Increasing water saturation also tends to retard 14C wave velocity but to a lesser extent. The governing equation has been applied using conditions that may possibly occur at the proposed Yucca Mountain repository. Calculations indicate that the 14C wave takes about 5900 years to reach the surface with a X 14g equal to 25 ppm. Diffusion and dispersion are not of major importance for these conditions. These calculations are approximate due to the number of assumptions involved. Discharge of 14C into the gas before the selected time would accelerate wave arrival and increase the amount of 14C reaching the surface.
NASA Technical Reports Server (NTRS)
Goorjian, Peter M.; Taflove, Allen
1992-01-01
The initial results for femtosecond electromagnetic soliton propagation and collision obtained from first principles, i.e., by a direct time integration of Maxwell's equations are reported. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit the modeling of 2D and 3D optical soliton propagation, scattering, and switching from the full-vector Maxwell's equations.
Estimation of the advection effects induced by surface heterogeneities in the surface energy budget
NASA Astrophysics Data System (ADS)
Cuxart, Joan; Wrenger, Burkhard; Martínez-Villagrasa, Daniel; Reuder, Joachim; Jonassen, Marius O.; Jiménez, Maria A.; Lothon, Marie; Lohou, Fabienne; Hartogensis, Oscar; Dünnermann, Jens; Conangla, Laura; Garai, Anirban
2016-07-01
The effect of terrain heterogeneities in one-point measurements is a continuous subject of discussion. Here we focus on the order of magnitude of the advection term in the equation of the evolution of temperature as generated by documented terrain heterogeneities and we estimate its importance as a term in the surface energy budget (SEB), for which the turbulent fluxes are computed using the eddy-correlation method. The heterogeneities are estimated from satellite and model fields for scales near 1 km or broader, while the smaller scales are estimated through direct measurements with remotely piloted aircraft and thermal cameras and also by high-resolution modelling. The variability of the surface temperature fields is not found to decrease clearly with increasing resolution, and consequently the advection term becomes more important as the scales become finer. The advection term provides non-significant values to the SEB at scales larger than a few kilometres. In contrast, surface heterogeneities at the metre scale yield large values of the advection, which are probably only significant in the first centimetres above the ground. The motions that seem to contribute significantly to the advection term in the SEB equation in our case are roughly those around the hectometre scales.
The connection of standard thin disk with advection-dominated accretion flow
NASA Astrophysics Data System (ADS)
Lin, Yi-qing; Lu, Ju-fu; G. U., Wei-min
2005-04-01
Using the standard Runge-Kutta method, a global solution of the basic equations describing black hole accretion flows is derived. It is proved that transition from a standard thin disk to an advection-dominated accretion flow is realizable in case of high viscosity, without introducing any additional mechanism of energy transfer or specifying any ad hoc outer boundary condition.
Diffusion and Advection using Cellular Potts Model
NASA Astrophysics Data System (ADS)
Dan, Debasis; Glazier, James
2005-03-01
The Cellular Potts Model (CPM) is a robust cell level methodology for simulation of biological tissues and morphogenesis. Standard diffusion solvers in the CPM use finite difference methods on the underlying CPM lattice. These methods have difficulty in simulating local advection in the ECM due to physiology and morphogenesis. To circumvent the problem of instabilities we simulate advection-diffusion within the framework of CPM using off-lattice finite-difference methods. We define a set of generalised fluid "cells" or particles which separate advection and diffusion from the lattice. Diffusion occurs between neighboring fluid cells by local averaging rules which approximate the Laplacian. CPM movement of the cells by spin flips handles the advection. The extension allows the CPM to model viscosity explicitly by including a relative velocity constraint on the fluid. The extended CPM correctly reproduces flow profiles of viscous fluids in cylindrical tube, during Stokes flow across a sphere and in flow in concentric cylindrical shells. We illustrate various conditions for diffusion including multiple instantaneous sources, continuous sources, moving sources and different boundary geometries and conditions to validate our approximation by comparing with analytical and established numerical solutions.
3D Flow Visualization Using Texture Advection
NASA Technical Reports Server (NTRS)
Kao, David; Zhang, Bing; Kim, Kwansik; Pang, Alex; Moran, Pat (Technical Monitor)
2001-01-01
Texture advection is an effective tool for animating and investigating 2D flows. In this paper, we discuss how this technique can be extended to 3D flows. In particular, we examine the use of 3D and 4D textures on 3D synthetic and computational fluid dynamics flow fields.
NASA Astrophysics Data System (ADS)
Fujioka, J.; Espinosa, A.
2015-11-01
In this article, we show that if the nonlinear Schrödinger (NLS) equation is generalized by simultaneously taking into account higher-order dispersion, a quintic nonlinearity, and self-steepening terms, the resulting equation is interesting as it has exact soliton solutions which may be (depending on the values of the coefficients) stable or unstable, standard or "embedded," fixed or "moving" (i.e., solitons which advance along the retarded-time axis). We investigate the stability of these solitons by means of a modified version of the Vakhitov-Kolokolov criterion, and numerical tests are carried out to corroborate that these solitons respond differently to perturbations. It is shown that this generalized NLS equation can be derived from a Lagrangian density which contains an auxiliary variable, and Noether's theorem is then used to show that the invariance of the action integral under infinitesimal gauge transformations generates a whole family of conserved quantities. Finally, we study if this equation has the Painlevé property.
Fujioka, J; Espinosa, A
2015-11-01
In this article, we show that if the nonlinear Schrödinger (NLS) equation is generalized by simultaneously taking into account higher-order dispersion, a quintic nonlinearity, and self-steepening terms, the resulting equation is interesting as it has exact soliton solutions which may be (depending on the values of the coefficients) stable or unstable, standard or "embedded," fixed or "moving" (i.e., solitons which advance along the retarded-time axis). We investigate the stability of these solitons by means of a modified version of the Vakhitov-Kolokolov criterion, and numerical tests are carried out to corroborate that these solitons respond differently to perturbations. It is shown that this generalized NLS equation can be derived from a Lagrangian density which contains an auxiliary variable, and Noether's theorem is then used to show that the invariance of the action integral under infinitesimal gauge transformations generates a whole family of conserved quantities. Finally, we study if this equation has the Painlevé property.
Gogosov, V.V.; Martynov, S.I.; Tsurikov, S.N.; Shaposhnikova, G.A.
1987-10-01
In the interest of establishing a scenario for the ultrasonic testing and quality control of magnetic liquids based on dispersions of magnetite the authors construct a mathematical model depicting the propagation of ultrasonic waves through the liquid under conditions of magnetization and magnetohydrodynamics imposed by an external magnetic field. The model analyzes the agglomerating properties of the magnetite particles and the effect of their agglomeration on ultrasonic wave propagation.
NASA Technical Reports Server (NTRS)
Joseph, Rose M.; Hagness, Susan C.; Taflove, Allen
1991-01-01
The initial results for femtosecond pulse propagation and scattering interactions for a Lorentz medium obtained by a direct time integration of Maxwell's equations are reported. The computational approach provides reflection coefficients accurate to better than 6 parts in 10,000 over the frequency range of dc to 3 x 10 to the 16th Hz for a single 0.2-fs Gaussian pulse incident upon a Lorentz-medium half-space. New results for Sommerfeld and Brillouin precursors are shown and compared with previous analyses. The present approach is robust and permits 2D and 3D electromagnetic pulse propagation directly from the full-vector Maxwell's equations.
NASA Technical Reports Server (NTRS)
Grant, F. C.
1972-01-01
The connection between the Van Kampen and Landau representations of the Vlasov equations has been extended to Fourier-Hermite expansions containing more than 1000 terms by taking advantage of the properties of tridiagonal matrices. These numerical results are regarded as conclusive indications of the nonuniformly convergent behavior of the approximation curve in the limit of an infinite number of terms and represent an extension of work begun by Grant (1967) and by Grant and Feix (1967).
NASA Astrophysics Data System (ADS)
Dubina, Sean Hyun; Wedgewood, Lewis Edward
2016-07-01
Ferrofluids are often favored for their ability to be remotely positioned via external magnetic fields. The behavior of particles in ferromagnetic clusters under uniformly applied magnetic fields has been computationally simulated using the Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. However, few methods have been established that effectively handle the basic principles of magnetic materials, namely, Maxwell's equations. An iterative constraint method was developed to satisfy Maxwell's equations when a uniform magnetic field is imposed on ferrofluids in a heterogeneous Brownian dynamics simulation that examines the impact of ferromagnetic clusters in a mesoscale particle collection. This was accomplished by allowing a particulate system in a simple shear flow to advance by a time step under a uniformly applied magnetic field, then adjusting the ferroparticles via an iterative constraint method applied over sub-volume length scales until Maxwell's equations were satisfied. The resultant ferrofluid model with constraints demonstrates that the magnetoviscosity contribution is not as substantial when compared to homogeneous simulations that assume the material's magnetism is a direct response to the external magnetic field. This was detected across varying intensities of particle-particle interaction, Brownian motion, and shear flow. Ferroparticle aggregation was still extensively present but less so than typically observed.
Capillary deposition of advected floating particles
NASA Astrophysics Data System (ADS)
Dressaire, Emilie; Debaisieux, Aymeric; Gregori, Federico
2016-11-01
The deposition and aggregation of particles flowing through a confined environment can dramatically hinder the transport of suspensions. Yet, the mechanisms responsible for the deposition of particles in shear flow are not fully understood. Here, we use an experimental model system in which floating particles are advected on the surface of a water channel and deposited on fixed obstacles through attractive capillary effects. By varying the flow rate of the liquid, the wetting properties and size of the particles and obstacles, we can tune the magnitude of the capillary and hydrodynamic forces that determine the probability of deposition and the equilibrium position on the substrate. We show that arrays of obstacles can be designed to efficiently capture the floating particles advected by the flow.
Distributed Parallel Particle Advection using Work Requesting
Muller, Cornelius; Camp, David; Hentschel, Bernd; Garth, Christoph
2013-09-30
Particle advection is an important vector field visualization technique that is difficult to apply to very large data sets in a distributed setting due to scalability limitations in existing algorithms. In this paper, we report on several experiments using work requesting dynamic scheduling which achieves balanced work distribution on arbitrary problems with minimal communication overhead. We present a corresponding prototype implementation, provide and analyze benchmark results, and compare our results to an existing algorithm.
NASA Astrophysics Data System (ADS)
Butler, N. L.; Hunt, J. R.; Tompkins, M. R.
2011-12-01
Hyporheic exchange can locally mitigate thermal stress caused by high water temperatures by upwelling water cooler than ambient stream temperatures and thus providing thermal refuge for critical cold water organisms like salmonids. Ten hyporheic exchange locations were identified by dye tracer experiments along a 16 km stretch of Deer Creek near Vina, California. Four months of continuous temperature measurements were made in the late summer of 2005 at each downwelling and upwelling location and revealed upwelled temperatures that were lagged in time and damped in amplitude. Upwelling hyporheic temperatures that could provide thermal refuge were observed in seven of the ten temperature records. This data was modeled by an analytical one-dimensional advection-diffusion equation solution using subsurface water velocity and the hydrodynamic dispersivity fitting parameters. At each location variations in upwelling temperature are explained by changing subsurface water velocities and flow pathways. The lag time in hyporheic heat flow ranged from a few hours to 44 hours over distances of 15 to 76 meters. The daily stream temperature variation was on the order of 10°C, which was reduced to 1 to 8°C in the upwelling hyporheic flow. At four locations, there was evidence that changes in stream flow produced changes in the amplitude and phase of the upwelling hyporheic water temperature by altering both the subsurface water velocity and hydrodynamic dispersivity. At two locations, additional cold water refuge was created by decreases in surface water flow because it reduced the estimated subsurface water velocity increasing the lag time between the peak surface water and subsurface water temperatures. Increases in surface water flow increased the dispersivity at three locations providing more cold water refuge by reducing the amplitude of the upwelling hyporheic temperature. Such changes alter thermal refuge for salmonids placing a new emphasis on managing surface water
NASA Astrophysics Data System (ADS)
Webb, G. M.; Dasgupta, B.; McKenzie, J. F.; Hu, Q.; Zank, G. P.
2014-03-01
In this paper advected invariants and conservation laws in ideal magnetohydrodynamics (MHD) and gas dynamics are obtained using Lie dragging techniques. There are different classes of invariants that are advected or Lie dragged with the flow. Simple examples are the advection of the entropy S (a 0-form), and the conservation of magnetic flux (an invariant 2-form advected with the flow). The magnetic flux conservation law is equivalent to Faraday's equation. The gauge condition for the magnetic helicity to be advected with the flow is determined. Different variants of the helicity in ideal fluid dynamics and MHD including: fluid helicity, cross helicity and magnetic helicity are investigated. The fluid helicity conservation law and the cross-helicity conservation law in MHD are derived for the case of a barotropic gas. If the magnetic field lies in the constant entropy surface, then the gas pressure can depend on both the entropy and the density. In these cases the conservation laws are local conservation laws. For non-barotropic gases, we obtain nonlocal conservation laws for fluid helicity and cross helicity by using Clebsch variables. These nonlocal conservation laws are the main new results of the paper. Ertel's theorem and potential vorticity, the Hollman invariant, and the Godbillon-Vey invariant for special flows for which the magnetic helicity is zero are also discussed.
Efficient mass transport by optical advection
Kajorndejnukul, Veerachart; Sukhov, Sergey; Dogariu, Aristide
2015-01-01
Advection is critical for efficient mass transport. For instance, bare diffusion cannot explain the spatial and temporal scales of some of the cellular processes. The regulation of intracellular functions is strongly influenced by the transport of mass at low Reynolds numbers where viscous drag dominates inertia. Mimicking the efficacy and specificity of the cellular machinery has been a long time pursuit and, due to inherent flexibility, optical manipulation is of particular interest. However, optical forces are relatively small and cannot significantly modify diffusion properties. Here we show that the effectiveness of microparticle transport can be dramatically enhanced by recycling the optical energy through an effective optical advection process. We demonstrate theoretically and experimentally that this new advection mechanism permits an efficient control of collective and directional mass transport in colloidal systems. The cooperative long-range interaction between large numbers of particles can be optically manipulated to create complex flow patterns, enabling efficient and tunable transport in microfluidic lab-on-chip platforms. PMID:26440069
An implicit dispersive transport algorithm for the US Geological Survey MOC3D solute-transport model
Kipp, K.L.; Konikow, L.F.; Hornberger, G.Z.
1998-01-01
This report documents an extension to the U.S. Geological Survey MOC3D transport model that incorporates an implicit-in-time difference approximation for the dispersive transport equation, including source/sink terms. The original MOC3D transport model (Version 1) uses the method of characteristics to solve the transport equation on the basis of the velocity field. The original MOC3D solution algorithm incorporates particle tracking to represent advective processes and an explicit finite-difference formulation to calculate dispersive fluxes. The new implicit procedure eliminates several stability criteria required for the previous explicit formulation. This allows much larger transport time increments to be used in dispersion-dominated problems. The decoupling of advective and dispersive transport in MOC3D, however, is unchanged. With the implicit extension, the MOC3D model is upgraded to Version 2. A description of the numerical method of the implicit dispersion calculation, the data-input requirements and output options, and the results of simulator testing and evaluation are presented. Version 2 of MOC3D was evaluated for the same set of problems used for verification of Version 1. These test results indicate that the implicit calculation of Version 2 matches the accuracy of Version 1, yet is more efficient than the explicit calculation for transport problems that are characterized by a grid Peclet number less than about 1.0.
Liu, Lianchi; Liu, Yi; Zybin, Sergey V; Sun, Huai; Goddard, William A
2011-10-13
The practical levels of density functional theory (DFT) for solids (LDA, PBE, PW91, B3LYP) are well-known not to account adequately for the London dispersion (van der Waals attraction) so important in molecular solids, leading to equilibrium volumes for molecular crystals ~10-15% too high. The ReaxFF reactive force field is based on fitting such DFT calculations and suffers from the same problem. In the paper we extend ReaxFF by adding a London dispersion term with a form such that it has low gradients (lg) at valence distances leaving the already optimized valence interactions intact but behaves as 1/R(6) for large distances. We derive here these lg corrections to ReaxFF based on the experimental crystal structure data for graphite, polyethylene (PE), carbon dioxide, and nitrogen and for energetic materials: hexahydro-1,3,5-trinitro-1,3,5-s-triazine (RDX), pentaerythritol tetranitrate (PETN), 1,3,5-triamino-2,4,6-trinitrobenzene (TATB), and nitromethane (NM). After this dispersion correction the average error of predicted equilibrium volumes decreases from 18.5 to 4.2% for the above systems. We find that the calculated crystal structures and equation of state with ReaxFF-lg are in good agreement with experimental results. In particular, we examined the phase transition between α-RDX and γ-RDX, finding that ReaxFF-lg leads to excellent agreement for both the pressure and volume of this transition occurring at ~4.8 GPa and ~2.18 g/cm(3) density from ReaxFF-lg vs 3.9 GPa and ~2.21 g/cm(3) from experiment. We expect ReaxFF-lg to improve the descriptions of the phase diagrams for other energetic materials.
Kukačka, Libor; Nosek, Štĕpán; Kellnerová, Radka; Jurčáková, Klára; Jaňour, Zbyněk
2012-01-01
The objective of this study is to determine processes of pollution ventilation in the X-shaped street intersection in an idealized symmetric urban area for the changing approach flow direction. A unique experimental setup for simultaneous wind tunnel measurement of the flow velocity and the tracer gas concentration in a high temporal resolution is assembled. Advective horizontal and vertical scalar fluxes are computed from averaged measured velocity and concentration data within the street intersection. Vertical advective and turbulent scalar fluxes are computed from synchronized velocity and concentration signals measured in the plane above the intersection. All the results are obtained for five approach flow directions. The influence of the approach flow on the advective and turbulent fluxes is determined. The contribution of the advective and turbulent flux to the ventilation is discussed. Wind direction with the best dispersive conditions in the area is found. The quadrant analysis is applied to the synchronized signals of velocity and concentration fluctuation to determine events with the dominant contribution to the momentum flux and turbulent scalar flux.
Kukačka, Libor; Nosek, Štĕpán; Kellnerová, Radka; Jurčáková, Klára; Jaňour, Zbyněk
2012-01-01
The objective of this study is to determine processes of pollution ventilation in the X-shaped street intersection in an idealized symmetric urban area for the changing approach flow direction. A unique experimental setup for simultaneous wind tunnel measurement of the flow velocity and the tracer gas concentration in a high temporal resolution is assembled. Advective horizontal and vertical scalar fluxes are computed from averaged measured velocity and concentration data within the street intersection. Vertical advective and turbulent scalar fluxes are computed from synchronized velocity and concentration signals measured in the plane above the intersection. All the results are obtained for five approach flow directions. The influence of the approach flow on the advective and turbulent fluxes is determined. The contribution of the advective and turbulent flux to the ventilation is discussed. Wind direction with the best dispersive conditions in the area is found. The quadrant analysis is applied to the synchronized signals of velocity and concentration fluctuation to determine events with the dominant contribution to the momentum flux and turbulent scalar flux. PMID:22649290
A computational method for sharp interface advection
Bredmose, Henrik; Jasak, Hrvoje
2016-01-01
We devise a numerical method for passive advection of a surface, such as the interface between two incompressible fluids, across a computational mesh. The method is called isoAdvector, and is developed for general meshes consisting of arbitrary polyhedral cells. The algorithm is based on the volume of fluid (VOF) idea of calculating the volume of one of the fluids transported across the mesh faces during a time step. The novelty of the isoAdvector concept consists of two parts. First, we exploit an isosurface concept for modelling the interface inside cells in a geometric surface reconstruction step. Second, from the reconstructed surface, we model the motion of the face–interface intersection line for a general polygonal face to obtain the time evolution within a time step of the submerged face area. Integrating this submerged area over the time step leads to an accurate estimate for the total volume of fluid transported across the face. The method was tested on simple two-dimensional and three-dimensional interface advection problems on both structured and unstructured meshes. The results are very satisfactory in terms of volume conservation, boundedness, surface sharpness and efficiency. The isoAdvector method was implemented as an OpenFOAM® extension and is published as open source. PMID:28018619
Gas phase dispersion in compost as a function of different water contents and air flow rates.
Sharma, Prabhakar; Poulsen, Tjalfe G
2009-07-21
Gas phase dispersion in a natural porous medium (yard waste compost) was investigated as a function of gas flow velocity and compost volumetric water content using oxygen and nitrogen as tracer gases. The compost was chosen because it has a very wide water content range and because it represents a wide range of porous media, including soils and biofilter media. Column breakthrough curves for oxygen and nitrogen were measured at relatively low pore gas velocities, corresponding to those observed in for instance soil vapor extraction systems or biofilters for air cleaning at biogas plants or composting facilities. Total gas mechanical dispersion-molecular diffusion coefficients were fitted from the breakthrough curves using a one-dimensional numerical solution to the advection-dispersion equation and used to determine gas dispersivities at different volumetric gas contents. The results showed that gas mechanical dispersion dominated over molecular diffusion with mechanical dispersion for all water contents and pore gas velocities investigated. Importance of mechanical dispersion increased with increasing pore gas velocity and compost water content. The results further showed that gas dispersivity was relatively constant at high values of compost gas-filled porosity but increased with decreasing gas-filled porosity at lower values of gas-filled porosity. Results finally showed that measurement uncertainty in gas dispersivity is generally highest at low values of pore gas velocity.
Wang Jianmin; Cheng Cheng; Li Yanrong
2012-04-01
We investigate the dynamics of clumps embedded in and confined by the advection-dominated accretion flows (ADAFs), in which collisions among the clumps are neglected. We start from the collisionless Boltzmann equation and assume that interaction between the clumps and the ADAF is responsible for transporting the angular momentum of clumps outward. The inner edge of the clumpy-ADAF is set to be the tidal radius of the clumps. We consider strong- and weak-coupling cases, in which the averaged properties of clumps follow the ADAF dynamics and are mainly determined by the black hole potential, respectively. We propose the analytical solution of the dynamics of clumps for the two cases. The velocity dispersion of clumps is one magnitude higher than the ADAF for the strong-coupling case. For the weak-coupling case, we find that the mean radial velocity of clumps is linearly proportional to the coefficient of the drag force. We show that the tidally disrupted clumps would lead to an accumulation of the debris to form a debris disk in the Shakura-Sunyaev regime. The entire hot ADAF will be efficiently cooled down by photons from the debris disk, giving rise to a collapse of the ADAF, and quench the clumpy accretion. Subsequently, evaporation of the collapsed ADAF drives resuscitate of a new clumpy-ADAF, resulting in an oscillation of the global clumpy-ADAF. Applications of the present model are briefly discussed to X-ray binaries, low ionization nuclear emission regions, and BL Lac objects.
Time Acceleration Methods for Advection on the Cubed Sphere
Archibald, Richard K; Evans, Katherine J; White III, James B; Drake, John B
2009-01-01
Climate simulation will not grow to the ultrascale without new algorithms to overcome the scalability barriers blocking existing implementations. Until recently, climate simulations concentrated on the question of whether the climate is changing. The emphasis is now shifting to impact assessments, mitigation and adaptation strategies, and regional details. Such studies will require significant increases in spatial resolution and model complexity while maintaining adequate throughput. The barrier to progress is the resulting decrease in time step without increasing single-thread performance. In this paper we demonstrate how to overcome this time barrier for the first standard test defined for the shallow-water equations on a sphere. This paper explains how combining a multiwavelet discontinuous Galerkin method with exact linear part time-evolution schemes can overcome the time barrier for advection equations on a sphere. The discontinuous Galerkin method is a high-order method that is conservative, flexible, and scalable. The addition of multiwavelets to discontinuous Galerkin provides a hierarchical scale structure that can be exploited to improve computational efficiency in both the spatial and temporal dimensions. Exact linear part time-evolution schemes are explicit schemes that remain stable for implicit-size time steps.
Convergent radial dispersion: a Laplace transform solution for aquifer tracer testing
Moench, A.F.
1989-01-01
A Laplace transform solution was obtained for the injection of a tracer in a well situated in a homogeneous aquifer where steady, horizontal, radially convergent flow has been established due to pumping at a second well. The standard advection-dispersion equation for mass transfer was used as the controlling equation. For boundary conditions, mass balances that account for mixing of the tracer with the fluid residing in the injection and pumping wells were used. The derived solution, which can be adapted for either resident or flux-averaged concentration, is of practical use only for the pumped well. This problem is of interest because it is easily applied to field determination of aquifer dispersivity and effective porosity. Breakthrough curves were obtained by numerical inversion of the Laplace transform solution. -from Author
Riparian seed dispersal: transport and depositional processes
NASA Astrophysics Data System (ADS)
Cunnings, A.; Johnson, E. A.; Martin, Y. E.
2012-04-01
Riparian tree population dynamics are linked to the physical processes controlled by the hydrogeomorphic setting. In particular, fluvial seed dispersal is influenced by a combination of factors including the hydrology, fluvial geomorphology, and seed dispersal traits. This study examines the influence of stream flow patterns on the transportation and deposition of buoyant seeds by applying a one dimensional transport model. Conceptually, the model separates the stream into two components: the main channel and transient storage /deposition zones. The hydrologic processes are governed by an advection-dispersion equation and numerically solved using the Crank-Nicolson method. Additional terms in the equation allow for model variation in the flow regime (lateral inflow and outflow) and the incorporation of a transient storage/deposition component where seeds may be detained. The model parameters are based on a bedrock-gravel bed river with pool-riffle morphology where we conducted field experimentation in Coastal Northern California. The riparian zone of the study reach is inhabited by White Alder (Alnus rhombifolia) which disperses buoyant seeds in late winter/early spring coinciding with the latter part of the wet, Mediterranean climate. Artificial seeds with similar characteristic traits of buoyancy, density and Bond Number to White Alder seeds were used to quantify transport times and identify storage areas. The model output captures a greater number of seeds during a receding hydrograph due to the increase in transient storage. Typically, this is found in shallow stream margins where the flow is divergent such as areas with back-eddies. In the field, this is associated with the ends of gravel bars or riffles where flow expansion causes secondary flows. The results demonstrate the importance of transient storage for seed transport and depositional processes and emphasize the need for improved measurement techniques, in lieu of empirical coefficients, to advance the
BUOYANT ADVECTION OF GASES IN UNSATURATED SOIL
Seely, Gregory E.; Falta, Ronald W.; Hunt, James R.
2010-01-01
In unsaturated soil, methane and volatile organic compounds can significantly alter the density of soil gas and induce buoyant gas flow. A series of laboratory experiments was conducted in a two-dimensional, homogeneous sand pack with gas permeabilities ranging from 110 to 3,000 darcy. Pure methane gas was injected horizontally into the sand and steady-state methane profiles were measured. Experimental results are in close agreement with a numerical model that represents the advective and diffusive components of methane transport. Comparison of simulations with and without gravitational acceleration permits identification of conditions where buoyancy dominates methane transport. Significant buoyant flow requires a Rayleigh number greater than 10 and an injected gas velocity sufficient to overcome dilution by molecular diffusion near the source. These criteria allow the extension of laboratory results to idealized field conditions for methane as well as denser-than-air vapors produced by volatilizing nonaqueous phase liquids trapped in unsaturated soil. PMID:20396624
NASA Astrophysics Data System (ADS)
Lester, D. R.; Trefry, M. G.; Metcalfe, G.
2016-11-01
The macroscopic spreading and mixing of solute plumes in saturated porous media is ultimately controlled by processes operating at the pore scale. Whilst the conventional picture of pore-scale mechanical dispersion and molecular diffusion leading to persistent hydrodynamic dispersion is well accepted, this paradigm is inherently two-dimensional (2D) in nature and neglects important three-dimensional (3D) phenomena. We discuss how the kinematics of steady 3D flow at the pore scale generate chaotic advection-involving exponential stretching and folding of fluid elements-the mechanisms by which it arises and implications of microscopic chaos for macroscopic dispersion and mixing. Prohibited in steady 2D flow due to topological constraints, these phenomena are ubiquitous due to the topological complexity inherent to all 3D porous media. Consequently 3D porous media flows generate profoundly different fluid deformation and mixing processes to those of 2D flow. The interplay of chaotic advection and broad transit time distributions can be incorporated into a continuous-time random walk (CTRW) framework to predict macroscopic solute mixing and spreading. We show how these results may be generalised to real porous architectures via a CTRW model of fluid deformation, leading to stochastic models of macroscopic dispersion and mixing which both honour the pore-scale kinematics and are directly conditioned on the pore-scale architecture.
Three-Dimensional Oil Dispersion Model in Campos basin, Brazil.
Oliveira, Bernardo Lopes Almeida de; Netto, Theodoro Antoun; Assad, Luiz Paulo de Freitas
2017-02-22
This paper presents the physical and mathematical formulation of a three-dimensional oil dispersion model that calculates the trajectory from the seafloor to the sea surface, its assumptions and constraints. It was developed by researchers that are familiar with oil spill dispersion and mathematical analysis. Oil dispersion is calculated through two computational routines. The first calculates the vertical dispersion along the water column and resamples the droplets when the oil reaches the surface. The second calculates the surface displacement of the spill. This model is based on the Eulerian Approach, and it uses numerical solution schemes in time and in space to solve the equation for advective-diffusive transport. A case study based on an actual accident that happened in the Campos Basin, in Rio de Janeiro State, considering the instant spill of 1.000 m(3) was used to evaluate the proposed model. After calculating the vertical transport, it was estimated that the area covered by the oil spill on the surface was about 35.685 m². After calculating the dispersion at the surface, the plume area was estimated as 20% of the initial area, resulting in a final area of 28.548 m².
Cho, Yeo-Myoung; Werner, David; Moffett, Kevan B; Luthy, Richard G
2010-08-01
Advective porewater movement and molecular diffusion are important factors affecting the mass transfer of hydrophobic organic compounds (HOCs) in marsh and mudflat sediments. This study assessed porewater movement in an intertidal mudflat in South Basin adjacent to Hunters Point Shipyard, San Francisco, CA, where a pilot-scale test of sorbent amendment assessed the in situ stabilization of polychlorinated biphenyls (PCBs). To quantify advective porewater movement within the top 0-60 cm sediment layer, we used temperature as a tracer and conducted heat transport analysis using 14-day data from multidepth sediment temperature logging stations and one-dimensional heat transport simulations. The best-fit conditions gave an average Darcy velocity of 3.8cm/d in the downward vertical direction for sorbent-amended sediment with a plausible range of 0 cm/d to 8 cm/d. In a limiting case with no net advection, the best-fit depth-averaged mechanical dispersion coefficient was 2.2x10(-7) m2/s with a range of 0.9x10(-7) m2/s to 5.6x10(-7) m2/s. The Peclet number for PCB mobilization showed that molecular diffusion would control PCB mass transfer from sediment to sorbent particles for the case of uniform distribution of sorbent. However, the advective flow and mechanical dispersion in the test site would significantly benefit the stabilization effect of heterogeneously distributed sorbent by acting to smooth out the heterogeneities and homogenizing pollutant concentrations across the entire bioactive zone. These measurements and modeling techniques on intertidal sediment porewater transport could be useful for the development of more reliable mass transfer models for the prediction of contaminant release within the sediment bed, the movement of HOCs in the intertidal aquatic environment, and in situ sequestration by sorbent addition.
Computation of traveling wave fronts for a nonlinear diffusion-advection model.
Mansour, M B A
2009-01-01
This paper utilizes a nonlinear reaction-diffusion-advection model for describing the spatiotemporal evolution of bacterial growth. The traveling wave solutions of the corresponding system of partial differential equations are analyzed. Using two methods, we then find such solutions numerically. One of the methods involves the traveling wave equations and solving an initial-value problem, which leads to accurate computations of the wave profiles and speeds. The second method is to construct time-dependent solutions by solving an initial-moving boundary-value problem for the PDE system, showing another approximation for such wave solutions.
NASA Astrophysics Data System (ADS)
Nefedov, Nikolay
2017-02-01
This is an extended variant of the paper presented at MURPHYS-HSFS 2016 conference in Barcelona. We discuss further development of the asymptotic method of differential inequalities to investigate existence and stability of sharp internal layers (fronts) for nonlinear singularly perturbed periodic parabolic problems and initial boundary value problems with blow-up of fronts for reaction-diffusion-advection equations. In particular, we consider periodic solutions with internal layer in the case of balanced reaction. For the initial boundary value problems we prove the existence of fronts and give their asymptotic approximation including the new case of blowing-up fronts. This case we illustrate by the generalised Burgers equation.
Modeling the advection of discontinuous quantities in Geophysical flows using Particle Level Sets
NASA Astrophysics Data System (ADS)
Aleksandrov, V.; Samuel, H.; Evonuk, M.
2010-12-01
Advection is one of the major processes that commonly acts on various scales in nature (core formation, mantle convective stirring, multi-phase flows in magma chambers, salt diapirism ...). While this process can be modeled numerically by solving conservation equations, various geodynamic scenarios involve advection of quantities with sharp discontinuities. Unfortunately, in these cases modeling numerically pure advection becomes very challenging, in particular because sharp discontinuities lead to numerical instabilities, which prevent the local use of high order numerical schemes. Several approaches have been used in computational geodynamics in order to overcome this difficulty, with variable amounts of success. Despite the use of correcting filters or non-oscillatory, shock-preserving schemes, Eulerian (fixed grid) techniques generally suffer from artificial numerical diffusion. Lagrangian approaches (dynamic grids or particles) tend to be more popular in computational geodynamics because they are not prone to excessive numerical diffusion. However, these approaches are generally computationally expensive, especially in 3D, and can suffer from spurious statistical noise. As an alternative to these aforementioned approaches, we have applied a relatively recent Particle Level set method [Enright et al., 2002] for modeling advection of quantities with the presence of sharp discontinuities. We have tested this improved method, which combines the best of Eulerian and Lagrangian approaches, against well known benchmarks and classical Geodynamic flows. In each case the Particle Level Set method accuracy equals or is better than other Eulerian and Lagrangian methods, and leads to significantly smaller computational cost, in particular in three-dimensional flows, where the reduction of computational time for modeling advection processes is most needed.
NASA Astrophysics Data System (ADS)
Samuel, Henri
2010-05-01
Advection is one of the major processes that commonly acts on various scales in nature (core formation, mantle convective stirring, multi-phase flows in magma chambers, salt diapirism ...). While this process can be modeled numerically by solving conservation equations, various geodynamic scenarios involve advection of quantities with sharp discontinuities. Unfortunately, in these cases modeling numerically pure advection becomes very challenging, in particular because sharp discontinuities lead to numerical instabilities, which prevent the local use of high order numerical schemes. Several approaches have been used in computational geodynamics in order to overcome this difficulty, with variable amounts of success. Despite the use of correcting filters or non-oscillatory, shock-preserving schemes, Eulerian (fixed grid) techniques generally suffer from artificial numerical diffusion. Lagrangian approaches (dynamic grids or particles) tend to be more popular in computational geodynamics because they are not prone to excessive numerical diffusion. However, these approaches are generally computationally expensive, especially in 3D, and can suffer from spurious statistical noise. As an alternative to these aforementioned approaches, I have applied a relatively recent Particle Level set method [Enright et al., 2002] for modeling advection of quantities with the presence of sharp discontinuities. I have adapted this improved method, which combines the best of Eulerian and Lagrangian approaches, and I have tested it against well known benchmarks and classical Geodynamic flows. In each case the Particle Level Set method accuracy equals or is better than other Eulerian and Lagrangian methods, and leads to significantly smaller computational cost, in particular in three-dimensional flows, where the reduction of computational time for modeling advection processes is most needed.
Advection, diffusion, and delivery over a network.
Heaton, Luke L M; López, Eduardo; Maini, Philip K; Fricker, Mark D; Jones, Nick S
2012-08-01
Many biological, geophysical, and technological systems involve the transport of a resource over a network. In this paper, we present an efficient method for calculating the exact quantity of the resource in each part of an arbitrary network, where the resource is lost or delivered out of the network at a given rate, while being subject to advection and diffusion. The key conceptual step is to partition the resource into material that does or does not reach a node over a given time step. As an example application, we consider resource allocation within fungal networks, and analyze the spatial distribution of the resource that emerges as such networks grow over time. Fungal growth involves the expansion of fluid filled vessels, and such growth necessarily involves the movement of fluid. We develop a model of delivery in growing fungal networks, and find good empirical agreement between our model and experimental data gathered using radio-labeled tracers. Our results lead us to suggest that in foraging fungi, growth-induced mass flow is sufficient to account for long-distance transport, if the system is well insulated. We conclude that active transport mechanisms may only be required at the very end of the transport pathway, near the growing tips.
Oxygen Advection and Diffusion in a Three Dimensional Vascular Anatomical Network
Fang, Qianqian; Sakadžić, Sava; Ruvinskaya, Lana; Devor, Anna; Dale, Anders M.; Boas, David A.
2008-01-01
There is an increasing need for quantitative and computationally affordable models for analyzing tissue metabolism and hemodynamics in microvascular networks. In this work, we develop a hybrid model to solve for the time-varying oxygen advection-diffusion equation in the vessels and tissue. To obtain a three-dimensional temporal evolution of tissue oxygen concentration for realistic complex vessel networks, we used a graph-based advection model combined with a finite-element based diffusion model and an implicit time-advancing scheme. We validated this algorithm for both static and dynamic conditions. We also applied it to a complex vascular network obtained from a rodent somatosensory cortex. Qualitative agreement was found with in-vivo experiments. PMID:18958033
Critical time scales for advection-diffusion-reaction processes
NASA Astrophysics Data System (ADS)
Ellery, Adam J.; Simpson, Matthew J.; McCue, Scott W.; Baker, Ruth E.
2012-04-01
The concept of local accumulation time (LAT) was introduced by Berezhkovskii and co-workers to give a finite measure of the time required for the transient solution of a reaction-diffusion equation to approach the steady-state solution [A. M. Berezhkovskii, C. Sample, and S. Y. Shvartsman, Biophys. J.BIOJAU0006-349510.1016/j.bpj.2010.07.045 99, L59 (2010); A. M. Berezhkovskii, C. Sample, and S. Y. Shvartsman, Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.83.051906 83, 051906 (2011)]. Such a measure is referred to as a critical time. Here, we show that LAT is, in fact, identical to the concept of mean action time (MAT) that was first introduced by McNabb [A. McNabb and G. C. Wake, IMA J. Appl. Math.IJAMDM0272-496010.1093/imamat/47.2.193 47, 193 (1991)]. Although McNabb's initial argument was motivated by considering the mean particle lifetime (MPLT) for a linear death process, he applied the ideas to study diffusion. We extend the work of these authors by deriving expressions for the MAT for a general one-dimensional linear advection-diffusion-reaction problem. Using a combination of continuum and discrete approaches, we show that MAT and MPLT are equivalent for certain uniform-to-uniform transitions; these results provide a practical interpretation for MAT by directly linking the stochastic microscopic processes to a meaningful macroscopic time scale. We find that for more general transitions, the equivalence between MAT and MPLT does not hold. Unlike other critical time definitions, we show that it is possible to evaluate the MAT without solving the underlying partial differential equation (pde). This makes MAT a simple and attractive quantity for practical situations. Finally, our work explores the accuracy of certain approximations derived using MAT, showing that useful approximations for nonlinear kinetic processes can be obtained, again without treating the governing pde directly.
Stevens, D.E.; Bretherton, S.
1996-12-01
This paper presents a new forward-in-time advection method for nearly incompressible flow, MU, and its application to an adaptive multilevel flow solver for atmospheric flows. MU is a modification of Leonard et al.`s UTOPIA scheme. MU, like UTOPIA, is based on third-order accurate semi-Lagrangian multidimensional upwinding for constant velocity flows. for varying velocity fields, MU is a second-order conservative method. MU has greater stability and accuracy than UTOPIA and naturally decomposes into a monotone low-order method and a higher-order accurate correction for use with flux limiting. Its stability and accuracy make it a computationally efficient alternative to current finite-difference advection methods. We present a fully second-order accurate flow solver for the anelastic equations, a prototypical low Mach number flow. The flow solver is based on MU which is used for both momentum and scalar transport equations. This flow solver can also be implemented with any forward-in-time advection scheme. The multilevel flow solver conserves discrete global integrals of advected quantities and includes adaptive mesh refinements. Its second-order accuracy is verified using a nonlinear energy conservation integral for the anelastic equations. For a typical geophysical problem in which the flow is most rapidly varying in a small part of the domain, the multilevel flow solver achieves global accuracy comparable to uniform-resolution simulation for 10% of the computational cost. 36 refs., 10 figs.
An advection-based model to increase the temporal resolution of PIV time series.
Scarano, Fulvio; Moore, Peter
A numerical implementation of the advection equation is proposed to increase the temporal resolution of PIV time series. The method is based on the principle that velocity fluctuations are transported passively, similar to Taylor's hypothesis of frozen turbulence. In the present work, the advection model is extended to unsteady three-dimensional flows. The main objective of the method is that of lowering the requirement on the PIV repetition rate from the Eulerian frequency toward the Lagrangian one. The local trajectory of the fluid parcel is obtained by forward projection of the instantaneous velocity at the preceding time instant and backward projection from the subsequent time step. The trajectories are approximated by the instantaneous streamlines, which yields accurate results when the amplitude of velocity fluctuations is small with respect to the convective motion. The verification is performed with two experiments conducted at temporal resolutions significantly higher than that dictated by Nyquist criterion. The flow past the trailing edge of a NACA0012 airfoil closely approximates frozen turbulence, where the largest ratio between the Lagrangian and Eulerian temporal scales is expected. An order of magnitude reduction of the needed acquisition frequency is demonstrated by the velocity spectra of super-sampled series. The application to three-dimensional data is made with time-resolved tomographic PIV measurements of a transitional jet. Here, the 3D advection equation is implemented to estimate the fluid trajectories. The reduction in the minimum sampling rate by the use of super-sampling in this case is less, due to the fact that vortices occurring in the jet shear layer are not well approximated by sole advection at large time separation. Both cases reveal that the current requirements for time-resolved PIV experiments can be revised when information is poured from space to time. An additional favorable effect is observed by the analysis in the frequency
Mechanistic analytical models for long-distance seed dispersal by wind.
Katul, G G; Porporato, A; Nathan, R; Siqueira, M; Soons, M B; Poggi, D; Horn, H S; Levin, S A
2005-09-01
We introduce an analytical model, the Wald analytical long-distance dispersal (WALD) model, for estimating dispersal kernels of wind-dispersed seeds and their escape probability from the canopy. The model is based on simplifications to well-established three-dimensional Lagrangian stochastic approaches for turbulent scalar transport resulting in a two-parameter Wald (or inverse Gaussian) distribution. Unlike commonly used phenomenological models, WALD's parameters can be estimated from the key factors affecting wind dispersal--wind statistics, seed release height, and seed terminal velocity--determined independently of dispersal data. WALD's asymptotic power-law tail has an exponent of -3/2, a limiting value verified by a meta-analysis for a wide variety of measured dispersal kernels and larger than the exponent of the bivariate Student t-test (2Dt). We tested WALD using three dispersal data sets on forest trees, heathland shrubs, and grassland forbs and compared WALD's performance with that of other analytical mechanistic models (revised versions of the tilted Gaussian Plume model and the advection-diffusion equation), revealing fairest agreement between WALD predictions and measurements. Analytical mechanistic models, such as WALD, combine the advantages of simplicity and mechanistic understanding and are valuable tools for modeling large-scale, long-term plant population dynamics.
Hydrodynamic dispersion of a neutral non-reacting solute in electroosmotic flow
S. K. Griffiths; R. H. Nilson
1999-06-01
Analytical methods are employed to determine the axial dispersion of a neutral non-reacting solute in an incompressible electroosmotic flow. In contrast to previous approaches, the dispersion is obtained here by solving the time-dependent diffusion-advection equation in transformed spatial and temporal coordinates to obtain the two-dimensional late-time concentration field. The coefficient of dispersion arises as a separation eigenvalue, and its value is obtained as a necessary condition for satisfying all of the required boundary conditions. Solutions based on the Debye-Huckel approximation are presented for both a circular tube and a channel of infinite width. These results recover the well-known solutions for dispersion in pressure-driven flows when the Debye length is very large. In this limit, the axial dispersion is proportional to the square of the Peclet number based on the characteristic transverse dimension of the tube or channel. In the tilt of very small Debye lengths, the authors find that the dispersion varies as the square of the Peclet number based on the Debye length. Simple approximations to the coefficient of dispersion as a function of the Debye length and Peclet number are also presented.
Designing for chaos: applications of chaotic advection at the microscale.
Stremler, Mark A; Haselton, F R; Aref, Hassan
2004-05-15
Chaotic advection can play an important role in efficient microfluidic mixers. We discuss a design paradigm that exploits chaotic advection and illustrate by two recent examples, namely enhancing gene expression profiling and constructing an in-line microfluidic mixing channel, how application of this paradigm has led to successful micromixers. We suggest that 'designing for chaos', that is, basing practical mixer design on chaotic advection analysis, is a promising approach to adopt in this developing field which otherwise has little to guide it and is constrained by issues of scale and manufacturability.
Dispersion controlled by permeable surfaces: surface properties and scaling
Ling, Bowen; Tartakovsky, Alexandre M.; Battiato, Ilenia
2016-07-19
Permeable and porous surfaces are common in natural and engineered systems. Flow and transport above such surfaces are significantly affected by the surface properties, e.g. matrix porosity and permeability. However, the relationship between such properties and macroscopic solute transport is largely unknown. In this work, we focus on mass transport in a two-dimensional channel with permeable porous walls under fully developed laminar flow conditions. By means of perturbation theory and asymptotic analysis, we derive the set of upscaled equations describing mass transport in the coupled channel–porous-matrix system and an analytical expression relating the dispersion coefficient with the properties of the surface, namely porosity and permeability. Our analysis shows that their impact on the dispersion coefficient strongly depends on the magnitude of the Péclet number, i.e. on the interplay between diffusive and advective mass transport. Additionally, we demonstrate different scaling behaviours of the dispersion coefficient for thin or thick porous matrices. Our analysis shows the possibility of controlling the dispersion coefficient, i.e. transverse mixing, by either active (i.e. changing the operating conditions) or passive mechanisms (i.e. controlling matrix effective properties) for a given Péclet number. By elucidating the impact of matrix porosity and permeability on solute transport, our upscaled model lays the foundation for the improved understanding, control and design of microporous coatings with targeted macroscopic transport features.
B.B. Rokhman
2007-09-15
This article considers the Eulerian continuum description of turbulent transfer of momentum and moment of momentum in a solid phase on the basis of the equations of transfer of the second and third moments of pulsations of the linear and angular velocities of particles. The pulsating characteristics of a gas are computed using the two-parameter model of turbulence generalized to the case of gas-dispersed turbulent flows.
A Streamline-Upwind Model for Filling Front Advection in Powder Injection Moulding
NASA Astrophysics Data System (ADS)
Larsen, Guillaume; Cheng, Zhi Qiang; Barriere, Thierry; Liu, Bao Sheng; Gelin, Jean-Claude
2010-06-01
The filling process of powder injection molding is modeled by the flows of two variably adjacent domains in the mold cavity. The feedstock is filled into the cavity while the air is expelled out by the injected feedstock [1]. Eulerian description is adopted. The filling patterns are determined by the solution of an advection equation, governed by the velocity field in both the feedstock flow and air flow [2]. In the real physics, the advance of filling front depends mainly on the flow of feedstock that locates behind the front. The flow of air in front of the injected material plays in fact no meaningful effect. However, the actual algorithm for solution of the advection equation takes equally the importance for both the flow of viscous feedstock and that of the slight air. Under such a condition, the injection flow of feedstock in simulation may be misdirected unrealistically by the velocity field in the air portion of the mold cavity. To correct this defect, an upwind scheme is proposed to reinforce the effect of upwind flow and reduce the effect of downstream flow. The present paper involves the investigation of an upwind algorithm for simulation of the filling state during powder injection molding. A Petrov-Galerkin upwind based method (SUPG) is adopted for numerical simulation of the transport equation instead of the Taylor-Galerkin method in previous work. In the proposed implementation of the Streamline-Upwind/Petrov-Galerkin (SUPG) approach. A stabilization method is used to prevent oscillations in the convection-dominated problems. It consists in the introduction of an artificial diffusion in streamline direction. Suitable modification of the test function is the important issue. It ensures the stable simulation of filling process and results in the more realistic prediction of filling patterns. The implementation of upwind scheme in mould filling state simulation, based on an advection equation and the whole velocity field of feedstock and air flow, makes
Manikandan, K; Senthilvelan, M
2016-07-01
We construct spatiotemporal localized envelope solutions of a (3 + 1)-dimensional nonlinear Schrödinger equation with varying coefficients such as dispersion, nonlinearity and gain parameters through similarity transformation technique. The obtained localized rational solutions can serve as prototypes of rogue waves in different branches of science. We investigate the characteristics of constructed localized solutions in detail when it propagates through six different dispersion profiles, namely, constant, linear, Gaussian, hyperbolic, logarithm, and exponential. We also obtain expressions for the hump and valleys of rogue wave intensity profiles for these six dispersion profiles and study the trajectory of it in each case. Further, we analyze how the intensity of another localized solution, namely, breather, changes when it propagates through the aforementioned six dispersion profiles. Our studies reveal that these localized solutions co-exist with the collapsing solutions which are already found in the (3 + 1)-dimensional nonlinear Schrödinger equation. The obtained results will help to understand the corresponding localized wave phenomena in related fields.
Clay with Desiccation Cracks is an Advection Dominated Environment
NASA Astrophysics Data System (ADS)
Baram, S.; Kurtzman, D.; Sher, Y.; Ronen, Z.; Dahan, O.
2012-04-01
, indicating deep soil evaporation. Daily fluctuation of the air temperature in the desiccation cracks supported thermally induced air convection within the cracks void and could explain the deep soil salinization process. Combination of all the abovementioned observations demonstrated that the formation of desiccation cracks network in dispersive clay sediments generates a bulk advection dominated environment for both air and water flow, and that the reference to clay sediments as "hydrologically safe" should to be reconsidered.
Overcoming diffusion-limited processes using enhanced advective fields
Rasmussen, T.C.
1995-12-31
Many subsurface cleanup activities focus on the remediation of organic contaminants using induced advective fields. Subsurface heterogeneities cause most advective transport to occur in more permeable zones, with transport from the lower permeability units being limited by diffusion to the higher permeable units. While diffusion rates can be enhanced using thermal sources, many of the treatment strategies, including pump and treat, vapor extraction and bioremediation, are limited by mass exchange rates between the higher and lower permeability sand and clay mixtures. Instead of relying on the enhancement of diffusion rates, it is proposed that remediation strategies should focus on the enhancement of induced advective transport rates through the lower permeability units. Injection-extraction strategies using crosshole and huff-and-puff methods are presented for maximizing advective transport through lower permeability units. Optimization of the design can incorporate diffusion-enhancement technologies, bionourishment, capillary confinement in the unsaturated zone, and DNAPL slurping.
Interpreting layer thickness advection in terms of eddy-topography interaction
NASA Astrophysics Data System (ADS)
Liu, Chuanyu; Köhl, Armin; Stammer, Detlef
2014-09-01
A parameterization for the spatial pattern of the eddy induced thickness advection parameter estimated from a dynamically consistent data assimilation procedure is presented. Values of the thickness advection parameter are predominantly negative (positive) over seamounts, and positive (negative) over the deep ocean in the southern (northern) hemisphere along strong currents; its magnitude is large at high latitudes but low in the tropical regions. Those characteristics motivate a parameterization based on the Coriolis parameter, the bottom depth and an eddy length scale. As a parameterization for an eddy streamfunction, the associated bolus velocities advect density anti-cyclonically (cyclonically) around seamounts (troughs). Although the parameterization has the same form as Holloway’s streamfunction for the Neptune effect, and is also related to eddy-topography interactions, Holloway’s streamfunction is in contrast applied to the momentum equation. The parameterization is independently confirmed by the flux-mean gradient relation from the output of a high resolution model. The effect of the proposed scheme is investigated using a channel model with idealized bottom topographies and a global ocean circulation model with realistic bottom topography. In agreement with the high resolution model, our scheme generates cold (warm) domes and cyclonic circulations over seamounts (troughs), which is consistent with the eddy movement in presence of the topographic β effect. This provides a different mechanism for eddy-topography interaction than the Neptune effect, which generates circulations of opposing sign.
An advection scheme based on the combination of particle mesh method and pure Lagrangian approach
NASA Astrophysics Data System (ADS)
Arsenic, Ilija; Mihailovic, Dragutin T.; Kapor, Darko
2011-11-01
Possibility of using pure Lagrangian approach in modeling transport phenomena is described in this paper. The application of pure Lagrangian approach in real atmospheric field induces highly irregular spatial distribution of grid points, after only a few time steps. In order to avoid problems caused by that irregularity, a quasi interpolation procedure is proposed. Proposed interpolation procedure is similar to the radial basis functions interpolation and does not impose any demands about spatial distribution of the grid points or about continuity and differentiability of the field that needs to be interpolated. Besides that, proposed procedure is explicitly mass conserving. Combination of particle mesh method and pure Lagrangian approach creates efficient transport scheme that does not produce any new local maxima and minima in advected field. In proposed advection scheme motion of points are performed in Lagrangian manner while spatial derivatives are evaluated on the basis of values interpolated onto regular grid. Applicability of proposed advection scheme in an unambiguous way is proved by performing "standard" numerical tests with (i) the slotted cylinder under solid body rotation, (ii) the test with Doswell's idealized cyclogenesis as well as (iii) integration of shallow water equations.
Constraints upon water advection in sediments of the Mariana Trough
Abbott, D.H.; Menke, W.; Morin, R.
1983-02-10
Thermal gradient measurements, consolidation tests, and pore water compositions from the Mariana Trough imply that water is moving through the sediments in areas with less than about 100 m of sediment cover. The maximum advection rates implied by the thermal measurements and consolidation tests may be as high as 10/sup -5/ cm s/sup -1/ but are most commonly in the range of 1 to 5 x 10/sup -6/ cm s/sup -1/. Theoretical calculations of the effect of the highest advection rates upon carbonate dissolution indicate that dissolution may be impeded or enhanced (depending upon the direction of flow) by a factor of 2 to 5 times the rate for diffusion alone. The average percentage of carbonate is consistently higher in two cores from the area with no advection or upward advection than the average percentage of carbonate in three cores from the area with downward advection. This increase in average amount of carbonate in cores with upward moving water or no movement cannot be attributed solely to differences in water depth or in amount of terrigenous dilution. If the sediment column acts as a passive boundary layer, then the water velocities necessary to affect chemical gradients of silica are in the range 10/sup -9/ to 10/sup -10/ cm s/sup -1/. However, if dissolution of silica occurs within the sediment column, then the advection velocities needed to affect chemical gradients are at least 3 x 10/sup -8/ cm s/sup -1/ and may be as high as 3 x 10/sup -6/ cm s/sup -1/. This order of magnitude increase in advection velocities when chemical reactions occur within the sediments is probably applicable to other cations in addition to silica. If so, then the advection velocities needed to affect heat flow (>10/sup -8/ cm s/sup -1/) and pore water chemical gradients are much nearer in magnitude than previously assumed.
Laboratory experiments on dispersive transport across interfaces: The role of flow direction
Berkowitz, B.; Cortis, A.; Dror, I.; Scher, H.
2009-04-01
We present experimental evidence of asymmetrical dispersive transport of a conservative tracer across interfaces between different porous materials. Breakthrough curves are measured for tracer pulses that migrate in a steady state flow field through a column that contains adjacent segments of coarse and fine porous media. The breakthrough curves show significant differences in behavior, with tracers migrating from fine medium to coarse medium arriving significantly faster than those from coarse medium to fine medium. As the flow rate increases, the differences between the breakthrough curves diminish. We argue that this behavior indicates the occurrence of significant, time-dependent tracer accumulation in the resident concentration profile across the heterogeneity interface. Conventional modeling using the advection-dispersion equation is demonstrated to be unable to capture this asymmetric behavior. However, tracer accumulation at the interface has been observed in particle-tracking simulations, which may be related to the asymmetry in the observed breakthrough curves.
A high-order discontinuous Galerkin method for unsteady advection-diffusion problems
NASA Astrophysics Data System (ADS)
Borker, Raunak; Farhat, Charbel; Tezaur, Radek
2017-03-01
A high-order discontinuous Galerkin method with Lagrange multipliers is presented for the solution of unsteady advection-diffusion problems in the high Péclet number regime. It operates directly on the second-order form of the governing equation and does not require any stabilization. Its spatial basis functions are chosen among the free-space solutions of the homogeneous form of the partial differential equation obtained after time-discretization. It also features Lagrange multipliers for enforcing a weak continuity of the approximated solution across the element interface boundaries. This leads to a system of differential-algebraic equations which are time-integrated by an implicit family of schemes. The numerical stability of these schemes and the well-posedness of the overall discretization method are supported by a theoretical analysis. The performance of this method is demonstrated for various high Péclet number constant-coefficient model flow problems.
An advective volume-balance model for flow in porous media
NASA Astrophysics Data System (ADS)
Malaga, Carlos; Mandujano, Francisco; Becerra, Julian
2016-11-01
Volume-balance models are used by petroleum engineers to simulate multiphase and multicomponent flow phenomena in porous media and the extraction process in oil reservoirs. In these models, mass conservation equations and Darcy's law are supplemented by a balance condition for the pore and fluid volumes. This provides a pressure equation suitable for simulating a compressible flow within a compressible solid matrix. Here we present an alternative interpretation of the volume-balance condition that includes the advective transport within a consolidated porous media. We obtain a modified equation for the time evolution of the pressure field. Preliminary numerical tests of phase separation due to gravity suggest the model reproduces qualitatively the physical phenomena. Fondo Sectorial CONACYT-SENER Grant Number 42536 (DGAJ-SPI-34-170412-217).
The role of advection and diffusion in waste disposal by sea urchin embryos
NASA Astrophysics Data System (ADS)
Clark, Aaron; Licata, Nicholas
2014-03-01
We determine the first passage probability for the absorption of waste molecules released from the microvilli of sea urchin embryos. We calculate a perturbative solution of the advection-diffusion equation for a linear shear profile similar to the fluid environment which the embryos inhabit. Rapid rotation of the embryo results in a concentration boundary layer of comparable thickness to the length of the microvilli. A comparison of the results to the regime of diffusion limited transport indicates that fluid flow is advantageous for efficient waste disposal.
Direct Measurements of Eddy Transport and Thermal Dispersion in a High Porosity Matrix
NASA Technical Reports Server (NTRS)
Niu, Yi; Simon, David; Gedeon, David
2004-01-01
Thermal losses from the hot end to the cold end of a Stirling cycle regenerator due to thermal dispersion through the regenerator matrix may significantly degrade the performance of the machine. Because of poor access to the void spaces within the porous medium, no direct measurements of thermal dispersion have been made and dispersion models have been derived indirectly. This is done by measuring the overall thermal performance of the regenerator and subtracting off the energy transfer caused by molecular conduction and advected enthalpy flows computed from volume-averaged fluid velocity and temperature. In the current program, a large-scale porous matrix consisting of stacked wire screens with a porosity of 90% is installed in a flow rig which is operated in a Reynolds number range that represents Stirling engine regenerator flow. Experiments are conducted to measure turbulent transport of momentum at the exit phase using hot-wires. The relationship of such turbulent transport terms to the thermal dispersion term in the volumetric-averaged energy equation for the regenerator matrix is developed and the measurements are used to determine cross-stream thermal dispersion. A dispersion model based upon the measurements is proposed and compared with models documented in the literature.
Dispersion in the Surfzone: Tracer Dispersion Studies
2011-09-30
objective is to improve understanding and modeling of dispersion of tracers (pol lution, fecal indicator bacteria, fine sediments) within the...discussed further here. Stochastic Particle Simulation for Surfzone Dispersion Drifter-derived diffusivities are time-dependent. In an unbounded...diffusion. Here HB06 particle trajectories are stochastically simulated with the Langevin equations with a shoreline boundary to explain the observed
A new Remesh-Lagrange technique for advecting temperature that minimizes numerical diffusion
NASA Astrophysics Data System (ADS)
Hasenclever, J.; Phipps Morgan, J.; Shi, C.
2007-12-01
The proper treatment of heat-advection is a generally underappreciated problem within CFD, yet particularly critical for calculating physically sound erosion in plume-lithosphere interactions and temperature sensitive melting processes. Typically, Eulerian (fixed-mesh) codes have been preferred to solve for fluid flow and they are almost essential for finite-difference-based algorithms. Unfortunately, the Eulerian approach introduces numerical artifacts into the solution of the advection-diffusion heat transport problem that can only be suppressed by adding 'too-diffusive' artificial diffusion to the equations, as for example in the Smolarkiewicz formulation for heat advection. We have developed a 'Remesh-Lagrange' method using a partly deforming finite element mesh and find it to be significantly more accurate than our previous methods. In several test scenarios we show the large improvement in accuracy that can be obtained by using a Lagrangian approach for 10-30 time steps (depending upon the distortion of the finite elements in the deformed Lagrangian mesh) and then regridding to the initial mesh. When an element becomes too distorted the nodes connected to it become fixed and we switch from Lagrange to a Semi-Lagrange formulation for these nodes. Instead of the standard 'linear backward' Semi-Lagrange we are also experimenting with a more accurate interpolation scheme for an unstructured mesh that additionally includes the nodal derivatives of the temperature field when calculating the value at the Semi-Lagrange traceback point. The same bicubic interpolation method for an unstructured grid is used to remesh the 'too-distorted' Lagrange grid back to the initial undistorted mesh. We compare the Remesh-Lagrange technique against the following Eulerian methods in a series of 2-D numerical experiments advecting stripes and Gaussian peaks in steady circulating flow: linear back-interpolation Semi-Lagrange method; bicubic back-interpolation Semi-Lagrange method
NASA Astrophysics Data System (ADS)
Mielikainen, Jarno; Huang, Bormin; Huang, Allen H.-L.
2015-05-01
The most widely used community weather forecast and research model in the world is the Weather Research and Forecast (WRF) model. Two distinct varieties of WRF exist. The one we are interested is the Advanced Research WRF (ARW) is an experimental, advanced research version featuring very high resolution. The WRF Nonhydrostatic Mesoscale Model (WRF-NMM) has been designed for forecasting operations. WRF consists of dynamics code and several physics modules. The WRF-ARW core is based on an Eulerian solver for the fully compressible nonhydrostatic equations. In the paper, we optimize a meridional (north-south direction) advection subroutine for Intel Xeon Phi coprocessor. Advection is of the most time consuming routines in the ARW dynamics core. It advances the explicit perturbation horizontal momentum equations by adding in the large-timestep tendency along with the small timestep pressure gradient tendency. We will describe the challenges we met during the development of a high-speed dynamics code subroutine for MIC architecture. Furthermore, lessons learned from the code optimization process will be discussed. The results show that the optimizations improved performance of the original code on Xeon Phi 7120P by a factor of 1.2x.
Advecting Procedural Textures for 2D Flow Animation
NASA Technical Reports Server (NTRS)
Kao, David; Pang, Alex; Moran, Pat (Technical Monitor)
2001-01-01
This paper proposes the use of specially generated 3D procedural textures for visualizing steady state 2D flow fields. We use the flow field to advect and animate the texture over time. However, using standard texture advection techniques and arbitrary textures will introduce some undesirable effects such as: (a) expanding texture from a critical source point, (b) streaking pattern from the boundary of the flowfield, (c) crowding of advected textures near an attracting spiral or sink, and (d) absent or lack of textures in some regions of the flow. This paper proposes a number of strategies to solve these problems. We demonstrate how the technique works using both synthetic data and computational fluid dynamics data.
Concentration polarization, surface currents, and bulk advection in a microchannel
NASA Astrophysics Data System (ADS)
Nielsen, Christoffer P.; Bruus, Henrik
2014-10-01
We present a comprehensive analysis of salt transport and overlimiting currents in a microchannel during concentration polarization. We have carried out full numerical simulations of the coupled Poisson-Nernst-Planck-Stokes problem governing the transport and rationalized the behavior of the system. A remarkable outcome of the investigations is the discovery of strong couplings between bulk advection and the surface current; without a surface current, bulk advection is strongly suppressed. The numerical simulations are supplemented by analytical models valid in the long channel limit as well as in the limit of negligible surface charge. By including the effects of diffusion and advection in the diffuse part of the electric double layers, we extend a recently published analytical model of overlimiting current due to surface conduction.
Development of a fast response dispersion model for virtual urban environments
NASA Astrophysics Data System (ADS)
Singh, Balwinder
According to a UN report, more than 50% of the total world's population resides in urban areas and this fraction is increasing. Urbanization has a wide range of potential environmental impacts, including those related to the dispersion of potentially dangerous substances emitted from activities such as combustion, industrial processing or from deliberate harmful releases. This research is primarily focused on the investigation of various factors which contribute to the dispersion of certain classes of materials in a complex urban environment and improving both of the fundamental components of a fast response dispersion modeling system---wind modeling and dispersion modeling. Specifically, new empirical parameterizations have been suggested for an existing fast response wind model for street canyon flow fields. These new parameterizations are shown to produce more favorable results when compared with the experimental data. It is also demonstrated that the use of Graphics Processing Unit (GPU) technology can enhance the efficiency of an urban Lagrangian dispersion model and can achieve near real-time particle advection. The GPU also enables real-time visualizations which can be used for creating virtual urban environments to aid emergency responders. The dispersion model based on the GPU architecture relies on the so-called "simplified Langevin equations (SLEs)" for particle advection. The full or generalized form of the Langevin equations (GLEs) is known for its stiffness which tends to generate unstable modes in particle trajectory, where a particle may travel significant distances in a small time step. A fractional step methodology has been used to implement the GLEs into an existing Lagrangian random walk model to partially circumvent the stiffness associated with the GLEs. Dispersion estimates from the GLEs-based model have been compared with the SLEs-based model and available wind tunnel data. The GLEs-based model is more dispersive than the SLEs-based model in
NASA Astrophysics Data System (ADS)
Bearon, R. N.; Bees, M. A.; Croze, O. A.
2012-12-01
There is much current interest in modelling suspensions of algae and other micro-organisms for biotechnological exploitation, and many bioreactors are of tubular design. Using generalized Taylor dispersion theory, we develop a population-level swimming-advection-diffusion model for suspensions of micro-organisms in a vertical pipe flow. In particular, a combination of gravitational and viscous torques acting on individual cells can affect their swimming behaviour, which is termed gyrotaxis. This typically leads to local cell drift and diffusion in a suspension of cells. In a flow in a pipe, small amounts of radial drift across streamlines can have a major impact on the effective axial drift and diffusion of the cells. We present a Galerkin method to calculate the local mean swimming velocity and diffusion tensor based on local shear for arbitrary flow rates. This method is validated with asymptotic results obtained in the limits of weak and strong shear. We solve the resultant swimming-advection-diffusion equation using numerical methods for the case of imposed Poiseuille flow and investigate how the flow modifies the dispersion of active swimmers from that of passive scalars. We establish that generalized Taylor dispersion theory predicts an enhancement of gyrotactic focussing in pipe flow with increasing shear strength, in contrast to earlier models. We also show that biased swimming cells may behave very differently to passive tracers, drifting axially at up to twice the rate and diffusing much less.
Optimal Stretching in Advection-Reaction-Diffusion Systems
NASA Astrophysics Data System (ADS)
Nevins, Thomas D.; Kelley, Douglas H.
2016-10-01
We investigate growth of the excitable Belousov-Zhabotinsky reaction in chaotic, time-varying flows. In slow flows, reacted regions tend to lie near vortex edges, whereas fast flows restrict reacted regions to vortex cores. We show that reacted regions travel toward vortex centers faster as flow speed increases, but nonreactive scalars do not. For either slow or fast flows, reaction is promoted by the same optimal range of the local advective stretching, but stronger stretching causes reaction blowout and can hinder reaction from spreading. We hypothesize that optimal stretching and blowout occur in many advection-diffusion-reaction systems, perhaps creating ecological niches for phytoplankton in the ocean.
Optimal Stretching in Advection-Reaction-Diffusion Systems.
Nevins, Thomas D; Kelley, Douglas H
2016-10-14
We investigate growth of the excitable Belousov-Zhabotinsky reaction in chaotic, time-varying flows. In slow flows, reacted regions tend to lie near vortex edges, whereas fast flows restrict reacted regions to vortex cores. We show that reacted regions travel toward vortex centers faster as flow speed increases, but nonreactive scalars do not. For either slow or fast flows, reaction is promoted by the same optimal range of the local advective stretching, but stronger stretching causes reaction blowout and can hinder reaction from spreading. We hypothesize that optimal stretching and blowout occur in many advection-diffusion-reaction systems, perhaps creating ecological niches for phytoplankton in the ocean.
Jet Magnetically Accelerated from Advection Dominated Accretion Flow
NASA Astrophysics Data System (ADS)
Gong, Xiao-Long; Jiang, Zhi-Xiong
2014-08-01
A jet model for the jet power arising from a steady, optically thin, advection dominated accretion flow (ADAF) around a Kerr black hole (BH) is proposed. We investigate the typical numerical solutions of ADAF, and calculate the jet power from an ADAF using a general relativistic version of electronic circuit theory. It is shown that the jet power concentrates in the inner region of the accretion flow, and the higher the degree to which the flow advection-dominated is, the lower the jet power from the ADAF is.
Fast multigrid solution of the advection problem with closed characteristics
Yavneh, I.; Venner, C.H.; Brandt, A.
1996-12-31
The numerical solution of the advection-diffusion problem in the inviscid limit with closed characteristics is studied as a prelude to an efficient high Reynolds-number flow solver. It is demonstrated by a heuristic analysis and numerical calculations that using upstream discretization with downstream relaxation-ordering and appropriate residual weighting in a simple multigrid V cycle produces an efficient solution process. We also derive upstream finite-difference approximations to the advection operator, whose truncation terms approximate {open_quotes}physical{close_quotes} (Laplacian) viscosity, thus avoiding spurious solutions to the homogeneous problem when the artificial diffusivity dominates the physical viscosity.
Self-advection of density perturbations on a sloping continental shelf
Ping-Tung Shaw; Csanady, G.T.
1983-05-01
Bottom water movement on the continental shelf is modeled by the nonlinear interaction between longshore bottom geostrophic flow and the density field. Bottom geostrophic velocity, subject to linear steady momentum equations with linear bottom friction, can be generated by along-isobath density variations over a sloping bottom. At the same time, the density field is slowly advected by the velocity field. Away from boundary layers, the interplay is governed by Burgers' equation, which shows the formation and self-propulsion of strong density gradients along an isobath. The direction of propagation of a dense water blob is to have shallow water on the right- (left-) hand side facing downstream in the Northern (Southern) Hemisphere. The propagation of a light water blob is opposite to that of a dense water blob.
Fractures as Advective Conduits at the Earth Atmosphere Interface
NASA Astrophysics Data System (ADS)
Dragila, M. I.; Weisbrod, N.; Nachshon, U.; Kamai, T.
2012-12-01
Understanding gas exchange between the Earth's upper crust and the atmosphere is vital and necessary because this phenomenon controls to a large extent many important processes including, the water cycle, agricultural activities, greenhouse gas emissions and more. From a hydrological aspect, water vapor transport is an extremely important process related to Earth-atmosphere gas exchange because it affects above ground water vapor concentration, soil water content and soil salinity. Traditionally, diffusion was considered the main mechanism of gas exchange between the atmosphere and vadose zone, driven by gas concentration gradients. While this assumption may be correct for many porous media, our laboratory and field-scale studies have shown that advective gas transport mechanisms are governing these fluxes in fractured rocks and cracked soils. Convection driven by thermal gradients (free convection) and wind induced (forced convection) were explored and both were found to play a major role in Earth-atmosphere gas exchange. Long-term laboratory experiments using fracture simulators in a customized climate controlled laboratory have shown that thermal convection occurs when nighttime thermal conditions prevail. This convective venting significantly enhances evaporation and subsequently salt precipitation on the fracture walls. Experiment results were used to develop an empirical relationship between temperature gradients, fracture aperture and convective gas flux through the fracture. Theoretical calculations show that thermal convection is indeed likely to play a major role in evaporation from fractures and can explain enhanced salt accumulation observed in surface-exposed fractures. Long-term field measurements, carried out continuously for 5+ years in a single fracture in the Israeli Negev Desert, verified the development of air convection cycles of 10-18 hours duration on a daily basis, with a peak in both convective flux and duration during the winter. During
Thermal Dispersion Within a Porous Medium Near a Solid Wall
NASA Technical Reports Server (NTRS)
Simon, T.; McFadden, G.; Ibrahim, M.
2006-01-01
The regenerator is a key component to Stirling cycle machine efficiency. Typical regenerators are of sintered fine wires or layers of fine-wire screens. Such porous materials are contained within solid-waH casings. Thermal energy exchange between the regenerator and the casing is important to cycle performance for the matrix and casing would not have the same axial temperature profile in an actual machine. Exchange from one to the other may allow shunting of thermal energy, reducing cycle efficiency. In this paper, temperature profiles within the near-wall region of the matrix are measured and thermal energy transport, termed thermal dispersion, is inferred. The data show how the wall affects thermal transport. Transport normal to the mean flow direction is by conduction within the solid and fluid and by advective transport within the matrix. In the near-wall region, both may be interrupted from their normal in-core pattern. Solid conduction paths are broken and scales of advective transport are damped. An equation is presented which describes this change for a wire screen mesh. The near-wall layer typically acts as an insulating layer. This should be considered in design or analysis. Effective thermal conductivity within the core is uniform. In-core transverse thermal effective conductivity values are compared to direct and indirect measurements reported elsewhere and to 3D numerical simulation results, computed previously and reported elsewhere. The 3-D CFD model is composed of six cylinders in cross flow, staggered in arrangement to match the dimensions and porosity of the matrix used in the experiments. The commercial code FLUENT is used to obtain the flow and thermal fields. The thermal dispersion and effective thermal conductivities for the matrix are computed from the results.
Ballarini, E; Bauer, S; Eberhardt, C; Beyer, C
2012-06-01
Transverse dispersion represents an important mixing process for transport of contaminants in groundwater and constitutes an essential prerequisite for geochemical and biodegradation reactions. Within this context, this work describes the detailed numerical simulation of highly controlled laboratory experiments using uranine, bromide and oxygen depleted water as conservative tracers for the quantification of transverse mixing in porous media. Synthetic numerical experiments reproducing an existing laboratory experimental set-up of quasi two-dimensional flow through tank were performed to assess the applicability of an analytical solution of the 2D advection-dispersion equation for the estimation of transverse dispersivity as fitting parameter. The fitted dispersivities were compared to the "true" values introduced in the numerical simulations and the associated error could be precisely estimated. A sensitivity analysis was performed on the experimental set-up in order to evaluate the sensitivities of the measurements taken at the tank experiment on the individual hydraulic and transport parameters. From the results, an improved experimental set-up as well as a numerical evaluation procedure could be developed, which allow for a precise and reliable determination of dispersivities. The improved tank set-up was used for new laboratory experiments, performed at advective velocities of 4.9 m d(-1) and 10.5 m d(-1). Numerical evaluation of these experiments yielded a unique and reliable parameter set, which closely fits the measured tracer concentration data. For the porous medium with a grain size of 0.25-0.30 mm, the fitted longitudinal and transverse dispersivities were 3.49×10(-4) m and 1.48×10(-5) m, respectively. The procedures developed in this paper for the synthetic and rigorous design and evaluation of the experiments can be generalized and transferred to comparable applications.
Tidal Mixing and Buoyancy Advection: Joint Influences on Lobster Distribution in Coastal Maine
NASA Astrophysics Data System (ADS)
Brooks, D. A.
2004-12-01
The Eastern Maine Coastal Current (EMCC) flows southwestward from the mouth of the Bay of Fundy to Penobscot Bay on the central Maine coast. Maximum non-tidal surface speeds reach 20-30 cm/s about 20 km offshore during April-May when the outflow from the Saint John River is strongest. Vigorous tides cause strong vertical and horizontal mixing, so that dispersal of neutral particles is influenced both by advection and tidal mixing. To survive, planktonic lobsters carried southwestward in the surface flow must settle to a nearshore cobble substrate. Larvae hatched near the Bay of Fundy can be advected to the central coast in 2-3 weeks, roughly the time needed to reach settlement stage. Over the same period, transverse tidal mixing is sufficient to raise nearshore larval concentrations to about half that offshore in the axis of the EMCC. Both processes may be necessary to explain the observed lobster distribution, which exhibits a distinct maximum in the central coastal region. The seasonal development of the EMCC is also influenced by winds and the larger circulation of the Gulf of Maine. This work is part of a multidisciplinary synthesis study funded by the NOAA Coastal Ocean Program.
Invasions in heterogeneous habitats in the presence of advection.
Vergni, Davide; Iannaccone, Sandro; Berti, Stefano; Cencini, Massimo
2012-05-21
We investigate invasions from a biological reservoir to an initially empty, heterogeneous habitat in the presence of advection. The habitat consists of a periodic alternation of favorable and unfavorable patches. In the latter the population dies at fixed rate. In the former it grows either with the logistic or with an Allee effect type dynamics, where the population has to overcome a threshold to grow. We study the conditions for successful invasions and the speed of the invasion process, which is numerically and analytically investigated in several limits. Generically advection enhances the downstream invasion speed but decreases the population size of the invading species, and can even inhibit the invasion process. Remarkably, however, the rate of population increase, which quantifies the invasion efficiency, is maximized by an optimal advection velocity. In models with Allee effect, differently from the logistic case, above a critical unfavorable patch size the population localizes in a favorable patch, being unable to invade the habitat. However, we show that advection, when intense enough, may activate the invasion process.
Black Hole Advective Accretion Disks with Optical Depth Transition
Artemove, Y.V.; Bisnovatyi-Kogan, G.S.; Igumenshchev, I.V.; Novikov, I.D.
2006-02-01
We have constructed numerically global solutions of advective accretion disks around black holes that describe a continuous transition between the effectively optically thick outer and optically thin inner disk regions. We have concentrated on models of accretion flows with large mass accretion rates, and we have employed a bridging formula for radiative losses at high and low effective optical depths.
Advective velocity and energy dissipation rate in an oscillatory flow.
Haider, Ziaul; Hondzo, Miki; Porte-Agel, Fernando
2005-07-01
Characterizing the transport processes at the sediment-water interface along sloping boundaries in lakes and reservoirs is of fundamental interest in lake and reservoir water quality management. The turbulent bottom boundary layer (TBBL) along a slope, induced by the breaking of internal waves in a linearly stratified fluid, was investigated through laboratory measurements. Fast response micro-scale conductivity and temperature probes in conjunction with laser-Doppler velocimetry were used to measure the time series of salinity, temperature, and velocity along a sloping boundary. Turbulent energy spectra were computed from the velocity data using a time-dependent advective velocity and Taylor's hypothesis. The energy spectra were used to estimate the energy dissipation rate at different positions in the TBBL. The advective velocity in this near-zero mean shear flow is based on an integral time scale (T(int)). The integral time scale is related to the average frequency of the spectral energy density of the flow velocity. The energy dissipation rate estimated from the variable advective velocity with an averaging time window equal to the integral time scale (T=T(int)) was 43% higher than the energy dissipation rate estimated from a constant advective velocity. The estimated dissipation rates with T=T(int) were comparable to values obtained by curve-fitting a theoretical Batchelor spectrum for the temperature gradient spectra. This study proposes the integral time scale to be used for the oscillatory flows as (a) a time-averaging window to estimate the advective velocity and associated energy dissipation level, and (b) a normalizing parameter in the energy spectrum.
Persistence of cluster synchronization under the influence of advection.
Guirey, Emma; Bees, Martin; Martin, Adrian; Srokosz, Meric
2010-05-01
We present a study on the emergence of spatial structure in plankton dynamics under the influence of stirring and mixing. A distribution of plankton is represented as a lattice of nonidentical, interacting, oscillatory plankton populations. Each population evolves according to (i) the internal biological dynamics represented by an NPZ model with population-specific phytoplankton growth rate, (ii) sub-grid-cell stirring and mixing parameterized by a nearest-neighbor coupling, and (iii) explicit advection resulting from a constant horizontal shear. Using the methods of synchronization theory, the emergent spatial structure of the simulation is investigated as a function of the coupling strength and rate of advection. Previous work using similar methods has neglected the effects of explicit stirring (i.e., at scales larger than the grid cell), leaving as an open question the relevance of the work to real marine systems. Here, we show that persistent spatial structure emerges for a range of coupling strengths for all realistic levels of surface ocean shear. Spatially, this corresponds to the formation of temporally evolving clusters of local synchronization. Increasing shear alters the spatial characteristics of this clustering by stretching and narrowing patches of synchronized dynamics. These patches are not stretched into stripes of synchronized abundance aligned with the flow, as may be expected, but instead lie at an angle to the flow. This study shows that advection does not diminish the relevance of conclusions from previous studies of spatial structure in plankton simulations. In fact, the inclusion of advection adds characteristic filamental structure, as observed in real-world plankton distributions. The results also show that the ability of coupled oscillators to synchronize depends strongly on the spatial arrangement of oscillator natural frequencies; under the influence of advection, therefore, the impact of the coupling strength on the emergent spatial
Influence of turbulent advection on a phytoplankton ecosystem with nonuniform carrying capacity.
McKiver, William J; Neufeld, Zoltán
2009-06-01
In this work we study a plankton ecosystem model in a turbulent flow. The plankton model we consider contains logistic growth with a spatially varying background carrying capacity and the flow dynamics are generated using the two-dimensional (2D) Navier-Stokes equations. We characterize the system in terms of a dimensionless parameter, gamma identical with TB/TF, which is the ratio of the ecosystem biological time scales TB and the flow time scales TF. We integrate this system numerically for different values of gamma until the mean plankton reaches a statistically stationary state and examine how the steady-state mean and variance of plankton depends on gamma. Overall we find that advection in the presence of a nonuniform background carrying capacity can lead to very different plankton distributions depending on the time scale ratio gamma. For small gamma the plankton distribution is very similar to the background carrying capacity field and has a mean concentration close to the mean carrying capacity. As gamma increases the plankton concentration is more influenced by the advection processes. In the largest gamma cases there is a homogenization of the plankton concentration and the mean plankton concentration approaches the harmonic mean, <1/K>(-1). We derive asymptotic approximations for the cases of small and large gamma. We also look at the dependence of the power spectra exponent, beta, on gamma where the power spectrum of plankton is proportional to k(-beta). We find that the power spectra exponent closely obeys beta=1+2/gamma as predicted by earlier studies using simple models of chaotic advection.
NASA Astrophysics Data System (ADS)
Rijnsburger, Sabine; van der Hout, Carola M.; van Tongeren, Onno; de Boer, Gerben J.; van Prooijen, Bram C.; Borst, Wil G.; Pietrzak, Julie D.
2016-05-01
This study identifies and unravels the processes that lead to stratification and destratification in the far field of a Region of Freshwater Influence (ROFI). We present measurements that are novel for two reasons: (1) measurements were carried out with two vessels that sailed simultaneously over two cross-shore transects; (2) the measurements were carried out in the far field of the Rhine ROFI, 80 km downstream from the river mouth. This unique four dimensional dataset allows the application of the 3D potential energy anomaly equation for one of the first times on field data. With this equation, the relative importance of the depth mean advection, straining and nonlinear processes over one tidal cycle is assessed. The data shows that the Rhine ROFI extends 80 km downstream and periodic stratification is observed. The analysis not only shows the important role of cross-shore tidal straining but also the significance of along-shore straining and depth mean advection. In addition, the nonlinear terms seem to be small. The presence of all the terms influences the timing of maximum stratification. The analysis also shows that the importance of each term varies in the cross-shore direction. One of the most interesting findings is that the data are not inline with several hypotheses on the functioning of straining and advection in ROFIs. This highlights the dynamic behaviour of the Rhine ROFI, which is valuable for understanding the distribution of fine sediments, contaminants and the protection of coasts.
Tu, Haohua; Liu, Yuan; Lægsgaard, Jesper; Sharma, Utkarsh; Siegel, Martin; Kopf, Daniel; Boppart, Stephen A.
2010-01-01
We quantitatively predict the observed continuum-like spectral broadening in a 90-mm weakly birefringent all-normal dispersion-flattened photonic crystal fiber pumped by 1041-nm 229-fs 76-MHz pulses from a solid-state Yb:KYW laser. The well-characterized continuum pulses span a bandwidth of up to 300 nm around the laser wavelength, allowing high spectral power density pulse shaping useful for various coherent control applications. We also identify the nonlinear polarization effect that limits the bandwidth of these continuum pulses, and therefore report the path toward a series of attractive alternative broadband coherent optical sources. PMID:21197060
Karniadakis, George Em
2014-03-11
The main objective of this project is to develop new computational tools for uncertainty quantifica- tion (UQ) of systems governed by stochastic partial differential equations (SPDEs) with applications to advection-diffusion-reaction systems. We pursue two complementary approaches: (1) generalized polynomial chaos and its extensions and (2) a new theory on deriving PDF equations for systems subject to color noise. The focus of the current work is on high-dimensional systems involving tens or hundreds of uncertain parameters.
NASA Astrophysics Data System (ADS)
Eslami, Parastou; Seo, Jung-Hee; Rahsepar, Amirali; George, Richard; Lardo, Albert; Mittal, Rajat
2014-11-01
Coronary computed tomography angiography (CTA) is a promising tool for assessment of coronary stenosis and plaque burden. Recent studies have shown the presence of axial contrast concentration gradients in obstructed arteries, but the mechanism responsible for this phenomenon is not well understood. We use computational fluid dynamics to study intracoronary contrast dispersion and the correlation of concentration gradients with intracoronary blood flow and stenotic severity. Data from our CFD patient-specific simulations reveals that contrast dispersions are generated by intracoronary advection effects, and therefore, encode the coronary flow velocity. This novel method- Transluminal Attenuation Flow Encoding (TAFE) - is used to estimate the flowrate in phantom studies as well as preclinical experiments. Our results indicate a strong correlation between the values estimated from TAFE and the values measured in these experiments. The flow physics of contrast dispersion associated with TAFE will be discussed. This work is funded by grants from Coulter Foundation and Maryland Innovation Initiative. The authors have pending patents in this technology and RM and ACL have other financial interests associated with TAFE.
NASA Astrophysics Data System (ADS)
Chrysikopoulos, Constantinos V.; Manariotis, Ioannis D.; Syngouna, Vasiliki I.
2014-05-01
Accurate prediction of colloid and biocolloid transport in porous media relies heavily on usage of suitable dispersion coefficients. The widespread procedure for dispersion coefficient determination consists of conducting conservative tracer experiments and subsequently fitting the collected breakthrough data with a selected advection-dispersion transport model. The fitted dispersion coefficient is assumed to characterize the porous medium and is often used thereafter to analyze experimental results obtained from the same porous medium with other solutes, colloids, and biocolloids. The classical advection-dispersion equation implies that Fick's first law of diffusion adequately describes the dispersion process, or that the dispersive flux is proportional to the concentration gradient. Therefore, the above-described procedure inherently assumes that the dispersive flux of all solutes, colloids and biocolloids under the same flow field conditions is exactly the same. Furthermore, the available mathematical models for colloid and biocoloid transport in porous media do not adequately account for gravity effects. Here an extensive laboratory study was undertaken in order to assess whether the dispersivity, which traditionally has been considered to be a property of the porous medium, is dependent on colloid particle size, interstitial velocity and length scale. The breakthrough curves were successfully simulated with a mathematical model describing colloid and biocolloid transport in homogeneous, water saturated porous media. The results demonstrated that the dispersivity increases very slowly with increasing interstitial velocity, and increases with column length. Furthermore, contrary to earlier results, which were based either on just a few experimental observations or experimental conditions leading to low mass recoveries, dispersivity was positively correlated with colloid particle size. Also, transport experiments were performed with biocolloids (bacteriophages:
Hagos, Samson M.; Feng, Zhe; Landu, Kiranmayi; Long, Charles N.
2014-09-11
Using observations from the 2011 AMIE/DYNAMO field campaign over the Indian Ocean and a high-resolution regional model simulation, the processes that lead to the rapid shallow-to-deep convection transitions associated with the initiation and eastward propagation of the Madden-Julian Oscillation (MJO) are examined. By tracking the evolution of the depth of several thousand individual model simulated precipitation features, the role of and the processes that control the observed midtropospheric moisture buildup ahead of the detection of deep convection are quantified at large and convection scales. The frequency of shallow-to-deep convection transitions is found to be sensitive to this midlevel moisture and large-scale uplift. This uplift along with the decline of large-scale drying by equator-ward advection causes the moisture buildup leading to the initiation of the MJO. Convection scale moisture variability and uplift, and large-scale zonal advection play secondary roles.
In situ measurements of advective solute transport in permeable shelf sands
NASA Astrophysics Data System (ADS)
Reimers, Clare E.; Stecher, Hilmar A.; Taghon, Gary L.; Fuller, Charlotte M.; Huettel, Markus; Rusch, Antje; Ryckelynck, Natacha; Wild, Christian
2004-01-01
Solute transport rates within the uppermost 2 cm of a rippled continental shelf sand deposit, with a mean grain size of 400-500 μm and permeabilities of 2.0-2.4×10 -11 m 2, have been measured in situ by detecting the breakthrough of a pulse of iodide after its injection into the bottom water. These tracer experiments were conducted on the USA Middle Atlantic Bight shelf at a water depth of ˜13 m using a small tethered tripod that carried a close-up video camera, acoustic current meter, motorized 1.5 liter "syringe", and a microprofiling system for positioning and operating a solid-state voltammetric microelectrode. When triggered on shipboard, the syringe delivered a 0.21 M solution of potassium iodide and red dye through five nozzles positioned around and above the buried tip of the voltammetric sensor for 0.65-5 min. Bottom turbulence rapidly mixed and dispersed the tracer, which then was carried into the bed by interfacial water flows associated with ripple topography. The advective downward transport to the sensor tip was timed by a sequence of repetitive voltammetric scans. The distance-averaged vertical velocity, expressed as the depth of the sensor tip in the sand divided by the time to iodide breakthrough, was found to vary from 6 to 53 cm h -1 and generally to decrease with sediment depth. Because of episodic pumping and dispersion associated with the greatest 5% of wave heights and current speeds recorded, some concentration vs. time responses showed evidence of uneven solute migration. For reasons of mass balance, the advective flow field in the surface layers of permeable beds includes regions of water intrusion, horizontal pore-water flow and upwelling which also may explain some of the observed uneven migration. Pore-water advection was also evident in oxygen profiles measured before and after tracer injection with the voltammetric sensor. These profiles showed irregular distributions and oxygen penetration depths of 4-4.5 cm. Sand cores from the
Impact of Ridge Induced Latent Heat Advection on Sea Ice Global Heat Budget.
NASA Astrophysics Data System (ADS)
Hudier, E.; Gosselin, J.
2008-12-01
The effects of permeability on ice keel induced latent heat fluxes are examined using pressure ridge density statistics computed from SAR images and a prognostic simulation of forced brine advection through the bottom ice layer. Under pressure gradients generated in the wake of an ice keel sea water is pushed into and brine pumped out of the bottom ice layer. This in turn causes a new thermodynamic equilibrium to be reached. At spring when the ice permeability increases, brine export combined with sea water import translates into an advective heat flow that is balanced by the latent heat absorbed by volume melting of brine channel walls. Sea ice within the sheltered areas behind keels is modelled as an anisotropic heteregeneous mushy layer. The non-linear equation system within each cell is implemented on a finite volume grid and include volume melt of the brine channels from which porosity, water density, temperature and salinity are computed. Outputs from these simulations are then combined with ridge distribution statistics to evaluate the global impact of latent heat absorbed due to volume melting in the wake of ridges. As anticipated, results are highly dependent on permeability, nevertheless, they show that pressure ridge induced melting within the ice is a significant component of the heat budget when compared with melting at the ice water interface. This work underlines needs for further researches to improve our understanding of ice permeability changes during the melt season, it also calls for better tools to extract pressure ridge characteristics from satellite images.
An adaptive multiresolution gradient-augmented level set method for advection problems
NASA Astrophysics Data System (ADS)
Schneider, Kai; Kolomenskiy, Dmitry; Nave, Jean-Chtristophe
2014-11-01
Advection problems are encountered in many applications, such as transport of passive scalars modeling pollution or mixing in chemical engineering. In some problems, the solution develops small-scale features localized in a part of the computational domain. If the location of these features changes in time, the efficiency of the numerical method can be significantly improved by adapting the partition dynamically to the solution. We present a space-time adaptive scheme for solving advection equations in two space dimensions. The third order accurate gradient-augmented level set method using a semi-Lagrangian formulation with backward time integration is coupled with a point value multiresolution analysis using Hermite interpolation. Thus locally refined dyadic spatial grids are introduced which are efficiently implemented with dynamic quad-tree data structures. For adaptive time integration, an embedded Runge-Kutta method is employed. The precision of the new fully adaptive method is analysed and speed up of CPU time and memory compression with respect to the uniform grid discretization are reported.
On the error propagation of semi-Lagrange and Fourier methods for advection problems.
Einkemmer, Lukas; Ostermann, Alexander
2015-02-01
In this paper we study the error propagation of numerical schemes for the advection equation in the case where high precision is desired. The numerical methods considered are based on the fast Fourier transform, polynomial interpolation (semi-Lagrangian methods using a Lagrange or spline interpolation), and a discontinuous Galerkin semi-Lagrangian approach (which is conservative and has to store more than a single value per cell). We demonstrate, by carrying out numerical experiments, that the worst case error estimates given in the literature provide a good explanation for the error propagation of the interpolation-based semi-Lagrangian methods. For the discontinuous Galerkin semi-Lagrangian method, however, we find that the characteristic property of semi-Lagrangian error estimates (namely the fact that the error increases proportionally to the number of time steps) is not observed. We provide an explanation for this behavior and conduct numerical simulations that corroborate the different qualitative features of the error in the two respective types of semi-Lagrangian methods. The method based on the fast Fourier transform is exact but, due to round-off errors, susceptible to a linear increase of the error in the number of time steps. We show how to modify the Cooley-Tukey algorithm in order to obtain an error growth that is proportional to the square root of the number of time steps. Finally, we show, for a simple model, that our conclusions hold true if the advection solver is used as part of a splitting scheme.
Modelling sensitivities to mixing and advection in a sill-basin estuarine system
NASA Astrophysics Data System (ADS)
Soontiens, Nancy; Allen, Susan E.
2017-04-01
This study investigates the sensitivity of a high resolution regional ocean model to several choices in mixing and advection. The oceanographic process examined is a deep water renewal event in the Juan de Fuca Strait-Strait of Georgia sill-basin estuarine system located on the west coast of North America. Previous observational work has shown that the timing of the renewal events is linked to the spring/neap tidal cycle, and in turn, is sensitive to the amount of vertical mixing induced by tidal currents interacting with sills and complicated bathymetry. It is found that the model's representation of deep water renewal is relatively insensitive to several mixing choices, including the vertical turbulence closure and direction of lateral mixing. No significant difference in deep or intermediate salinity was found between cases that used k - ɛ versus k - ω closures and isoneutral versus horizontal lateral mixing. Modifications that had a stronger effect included those that involved advection such as modifying the salinity of the open boundary conditions which supply the source waters for the renewal event. The strongest impact came from the removal of the Hollingsworth instability, a kinetic energy sink in the energy-enstrophy discretization of the momentum equations. A marked improvement to the salinity of the deep water renewal suggests that the removal of the Hollingsworth instability will correct a fresh drift in the deep and intermediate waters in an operational version of this model.
Phase Segregation of Passive Advective Particles in an Active Medium
NASA Astrophysics Data System (ADS)
Das, Amit; Polley, Anirban; Rao, Madan
2016-02-01
Localized contractile configurations or asters spontaneously appear and disappear as emergent structures in the collective stochastic dynamics of active polar actomyosin filaments. Passive particles which (un)bind to the active filaments get advected into the asters, forming transient clusters. We study the phase segregation of such passive advective scalars in a medium of dynamic asters, as a function of the aster density and the ratio of the rates of aster remodeling to particle diffusion. The dynamics of coarsening shows a violation of Porod behavior; the growing domains have diffuse interfaces and low interfacial tension. The phase-segregated steady state shows strong macroscopic fluctuations characterized by multiscaling and intermittency, signifying rapid reorganization of macroscopic structures. We expect these unique nonequilibrium features to manifest in the actin-dependent molecular clustering at the cell surface.
Chaotic Advection in a Bounded 3-Dimensional Potential Flow
NASA Astrophysics Data System (ADS)
Metcalfe, Guy; Smith, Lachlan; Lester, Daniel
2012-11-01
3-dimensional potential, or Darcy flows, are central to understanding and designing laminar transport in porous media; however, chaotic advection in 3-dimensional, volume-preserving flows is still not well understood. We show results of advecting passive scalars in a transient 3-dimensional potential flow that consists of a steady dipole flow and periodic reorientation. Even for the most symmetric reorientation protocol, neither of the two invarients of the motion are conserved; however, one invarient is closely shadowed by a surface of revolution constructed from particle paths of the steady flow, creating in practice an adiabatic surface. A consequence is that chaotic regions cover 3-dimensional space, though tubular regular regions are still transport barriers. This appears to be a new mechanism generating 3-dimensional chaotic orbits. These results contast with the experimental and theoretical results for chaotic scalar transport in 2-dimensional Darcy flows. Wiggins, J. Fluid Mech. 654 (2010).
Aerosol particles and the formation of advection fog
NASA Technical Reports Server (NTRS)
Hung, R. J.; Liaw, G. S.; Vaughan, O. H., Jr.
1979-01-01
A study of numerical simulation of the effects of concentration, particle size, mass of nuclei, and chemical composition on the dynamics of warm fog formation, particularly the formation of advection fog, is presented. This formation is associated with the aerosol particle characteristics, and both macrophysical and microphysical processes are considered. In the macrophysical model, the evolution of wind components, water vapor content, liquid water content, and potential temperature under the influences of vertical turbulent diffusion, turbulent momentum, and turbulent energy transfers are taken into account. In the microphysical model, the supersaturation effect is incorporated with the surface tension and hygroscopic material solution. It is shown that the aerosol particles with the higher number density, larger size nuclei, the heavier nuclei mass, and the higher ratio of the Van't Hoff factor to the molecular weight favor the formation of the lower visibility advection fogs with stronger vertical energy transfer during the nucleation and condensation time period.
Advective-diffusive contaminant migration in unsaturated sand and gravel
Rowe, R.K.; Badv, K.
1996-12-01
A method is presented for estimating the diffusion coefficients for chloride and sodium in unsaturated coarse sand and fine gravel based on parameters obtained from saturated diffusion tests conducted for similar material. The method is tested by comparing the observed and predicted diffusion profiles through unsaturated soil. The method is shown to work well for predicting the advective-diffusive migration of chloride and sodium through a two-layer soil system consisting of a compacted clayey silt underlain by an unsaturated fine gravel. Over the range of conditions examined, it is concluded that existing solute transport theory along with the proposed procedure for estimating the unsaturated diffusion coefficients can adequately predict chloride and sodium diffusion through both unsaturated coarse sand and fine gravel as well as predict advective-diffusive transport through a compacted clayey layer and underlying unsaturated fine gravel.
Spectral Theory of Advective Diffusion in the Ocean
2013-09-19
to study this enhancement of sea ice thermal conductivity and better understand temperature data collected during a 2007 Antarctic expedition. 15...conductivity and better understand temperature data collected during a 2007 Antarctic expedition. Activities and Findings: 1. Advection-enhanced...critically on the properties of this Hilbert space. More specifically, it is only on a special subset of this space that the random operator is Hermitian
Stability of explicit advection schemes. The balance point location rule
NASA Astrophysics Data System (ADS)
Leonard, B. P.
2002-02-01
This paper introduces the balance point location rule, providing specific necessary and sufficient conditions for constructing unconditionally stable explicit advection schemes, in both semi-Lagrangian and flux-form Eulerian formulations. The rule determines how the spatial stencil is placed on the computational grid. It requires the balance point (the center of the stencil in index space) to be located in the same patch as the departure point for semi-Lagrangian schemes or the same cell as the sweep point for Eulerian schemes. Centering the stencil in this way guarantees stability, regardless of the size of the time step. In contrast, the original Courant-Friedrichs-Lewy (CFL) condition requiring the stencil merely to include the departure (sweep) point, although necessary, is not sufficient for guaranteeing stability. The CFL condition is of limited practical value, whereas the balance point location rule always gives precise and easily implemented prescriptions for constructing stable algorithms. The rule is also helpful in correcting a number of misconceptions that have arisen concerning explicit advection schemes. In particular, explicit Eulerian schemes are widely believed to be inefficient because of stability constraints on the time step, dictated by a narrow interpretation of the CFL condition requiring the Courant number to be less than or equal to one. However, such constraints apply only to a particular class of advection schemes resulting for centering the stencil on the arrival point, when in fact the sole function of the stencil is to estimate the departure (sweep) point value - the arrival point has no relevance in determining the placement of the stencil. Unconditionally stable explicit Eulerian advection schemes are efficient and accurate, comparable in operation count to semi-Lagrangian schemes of the same order, but because of their flux-based formulation, they have the added advantage of being inherently conservative. Copyright
An ELLAM Approximation for Advective-Dispersive Transport with Nonlinear Sorption
2005-02-28
1, Cass T. Miller a aCenter for the Integrated Study of the Environment, Department of Environmental Sciences and Engineering , University of North...Carolina, Chapel Hill, North Carolina 27599-7431, USA bU.S. Army Engineer Research and Development Center, Coastal and Hydraulics Laboratory, 3909 Halls...Center for Integrated Study of the Environment,Department of Environmental Sciences and Engineering ,Chapel Hill,NC,27599-7431 8. PERFORMING
Dispersion of aerosol particles in the atmosphere: Fukushima
NASA Astrophysics Data System (ADS)
Haszpra, Tímea; Lagzi, István; Tél, Tamás
2013-04-01
Investigation of dispersion and deposition of aerosol particles in the atmosphere is an essential issue, because they have an effect on the biosphere and atmosphere. Moreover, aerosol particles have different transport properties and chemical and physical transformations in the atmosphere compared to gas phase air pollutants. The motion of a particle is described by a set of ordinary differential equations. The large-scale dynamics in the horizontal direction can be described by the equations of passive scalar advection, but in the vertical direction a well-defined terminal velocity should be taken into account as a term added to the vertical wind component. In the planetary boundary layer turbulent diffusion has an important role in the particle dispersion, which is taken into account by adding stochastic terms to the deterministic equations above. Wet deposition is also an essential process in the lower levels of the atmosphere, however, its precise parameterization is a challenge. For the simulations the wind field and other necessary data were taken from the ECMWF ERA-Interim database. In the case of the Fukushima Daiichi nuclear disaster (March-April 2011) radioactive aerosol particles were also released in the planetary boundary layer. Simulations (included the continuous and varying emission from the nuclear power plant) will be presented for the period of 14-23 March. Results show that wet deposition also has to be taken into consideration in the lower levels of the atmosphere. Furthermore, dynamical system characteristics are evaluated for the aerosol particle dynamics. The escape rate of particles was estimated both with and without turbulent diffusion, and in both cases when there was no wet deposition and also when wet deposition was taken into consideration.
Modeling breakup and relaxation of Newtonian droplets using the advected phase-field approach
NASA Astrophysics Data System (ADS)
Beaucourt, J.; Biben, T.; Leyrat, A.; Verdier, C.
2007-02-01
The relaxation and breakup of Newtonian droplets is considered using the advected field approach. This method allows one to follow the deformation of interfaces using an order parameter field [Biben , Europhys. Lett. 63, 623 (2003)] based on a Ginzburg-Landau equation. Using this method, it is possible to follow the breakup of droplets and stability curves can be obtained in both two- and three-dimensional shear and elongational flows. Finally, relaxation of a droplet is considered, following the application of an elongational flow. The results are compared with previous experimental data [Ha and Leal, Phys. Fluids 13, 1568 (2001)], and are found to be in satisfactory agreement. The method is general enough to be applied to other non-Newtonian fluids, such as Oldroyd-B fluids or viscoplastic materials.
NASA Technical Reports Server (NTRS)
Zhou, YE; Vahala, George
1993-01-01
The advection of a passive scalar by incompressible turbulence is considered using recursive renormalization group procedures in the differential sub grid shell thickness limit. It is shown explicitly that the higher order nonlinearities induced by the recursive renormalization group procedure preserve Galilean invariance. Differential equations, valid for the entire resolvable wave number k range, are determined for the eddy viscosity and eddy diffusivity coefficients, and it is shown that higher order nonlinearities do not contribute as k goes to 0, but have an essential role as k goes to k(sub c) the cutoff wave number separating the resolvable scales from the sub grid scales. The recursive renormalization transport coefficients and the associated eddy Prandtl number are in good agreement with the k-dependent transport coefficients derived from closure theories and experiments.
Runkel, Robert L.; Chapra, Steven C.
1993-01-01
Several investigators have proposed solute transport models that incorporate the effects of transient storage. Transient storage occurs in small streams when portions of the transported solute become isolated in zones of water that are immobile relative to water in the main channel (e.g., pools, gravel beds). Transient storage is modeled by adding a storage term to the advection-dispersion equation describing conservation of mass for the main channel. In addition, a separate mass balance equation is written for the storage zone. Although numerous applications of the transient storage equations may be found in the literature, little attention has been paid to the numerical aspects of the approach. Of particular interest is the coupled nature of the equations describing mass conservation for the main channel and the storage zone. In the work described herein, an implicit finite difference technique is developed that allows for a decoupling of the governing differential equations. This decoupling method may be applied to other sets of coupled equations such as those describing sediment-water interactions for toxic contaminants. For the case at hand, decoupling leads to a 50% reduction in simulation run time. Computational costs may be further reduced through efficient application of the Thomas algorithm. These techniques may be easily incorporated into existing codes and new applications in which simulation run time is of concern.
NASA Astrophysics Data System (ADS)
Lueptow, Richard M.; Schlick, Conor P.; Umbanhowar, Paul B.; Ottino, Julio M.
2013-11-01
We investigate chaotic advection and diffusion in competitive autocatalytic reactions. To study this subject, we use a computationally efficient method for solving advection-reaction-diffusion equations for periodic flows using a mapping method with operator splitting. In competitive autocatalytic reactions, there are two species, B and C, which both react autocatalytically with species A (A +B -->2B and A +C -->2C). If there is initially a small amount of spatially localized B and C and a large amount of A, all three species will be advected by the velocity field, diffuse, and react until A is completely consumed and only B and C remain. We find that the small scale interactions associated with the chaotic velocity field, specifically the local finite-time Lyapunov exponents (FTLEs), can accurately predict the final average concentrations of B and C after the reaction is complete. The species, B or C, that starts in the region with the larger FTLE has, with high probability, the larger average concentration at the end of the reaction. If species B and C start in regions having similar FTLEs, their average concentrations at the end of the reaction will also be similar. Funded by NSF Grant CMMI-1000469.
Magnetic flux and heat losses by diffusive, advective, and Nernst effects in MagLIF-like plasma
Velikovich, A. L. Giuliani, J. L.; Zalesak, S. T.
2014-12-15
The MagLIF approach to inertial confinement fusion involves subsonic/isobaric compression and heating of a DT plasma with frozen-in magnetic flux by a heavy cylindrical liner. The losses of heat and magnetic flux from the plasma to the liner are thereby determined by plasma advection and gradient-driven transport processes, such as thermal conductivity, magnetic field diffusion and thermomagnetic effects. Theoretical analysis based on obtaining exact self-similar solutions of the classical collisional Braginskii's plasma transport equations in one dimension demonstrates that the heat loss from the hot plasma to the cold liner is dominated by the transverse heat conduction and advection, and the corresponding loss of magnetic flux is dominated by advection and the Nernst effect. For a large electron Hall parameter ω{sub e}τ{sub e} effective diffusion coefficients determining the losses of heat and magnetic flux are both shown to decrease with ω{sub e}τ{sub e} as does the Bohm diffusion coefficient, which is commonly associated with low collisionality and two-dimensional transport. This family of exact solutions can be used for verification of codes that model the MagLIF plasma dynamics.
Velikovich, A. L.; Giuliani, J. L.; Zalesak, S. T.
2015-04-15
The magnetized liner inertial fusion (MagLIF) approach to inertial confinement fusion [Slutz et al., Phys. Plasmas 17, 056303 (2010); Cuneo et al., IEEE Trans. Plasma Sci. 40, 3222 (2012)] involves subsonic/isobaric compression and heating of a deuterium-tritium plasma with frozen-in magnetic flux by a heavy cylindrical liner. The losses of heat and magnetic flux from the plasma to the liner are thereby determined by plasma advection and gradient-driven transport processes, such as thermal conductivity, magnetic field diffusion, and thermomagnetic effects. Theoretical analysis based on obtaining exact self-similar solutions of the classical collisional Braginskii's plasma transport equations in one dimension demonstrates that the heat loss from the hot compressed magnetized plasma to the cold liner is dominated by transverse heat conduction and advection, and the corresponding loss of magnetic flux is dominated by advection and the Nernst effect. For a large electron Hall parameter (ω{sub e}τ{sub e}≫1), the effective diffusion coefficients determining the losses of heat and magnetic flux to the liner wall are both shown to decrease with ω{sub e}τ{sub e} as does the Bohm diffusion coefficient cT/(16eB), which is commonly associated with low collisionality and two-dimensional transport. We demonstrate how this family of exact solutions can be used for verification of codes that model the MagLIF plasma dynamics.
NASA Astrophysics Data System (ADS)
Velikovich, A. L.; Giuliani, J. L.; Zalesak, S. T.
2015-04-01
The magnetized liner inertial fusion (MagLIF) approach to inertial confinement fusion [Slutz et al., Phys. Plasmas 17, 056303 (2010); Cuneo et al., IEEE Trans. Plasma Sci. 40, 3222 (2012)] involves subsonic/isobaric compression and heating of a deuterium-tritium plasma with frozen-in magnetic flux by a heavy cylindrical liner. The losses of heat and magnetic flux from the plasma to the liner are thereby determined by plasma advection and gradient-driven transport processes, such as thermal conductivity, magnetic field diffusion, and thermomagnetic effects. Theoretical analysis based on obtaining exact self-similar solutions of the classical collisional Braginskii's plasma transport equations in one dimension demonstrates that the heat loss from the hot compressed magnetized plasma to the cold liner is dominated by transverse heat conduction and advection, and the corresponding loss of magnetic flux is dominated by advection and the Nernst effect. For a large electron Hall parameter ( ωeτe≫1 ), the effective diffusion coefficients determining the losses of heat and magnetic flux to the liner wall are both shown to decrease with ωeτe as does the Bohm diffusion coefficient c T /(16 e B ) , which is commonly associated with low collisionality and two-dimensional transport. We demonstrate how this family of exact solutions can be used for verification of codes that model the MagLIF plasma dynamics.
Griffith, Boyce E.; Peskin, Charles S.
2010-01-01
We describe an immersed boundary method for problems of fluid-solute-structure interaction. The numerical scheme employs linearly implicit timestepping, allowing for the stable use of timesteps that are substantially larger than those permitted by an explicit method, and local mesh refinement, making it feasible to resolve the steep gradients associated with the space charge layers as well as the chemical potential, which is used in our formulation to control the permeability of the membrane to the (possibly charged) solute. Low Reynolds number fluid dynamics are described by the time-dependent incompressible Stokes equations, which are solved by a cell-centered approximate projection method. The dynamics of the chemical species are governed by the advection-electrodiffusion equations, and our semi-implicit treatment of these equations results in a linear system which we solve by GMRES preconditioned via a fast adaptive composite-grid (FAC) solver. Numerical examples demonstrate the capabilities of this methodology, as well as its convergence properties. PMID:20454540
NASA Astrophysics Data System (ADS)
Wilderbuer, Thomas; Duffy-Anderson, Janet T.; Stabeno, Phyllis; Hermann, Albert
2016-05-01
In an effort to better understand the physics of the eastern Bering Sea shelf current as it relates to flatfish advection to favorable near-shore areas, sets of multiple, satellite-tracked, oceanic drifters were released in 2010, 2012 and 2013. The release sites and dates were chosen to coincide with known spawning locations for northern rock sole (Lepidopsetta polyxystra) and known time of larval emergence. The drifters were drogued 5-each at 20 and 40 m in 2010 and 2012, and 4 at 40 m and 2 at 20 m in 2013. The locations of drifters were used to calculate divergence over a 90-day period that corresponds to the larval pelagic duration of Bering Sea shelf northern rock sole. Results indicate that there are alternating periods of positive and negative divergence with an overall trend toward drifter separation after 90 days, roughly the end of the rock sole planktonic larval period. Examination of the drifter behavior at the hourly scale indicates that semi-daily tidal forcing is the primary mechanism of drifter divergence and convergence. Field observations of early-stage northern rock sole larval distributions over the same period indicate that predominant oceanographic advection is northerly over the continental shelf among preflexion stages, though juveniles are predominantly found in nursery areas located ~ 400 km eastward and inshore. Evidence from drifter deployments suggests that behavioral movements during the postflexion and early juvenile larval phases that optimize eastward periodicity of tidal cycles is a viable mechanism to enhance eastward movement of northern rock sole larvae to favorable nursery grounds. A regional ocean modeling system (ROMS) was implemented to track the different rates of dispersion in simulations both with and without tidal forcing, and was used to estimate effective horizontal eddy diffusion in the case of both isobaric (fixed-depth) and Lagrangian (neutrally buoyant) particles. The addition of tidal forcing had a pronounced
Analyzing critical propagation in a reaction-diffusion-advection model using unstable slow waves.
Kneer, Frederike; Obermayer, Klaus; Dahlem, Markus A
2015-02-01
The effect of advection on the propagation and in particular on the critical minimal speed of traveling waves in a reaction-diffusion model is studied. Previous theoretical studies estimated this effect on the velocity of stable fast waves and predicted the existence of a critical advection strength below which propagating waves are not supported anymore. In this paper, an analytical expression for the advection-velocity relation of the unstable slow wave is derived. In addition, the critical advection strength is calculated taking into account the unstable slow wave solution. We also analyze a two-variable reaction-diffusion-advection model numerically in a wide parameter range. Due to the new control parameter (advection) we can find stable wave propagation in the otherwise non-excitable parameter regime, if the advection strength exceeds a critical value. Comparing theoretical predictions to numerical results, we find that they are in good agreement. Theory provides an explanation for the observed behaviour.
NASA Technical Reports Server (NTRS)
Douglass, A.; Kawa, S. R.; Einaudi, Franco (Technical Monitor)
2000-01-01
Three dimensional chemistry and transport models (CTMs) contain a set of coupled continuity equations which describe the evolution of constituents such as ozone and other minor species which affect ozone. Both advection and photochemical processes contribute to constituent evolution, and a CTM provides a means to evaluate these contributions separately. Such evaluation is particularly useful when both terms are important to the modeled tendency. An example is the ozone tendency in the high latitude winter lower stratosphere, where advection tends to increase ozone, and catalytic processes involving chlorine radicals tend to decrease ozone. The Goddard three dimensional chemistry and transport model uses meteorological fields from the Goddard Earth Observing System Data Assimilation System, thus the modeled ozone evolution may reproduce the observed evolution and provide a test of the model representation of photochemical processes if the transport is shown to be modeled appropriately. We have investigated the model advection further using diabatic trajectory calculations. For long lived constituents such as N2O, the model field for a particular time on a potential temperature surface is compared with a field produced by calculating 15 day back trajectories for a fixed latitude longitude grid, and mapping model N2O at the terminus of the back trajectories onto the initial grid. This provides a quantitative means to evaluate two aspects of the CTM transport: one, the model horizontal gradient between middle latitudes and the polar vortex is compared with the gradient produced using the non-diffusive trajectory calculation; two, the model vertical advection, which is produced by the divergence of the horizontal winds, is compared with the vertical transport expected from diabatic cooling.
NASA Astrophysics Data System (ADS)
Vinsard, G.; Dufour, S.; Saatdjian, E.; Mota, J. P. B.
2016-03-01
Chaotic advection can effectively enhance the heat transfer rate between a boundary and fluids with high Prandtl number. These fluids are usually highly viscous and thus turbulent agitation is not a viable solution since the energy required to mix the fluid would be prohibitive. Here, we analyze previously obtained results on chaotic advection and heat transfer in two similar 2-D periodic flows and on their corresponding 3-D periodic flows when an axial velocity component is superposed. The two flows studied are the flow between eccentric rotating cylinders and the flow between confocal ellipses. For both of these flows the analysis is simplified because the Stokes equations can be solved analytically to obtain a closed form solution. For both 2-D periodic flows, we show that chaotic heat transfer is enhanced by the displacement of the saddle point location during one period. Furthermore, the enhancement by chaotic advection in the elliptical geometry is approximately double that obtained in the cylindrical geometry because there are two saddle points instead of one. We also explain why, for high eccentricity ratios, there is no heat transfer enhancement in the cylindrical geometry. When an axial velocity component is added to both of these flows so that they become 3-D, previous work has shown that there is an optimum modulation frequency for which chaotic advection and heat transfer enhancement is a maximum. Here we show that the optimum modulation frequency can be derived from results without an axial flow. We also explain by physical arguments other previously unanswered questions in the published data.
High-Order Residual-Distribution Hyperbolic Advection-Diffusion Schemes: 3rd-, 4th-, and 6th-Order
NASA Technical Reports Server (NTRS)
Mazaheri, Alireza R.; Nishikawa, Hiroaki
2014-01-01
In this paper, spatially high-order Residual-Distribution (RD) schemes using the first-order hyperbolic system method are proposed for general time-dependent advection-diffusion problems. The corresponding second-order time-dependent hyperbolic advection- diffusion scheme was first introduced in [NASA/TM-2014-218175, 2014], where rapid convergences over each physical time step, with typically less than five Newton iterations, were shown. In that method, the time-dependent hyperbolic advection-diffusion system (linear and nonlinear) was discretized by the second-order upwind RD scheme in a unified manner, and the system of implicit-residual-equations was solved efficiently by Newton's method over every physical time step. In this paper, two techniques for the source term discretization are proposed; 1) reformulation of the source terms with their divergence forms, and 2) correction to the trapezoidal rule for the source term discretization. Third-, fourth, and sixth-order RD schemes are then proposed with the above techniques that, relative to the second-order RD scheme, only cost the evaluation of either the first derivative or both the first and the second derivatives of the source terms. A special fourth-order RD scheme is also proposed that is even less computationally expensive than the third-order RD schemes. The second-order Jacobian formulation was used for all the proposed high-order schemes. The numerical results are then presented for both steady and time-dependent linear and nonlinear advection-diffusion problems. It is shown that these newly developed high-order RD schemes are remarkably efficient and capable of producing the solutions and the gradients to the same order of accuracy of the proposed RD schemes with rapid convergence over each physical time step, typically less than ten Newton iterations.
Visualizing Vector Fields Using Line Integral Convolution and Dye Advection
NASA Technical Reports Server (NTRS)
Shen, Han-Wei; Johnson, Christopher R.; Ma, Kwan-Liu
1996-01-01
We present local and global techniques to visualize three-dimensional vector field data. Using the Line Integral Convolution (LIC) method to image the global vector field, our new algorithm allows the user to introduce colored 'dye' into the vector field to highlight local flow features. A fast algorithm is proposed that quickly recomputes the dyed LIC images. In addition, we introduce volume rendering methods that can map the LIC texture on any contour surface and/or translucent region defined by additional scalar quantities, and can follow the advection of colored dye throughout the volume.
Update on Advection-Diffusion Purge Flow Model
NASA Technical Reports Server (NTRS)
Brieda, Lubos
2015-01-01
Gaseous purge is commonly used in sensitive spacecraft optical or electronic instruments to prevent infiltration of contaminants and/or water vapor. Typically, purge is sized using simplistic zero-dimensional models that do not take into account instrument geometry, surface effects, and the dependence of diffusive flux on the concentration gradient. For this reason, an axisymmetric computational fluid dynamics (CFD) simulation was recently developed to model contaminant infiltration and removal by purge. The solver uses a combined Navier-Stokes and Advection-Diffusion approach. In this talk, we report on updates in the model, namely inclusion of a particulate transport model.
Subsurface barrier design alternatives for confinement and controlled advection flow
Phillips, S.J.; Stewart, W.E.; Alexander, R.G.; Cantrell, K.J.; McLaughlin, T.J.
1994-02-01
Various technologies and designs are being considered to serve as subsurface barriers to confine or control contaminant migration from underground waste storage or disposal structures containing radioactive and hazardous wastes. Alternatives including direct-coupled flood and controlled advection designs are described as preconceptual examples. Prototype geotechnical equipment for testing and demonstration of these alternative designs tested at the Hanford Geotechnical Development and Test Facility and the Hanford Small-Tube Lysimeter Facility include mobile high-pressure injectors and pumps, mobile transport and pumping units, vibratory and impact pile drivers, and mobile batching systems. Preliminary laboratory testing of barrier materials and additive sequestering agents have been completed and are described.
Is Chaotic Advection Inherent to Porous Media Flow?
NASA Astrophysics Data System (ADS)
Lester, Daniel; Metcalfe, Guy; Trefry, Mike
2013-11-01
All porous media, including granular and packed media, fractured and open networks, are typified by the inherent topological complexity of the pore-space. This topological complexity admits a large number density of stagnation points under steady Stokes flow, which in turn generates a 3D fluid mechanical analouge of the Bakers map, termed the Baker's flow. We demonstrate that via this mechanism, chaotic advection at the pore-scale is inherent to almost all porous media under reasonable conditions, and such dynamics have significant implications for a range of fluid-borne processes including transport and mixing, chemical reactions and biological activity.
Helical turbulent Prandtl number in the A model of passive vector advection
NASA Astrophysics Data System (ADS)
Hnatič, M.; Zalom, P.
2016-11-01
Using the field theoretic renormalization group technique in the two-loop approximation, turbulent Prandtl numbers are obtained in the general A model of passive vector advected by fully developed turbulent velocity field with violation of spatial parity introduced via the continuous parameter ρ ranging from ρ =0 (no violation of spatial parity) to |ρ |=1 (maximum violation of spatial parity). Values of A represent a continuously adjustable parameter which governs the interaction structure of the model. In nonhelical environments, we demonstrate that A is restricted to the interval -1.723 ≤A ≤2.800 (rounded to 3 decimal places) in the two-loop order of the field theoretic model. However, when ρ >0.749 (rounded to 3 decimal places), the restrictions may be removed, which means that presence of helicity exerts a stabilizing effect onto the possible stationary regimes of the system. Furthermore, three physically important cases A ∈{-1 ,0 ,1 } are shown to lie deep within the allowed interval of A for all values of ρ . For the model of the linearized Navier-Stokes equations (A =-1 ) up to date unknown helical values of the turbulent Prandtl number have been shown to equal 1 regardless of parity violation. Furthermore, we have shown that interaction parameter A exerts strong influence on advection-diffusion processes in turbulent environments with broken spatial parity. By varying A continuously, we explain high stability of the kinematic MHD model (A =1 ) against helical effects as a result of its proximity to the A =0.912 (rounded to 3 decimal places) case where helical effects are completely suppressed. Contrary, for the physically important A =0 model, we show that it lies deep within the interval of models where helical effects cause the turbulent Prandtl number to decrease with |ρ | . We thus identify internal structure of interactions given by the parameter A , and not the vector character of the admixture itself being the dominant factor influencing
Helical turbulent Prandtl number in the A model of passive vector advection.
Hnatič, M; Zalom, P
2016-11-01
Using the field theoretic renormalization group technique in the two-loop approximation, turbulent Prandtl numbers are obtained in the general A model of passive vector advected by fully developed turbulent velocity field with violation of spatial parity introduced via the continuous parameter ρ ranging from ρ=0 (no violation of spatial parity) to |ρ|=1 (maximum violation of spatial parity). Values of A represent a continuously adjustable parameter which governs the interaction structure of the model. In nonhelical environments, we demonstrate that A is restricted to the interval -1.723≤A≤2.800 (rounded to 3 decimal places) in the two-loop order of the field theoretic model. However, when ρ>0.749 (rounded to 3 decimal places), the restrictions may be removed, which means that presence of helicity exerts a stabilizing effect onto the possible stationary regimes of the system. Furthermore, three physically important cases A∈{-1,0,1} are shown to lie deep within the allowed interval of A for all values of ρ. For the model of the linearized Navier-Stokes equations (A=-1) up to date unknown helical values of the turbulent Prandtl number have been shown to equal 1 regardless of parity violation. Furthermore, we have shown that interaction parameter A exerts strong influence on advection-diffusion processes in turbulent environments with broken spatial parity. By varying A continuously, we explain high stability of the kinematic MHD model (A=1) against helical effects as a result of its proximity to the A=0.912 (rounded to 3 decimal places) case where helical effects are completely suppressed. Contrary, for the physically important A=0 model, we show that it lies deep within the interval of models where helical effects cause the turbulent Prandtl number to decrease with |ρ|. We thus identify internal structure of interactions given by the parameter A, and not the vector character of the admixture itself being the dominant factor influencing diffusion-advection
Horizontal advection, diffusion and plankton spectra at the sea surface.
NASA Astrophysics Data System (ADS)
Bracco, A.; Clayton, S.; Pasquero, C.
2009-04-01
Plankton patchiness is ubiquitous in the oceans, and various physical and biological processes have been proposed as its generating mechanisms. However, a coherent statement on the problem is missing, due to both a small number of suitable observations and to an incomplete understanding of the properties of reactive tracers in turbulent media. Abraham (1998) suggested that horizontal advection may be the dominant process behind the observed distributions of phytoplankton and zooplankton, acting to mix tracers with longer reaction times (Rt) down to smaller scales. Conversely, Mahadevan and Campbell (2002) attributed the relative distributions of sea surface temperature and phytoplankton to small scale upwelling, where tracers with longer Rt are able to homogenize more than those with shorter reaction times. Neither of the above mechanisms can explain simultaneously the (relative) spectral slopes of temperature, phytoplankton and zooplankton. Here, with a simple advection model and a large suite of numerical experiments, we concentrate on some of the physical processes influencing the relative distributions of tracers at the ocean surface, and we investigate: 1) the impact of the spatial scale of tracer supply; 2) the role played by coherent eddies on the distribution of tracers with different Rt; 3) the role of diffusion (so far neglected). We show that diffusion determines the distribution of temperature, regardless of the nature of the forcing. We also find that coherent structures together with differential diffusion of tracers with different Rt impact the tracer distributions. This may help in understanding the highly variable nature of observed plankton spectra.
Advection-Based Sparse Data Management for Visualizing Unsteady Flow.
Guo, Hanqi; Zhang, Jiang; Liu, Richen; Liu, Lu; Yuan, Xiaoru; Huang, Jian; Meng, Xiangfei; Pan, Jingshan
2014-12-01
When computing integral curves and integral surfaces for large-scale unsteady flow fields, a major bottleneck is the widening gap between data access demands and the available bandwidth (both I/O and in-memory). In this work, we explore a novel advection-based scheme to manage flow field data for both efficiency and scalability. The key is to first partition flow field into blocklets (e.g. cells or very fine-grained blocks of cells), and then (pre)fetch and manage blocklets on-demand using a parallel key-value store. The benefits are (1) greatly increasing the scale of local-range analysis (e.g. source-destination queries, streak surface generation) that can fit within any given limit of hardware resources; (2) improving memory and I/O bandwidth-efficiencies as well as the scalability of naive task-parallel particle advection. We demonstrate our method using a prototype system that works on workstation and also in supercomputing environments. Results show significantly reduced I/O overhead compared to accessing raw flow data, and also high scalability on a supercomputer for a variety of applications.
Local and nonlocal advection of a passive scalar
NASA Astrophysics Data System (ADS)
Scott, R. K.
2006-11-01
Passive and active scalar mixing is examined in a simple one-parameter family of two-dimensional flows based on quasi-geostrophic dynamics, in which the active scalar, the quasi-geostrophic potential vorticity, is confined to a single horizontal surface (so-called surface quasi-geostrophic dynamics) and in which a passive scalar field is also advected by the (horizontal, two-dimensional) velocity field at a finite distance from the surface. At large distances from the surface the flow is determined by the largest horizontal scales, the flow is spectrally nonlocal, and a chaotic advection-type regime dominates. At small distances, z, scaling arguments suggest a transition wavenumber kc˜1/2z, where the slope of the passive scalar spectrum changes from k-5/3, determined by local dynamics, to k-1, determined by nonlocal dynamics, analogous to the transition to a k-1 slope in the Batchelor regime in three-dimensional turbulence. Direct numerical simulations reproduce the qualitative aspects of this transition. Other characteristics of the simulated scalar fields, such as the relative dominance of coherent or filamentary structures, are also shown to depend strongly on the degree of locality.
THE ADVECTION OF SUPERGRANULES BY THE SUN'S AXISYMMETRIC FLOWS
Hathaway, David H.; Williams, Peter E.; Rosa, Kevin Dela; Cuntz, Manfred E-mail: peter.williams@nasa.go
2010-12-10
We show that the motions of supergranules are consistent with a model in which they are simply advected by the axisymmetric flows in the Sun's surface shear layer. We produce a 10 day series of simulated Doppler images at a 15 minute cadence that reproduces most spatial and temporal characteristics seen in the SOHO/MDI Doppler data. Our simulated data have a spectrum of cellular flows with just two components-a granule component that peaks at spherical wavenumbers of about 4000 and a supergranule component that peaks at wavenumbers of about 110. We include the advection of these cellular components by the axisymmetric flows-differential rotation and meridional flow-whose variations with latitude and depth (wavenumber) are consistent with observations. We mimic the evolution of the cellular pattern by introducing random variations to the phases of the spectral components at rates that reproduce the levels of cross-correlation as functions of time and latitude. Our simulated data do not include any wave-like characteristics for the supergranules yet can reproduce the rotation characteristics previously attributed to wave-like behavior. We find rotation rates which appear faster than the actual rotation rates and attribute this to projection effects. We find that the measured meridional flow does accurately represent the actual flow and that the observations indicate poleward flow to 65{sup 0}-70{sup 0} latitude with equatorward countercells in the polar regions.
Transient responses to spatial perturbations in advective systems.
Anderson, Kurt E; Nisbet, Roger M; McCauley, Edward
2008-07-01
We study the transient dynamics, following a spatially-extended perturbation of models describing populations residing in advective media such as streams and rivers. Our analyses emphasize metrics that are independent of initial perturbations-resilience, reactivity, and the amplification envelope-and relate them to component spatial wavelengths of the perturbation using spatial Fourier transforms of the state variables. This approach offers a powerful way of understanding the influence of spatial scale on the initial dynamics of a population following a spatially variable environmental perturbation, an important property in determining the ecological implications of transient dynamics in advective systems. We find that asymptotically stable systems may exhibit transient amplification of perturbations (i.e., have positive reactivity) for some spatial wavelengths and not others. Furthermore, the degree and duration of amplification varies strongly with spatial wavelength. For two single-population models, there is a relationship between transient dynamics and the response length that characterizes the steady state response to spatial perturbations: a long response length implies that peak amplification of perturbations is small and occurs fast. This relationship holds less generally in a specialist consumer-resource model, likely due to the model's tendency for flow-induced instabilities at an alternative characteristic spatial scale.
A cryogenic circulating advective multi-pass absorption cell
NASA Astrophysics Data System (ADS)
Stockett, M. H.; Lawler, J. E.
2012-03-01
A novel absorption cell has been developed to enable a spectroscopic survey of a broad range of polycyclic aromatic hydrocarbons (PAH) under astrophysically relevant conditions and utilizing a synchrotron radiation continuum to test the still controversial hypothesis that these molecules or their ions could be carriers of the diffuse interstellar bands. The cryogenic circulating advective multi-pass absorption cell resembles a wind tunnel; molecules evaporated from a crucible or injected using a custom gas feedthrough are entrained in a laminar flow of cryogenically cooled buffer gas and advected into the path of the synchrotron beam. This system includes a multi-pass optical White cell enabling absorption path lengths of hundreds of meters and a detection sensitivity to molecular densities on the order of 107 cm-3. A capacitively coupled radio frequency dielectric barrier discharge provides ionized and metastable buffer gas atoms for ionizing the candidate molecules via charge exchange and the Penning effect. Stronger than expected clustering of PAH molecules has slowed efforts to record gas phase PAH spectra at cryogenic temperatures, though such clusters may play a role in other interstellar phenomena.
A cryogenic circulating advective multi-pass absorption cell.
Stockett, M H; Lawler, J E
2012-03-01
A novel absorption cell has been developed to enable a spectroscopic survey of a broad range of polycyclic aromatic hydrocarbons (PAH) under astrophysically relevant conditions and utilizing a synchrotron radiation continuum to test the still controversial hypothesis that these molecules or their ions could be carriers of the diffuse interstellar bands. The cryogenic circulating advective multi-pass absorption cell resembles a wind tunnel; molecules evaporated from a crucible or injected using a custom gas feedthrough are entrained in a laminar flow of cryogenically cooled buffer gas and advected into the path of the synchrotron beam. This system includes a multi-pass optical White cell enabling absorption path lengths of hundreds of meters and a detection sensitivity to molecular densities on the order of 10(7) cm(-3). A capacitively coupled radio frequency dielectric barrier discharge provides ionized and metastable buffer gas atoms for ionizing the candidate molecules via charge exchange and the Penning effect. Stronger than expected clustering of PAH molecules has slowed efforts to record gas phase PAH spectra at cryogenic temperatures, though such clusters may play a role in other interstellar phenomena.
Observation of Magnetic Reconnection Driven by Granular Scale Advection
NASA Astrophysics Data System (ADS)
Zeng, Zhichen; Cao, W.; Ji, H.
2013-07-01
We report the first evidence of magnetic reconnection driven by advection in a rapidly developing large granule, using high spatial resolution observations of a small surge event (base size 4‧‧ by 4‧‧) with the 1.6 meter aperture New Solar Telescope (NST) at Big Bear Solar Observatory. The observations were carried out in narrow-band (0.5 Å) Helium I 10830 Å and broad-band (10 Å) TiO 7057 Å. Since He I 10830 Å triplet has very high excitation level and is optically thin, its filtergrams enable us to investigate the surge from the photosphere through the chromosphere into the lower corona. Simultaneous space data from Atmospheric Imaging Assembly (AIA) and Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) were used in the analysis. It is shown that the surge is spatio-temporally associated with magnetic flux emergence in the rapidly developing large granule. During the development of the granule, its advecting flow ( 2 km/ s) squeezed the magnetic flux into an intergranular lane area, where a magnetic flux concentration was formed and the neighboring flux with opposite magnetic polarity was cancelled. During the cancellation, the surge was produced as absorption in He I 10830 Å filtergrams while simultaneous EUV brightening occurred at its base. The observations clearly indicate evidence of finest-scale reconnection process driven by the granule’s motion.
Observation of Magnetic Reconnection Driven by Granular Scale Advection
NASA Astrophysics Data System (ADS)
Zeng, Zhicheng; Cao, Wenda; Ji, Haisheng
2013-06-01
We report the first evidence of magnetic reconnection driven by advection in a rapidly developing large granule using high spatial resolution observations of a small surge event (base size ~ 4'' × 4'') with the 1.6 m aperture New Solar Telescope at the Big Bear Solar Observatory. The observations were carried out in narrowband (0.5 Å) He I 10830 Å and broadband (10 Å) TiO 7057 Å. Since He I 10830 Å triplet has a very high excitation level and is optically thin, its filtergrams enable us to investigate the surge from the photosphere through the chromosphere into the lower corona. Simultaneous space data from the Atmospheric Imaging Assembly and Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory were used in the analysis. It is shown that the surge is spatio-temporally associated with magnetic flux emergence in the rapidly developing large granule. During the development of the granule, its advecting flow (~2 km s-1) squeezed the magnetic flux into an intergranular lane area, where a magnetic flux concentration was formed and the neighboring flux with opposite magnetic polarity was canceled. During the cancellation, the surge was produced as absorption in He I 10830 Å filtergrams while simultaneous EUV brightening occurred at its base. The observations clearly indicate evidence of a finest-scale reconnection process driven by the granule's motion.
Positivity-preserving numerical schemes for multidimensional advection
NASA Technical Reports Server (NTRS)
Leonard, B. P.; Macvean, M. K.; Lock, A. P.
1993-01-01
This report describes the construction of an explicit, single time-step, conservative, finite-volume method for multidimensional advective flow, based on a uniformly third-order polynomial interpolation algorithm (UTOPIA). Particular attention is paid to the problem of flow-to-grid angle-dependent, anisotropic distortion typical of one-dimensional schemes used component-wise. The third-order multidimensional scheme automatically includes certain cross-difference terms that guarantee good isotropy (and stability). However, above first-order, polynomial-based advection schemes do not preserve positivity (the multidimensional analogue of monotonicity). For this reason, a multidimensional generalization of the first author's universal flux-limiter is sought. This is a very challenging problem. A simple flux-limiter can be found; but this introduces strong anisotropic distortion. A more sophisticated technique, limiting part of the flux and then restoring the isotropy-maintaining cross-terms afterwards, gives more satisfactory results. Test cases are confined to two dimensions; three-dimensional extensions are briefly discussed.
A cryogenic circulating advective multi-pass absorption cell
Stockett, M. H.; Lawler, J. E.
2012-03-15
A novel absorption cell has been developed to enable a spectroscopic survey of a broad range of polycyclic aromatic hydrocarbons (PAH) under astrophysically relevant conditions and utilizing a synchrotron radiation continuum to test the still controversial hypothesis that these molecules or their ions could be carriers of the diffuse interstellar bands. The cryogenic circulating advective multi-pass absorption cell resembles a wind tunnel; molecules evaporated from a crucible or injected using a custom gas feedthrough are entrained in a laminar flow of cryogenically cooled buffer gas and advected into the path of the synchrotron beam. This system includes a multi-pass optical White cell enabling absorption path lengths of hundreds of meters and a detection sensitivity to molecular densities on the order of 10{sup 7} cm{sup -3}. A capacitively coupled radio frequency dielectric barrier discharge provides ionized and metastable buffer gas atoms for ionizing the candidate molecules via charge exchange and the Penning effect. Stronger than expected clustering of PAH molecules has slowed efforts to record gas phase PAH spectra at cryogenic temperatures, though such clusters may play a role in other interstellar phenomena.
Chaotic advection in 2D anisotropic porous media
NASA Astrophysics Data System (ADS)
Varghese, Stephen; Speetjens, Michel; Trieling, Ruben; Toschi, Federico
2015-11-01
Traditional methods for heat recovery from underground geothermal reservoirs employ a static system of injector-producer wells. Recent studies in literature have shown that using a well-devised pumping scheme, through actuation of multiple injector-producer wells, can dramatically enhance production rates due to the increased scalar / heat transport by means of chaotic advection. However the effect of reservoir anisotropy on kinematic mixing and heat transport is unknown and has to be incorporated and studied for practical deployment in the field. As a first step, we numerically investigate the effect of anisotropy (both magnitude and direction) on (chaotic) advection of passive tracers in a time-periodic Darcy flow within a 2D circular domain driven by periodically reoriented diametrically opposite source-sink pairs. Preliminary results indicate that anisotropy has a significant impact on the location, shape and size of coherent structures in the Poincare sections. This implies that the optimal operating parameters (well spacing, time period of well actuation) may vary strongly and must be carefully chosen so as to enhance subsurface transport. This work is part of the research program of the Foundation for Fundamental Research on Matter (FOM), which is part of Netherlands Organisation for Scientific Research (NWO). This research program is co-financed by Shell Global Solutions International B.V.
2011-06-16
introduce this anti-diffusive WENO scheme for Eq . (11). 5 Let xi, i = 1, . . . , N be a uniform (for simplicity) mesh of the computational domain, with mesh...example is the model problem of [23]. Consider Eq . (4) with f(u) = u, the source term given by Eq . ( 5 ), and the initial condition: u(x, 0) = { 1, x ≤ 0.3...should be always zero. However, if µ in the source term Eq . ( 5 ) is very large, the numerical errors of u in the transition region can result in large
NASA Astrophysics Data System (ADS)
Stevens, D.; Power, H.
2015-10-01
We propose a node-based local meshless method for advective transport problems that is capable of operating on centrally defined stencils and is suitable for shock-capturing purposes. High spatial convergence rates can be achieved; in excess of eighth-order in some cases. Strongly-varying smooth profiles may be captured at infinite Péclet number without instability, and for discontinuous profiles the solution exhibits neutrally stable oscillations that can be damped by introducing a small artificial diffusion parameter, allowing a good approximation to the shock-front to be maintained for long travel times without introducing spurious oscillations. The proposed method is based on local collocation with radial basis functions (RBFs) in a "finite collocation" configuration. In this approach the PDE governing and boundary equations are enforced directly within the local RBF collocation systems, rather than being reconstructed from fixed interpolating functions as is typical of finite difference, finite volume or finite element methods. In this way the interpolating basis functions naturally incorporate information from the governing PDE, including the strength and direction of the convective velocity field. By using these PDE-enhanced interpolating functions an "implicit upwinding" effect is achieved, whereby the flow of information naturally respects the specifics of the local convective field. This implicit upwinding effect allows high-convergence solutions to be obtained on centred stencils for advection problems. The method is formulated using a high-convergence implicit timestepping algorithm based on Richardson extrapolation. The spatial and temporal convergence of the proposed approach is demonstrated using smooth functions with large gradients. The capture of discontinuities is then investigated, showing how the addition of a dynamic stabilisation parameter can damp the neutrally stable oscillations with limited smearing of the shock front.
Monitoring the Biophysical Properties along Lagrangian Advection Pathways in the Amazon River Plume
NASA Astrophysics Data System (ADS)
Fournier, S.; Gaultier, L.; Vandemark, D. C.; Salisbury, J.; Lee, T.; Gierach, M. M.
2015-12-01
Large rivers are important biogeochemistry. The freshwater inputs associated with major river plumes modify the local and regional sea surface salinity (SSS) and in the mean time carry a large amount of organic and inorganic particulates into the ocean. Monitoring of the spatial and temporal variability of river plumes extension is therefore important to the physics and biophysical interaction at regional scales. With the launches of the NASA Aquarius/Sac-D missions and the ESA Soil Moisture and Ocean Salinity (SMOS), we are now able to use the low-resolution SSS observations in combination with altimetry and high-resolution ocean color observations to monitor the physical and biogeochemical properties of river plumes. Our study focuses on the Amazon River, the world's largest river in terms of discharge. Waters from the Amazon River are carried northwestward across the equator along the Brazilian shelf by the North Brazilian Current (NBC) and eastward along the North Equatorial Counter Current. Large oceanic rings shed off the NBC retroflection near 8∘N in the North Tropical Atlantic Ocean. Large-scale gradients of SSS, colored detrital matter (cdm) and sea surface temperature (SST) associated with these rings are visible from space using SSS, SST and ocean color sensors. These rings carry freshwaters highly concentrated in organic and inorganic matter towards the Caribbean Sea and offshore. In this study, the surface properties of the river plume oligotrophic waters trapped into these large eddies are analyzed. We use a Lagrangian advection method to track the particles trapped in NBC rings and follow their biophysical properties along the northwestward trajectories using measurements from Aquarius, SMOS, and Aqua MODIS. The pathways of the Amazon plume waters can therefore be analyzed, enabling an investigation of the physical and biogeochemical processes associated with the Amazon River freshwaters as they are advected and mixed from the river mouth to the
On the error propagation of semi-Lagrange and Fourier methods for advection problems☆
Einkemmer, Lukas; Ostermann, Alexander
2015-01-01
In this paper we study the error propagation of numerical schemes for the advection equation in the case where high precision is desired. The numerical methods considered are based on the fast Fourier transform, polynomial interpolation (semi-Lagrangian methods using a Lagrange or spline interpolation), and a discontinuous Galerkin semi-Lagrangian approach (which is conservative and has to store more than a single value per cell). We demonstrate, by carrying out numerical experiments, that the worst case error estimates given in the literature provide a good explanation for the error propagation of the interpolation-based semi-Lagrangian methods. For the discontinuous Galerkin semi-Lagrangian method, however, we find that the characteristic property of semi-Lagrangian error estimates (namely the fact that the error increases proportionally to the number of time steps) is not observed. We provide an explanation for this behavior and conduct numerical simulations that corroborate the different qualitative features of the error in the two respective types of semi-Lagrangian methods. The method based on the fast Fourier transform is exact but, due to round-off errors, susceptible to a linear increase of the error in the number of time steps. We show how to modify the Cooley–Tukey algorithm in order to obtain an error growth that is proportional to the square root of the number of time steps. Finally, we show, for a simple model, that our conclusions hold true if the advection solver is used as part of a splitting scheme. PMID:25844018
Mechanistic models of plant seed dispersal by wind in heterogeneous landscapes
NASA Astrophysics Data System (ADS)
Trakhtenbrot, A.; Katul, G. G.; Nathan, R.
2010-12-01
Seed dispersal, and especially long-distance dispersal (LDD), is a key process in plant population survival, colonization, and gene flow. Its importance is amplified by the man-induced habitat fragmentation, climate change and invasions of exotic species. Mechanistic seed dispersal models are central to quantitative prediction of dispersal patterns and understanding their underlying mechanisms. For wind dispersal, most current mechanistic models assume homogenous environment. Although both topography and sharp transitions in vegetation stature profoundly affect wind flow, accounting for these effects via simplified models remains a vexing research problem. Such simplified models are needed to inform ecosystem managers about consequences of landscape fragmentation. We modified the Coupled Eulerian-Lagrangian closure (CELC) mechanistic dispersal model to represent scenarios of wind flow over a sharp transition from short to tall vegetation or over forested hilly terrain, and predicted the resulting dispersal distances and direction. We parameterized the wind and vegetation factors using measurements taken on a hill with short height Mediterranean shrubland and pine forest vegetation at Mt. Pithulim, Israel. For the short-to-tall vegetation transition scenario, the main feature of the modeled wind field is an exponential decay of the mean horizontal wind velocity, assuming that the mean momentum equation simplifies to a balance between the advective acceleration and the drag force terms. As a consequence of the incompressibility condition, this exponential decay leads to strong upward mean vertical velocity component. We found that for seed release downwind of the edge, the simulated median (short) and 99-th percentile (long) distances were longer than those for the homogeneous tall vegetation scenario. For seed release upwind of the edge the effect on dispersal distance was more complex and depended on the release height and he seed terminal velocity of the seeds
CFD modeling of the dispersion of contaminants in the Clinch River
Wendel, M.W.; Williams, P.T.; Platfoot, J.H.
1997-08-01
The purpose of this work is to develop a multi-dimensional, transient computational fluid dynamics (CFD) model for the entrance region of the confluence of White Oak Creek and the Clinch River that will produce accurate predictions for dispersion of contaminants within a segment of the river. The objective is to develop the capability to predict the multi-dimensional distribution of contaminant concentration in the Clinch River. The numerical model was defined using the commercial computational-fluid-dynamics (CFD) computer program CFX Version 4, developed by AEA Technology Engineering Software, Inc. the program solves the Navier-Stokes, energy and species-transport equations with the SIMPLEC finite-volume method. A scalar advection-diffusion equation was defined to represent transport of the contaminant within the flow field. CFX has a multiblock capability that allows an accurate representation of the true river geometry. The present study represents the first application of a general-purpose turbulence model to the Clinch River dispersion problem.
Bachand, P.A.M.; S. Bachand,; Fleck, Jacob A.; Anderson, Frank E.; Windham-Myers, Lisamarie
2014-01-01
The current state of science and engineering related to analyzing wetlands overlooks the importance of transpiration and risks data misinterpretation. In response, we developed hydrologic and mass budgets for agricultural wetlands using electrical conductivity (EC) as a natural conservative tracer. We developed simple differential equations that quantify evaporation and transpiration rates using flowrates and tracer concentrations atwetland inflows and outflows. We used two ideal reactormodel solutions, a continuous flowstirred tank reactor (CFSTR) and a plug flow reactor (PFR), to bracket real non-ideal systems. From those models, estimated transpiration ranged from 55% (CFSTR) to 74% (PFR) of total evapotranspiration (ET) rates, consistent with published values using standard methods and direct measurements. The PFR model more appropriately represents these nonideal agricultural wetlands in which check ponds are in series. Using a fluxmodel, we also developed an equation delineating the root zone depth at which diffusive dominated fluxes transition to advective dominated fluxes. This relationship is similar to the Peclet number that identifies the dominance of advective or diffusive fluxes in surface and groundwater transport. Using diffusion coefficients for inorganic mercury (Hg) and methylmercury (MeHg) we calculated that during high ET periods typical of summer, advective fluxes dominate root zone transport except in the top millimeters below the sediment–water interface. The transition depth has diel and seasonal trends, tracking those of ET. Neglecting this pathway has profound implications: misallocating loads along different hydrologic pathways; misinterpreting seasonal and diel water quality trends; confounding Fick's First Law calculations when determining diffusion fluxes using pore water concentration data; and misinterpreting biogeochemicalmechanisms affecting dissolved constituent cycling in the root zone. In addition,our understanding of internal
Bachand, P A M; Bachand, S; Fleck, J; Anderson, F; Windham-Myers, L
2014-06-15
The current state of science and engineering related to analyzing wetlands overlooks the importance of transpiration and risks data misinterpretation. In response, we developed hydrologic and mass budgets for agricultural wetlands using electrical conductivity (EC) as a natural conservative tracer. We developed simple differential equations that quantify evaporation and transpiration rates using flow rates and tracer concentrations at wetland inflows and outflows. We used two ideal reactor model solutions, a continuous flow stirred tank reactor (CFSTR) and a plug flow reactor (PFR), to bracket real non-ideal systems. From those models, estimated transpiration ranged from 55% (CFSTR) to 74% (PFR) of total evapotranspiration (ET) rates, consistent with published values using standard methods and direct measurements. The PFR model more appropriately represents these non-ideal agricultural wetlands in which check ponds are in series. Using a flux model, we also developed an equation delineating the root zone depth at which diffusive dominated fluxes transition to advective dominated fluxes. This relationship is similar to the Peclet number that identifies the dominance of advective or diffusive fluxes in surface and groundwater transport. Using diffusion coefficients for inorganic mercury (Hg) and methylmercury (MeHg) we calculated that during high ET periods typical of summer, advective fluxes dominate root zone transport except in the top millimeters below the sediment-water interface. The transition depth has diel and seasonal trends, tracking those of ET. Neglecting this pathway has profound implications: misallocating loads along different hydrologic pathways; misinterpreting seasonal and diel water quality trends; confounding Fick's First Law calculations when determining diffusion fluxes using pore water concentration data; and misinterpreting biogeochemical mechanisms affecting dissolved constituent cycling in the root zone. In addition, our understanding of
NASA Astrophysics Data System (ADS)
Mahesha, Chaitra
A unique processing technique based on chaotic advection developed at Clemson University and shown to controllably produce structured materials in the past was employed to produce structured nanocomposites with a high degree of clay orientation as well as localization of platelets within layers of nanoscale thicknesses. Continuous lengths of nanocomposites with different clay contents were extruded in the form of films by feeding separately melts of virgin polyamide-6 polymer and polyamide 6-clay masterbatch into a continuous chaotic advection blender. A variety of composite structures were producible at fixed clay compositions. The internal structure was characterized by transmission electron microscopy (TEM), x-ray diffraction (XRD) and differential scanning calorimetry (DSC). Nanocomposites with novel in-situ multi-layered structures and a high degree of platelet orientation were formed by the recursive stretching and folding of the melt domains due to chaotic advection. Clay platelets were localized within discrete regions to form alternating virgin and platelet-rich layers leading to a hierarchical structure with multiple nano-scales. The thicknesses of the layers reduced with prolonged chaotic advection, eventually leading to nanocomposites in which the multi-layering was no longer discernible. The oriented platelets appeared to be homogenously dispersed through the bulk of the nanocomposite. Investigation of the morphology of the matrix by XRD showed that the homogeneity of the crystalline phase and the orientation of polymer chains parallel to the film surface increased with increased chaotic advection. Also, as the layer thickness reduced, the number of polymer chains restricted by clay platelets increased causing the gamma-crystalline fraction to increase. While XRD results suggested a change in total crystallinity with chaotic advection and clay content but without a specific trend, no change in crystallinity was measured by DSC. Such contradictions are
NASA Astrophysics Data System (ADS)
Mudunuru, M. K.; Shabouei, M.; Nakshatrala, K.
2015-12-01
Advection-diffusion-reaction (ADR) equations appear in various areas of life sciences, hydrogeological systems, and contaminant transport. Obtaining stable and accurate numerical solutions can be challenging as the underlying equations are coupled, nonlinear, and non-self-adjoint. Currently, there is neither a robust computational framework available nor a reliable commercial package known that can handle various complex situations. Herein, the objective of this poster presentation is to present a novel locally conservative non-negative finite element formulation that preserves the underlying physical and mathematical properties of a general linear transient anisotropic ADR equation. In continuous setting, governing equations for ADR systems possess various important properties. In general, all these properties are not inherited during finite difference, finite volume, and finite element discretizations. The objective of this poster presentation is two fold: First, we analyze whether the existing numerical formulations (such as SUPG and GLS) and commercial packages provide physically meaningful values for the concentration of the chemical species for various realistic benchmark problems. Furthermore, we also quantify the errors incurred in satisfying the local and global species balance for two popular chemical kinetics schemes: CDIMA (chlorine dioxide-iodine-malonic acid) and BZ (Belousov--Zhabotinsky). Based on these numerical simulations, we show that SUPG and GLS produce unphysical values for concentration of chemical species due to the violation of the non-negative constraint, contain spurious node-to-node oscillations, and have large errors in local and global species balance. Second, we proposed a novel finite element formulation to overcome the above difficulties. The proposed locally conservative non-negative computational framework based on low-order least-squares finite elements is able to preserve these underlying physical and mathematical properties
Moments of action provide insight into critical times for advection-diffusion-reaction processes.
Ellery, Adam J; Simpson, Matthew J; McCue, Scott W; Baker, Ruth E
2012-09-01
Berezhkovskii and co-workers introduced the concept of local accumulation time as a finite measure of the time required for the transient solution of a reaction-diffusion equation to effectively reach steady state [Biophys J. 99, L59 (2010); Phys. Rev. E 83, 051906 (2011)]. Berezhkovskii's approach is a particular application of the concept of mean action time (MAT) that was introduced previously by McNabb [IMA J. Appl. Math. 47, 193 (1991)]. Here, we generalize these previous results by presenting a framework to calculate the MAT, as well as the higher moments, which we call the moments of action. The second moment is the variance of action time, the third moment is related to the skew of action time, and so on. We consider a general transition from some initial condition to an associated steady state for a one-dimensional linear advection-diffusion-reaction partial differential equation (PDE). Our results indicate that it is possible to solve for the moments of action exactly without requiring the transient solution of the PDE. We present specific examples that highlight potential weaknesses of previous studies that have considered the MAT alone without considering higher moments. Finally, we also provide a meaningful interpretation of the moments of action by presenting simulation results from a discrete random-walk model together with some analysis of the particle lifetime distribution. This work shows that the moments of action are identical to the moments of the particle lifetime distribution for certain transitions.
NASA Astrophysics Data System (ADS)
Antonov, N. V.; Gulitskiy, N. M.; Kostenko, M. M.; Lučivjanský, T.
2017-03-01
The field theoretic renormalization group (RG) and the operator product expansion (OPE) are applied to the model of a density field advected by a random turbulent velocity field. The latter is governed by the stochastic Navier-Stokes equation for a compressible fluid. The model is considered near the special space dimension d = 4. It is shown that various correlation functions of the scalar field exhibit anomalous scaling behaviour in the inertial-convective range. The scaling properties in the RG+OPE approach are related to fixed points of the renormalization group equations. In comparison with physically interesting case d = 3, at d = 4 additional Green function has divergences which affect the existence and stability of fixed points. From calculations it follows that a new regime arises there and then by continuity moves into d = 3. The corresponding anomalous exponents are identified with scaling dimensions of certain composite fields and can be systematically calculated as series in y (the exponent, connected with random force) and ɛ = 4 - d. All calculations are performed in the leading one-loop approximation.
NASA Astrophysics Data System (ADS)
Pardini, Federica; Spanu, Antonio; de'Michieli Vitturi, Mattia; Salvetti, Maria Vittoria; Neri, Augusto
2016-02-01
We present the results of uncertainty quantification and sensitivity analysis applied to volcanic ash dispersal from weak plumes with focus on the uncertainties associated to the original grain size distribution of the mixture. The Lagrangian particle model Lagrangian Particles Advection Code is used to simulate the transport of inertial particles under the action of realistic atmospheric conditions. The particle motion equations are derived by expressing the particle acceleration as the sum of forces acting along its trajectory, with the drag force calculated as a function of particle diameter, density, shape, and Reynolds number. Simulations are representative of a weak plume event of Mount Etna (Italy) and aimed at quantifying the effect on the dispersal process of the uncertainty in the mean and standard deviation of a lognormal function describing the initial grain size distribution and in particle sphericity. In order to analyze the sensitivity of particle dispersal to these uncertain variables with a reasonable number of simulations, response surfaces in the parameter space are built by using the generalized polynomial chaos expansion technique. The mean diameter and standard deviation of particle size distribution, and their probability density functions, at various distances from the source, both airborne and on ground, are quantified. Results highlight that uncertainty ranges in these quantities are drastically reduced with distance from source, making them largely dependent just on the location. Moreover, at a given distance from source, the distribution is mostly controlled by particle sphericity, particularly on the ground, whereas in air also mean diameter and sorting play a main role.
On the hydro-dispersive equivalence between multi-layered mineral barriers
NASA Astrophysics Data System (ADS)
Guyonnet, D.; Perrochet, P.; Côme, B.; Seguin, J.-J.; Parriaux, A.
2001-10-01
In the context of municipal solid waste and hazardous waste disposal, the notion of "equivalence" between different barrier designs appears in regulatory documents from several industrialized countries. While in the past, equivalence has been thought of mainly in terms of contaminant travel times, in recent years it has been defined more in terms of the magnitude of a disposal site's potential impact on groundwater resources. This paper presents some original analytical solutions to the problem of contaminant migration through a multi-layered mineral barrier. The solutions account for the two major mechanisms of subsurface contaminant migration, namely, advection and diffusion-dispersion. An example application using the proposed solutions and a numerical model illustrates how one multi-layered mineral barrier can be considered superior to another from a strictly hydro-dispersive viewpoint. The influence of partial saturation of the mineral barrier is investigated using a numerical solution to the Richards equation for unsaturated flow. It is emphasized that conclusions relative to the superiority of one multi-layered barrier, with respect to another, should not only consider hydro-dispersive aspects, but also other processes such as the mechanical and chemical evolutions of the different barrier components. Although such phenomena are poorly addressed by existing models, failure to take them into account, at least in a qualitative fashion, may lead to unconservative conclusions with respect to barrier equivalence.
Optimization of one-way wave equations.
Lee, M.W.; Suh, S.Y.
1985-01-01
The theory of wave extrapolation is based on the square-root equation or one-way equation. The full wave equation represents waves which propagate in both directions. On the contrary, the square-root equation represents waves propagating in one direction only. A new optimization method presented here improves the dispersion relation of the one-way wave equation. -from Authors
Colloid particle size-dependent dispersivity
NASA Astrophysics Data System (ADS)
Chrysikopoulos, C. V.; Katzourakis, V. E.
2014-12-01
Laboratory and field studies have demonstrated that dispersion coefficients evaluated by fitting advection-dispersion transport models to nonreactive tracer breakthrough curves do not adequately describe colloid transport under the same flow field conditions. Here an extensive laboratory study was undertaken to assess whether the dispersivity, which traditionally has been considered to be a property of the porous medium, is dependent on colloid particle size and interstitial velocity. A total of 49 colloid transport experiments were performed in columns packed with glass beads under chemically unfavorable colloid attachment conditions. Nine different colloid diameters, and various flow velocities were examined. The breakthrough curves were successfully simulated with a mathematical model describing colloid transport in homogeneous, water saturated porous media. The results demonstrated that the dispersivity is positively correlated with colloid particle size, and increases with increasing velocity.
The General Fishbone Like Dispersion Relation
NASA Astrophysics Data System (ADS)
Zonca, Fulvio
2015-12-01
The following sections are included: * Introduction * Motivation and outline * Fundamental equations * The collisionless gyrokinetic equation * Vorticity equation * Quasi-neutrality condition * Perpendicular Ampère's law * Studying collective modes in burning plasmas * Ideal plasma equilibrium in the low-β limit * Approximations for the energetic population * Characteristic frequencies of particle motions * Alfvén wave frequency and wavelength orderings * Applications of the general theoretical framework * The general fishbone like dispersion relation * Properties of the fishbone like dispersion relation * Derivation of the fishbone like dispersion relation * Special cases of the fishbone like dispersion relation * Toroidal Alfvén Eigenmodes (TAE) * Alfvén Cascades * Summary and discussions * Acknowledgments * References
Thermally driven advection for radioxenon transport from an underground nuclear explosion
NASA Astrophysics Data System (ADS)
Sun, Yunwei; Carrigan, Charles R.
2016-05-01
Barometric pumping is a ubiquitous process resulting in migration of gases in the subsurface that has been studied as the primary mechanism for noble gas transport from an underground nuclear explosion (UNE). However, at early times following a UNE, advection driven by explosion residual heat is relevant to noble gas transport. A rigorous measure is needed for demonstrating how, when, and where advection is important. In this paper three physical processes of uncertain magnitude (oscillatory advection, matrix diffusion, and thermally driven advection) are parameterized by using boundary conditions, system properties, and source term strength. Sobol' sensitivity analysis is conducted to evaluate the importance of all physical processes influencing the xenon signals. This study indicates that thermally driven advection plays a more important role in producing xenon signals than oscillatory advection and matrix diffusion at early times following a UNE, and xenon isotopic ratios are observed to have both time and spatial dependence.
NASA Astrophysics Data System (ADS)
Hammer, Daniel X.; Noojin, Gary D.; Thomas, Robert J.; Stolarski, David J.; Rockwell, Benjamin A.; Welch, Ashley J.
1999-06-01
Spectrally resolved white-light interferometry (SRWLI) was used to measure the wavelength dependence of refractive index (i.e., dispersion) for various ocular components. The accuracy of the technique was assessed by measurement of fused silica and water, the refractive indices of which have been measured at several different wavelengths. The dispersion of bovine and rabbit aqueous and vitreous humor was measured from 400 to 1100 nm. Also, the dispersion was measured from 400 to 700 nm for aqueous and vitreous humor extracted from goat and rhesus monkey eyes. For the humors, the dispersion did not deviate significantly from water. In an additional experiment, the dispersion of aqueous and vitreous humor that had aged up to a month was compared to freshly harvested material. No difference was found between the fresh and aged media. An unsuccessful attempt was also made to use the technique for dispersion measurement of bovine cornea and lens. Future refinement may allow measurement of the dispersion of cornea and lens across the entire visible and near-infrared wavelength band. The principles of white- light interferometry including image analysis, measurement accuracy, and limitations of the technique, are discussed. In addition, alternate techniques and previous measurements of ocular dispersion are reviewed.
Periáñez, R; Bezhenar, R; Iosjpe, M; Maderich, V; Nies, H; Osvath, I; Outola, I; de With, G
2015-01-01
Four radionuclide dispersion models have been applied to simulate the transport and distribution of (137)Cs fallout from Chernobyl accident in the Baltic Sea. Models correspond to two categories: box models and hydrodynamic models which solve water circulation and then an advection/diffusion equation. In all cases, interactions of dissolved radionuclides with suspended matter and bed sediments are included. Model results have been compared with extensive field data obtained from HELCOM database. Inventories in the water column and seabed, as well as (137)Cs concentrations along 5 years in water and sediments of several sub-basins of the Baltic, have been used for model comparisons. Values predicted by the models for the target magnitudes are very similar and close to experimental values. Results suggest that some processes are not very relevant for radionuclide transport within the Baltic Sea, for instance the roles of the ice cover and, surprisingly, water stratification. Also, results confirm previous findings concerning multi-model applications.
NASA Astrophysics Data System (ADS)
Chamecki, Marcelo; Meneveau, Charles; Parlange, Marc B.
2008-11-01
A framework to simulate pollen dispersal in the atmospheric boundary layer based on the large eddy simulation technique is developed. Pollen is represented by a continuum concentration field and is evolved following an advection-diffusion equation including a gravitational settling term. The approach is validated against classical data on point-source releases and our own field data for a natural ragweed field. The LES is further used as a tool to investigate the effect of source size on the patterns of pollen ground deposition, an issue of fundamental importance in the development of policies for genetically modified crops. The cross-wind integrated deposition is shown to scale with the pollen boundary-layer height at the trailing edge of the field and a simple practical expression based on the development of the pollen boundary layer is proposed to scale results from small test fields to realistic agricultural conditions.
Unification of some advection schemes in two dimensions
NASA Technical Reports Server (NTRS)
Sidilkover, D.; Roe, P. L.
1995-01-01
The relationship between two approaches towards construction of genuinely two-dimensional upwind advection schemes is established. One of these approaches is of the control volume type applicable on structured cartesian meshes. It resulted in the compact high resolution schemes capable of maintaining second order accuracy in both homogeneous and inhomogeneous cases. Another one is the fluctuation splitting approach, which is well suited for triangular (and possibly) unstructured meshes. Understanding the relationship between these two approaches allows us to formulate here a new fluctuation splitting high resolution (i.e. possible use of artificial compression, while maintaining positivity property) scheme. This scheme is shown to be linearity preserving in inhomogeneous as well as homogeneous cases.
Mobile scintillometry to study heat advection over heterogeneous surfaces
NASA Astrophysics Data System (ADS)
Kleissl, J.
2007-12-01
Large Aperture Scintillometer (LAS) receivers measure the structure parameter of the refractive index from intensity fluctuations of the transmitter beam. Due to the spatial averaging over 1-4 km employed by this emerging technique the constraints for long temporal averaging (15-30 min) and associated uncertainties that have to be met by other flux measurement techniques do not apply for LASs. In this paper the constraints for temporal averaging of LASs will be examined as a function of environmental conditions and transect geometry. Moreover, analysis of data from a mobile LAS measurement across a surface gradient from rough and dry to smoother and wet will be presented. In this experiment the LAS was mounted on a pickup truck, allowing for quick redeployment of the transect after meaurement. The potential for the use of LAS to study local advection of heat in riparian or irrigated areas in the semi-arid southwest will be evaluated.
Microscale chaotic advection enables robust convective DNA replication.
Priye, Aashish; Hassan, Yassin A; Ugaz, Victor M
2013-11-05
The ability of chaotic advection under microscale confinement to direct chemical processes along accelerated kinetic pathways has been recognized for some time. However, practical applications have been slow to emerge because optimal results are often counterintuitively achieved in flows that appear to possess undesirably high disorder. Here we present a 3D time-resolved analysis of polymerase chain reaction (PCR)-mediated DNA replication across a broad ensemble of geometric states. The resulting parametric map reveals an unexpectedly wide operating regime where reaction rates remain constant over 2 orders of magnitude of the Rayleigh number, encompassing virtually any realistic PCR condition (temperature, volume, gravitational alignment), a level of robustness previously thought unattainable in the convective format.
Dependence of advection-diffusion-reaction on flow coherent structures
NASA Astrophysics Data System (ADS)
Tang, Wenbo; Luna, Christopher
2013-10-01
A study on an advection-diffusion-reaction system is presented. Variability of the reaction process in such a system triggered by a highly localized source is quantified. It is found, for geophysically motivated parameter regimes, that the difference in bulk concentration subject to realizations of different source locations is highly correlated with the local flow topology of the source. Such flow topologies can be highlighted by Lagrangian coherent structures. Reaction is relatively enhanced in regions of strong stretching, and relatively suppressed in regions where vortices are present. In any case, the presence of a divergence-free background flow helps speed up the reaction process, especially when the flow is time-dependent. Probability density of various quantities characterizing the reaction processes is also obtained. This reveals the inherent complexity of the reaction-diffusion process subject to nonlinear background stirring.
Advection in polar and sub-polar environments: Impacts on high latitude marine ecosystems
NASA Astrophysics Data System (ADS)
Hunt, George L.; Drinkwater, Kenneth F.; Arrigo, Kevin; Berge, Jørgen; Daly, Kendra L.; Danielson, Seth; Daase, Malin; Hop, Haakon; Isla, Enrique; Karnovsky, Nina; Laidre, Kristin; Mueter, Franz J.; Murphy, Eugene J.; Renaud, Paul E.; Smith, Walker O.; Trathan, Philip; Turner, John; Wolf-Gladrow, Dieter
2016-12-01
We compare and contrast the ecological impacts of atmospheric and oceanic circulation patterns on polar and sub-polar marine ecosystems. Circulation patterns differ strikingly between the north and south. Meridional circulation in the north provides connections between the sub-Arctic and Arctic despite the presence of encircling continental landmasses, whereas annular circulation patterns in the south tend to isolate Antarctic surface waters from those in the north. These differences influence fundamental aspects of the polar ecosystems from the amount, thickness and duration of sea ice, to the types of organisms, and the ecology of zooplankton, fish, seabirds and marine mammals. Meridional flows in both the North Pacific and the North Atlantic oceans transport heat, nutrients, and plankton northward into the Chukchi Sea, the Barents Sea, and the seas off the west coast of Greenland. In the North Atlantic, the advected heat warms the waters of the southern Barents Sea and, with advected nutrients and plankton, supports immense biomasses of fish, seabirds and marine mammals. On the Pacific side of the Arctic, cold waters flowing northward across the northern Bering and Chukchi seas during winter and spring limit the ability of boreal fish species to take advantage of high seasonal production there. Southward flow of cold Arctic waters into sub-Arctic regions of the North Atlantic occurs mainly through Fram Strait with less through the Barents Sea and the Canadian Archipelago. In the Pacific, the transport of Arctic waters and plankton southward through Bering Strait is minimal. In the Southern Ocean, the Antarctic Circumpolar Current and its associated fronts are barriers to the southward dispersal of plankton and pelagic fishes from sub-Antarctic waters, with the consequent evolution of Antarctic zooplankton and fish species largely occurring in isolation from those to the north. The Antarctic Circumpolar Current also disperses biota throughout the Southern Ocean
Examination of the evolution of radiation and advection fogs. Final report
Orgill, M.M.
1993-01-01
A literature study was done on radiation and advection fog evolution. For radiation fog, six stages of fog evolution have been identified -- (1) precursor, (2) sunset, (3) conditioning, (4) mature, (5) sunrise, and (6) dissipation. The evolution of advection fog models has been in parallel with radiation fog models, but no identified stages in the evolution of advection fog have been proposed: (1) precursor, (2) initiation, (3) mature, and (4) dissipation. Radiation and advection fog models will require greater sophistication in order to study fog spatial and temporal variability. Physical aspects that require further study are discussed.
How Hydrate Saturation Anomalies are Diffusively Constructed and Advectively Smoothed
NASA Astrophysics Data System (ADS)
Rempel, A. W.; Irizarry, J. T.; VanderBeek, B. P.; Handwerger, A. L.
2015-12-01
The physical processes that control the bulk characteristics of hydrate reservoirs are captured reasonably well by long-established model formulations that are rooted in laboratory-verified phase equilibrium parameterizations and field-based estimates of in situ conditions. More detailed assessments of hydrate distribution, especially involving the occurrence of high-saturation hydrate anomalies have been more difficult to obtain. Spatial variations in sediment properties are of central importance for modifying the phase behavior and promoting focussed fluid flow. However, quantitative predictions of hydrate anomaly development cannot be made rigorously without also addressing the changes in phase behavior and mechanical balances that accompany changes in hydrate saturation level. We demonstrate how pore-scale geometrical controls on hydrate phase stability can be parameterized for incorporation in simulations of hydrate anomaly development along dipping coarse-grained layers embedded in a more fine-grained background that is less amenable to fluid transport. Model simulations demonstrate how hydrate anomaly growth along coarse-layer boundaries is promoted by diffusive gas transport from the adjacent fine-grained matrix, while advective transport favors more distributed growth within the coarse-grained material and so effectively limits the difference between saturation peaks and background levels. Further analysis demonstrates how sediment contacts are unloaded once hydrate saturation reaches sufficient levels to form a load-bearing skeleton that can evolve to produce segregated nodules and lenses. Decomposition of such growth forms poses a significant geohazard that is expected to be particularly sensitive to perturbations induced by gas extraction. The figure illustrates the predicted evolution of hydrate saturation Sh in a coarse-grained dipping layer showing how prominent bounding hydrate anomalies (spikes) supplied by diffusive gas transport at early times
Sensitivity of Age-of-Air Calculations to the Choice of Advection Scheme
NASA Technical Reports Server (NTRS)
Eluszkiewicz, Janusz; Hemler, Richard S.; Mahlman, Jerry D.; Bruhwiler, Lori; Takacs, Lawrence L.
2000-01-01
The age of air has recently emerged as a diagnostic of atmospheric transport unaffected by chemical parameterizations, and the features in the age distributions computed in models have been interpreted in terms of the models' large-scale circulation field. This study shows, however, that in addition to the simulated large-scale circulation, three-dimensional age calculations can also be affected by the choice of advection scheme employed in solving the tracer continuity equation, Specifically, using the 3.0deg latitude X 3.6deg longitude and 40 vertical level version of the Geophysical Fluid Dynamics Laboratory SKYHI GCM and six online transport schemes ranging from Eulerian through semi-Lagrangian to fully Lagrangian, it will be demonstrated that the oldest ages are obtained using the nondiffusive centered-difference schemes while the youngest ages are computed with a semi-Lagrangian transport (SLT) scheme. The centered- difference schemes are capable of producing ages older than 10 years in the mesosphere, thus eliminating the "young bias" found in previous age-of-air calculations. At this stage, only limited intuitive explanations can be advanced for this sensitivity of age-of-air calculations to the choice of advection scheme, In particular, age distributions computed online with the National Center for Atmospheric Research Community Climate Model (MACCM3) using different varieties of the SLT scheme are substantially older than the SKYHI SLT distribution. The different varieties, including a noninterpolating-in-the-vertical version (which is essentially centered-difference in the vertical), also produce a narrower range of age distributions than the suite of advection schemes employed in the SKYHI model. While additional MACCM3 experiments with a wider range of schemes would be necessary to provide more definitive insights, the older and less variable MACCM3 age distributions can plausibly be interpreted as being due to the semi-implicit semi
Madankan, R.; Pouget, S.; Singla, P.; Bursik, M.; Dehn, J.; Jones, M.; Patra, A.; Pavolonis, M.; Pitman, E.B.; Singh, T.; Webley, P.
2014-08-15
Volcanic ash advisory centers are charged with forecasting the movement of volcanic ash plumes, for aviation, health and safety preparation. Deterministic mathematical equations model the advection and dispersion of these plumes. However initial plume conditions – height, profile of particle location, volcanic vent parameters – are known only approximately at best, and other features of the governing system such as the windfield are stochastic. These uncertainties make forecasting plume motion difficult. As a result of these uncertainties, ash advisories based on a deterministic approach tend to be conservative, and many times over/under estimate the extent of a plume. This paper presents an end-to-end framework for generating a probabilistic approach to ash plume forecasting. This framework uses an ensemble of solutions, guided by Conjugate Unscented Transform (CUT) method for evaluating expectation integrals. This ensemble is used to construct a polynomial chaos expansion that can be sampled cheaply, to provide a probabilistic model forecast. The CUT method is then combined with a minimum variance condition, to provide a full posterior pdf of the uncertain source parameters, based on observed satellite imagery. The April 2010 eruption of the Eyjafjallajökull volcano in Iceland is employed as a test example. The puff advection/dispersion model is used to hindcast the motion of the ash plume through time, concentrating on the period 14–16 April 2010. Variability in the height and particle loading of that eruption is introduced through a volcano column model called bent. Output uncertainty due to the assumed uncertain input parameter probability distributions, and a probabilistic spatial-temporal estimate of ash presence are computed.
Swain, E.D.; Chin, D.A.
2003-01-01
A predominant cause of dispersion in groundwater is advective mixing due to variability in seepage rates. Hydraulic conductivity variations have been extensively researched as a cause of this seepage variability. In this paper the effect of variations in surface recharge to a shallow surficial aquifer is investigated as an important additional effect. An analytical formulation has been developed that relates aquifer parameters and the statistics of recharge variability to increases in the dispersivity. This is accomplished by solving Fourier transforms of the small perturbation forms of the groundwater flow equations. Two field studies are presented in this paper to determine the statistics of recharge variability for input to the analytical formulation. A time series of water levels at a continuous groundwater recorder is used to investigate the temporal statistics of hydraulic head caused by recharge, and a series of infiltrometer measurements are used to define the spatial variability in the recharge parameters. With these field statistics representing head fluctuations due to recharge, the analytical formulation can be used to compute the dispersivity without an explicit representation of the recharge boundary. Results from a series of numerical experiments are used to define the limits of this analytical formulation and to provide some comparison. A sophisticated model has been developed using a particle-tracking algorithm (modified to account for temporal variations) to estimate groundwater dispersion. Dispersivity increases of 9 percent are indicated by the analytical formulation for the aquifer at the field site. A comparison with numerical model results indicates that the analytical results are reasonable for shallow surficial aquifers in which two-dimensional flow can be assumed.
Modeling velocity in gradient flows with coupled-map lattices with advection.
Lind, Pedro G; Corte-Real, João; Gallas, Jason A C
2002-07-01
We introduce a simple model to investigate large scale behavior of gradient flows based on a lattice of coupled maps which, in addition to the usual diffusive term, incorporates advection, as an asymmetry in the coupling between nearest neighbors. This diffusive-advective model predicts traveling patterns to have velocities obeying the same scaling as wind velocities in the atmosphere, regarding the advective parameter as a sort of geostrophic wind. In addition, the velocity and wavelength of traveling wave solutions are studied. In general, due to the presence of advection, two regimes are identified: for strong diffusion the velocity varies linearly with advection, while for weak diffusion a power law is found with a characteristic exponent proportional to the diffusion.
A general mechanism for “inexact” phase differences in reaction-diffusion-advection systems
NASA Astrophysics Data System (ADS)
Satnoianu, Razvan A.; Menzinger, Michael
2002-11-01
‘Inexact’ phase differences that may take any value in the range [0, π], between the chemical morphogens diffusing in an embryo, have been proposed [M.A. Russell, Dev. Biol. 108 (1985) 269] to improve the positional information theory [L. Wolpert, J. Theor. Biol. 25 (1969) 1] by encoding this information with higher resolution than that provided by other mechanisms. Reaction-diffusion systems, including Turing systems, show only ‘exact’ phase differences 0 and/or π. We demonstrate here that inexact phase differences arise naturally in reactive flows described by reaction-diffusion-advection equations and illustrate them by the stationary waves in open flows (flow- and diffusion-distributed structures FDS [R.A. Satnoianu, M. Menzinger, Phys. Rev. E 62 (2000) 113; R.A. Satnoianu, P.K. Maini, M. Menzinger, Physica D 160 (2001) 79] and travelling waves in differential-induced flow systems (DIFI) [A.B. Rovinsky, M. Menzinger, Phys. Rev. Lett. 70 (1993) 778; R.A. Satnoianu, J.H. Merkin, S.K. Scott, Physica D 124 (1998) 345]. The ability of cells in a developing organism to read phase differences in addition to morphogen concentrations would endow them with a robust mechanism for producing segmentation patterns that is richer, shows higher spatial resolution and is more stable than Turing's and Wolpert's positional information mechanisms.
A validated 2-D diffusion-advection model for prediction of drift from ground boom sprayers
NASA Astrophysics Data System (ADS)
Baetens, K.; Ho, Q. T.; Nuyttens, D.; De Schampheleire, M.; Melese Endalew, A.; Hertog, M. L. A. T. M.; Nicolaï, B.; Ramon, H.; Verboven, P.
Correct field drift prediction is a key element in environmental risk assessment of spraying applications. A reduced order drift prediction model based on the diffusion-advection equation is presented. It allows fast assessment of the drift potential of specific ground boom applications under specific environmental wind conditions that obey the logarithmic wind profile. The model was calibrated based on simulations with a validated Computational Fluid Dynamics (CFD) model. Validation of both models against 38 carefully conducted field experiments is successfully performed for distances up to 20 m from the field edge, for spraying on flat pasture land. The reduced order model succeeded in correct drift predictions for different nozzle types, wind velocities, boom heights and spray pressures. It used 4 parameters representing the physical aspects of the drift cloud; the height of the cloud at the field edge, the mass flux crossing the field edge, the settling velocity of the droplets and the turbulence. For the parameter set and range considered, it is demonstrated for the first time that the effect of the droplet diameter distribution of the different nozzle types on the amount of deposition spray drift can be evaluated by a single parameter, i.e., the volume fraction of droplets with a diameter smaller than 191 μm. The reduced order model can be solved more than 4 orders of magnitude faster than the comprehensive CFD model.
NASA Astrophysics Data System (ADS)
Fries, Dan; Ochs, Bradley; Ranjan, Devesh; Menon, Suresh
2016-11-01
A new facility has been developed at the Georgia Institute of Technology to study sub- and supersonic combustion, which is based on classical flame bomb studies but incorporates a mean flow, allowing for a wider variety of turbulent conditions and the inclusion of effects like compressibility, while supporting shear-free spherical flames. Homogeneous, isotropic turbulence is generated via an active vane grid. Methane-air flame kernels advecting with the mean flow are generated using Laser Induced Breakdown ignition. The facility is accessing the thin reaction zone regime with uRMS' /SL0 = 6 . 9 - 22 , L11 /δF = 44 - 68 and Reλ = 190 - 550 . The flame kernels are probed with OH-Planar Laser Induced Fluorescence (PLIF). To validate the facility, results at Ū = 30 m/s are compared to existing data using a scaling derived from a spectral closure of the G-equation. This indicates the reacting flow remains Galilean invariant under the given conditions. The differences between global and local turbulent consumption speeds derived from OH-PLIF results are discussed with a focus on modeling efforts. The curvature of flame wrinkles is evaluated to examine the impact of different turbulent scales on flame development. This work was supported by the Air Force Office of Scientific Research under basic research Grant FA9550-15-1-0512 (Project monitor: Dr. Chiping Li).
NASA Astrophysics Data System (ADS)
Johnson, Joel P. L.; Delbecq, Katie; Kim, Wonsuck; Mohrig, David
2016-01-01
A goal of paleotsunami research is to quantitatively reconstruct wave hydraulics from sediment deposits in order to better understand coastal hazards. Simple models have been proposed to predict wave heights and velocities, based largely on deposit grain size distributions (GSDs). Although seemingly consistent with some recent tsunamis, little independent data exist to test these equations. We conducted laboratory experiments to evaluate inversion assumptions and uncertainties. A computer-controlled lift gate instantaneously released 6.5 m3 of water into a 32 m flume with shallow ponded water, creating a hydraulic bore that transported sand from an upstream source dune. Differences in initial GSDs and ponded water depths influenced entrainment, transport, and deposition. While the source dune sand was fully suspendable based on size alone, experimental tsunamis produced deposits dominated by bed load sand transport in the upstream 1/3 of the flume and suspension-dominated transport downstream. The suspension deposits exhibited downstream fining and thinning. At 95% confidence, a published advection-settling model predicts time-averaged flow depths to approximately a factor of two, and time-averaged downstream flow velocities to within a factor of 1.5. Finally, reasonable scaling is found between flume and field cases by comparing flow depths, inundation distances, Froude numbers, Rouse numbers and grain size trends in suspension-dominated tsunami deposits, justifying laboratory study of sediment transport and deposition by tsunamis.
A nonlocal and periodic reaction-diffusion-advection model of a single phytoplankton species.
Peng, Rui; Zhao, Xiao-Qiang
2016-02-01
In this article, we are concerned with a nonlocal reaction-diffusion-advection model which describes the evolution of a single phytoplankton species in a eutrophic vertical water column where the species relies solely on light for its metabolism. The new feature of our modeling equation lies in that the incident light intensity and the death rate are assumed to be time periodic with a common period. We first establish a threshold type result on the global dynamics of this model in terms of the basic reproduction number R0. Then we derive various characterizations of R0 with respect to the vertical turbulent diffusion rate, the sinking or buoyant rate and the water column depth, respectively, which in turn give rather precise conditions to determine whether the phytoplankton persist or become extinct. Our theoretical results not only extend the existing ones for the time-independent case, but also reveal new interesting effects of the modeling parameters and the time-periodic heterogeneous environment on persistence and extinction of the phytoplankton species, and thereby suggest important implications for phytoplankton growth control.
Dispersive radiation induced by shock waves in passive resonators.
Malaguti, Stefania; Conforti, Matteo; Trillo, Stefano
2014-10-01
We show that passive Kerr resonators pumped close to zero dispersion wavelengths on the normal dispersion side can develop the resonant generation of linear waves driven by cavity (mixed dispersive-dissipative) shock waves. The resonance mechanism can be successfully described in the framework of the generalized Lugiato-Lefever equation with higher-order dispersive terms. Substantial differences with radiation from cavity solitons and purely dispersive shock waves dispersion are highlighted.
Advective hydrogel membrane chromatography for monoclonal antibody purification in bioprocessing.
Hou, Ying; Brower, Mark; Pollard, David; Kanani, Dharmesh; Jacquemart, Renaud; Kachuik, Bradley; Stout, James
2015-01-01
Protein A chromatography is widely employed for the capture and purification of monoclonal antibodies (mAbs). Because of the high cost of protein A resins, there is a significant economic driving force to seek new downstream processing strategies. Membrane chromatography has emerged as a promising alternative to conventional resin based column chromatography. However, to date, the application has been limited to mostly ion exchange flow through (FT) mode. Recently, significant advances in Natrix hydrogel membrane has resulted in increased dynamic binding capacities for proteins, which makes membrane chromatography much more attractive for bind/elute operations. The dominantly advective mass transport property of the hydrogel membrane has also enabled Natrix membrane to be run at faster volumetric flow rates with high dynamic binding capacities. In this work, the potential of using Natrix weak cation exchange membrane as a mAb capture step is assessed. A series of cycle studies was also performed in the pilot scale device (> 30 cycles) with good reproducibility in terms of yield and product purities, suggesting potential for improved manufacturing flexibility and productivity. In addition, anion exchange (AEX) hydrogel membranes were also evaluated with multiple mAb programs in FT mode. Significantly higher binding capacity for impurities (support mAb loads up to 10Kg/L) and 40X faster processing speed were observed compared with traditional AEX column chromatography. A proposed protein A free mAb purification process platform could meet the demand of a downstream purification process with high purity, yield, and throughput.
MAST solution of advection problems in irrotational flow fields
NASA Astrophysics Data System (ADS)
Aricò, Costanza; Tucciarelli, Tullio
2007-03-01
A new numerical-analytical Eulerian procedure is proposed for the solution of convection-dominated problems in the case of existing scalar potential of the flow field. The methodology is based on the conservation inside each computational elements of the 0th and 1st order effective spatial moments of the advected variable. This leads to a set of small ODE systems solved sequentially, one element after the other over all the computational domain, according to a MArching in Space and Time technique. The proposed procedure shows the following advantages: (1) it guarantees the local and global mass balance; (2) it is unconditionally stable with respect to the Courant number, (3) the solution in each cell needs information only from the upstream cells and does not require wider and wider stencils as in most of the recently proposed higher-order methods; (4) it provides a monotone solution. Several 1D and 2D numerical test have been performed and results have been compared with analytical solutions, as well as with results provided by other recent numerical methods.
Jet-dominated advective systems of all mass scales
NASA Astrophysics Data System (ADS)
Körding, Elmar; Fender, R.
We show that the radio emission of black hole (BH) and neutron star (NS) X-ray binaries (XRBs) follows the analytical prediction of a jet model where the jet carries a constant fraction of the accretion power. The radio emission can therefore be used as a tracer of the accretion rate. This measure is normalised with efficiently radiating objects. As it is independent of the X-ray fluxes, the measure allows us to compare the accretion rate dependency of the bolometric X-ray lumi- nosity of BHs and NSs. For NSs, it scales linearly with accretion rate while the scaling for BHs is quadratic - as expected for inefficient accretion flows. We find the same behaviour in AGN. This new approach uses the jet power to obtain the accretion rate. Thus, we know both the jet power and the radiated power of an accreting BH. This allows us to show that some accretion power is likely to be advected into the black hole, while the jet power dominates over the bolometric luminosity of a hard state BH.
Sea breezes and advective effects in southwest James Bay
NASA Technical Reports Server (NTRS)
Mckendry, Ian; Roulet, Nigel
1994-01-01
Observations from a transect extending 100 km inland during the Northern Wetlands Study (NOWES) in 1990 show that the sea breeze develops on approximately 25% of days during summer and may penetrate up to 100 km inland on occasions. The sea breeze exhibits a marked diurnal clockwise rotation as a result of the Coriolis effect along the unobstructed coastline. The marine advective effect is shown to depend on gradient wind direction. With northwesterly upper level flow the sea breeze tends to be northeasterly in direction and is associated with decreased temperatures and vapor pressure deficits (VPD). With southwesterly upper level flow the sea breeze tends to have a southeasterly direction and less effect on temperatures and VPD. This is attributed to shorter residence times of air parcels over water. For two cases, Colorado State University mesoscale model simulations show good agreement with surface wind observations and suggest that under northwesterly gradient flow, Bowen ratios are increased in the onshore flow along western James Bay, while during southwesterly gradient flow these effects are negligible. These results have implications for the interpretation of local climate, ecology, and hydrology as well as land-based and airborne turbulent flux measurements made during NOWES.
Authalic parameterization of general surfaces using Lie advection.
Zou, Guangyu; Hu, Jiaxi; Gu, Xianfeng; Hua, Jing
2011-12-01
Parameterization of complex surfaces constitutes a major means of visualizing highly convoluted geometric structures as well as other properties associated with the surface. It also enables users with the ability to navigate, orient, and focus on regions of interest within a global view and overcome the occlusions to inner concavities. In this paper, we propose a novel area-preserving surface parameterization method which is rigorous in theory, moderate in computation, yet easily extendable to surfaces of non-disc and closed-boundary topologies. Starting from the distortion induced by an initial parameterization, an area restoring diffeomorphic flow is constructed as a Lie advection of differential 2-forms along the manifold, which yields equality of the area elements between the domain and the original surface at its final state. Existence and uniqueness of result are assured through an analytical derivation. Based upon a triangulated surface representation, we also present an efficient algorithm in line with discrete differential modeling. As an exemplar application, the utilization of this method for the effective visualization of brain cortical imaging modalities is presented. Compared with conformal methods, our method can reveal more subtle surface patterns in a quantitative manner. It, therefore, provides a competitive alternative to the existing parameterization techniques for better surface-based analysis in various scenarios.
NASA Astrophysics Data System (ADS)
Naveed, M.; Kawamoto, K.; Hamamoto, S.; Sakaki, T.; Moldrup, P.; Komatsu, T.
2010-12-01
The transport and fate of gases in the soil are governed by gas advection, diffusion and dispersion phenomena. Among three gas transport phenomena, gas dispersion is least understood. Main objective of this study is to investigate the gas dispersion phenomena, emphasising on the effect of moisture content, sand particle shape, particle size, particle size distribution, and scale dependency on gas dispersion. One dimensional laboratory column experiments, in an apparatus consisting of an acrylic column attached to inlet and outlet chambers (Hamamoto et al., SSAJ, 2009), were conducted for the measurements of gas dispersion coefficient (DH). Various types of sands (Narita and Toyoura sands from Japan, and Granusils and Accusands from United States) and glass beads with variable moisture contents were used as porous media. Shape of the sand particles were characterized in terms of sphericity and roundness. The changes in the oxygen concentration within the soil column and in the inlet and outlet chambers were monitored. In addition the air pressure at inlet and middle of the soil column was also monitored to ensure the uniform density of porous media along the column. The measured breakthrough curves were fitted with the analytical solution of the advection dispersion equation to determine dispersion coefficients. The measured dispersion coefficient (DH) showed linear increase with pore velocity (u0). Measured dispersivity (λ= DH/u0) increases with decrease in air filled porosity induced by adding moisture contents in sands. Its values varies from 0 to 3 cm on decreasing air filled porosity from 0.50 (air dry) to 0.25 (field capacity). Shape of the sand particles has no significant effect on gas dispersion. When gas dispersion phenomena was studied on different shape of the sand particles at various air filled porosities, it was found that for angular sand particles initially gas dispersivity increases more rapidly as compared to rounded sand particles and finally
Boltzmann equations for neutrinos with flavor mixings
NASA Astrophysics Data System (ADS)
Yamada, Shoichi
2000-11-01
With a view of applications to the simulations of supernova explosions and protoneutron star cooling, we derive the Boltzmann equations for the neutrino transport with flavor mixing based on the real time formalism of the nonequilibrium field theory and the gradient expansion of the Green function. The relativistic kinematics is properly taken into account. The advection terms are derived in the mean field approximation for the neutrino self-energy while the collision terms are obtained in the Born approximation. The resulting equations take the familiar form of the Boltzmann equation with corrections due to mixing both in the advection part and in the collision part. These corrections are essentially the same as those derived by Sirera et al. for the advection terms and those by Raffelt et al. for the collision terms, respectively, though the formalism employed here is different from theirs. The derived equations will be easily implemented in numerical codes employed in the simulations of supernova explosions and protoneutron star cooling.
NASA Astrophysics Data System (ADS)
Zhang, Yi; Yu, Rucong; Li, Jian
2017-03-01
An Eulerian flux-form advection scheme, called the Two-step Shape-Preserving Advection Scheme (TSPAS), was generalized and implemented on a spherical icosahedral hexagonal grid (also referred to as a geodesic grid) to solve the transport equation. The C grid discretization was used for the spatial discretization. To implement TSPAS on an unstructured grid, the original finite-difference scheme was further generalized. The two-step integration utilizes a combination of two separate schemes (a low-order monotone scheme and a high-order scheme that typically cannot ensure monotonicity) to calculate the fluxes at the cell walls (one scheme corresponds to one cell wall). The choice between these two schemes for each edge depends on a pre-updated scalar value using slightly increased fluxes. After the determination of an appropriate scheme, the final integration at a target cell is achieved by summing the fluxes that are computed by the different schemes. The conservative and shape-preserving properties of the generalized scheme are demonstrated. Numerical experiments are conducted at several horizontal resolutions. TSPAS is compared with the Flux Corrected Transport (FCT) approach to demonstrate the differences between the two methods, and several transport tests are performed to examine the accuracy, efficiency and robustness of the two schemes.
von Kameke, A; Huhn, F; Muñuzuri, A P; Pérez-Muñuzuri, V
2013-02-22
In the absence of advection, reaction-diffusion systems are able to organize into spatiotemporal patterns, in particular spiral and target waves. Whenever advection is present that can be parametrized in terms of effective or turbulent diffusion D(*), these patterns should be attainable on a much greater, boosted length scale. However, so far, experimental evidence of these boosted patterns in a turbulent flow was lacking. Here, we report the first experimental observation of boosted target and spiral patterns in an excitable chemical reaction in a quasi-two-dimensional turbulent flow. The wave patterns observed are ~50 times larger than in the case of molecular diffusion only. We vary the turbulent diffusion coefficient D(*) of the flow and find that the fundamental Fisher-Kolmogorov-Petrovsky-Piskunov equation, v(f) proportional sqrt[D(*)], for the asymptotic speed of a reactive wave remains valid. However, not all measures of the boosted wave scale with D(*) as expected from molecular diffusion, since the wave fronts turn out to be highly filamentous.
Moments of action provide insight into critical times for advection-diffusion-reaction processes
NASA Astrophysics Data System (ADS)
Ellery, Adam J.; Simpson, Matthew J.; McCue, Scott W.; Baker, Ruth E.
2012-09-01
Berezhkovskii and co-workers introduced the concept of local accumulation time as a finite measure of the time required for the transient solution of a reaction-diffusion equation to effectively reach steady state [Biophys J.BIOJAU0006-349510.1016/j.bpj.2010.07.045 99, L59 (2010); Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.83.051906 83, 051906 (2011)]. Berezhkovskii's approach is a particular application of the concept of mean action time (MAT) that was introduced previously by McNabb [IMA J. Appl. Math.IJAMDM0272-496010.1093/imamat/47.2.193 47, 193 (1991)]. Here, we generalize these previous results by presenting a framework to calculate the MAT, as well as the higher moments, which we call the moments of action. The second moment is the variance of action time, the third moment is related to the skew of action time, and so on. We consider a general transition from some initial condition to an associated steady state for a one-dimensional linear advection-diffusion-reaction partial differential equation (PDE). Our results indicate that it is possible to solve for the moments of action exactly without requiring the transient solution of the PDE. We present specific examples that highlight potential weaknesses of previous studies that have considered the MAT alone without considering higher moments. Finally, we also provide a meaningful interpretation of the moments of action by presenting simulation results from a discrete random-walk model together with some analysis of the particle lifetime distribution. This work shows that the moments of action are identical to the moments of the particle lifetime distribution for certain transitions.
Spectral Models Based on Boussinesq Equations
2006-10-03
equations assume periodic solutions apriori. This, however, also forces the question of which extended Boussinesq model to use. Various one- equation ... equations of Nwogu (1993), without the traditional reduction to a one- equation model. Optimal numerical techniques to solve this system of equations are...A. and Madsen, P. A. (2004). "Boussinesq evolution equations : numerical efficiency, breaking and amplitude dispersion," Coastal Engineering, 51, 1117
ERIC Educational Resources Information Center
Budiansky, Stephen
1980-01-01
This article discusses the need for more accurate and complete input data and field verification of the various models of air pollutant dispension. Consideration should be given to changing the form of air quality standards based on enhanced dispersion modeling techniques. (Author/RE)
Verification of Advective Bar Elements Implemented in the Aria Thermal Response Code.
Mills, Brantley
2016-01-01
A verification effort was undertaken to evaluate the implementation of the new advective bar capability in the Aria thermal response code. Several approaches to the verification process were taken : a mesh refinement study to demonstrate solution convergence in the fluid and the solid, visually examining the mapping of the advective bar element nodes to the surrounding surfaces, and a comparison of solutions produced using the advective bars for simple geometries with solutions from commercial CFD software . The mesh refinement study has shown solution convergence for simple pipe flow in both temperature and velocity . Guidelines were provided to achieve appropriate meshes between the advective bar elements and the surrounding volume. Simulations of pipe flow using advective bars elements in Aria have been compared to simulations using the commercial CFD software ANSYS Fluent (r) and provided comparable solutions in temperature and velocity supporting proper implementation of the new capability. Verification of Advective Bar Elements iv Acknowledgements A special thanks goes to Dean Dobranich for his guidance and expertise through all stages of this effort . His advice and feedback was instrumental to its completion. Thanks also goes to Sam Subia and Tolu Okusanya for helping to plan many of the verification activities performed in this document. Thank you to Sam, Justin Lamb and Victor Brunini for their assistance in resolving issues encountered with running the advective bar element model. Finally, thanks goes to Dean, Sam, and Adam Hetzler for reviewing the document and providing very valuable comments.
STANDING SHOCK INSTABILITY IN ADVECTION-DOMINATED ACCRETION FLOWS
Le, Truong; Wood, Kent S.; Wolff, Michael T.; Becker, Peter A.; Putney, Joy
2016-03-10
Depending on the values of the energy and angular momentum per unit mass in the gas supplied at large radii, inviscid advection-dominated accretion flows can display velocity profiles with either preshock deceleration or preshock acceleration. Nakayama has shown that these two types of flow configurations are expected to have different stability properties. By employing the Chevalier and Imamura linearization method and the Nakayama instability boundary conditions, we discover that there are regions of parameter space where disks/shocks with outflows can be stable or unstable. In regions of instability, we find that preshock deceleration is always unstable to the zeroth mode with zero frequency of oscillation, but is always stable to the fundamental mode and overtones. Furthermore, we also find that preshock acceleration is always unstable to the zeroth mode and that the fundamental mode and overtones become increasingly less stable as the shock location moves away from the horizon when the disk half-height expands above ∼12 gravitational radii at the shock radius. In regions of stability, we demonstrate the zeroth mode to be stable for the velocity profiles that exhibit preshock acceleration and deceleration. Moreover, for models that are linearly unstable, our model suggests the possible existence of quasi-periodic oscillations (QPOs) with ratios 2:3 and 3:5. These ratios are believed to occur in stellar and supermassive black hole candidates, for example, in GRS 1915+105 and Sgr A*, respectively. We expect that similar QPO ratios also exist in regions of stable shocks.
The distortion of the level set gradient under advection
NASA Astrophysics Data System (ADS)
Trujillo, Mario F.; Anumolu, Lakshman; Ryddner, Doug
2017-04-01
The practice of periodically reinitializing the level set function is well established in two-phase flow applications as a way of controlling the growth of anomalies and/or numerical errors. In the present work, the underlying roots of this anomalous growth are studied, where it is established that the augmentation of the magnitude of the level set gradient (| ∇ϕ |) is directly connected to the nature of the flow field; hence, it is not necessarily the result of some type of numerical error. More specifically, for a general flow field advecting the level set function, it is shown that the eigenpairs of the strain rate tensor are responsible for the rate of change of | ∇ϕ | along a fluid particle trajectory. This straining action not only affects the magnitude of | ∇ϕ |, but the general character of ϕ, and consequently contributes to the growth in numerical error. These numerical consequences are examined by adopting the Gradient Augmented Level Set method. Specifically, it is shown that the local error for ϕ is directly connected to the size of | ∇ϕ | and to the magnitude of the second and fourth order derivatives of ϕ. These analytical findings are subsequently supported by various examples. The role of reinitialization is discussed, where it is shown that in cases where the zero level set contour has a local radius of curvature that is below the local grid resolution, reinitialization exacerbates rather than diminishes the degree of error. For other cases, where the interface is well resolved, reinitialization helps stabilize the error as intended.
The contiguous domains of Arctic Ocean advection: Trails of life and death
NASA Astrophysics Data System (ADS)
Wassmann, P.; Kosobokova, K. N.; Slagstad, D.; Drinkwater, K. F.; Hopcroft, R. R.; Moore, S. E.; Ellingsen, I.; Nelson, R. J.; Carmack, E.; Popova, E.; Berge, J.
2015-12-01
The central Arctic Ocean is not isolated, but tightly connected to the northern Pacific and Atlantic Oceans. Advection of nutrient-, detritus- and plankton-rich waters into the Arctic Ocean forms lengthy contiguous domains that connect subarctic with the arctic biota, supporting both primary production and higher trophic level consumers. In turn, the Arctic influences the physical, chemical and biological oceanography of adjacent subarctic waters through southward fluxes. However, exports of biomass out of the Arctic Ocean into both the Pacific and Atlantic Oceans are thought to be far smaller than the northward influx. Thus, Arctic Ocean ecosystems are net biomass beneficiaries through advection. The biotic impact of Atlantic- and Pacific-origin taxa in arctic waters depends on the total supply of allochthonously-produced biomass, their ability to survive as adults and their (unsuccessful) reproduction in the new environment. Thus, advective transport can be thought of as trails of life and death in the Arctic Ocean. Through direct and indirect (mammal stomachs, models) observations this overview presents information about the advection and fate of zooplankton in the Arctic Ocean, now and in the future. The main zooplankton organisms subjected to advection into and inside the Arctic Ocean are (a) oceanic expatriates of boreal Atlantic and Pacific origin, (b) oceanic Arctic residents and (c) neritic Arctic expatriates. As compared to the Pacific gateway the advective supply of zooplankton biomass through the Atlantic gateways is 2-3 times higher. Advection characterises how the main planktonic organisms interact along the contiguous domains and shows how the subarctic production regimes fuel life in the Arctic Ocean. The main differences in the advective regimes through the Pacific and Atlantic gateways are presented. The Arctic Ocean is, at least in some regions, a net heterotrophic ocean that - during the foreseeable global warming trend - will more and more rely
Horizontal Advection and Mixing of Pollutants in the Urban Atmospheric Environment
NASA Astrophysics Data System (ADS)
Magnusson, S. P.; Entekhabi, D.; Britter, R.; Norford, L.; Fernando, H. J.
2013-12-01
Although urban air quality and its impacts on the public health have long been studied, the increasing urbanization is raising concerns on how to better control and mitigate these health impacts. A necessary element in predicting exposure levels is fundamental understanding of flow and dispersion in urban canyons. The complex topology of building structures and roads requires the resolution of turbulence phenomena within urban canyons. The use of dense and low porosity construction material can lead to rapid heating in response to direct solar exposure due to large thermal mass. Hence thermal and buoyancy effects may be as important as mechanically-forced or shear-induced flows. In this study, the transport of pollutants within the urban environment, as well as the thermal and advection effects, are investigated. The focus is on the horizontal transport or the advection effects within the urban environment. With increased urbanization and larger and more spread cities, concern about how the upstream air quality situation can affect downstream areas. The study also examines the release and the dispersion of hazardous material. Due to the variety and complexity of urban areas around the world, the urban environment is simplified into adjacent two-dimensional urban street canyons. Pollutants are released inside each canyon. Computational Fluid Dynamics (CFD) simulations are applied to evaluate and quantify the flow rate out of each canyon and also the exchange of pollutants between the canyons. Imagine a row of ten adjacent urban street canyons of aspect ratio 1 with horizontal flow perpendicular to it as shown in the attached figure. C is the concentration of pollutants. The first digit indicates in what canyon the pollutant is released and the second digit indicates the location of that pollutant. For example, C3,4 is the concentration of pollutant released inside canyon 3 measured in canyon 4. The same amount of pollution is released inside the ten street canyons
Evaluation of dispersivity coefficients by means of a laboratory image analysis
NASA Astrophysics Data System (ADS)
Citarella, Donato; Cupola, Fausto; Tanda, Maria Giovanna; Zanini, Andrea
2015-01-01
This paper describes the application of an innovative procedure that allows the estimation of longitudinal and transverse dispersivities in an experimental plume devised in a laboratory sandbox. The phenomenon of transport in porous media is studied using sodium fluorescein as tracer. The fluorescent excitation was achieved by using blue light and the concentration data were obtained through the processing of side wall images collected with a high resolution color digital camera. After a calibration process, the relationship between the luminosity of the emitted fluorescence and the fluorescein concentration was determined at each point of the sandbox. The relationships were used to describe the evolution of the transport process quantitatively throughout the entire domain. Some check tests were performed in order to verify the reliability of the experimental device. Numerical flow and transport models of the sandbox were developed and calibrated comparing computed and observed flow rates and breakthrough curves. The estimation of the dispersivity coefficients was carried out by analyzing the concentration field deduced from the images collected during the experiments; the dispersivity coefficients were evaluated in the domain zones where the tracer affected the porous medium under the hypothesis that the transport phenomenon is described by advection-dispersion equation (ADE) and by computing the differential components of the concentration by means of a numerical leap-frog scheme. The values determined agree with the ones referred in literature for similar media and with the coefficients obtained by calibrating the numerical model. Very interesting considerations have been made from the analysis of the performance of the methodology at different locations in the flow domain and phases of the plume evolution.
A New Methodology For Estimating CO2 Advective Fluxes In Complex Terrain
NASA Astrophysics Data System (ADS)
Montagnani, L.; Manca, G.; Canepa, E.; Georgieva, E.; Kerschbaumer, G.; Minerbi, S.; Seufert, G.
2007-12-01
A key problem in using the eddy correlation (EC) technique for estimating the carbon dioxide Net Ecosystem Exchange (NEE) of terrestrial ecosystems is the potential bias caused by advective fluxes of CO2. Advective fluxes are often not considered since they are difficult to identify and to quantify, especially in complex mountainous terrain with highly variable wind patterns and drainage flows. We propose a methodology to estimate these fluxes based on a full 3-Dimensional (3D) approach applied to the topographically complex alpine forest site of Renon (1736 m a.s.l.). This is an aerodynamic method based on the computation of advective fluxes across the aerial faces of a control volume including the plant ecosystem. Data used for the computation of CO2 advective fluxes were collected during an extensive field campaign performed in 2005 in the framework of CarboEurope-IP research project. Vertical profiles of wind, air temperature and CO2 concentration have been measured at five towers and a spatial interpolation was performed in order to get 3D fields of such variables. The frame of reference used was orthogonal and the vertical direction was parallel to the gravity. Each anemometer was aligned in this frame of reference and no rotations were applied to the wind velocity components. The analysis of the 3D fields of wind velocity, CO2 mixing ratio and air density highlighted the spatial heterogeneity of CO2 source/sink strength and the strong de-coupling between air flow below and above the canopy during stable nights. The total CO2 advection calculated using the proposed methodology exhibited prevailing positive values during the night-time period. Advective fluxes estimated during windy nights were of the same magnitude and sign of vertical turbulent flux measured above canopy by the EC technique. This observation suggests that the friction velocity correction routinely applied to night-time periods may not be efficient at the Renon site. During light windy nights
Longitudinal dispersion modeling in small streams
NASA Astrophysics Data System (ADS)
Pekarova, Pavla; Pekar, Jan; Miklanek, Pavol
2014-05-01
The environmental problems caused by the increasing of pollutant loads discharged into natural water bodies are very complex. For that reason the cognition of transport mechanism and mixing characteristics in natural streams is very important. The mathematical and numerical models have become very useful tools for solving the water management problems. The mathematical simulations based on numerical models of pollution mixing in streams can be used (for example) for prediction of spreading of accidental contaminant waves in rivers. The paper deals with the estimation of the longitudinal dispersion coefficients and with the numerical simulation of transport and transformation of accidental pollution in the small natural streams. There are different ways of solving problems of pollution spreading in open channels, in natural rivers. One of them is the hydrodynamic approach, which endeavours to understand and quantify the spreading phenomenon in a stream. The hydrodynamic models are based on advection-diffusion equation and the majority of them are one-dimensional models. Their disadvantage is inability to simulate the spread of pollution until complete dispersion of pollutant across the stream section is finished. Two-dimensional mixing models do not suffer from these limitations. On the other hand, the one-dimensional models are simpler than two-dimensional ones, they need not so much input data and they are often swifter. Three-dimensional models under conditions of natural streams are applicable with difficulties (or inapplicable) for their complexity and demands on accuracy and amount of input data. As there was mentioned above the two-dimensional models can be used also until complete dispersion of pollutant across the stream section is not finished, so we decided to apply the two-dimensional model SIRENIE. Experimental microbasin Rybarik is the part of the experimental Mostenik brook basin of IH SAS Bratislava. It was established as a Field Hydrological
Technology Transfer Automated Retrieval System (TEKTRAN)
Because the Surface Energy Balance Algorithm for Land (SEBAL) tends to underestimate ET under conditions of advection, the model was modified by incorporating an advection component as part of the energy usable for crop evapotranspiration (ET). The modification involved the estimation of advected en...
NASA Astrophysics Data System (ADS)
Atis, S.; Saha, S.; Auradou, H.; Martin, J.; Rakotomalala, N.; Talon, L.; Salin, D.
2012-09-01
Autocatalytic reaction fronts between two reacting species in the absence of fluid flow, propagate as solitary waves. The coupling between autocatalytic reaction front and forced simple hydrodynamic flows leads to stationary fronts whose velocity and shape depend on the underlying flow field. We address the issue of the chemico-hydrodynamic coupling between forced advection in porous media and self-sustained chemical waves. Towards that purpose, we perform experiments over a wide range of flow velocities with the well characterized iodate arsenious acid and chlorite-tetrathionate autocatalytic reactions in transparent packed beads porous media. The characteristics of these porous media such as their porosity, tortuosity, and hydrodynamics dispersion are determined. In a pack of beads, the characteristic pore size and the velocity field correlation length are of the order of the bead size. In order to address these two length scales separately, we perform lattice Boltzmann numerical simulations in a stochastic porous medium, which takes into account the log-normal permeability distribution and the spatial correlation of the permeability field. In both experiments and numerical simulations, we observe stationary fronts propagating at a constant velocity with an almost constant front width. Experiments without flow in packed bead porous media with different bead sizes show that the front propagation depends on the tortuous nature of diffusion in the pore space. We observe microscopic effects when the pores are of the size of the chemical front width. We address both supportive co-current and adverse flows with respect to the direction of propagation of the chemical reaction. For supportive flows, experiments and simulations allow observation of two flow regimes. For adverse flow, we observe upstream and downstream front motion as well as static front behaviors over a wide range of flow rates. In order to understand better these observed static state fronts, flow
Does the Rayleigh equation apply to evaluate field isotope data in contaminant hydrogeology?
Abe, Yumiko; Hunkeler, Daniel
2006-03-01
Stable isotope data have been increasingly used to assess in situ biodegradation of organic contaminants in groundwater. The data are usually evaluated using the Rayleigh equation to evaluate whether isotope data follow a Rayleigh trend, to calculate the extent of contaminant biodegradation, or to estimate first-order rate constants. However, the Rayleigh equation was developed for homogeneous systems while in the subsurface, contaminants can migrate at different velocities due to physical heterogeneity. This paper presents a method to quantify the systematic effect that is introduced by applying the Rayleigh equation to field isotope data. For this purpose, the travel time distribution between source and sampling point is characterized by an analytical solution to the advection-dispersion equation. The systematic effect was evaluated as a function of the magnitude of physical heterogeneity, geometry of the contaminant plume, and degree of biodegradation. Results revealed that the systematic effect always leads to an underestimation of the actual values of isotope enrichment factors, the extent of biodegradation, or first-order rate constants, especially in the dispersion-dominant region representing a higher degree of physical heterogeneity. A substantial systematic effect occurs especially for the quantification of first-order rate constants (up to 50% underestimation of actual rate) while it is relatively small for quantification of the extent of biodegradation (< 5% underestimation of actual degree of biodegradation). The magnitude of the systematic effect is in the same range as the uncertainty due to uncertainty of the analytical data, of the isotope enrichment factor, and the average travel time.
Sabelnikov, V A; Petrova, N N; Lipatnikov, A N
2016-10-01
Within the framework of the Maxwell-Cattaneo relaxation model extended to reaction-diffusion systems with nonlinear advection, travelling wave (TW) solutions are analytically investigated by studying a normalized reaction-telegraph equation in the case of the reaction and advection terms described by quadratic functions. The problem involves two governing parameters: (i) a ratio φ^{2} of the relaxation time in the Maxwell-Cattaneo model to the characteristic time scale of the reaction term, and (ii) the normalized magnitude N of the advection term. By linearizing the equation at the leading edge of the TW, (i) necessary conditions for the existence of TW solutions that are smooth in the entire interval of -∞<ζ<∞ are obtained, (ii) the smooth TW speed is shown to be less than the maximal speed φ^{-1} of the propagation of a substance, (iii) the lowest TW speed as a function of φ and N is determined. If the necessary condition of N>φ-φ^{-1} does not hold, e.g., if the magnitude N of the nonlinear advection is insufficiently high in the case of φ^{2}>1, then, the studied equation admits piecewise smooth TW solutions with sharp leading fronts that propagate at the maximal speed φ^{-1}, with the substance concentration or its spatial derivative jumping at the front. An increase in N can make the solution smooth in the entire spatial domain. Moreover, an explicit TW solution to the considered equation is found provided that N>φ. Subsequently, by invoking a principle of the maximal decay rate of TW solution at its leading edge, relevant TW solutions are selected in a domain of (φ,N) that admits the smooth TWs. Application of this principle to the studied problem yields transition from pulled (propagation speed is controlled by the TW leading edge) to pushed (propagation speed is controlled by the entire TW structure) TW solutions at N=N_{cr}=sqrt[1+φ^{2}], with the pulled (pushed) TW being relevant at smaller (larger) N. An increase in the normalized
NASA Technical Reports Server (NTRS)
Frost, W.; Christensen, L. S.; Collins, F. G.; Camp, D. W.
1980-01-01
A study of economically viable techniques for dispersing warm fog at commercial airports is presented. Five fog dispersion techniques are examined: evaporation suppression, downwash, mixing, seeding with hygroscopic material, thermal techniques, and charged particle techniques. Thermal techniques, although effective, were found to be too expensive for routine airport operations, and detrimental to the environment. Seeding or helicopter downwash are practical for small-scale or temporary fog clearing, but are probably not useful for airport operations on a routine basis. Considerable disagreement exists on the capability of charged particle techniques, which stems from the fact that different assumptions and parameter values are used in the analytical models. Recommendations resulting from the review of this technique are listed, and include: experimental measurements of the parameters in question; a study to ascertain possible safety hazards, such as increased electrical activity or fuel ignition during refueling operations which could render charged particle techniques impractical; and a study of a single charged particle generator.
Performance of Steady-State Dispersion Models Under Low Wind-Speed Conditions
NASA Astrophysics Data System (ADS)
Qian, Wenjun; Venkatram, Akula
2011-03-01
We examine the performance of two steady-state models, a numerical solution of the advection-diffusion equation and the Gaussian plume-model-based AERMOD (the American Meteorological Society/Environmental Protection Agency Regulatory Model), to predict dispersion for surface releases under low wind-speed conditions. A comparison of model estimates with observations from two tracer studies, the Prairie Grass experiment and the Idaho Falls experiment indicates that about 50% of the concentration estimates are within a factor of two of the observations, but the scatter is large: the 95% confidence interval of the ratio of the observed to estimated concentrations is about 4. The model based on the numerical solution of the diffusion equation in combination with the model of Eckman (1994, Atmos Environ 28:265-272) for horizontal spread performs better than AERMOD in explaining the observations. Accounting for meandering of the wind reduces some of the overestimation of concentrations at low wind speeds. The results deteriorate when routine one-level observations are used to construct model inputs. An empirical modification to the similarity estimate of the surface friction velocity reduces the underestimation at low wind speeds.
Divergence of reference evapotranspiration estimates under advective tropical conditions
Technology Transfer Automated Retrieval System (TEKTRAN)
Standardized reference evapotranspiration (ET) and crop specific coefficients are frequently used to assess crop water use in irrigated agriculture. However, equations for calculating reference ET have not been well validated in more humid environments where optimal crop yields can depend on supplem...
Black Hole Event Horizons and Advection-Dominated Accretion
NASA Technical Reports Server (NTRS)
McClintock, Jeffrey; Mushotzky, Richard F. (Technical Monitor)
2001-01-01
The XMM data on black-hole X-ray novae are only now becoming available and they have so far not been included in any publications. This work is part of a larger project that makes use of both XMM and Chandra data. Our first publication on the Chandra results is the following: "New Evidence for Black Hole Event Horizons from Chandra" by M.R. Garcia, J.E. McClintock, R. Narayan, P. Callanan, D. Barret and S. Murray (2001, ApJ, 553, L47). Therein we present the luminosities of the two black-hole X-ray novae, GRO J0422+22 and 4U1 543-47, which were observed by Chandra. These results are combined with the luminosities of four additional black-hole X-ray novae, which were observed as part of a Chandra GTO program (PI: S. Murray). The very low, but nonzero, quiescent X-ray luminosities of these black hole binaries is very difficult to understand in the context of standard viscous accretion disk theory. The principal result of this work is that X-ray novae that contain black hole primaries are about 100 times fainter that X-ray novae that contain neutron star primaries. This result had been suggested in earlier work, but the present work very firmly establishes this large luminosity difference. The result is remarkable because the black-hole and the neutron-star systems are believed to be similar in many respects. Most importantly, the mass transfer rate from the secondary star is believed to be very comparable for the two kinds of systems for similar orbital periods. The advection-dominated accretion flow (ADAF) model provides a natural framework for understanding the extraordinarily low luminosities of the black hole systems and the hundred-fold greater luminosities of the neutron star systems. The chief feature of an ADAF is that the heat energy in the accreting gas is trapped in the gas and travels with it, rather than being radiated promptly. Thus the accreting gas reaches the central object with a huge amount of thermal energy. If the accretor is a black hole, the
Dispersion in alluvial convergent estuaries
NASA Astrophysics Data System (ADS)
Zhang, Zhilin; Savenije, Hubert H. G.
2016-04-01
The Van der Burgh's equation for longitudinal effective dispersion is a purely empirical method with practical implications. Its application to the effective tidal average dispersion under equilibrium conditions appears to have excellent performance in a wide range of alluvial estuaries. In this research, we try to find out the physical meaning of Van der Burgh's coefficient. Researchers like MacCready, Fischer, Kuijper, Hansen and Rattray have tried to split up dispersion into its constituents which did not do much to explain overall behaviour. In addition, traditional literature on dispersion is mostly related to flumes with constant cross-section. This research is about understanding the Van der Burgh's coefficient facing the fact that natural estuaries have exponentially varying cross-section. The objective is to derive a simple 1-D model considering both longitudinal and lateral mixing processes based on field observations (theoretical derivation). To that effect, we connect dispersion with salinity using the salt balance equation. Then we calculate the salinity along the longitudinal direction and compare it to the observed salinity. Calibrated dispersion coefficients in a range of estuaries are then compared with new expressions for the Van der Burgh's coefficient K and it is analysed if K varies from estuary to estuary. The set of reliable data used will be from estuaries: Kurau, Perak, Bernam, Selangor, Muar, Endau, Maputo, Thames, Corantijn, Sinnamary, Mae Klong, Lalang, Limpopo, Tha Chin, Chao Phraya, Edisto and Elbe.
Rigorous upper bounds for fluid and plasma transport due to passive advection
Krommes, J.A.; Smith, R.A.; Kim, C.B.
1987-07-01
The formulation of variational principles for transport due to passive advection is described. A detailed account of the work has been published elsewhere. In the present paper, the motivations, philosophy, and implications of the method are briefly discussed. 15 refs.
NASA Astrophysics Data System (ADS)
Gusti, T. P.; Hertanti, D. R.; Bahsan, E.; Soeryantono, H.
2013-12-01
Particle-based numerical methods, such as Smoothed Particle Hydrodynamics (SPH), may be able to simulate some hydrodynamic and morphodynamic behaviors better than grid-based numerical methods. This study simulates hydrodynamics in meanders and advection and turbulent diffusion in straight river channels using Microsoft Excel and Visual Basic. The simulators generate three-dimensional data for hydrodynamics and one-dimensional data for advection-turbulent diffusion. Fluid at rest, sloshing, and helical flow are simulated in the river meanders. Spill loading and step loading are done to simulate concentration patterns associated with advection-turbulent diffusion. Results indicate that helical flow is formed due to disturbance in morphology and particle velocity in the stream and the number of particles does not have a significant effect on the pattern of advection-turbulent diffusion concentration.
The impact of advection on stratification and chlorophyll variability in the equatorial Pacific
NASA Astrophysics Data System (ADS)
Dave, Apurva C.; Lozier, M. Susan
2015-06-01
Previously reported global-scale correlations between interannual variability in upper ocean stratification and chlorophyll a (a proxy for phytoplankton biomass) have been shown to be driven by strong associations between the two properties in the central and western equatorial Pacific. Herein, we present evidence that these correlations are not causal but instead result from the advection of heat, salt, and nutrients in the region. Specifically, we demonstrate that stratification and chlorophyll are simultaneously influenced by shifts in the horizontal advective inputs of cold/saline/nutrient-rich waters from upwelling regions to the east and warm/fresh/nutrient-poor waters to the west. We find that horizontal advection contributes substantially to the annual surface layer nutrient budget and, together with vertical advection, significantly impacts interannual variability in chlorophyll. These results highlight the importance of a three-dimensional framework for examining nutrient supply in the upper ocean—a crucial requirement for assessing future marine ecosystem responses to a changing climate.
Sensitivity of solute advective travel time to porosities of hydrogeologic units.
Zhu, Jianting; Pohlmann, Karl F; Chapman, Jenny B; Russell, Charles E; Carroll, Rosemary W H; Shafer, David S
2010-01-01
An integral approach is proposed to quantify uncertainty and sensitivity of advective travel time to the effective porosities of hydrogeologic units (HGUs) along groundwater flow paths. The approach is applicable in situations where a groundwater flow model exists, but a full solute transport model is not available. The approach can be used to: (1) determine HGUs whose porosities are influential to the solute advective travel time; and (2) apportion uncertainties of solute advective travel times to the uncertainty contributions from individual HGU porosities. A simple one-dimensional steady-state flow example is used to illustrate the approach. Advective travel times of solutes are obtained based on the one-dimensional steady-state flow results in conjunction with the HGU porosities. The approach can be easily applicable to more complex multi-dimensional cases where advective solute travel time can be calculated based on simulated flow results from groundwater flow models. This approach is particularly valuable for optimizing limited resources when designing field characterization programs for uncertainty reduction by identifying HGUs that contribute most to the estimation uncertainty of advective travel times of solutes.
Dispersion compensation in slot photonic crystal waveguide
NASA Astrophysics Data System (ADS)
Plastun, Alexander; Konyukhov, Andrey
2015-03-01
Dispersion tailoring using photonic crystal cladding for slot waveguide is proposed. Numerical modeling based on the Maxwell equation for Te and TM modes of the photonic crystal is performed. Slot waveguide provide high intencity at the central area. Photonic crystal cladding of the slot waveguide allow us to compensate high values of the host glass dispersion.
Ginzburg, Irina
2017-01-01
Impact of the unphysical tangential advective-diffusion constraint of the bounce-back (BB) reflection on the impermeable solid surface is examined for the first four moments of concentration. Despite the number of recent improvements for the Neumann condition in the lattice Boltzmann method-advection-diffusion equation, the BB rule remains the only known local mass-conserving no-flux condition suitable for staircase porous geometry. We examine the closure relation of the BB rule in straight channel and cylindrical capillary analytically, and show that it excites the Knudsen-type boundary layers in the nonequilibrium solution for full-weight equilibrium stencil. Although the d2Q5 and d3Q7 coordinate schemes are sufficient for the modeling of isotropic diffusion, the full-weight stencils are appealing for their advanced stability, isotropy, anisotropy and anti-numerical-diffusion ability. The boundary layers are not covered by the Chapman-Enskog expansion around the expected equilibrium, but they accommodate the Chapman-Enskog expansion in the bulk with the closure relation of the bounce-back rule. We show that the induced boundary layers introduce first-order errors in two primary transport properties, namely, mean velocity (first moment) and molecular diffusion coefficient (second moment). As a side effect, the Taylor-dispersion coefficient (second moment), skewness (third moment), and kurtosis (fourth moment) deviate from their physical values and predictions of the fourth-order Chapman-Enskog analysis, even though the kurtosis error in pure diffusion does not depend on grid resolution. In two- and three-dimensional grid-aligned channels and open-tubular conduits, the errors of velocity and diffusion are proportional to the diagonal weight values of the corresponding equilibrium terms. The d2Q5 and d3Q7 schemes do not suffer from this deficiency in grid-aligned geometries but they cannot avoid it if the boundaries are not parallel to the coordinate lines. In order
NASA Astrophysics Data System (ADS)
Ginzburg, Irina
2017-01-01
Impact of the unphysical tangential advective-diffusion constraint of the bounce-back (BB) reflection on the impermeable solid surface is examined for the first four moments of concentration. Despite the number of recent improvements for the Neumann condition in the lattice Boltzmann method-advection-diffusion equation, the BB rule remains the only known local mass-conserving no-flux condition suitable for staircase porous geometry. We examine the closure relation of the BB rule in straight channel and cylindrical capillary analytically, and show that it excites the Knudsen-type boundary layers in the nonequilibrium solution for full-weight equilibrium stencil. Although the d2Q5 and d3Q7 coordinate schemes are sufficient for the modeling of isotropic diffusion, the full-weight stencils are appealing for their advanced stability, isotropy, anisotropy and anti-numerical-diffusion ability. The boundary layers are not covered by the Chapman-Enskog expansion around the expected equilibrium, but they accommodate the Chapman-Enskog expansion in the bulk with the closure relation of the bounce-back rule. We show that the induced boundary layers introduce first-order errors in two primary transport properties, namely, mean velocity (first moment) and molecular diffusion coefficient (second moment). As a side effect, the Taylor-dispersion coefficient (second moment), skewness (third moment), and kurtosis (fourth moment) deviate from their physical values and predictions of the fourth-order Chapman-Enskog analysis, even though the kurtosis error in pure diffusion does not depend on grid resolution. In two- and three-dimensional grid-aligned channels and open-tubular conduits, the errors of velocity and diffusion are proportional to the diagonal weight values of the corresponding equilibrium terms. The d2Q5 and d3Q7 schemes do not suffer from this deficiency in grid-aligned geometries but they cannot avoid it if the boundaries are not parallel to the coordinate lines. In order
Parkhurst, D.L.
1995-01-01
PHREEQC is a computer program written in the C pwgranuning language that is designed to perform a wide variety of aqueous geochemical calculations. PHREEQC is based on an ion-association aqueous model and has capabilities for (1) speciation and saturation-index calculations, (2) reaction-path and advective-transport calculations involving specified irreversible reactions, mixing of solutions, mineral and gas equilibria surface-complex-ation reactions, and ion-exchange reactions, and (3) inverse modeling, which finds sets of mineral and gas mole transfers that account for composition differences between waters, within specified compositional uncertainties. PHREEQC is derived from the Fortran program PHREEQE, but it has been completely rewritten in C with the addition many new capabilities. New features include the capabilities to use redox couples to distribute redox elements among their valence states in speciation calculations; to model ion-exchange and surface-compiexation reactions; to model reactions with a fixed-pressure, multicomponent gas phase (that is, a gas bubble); to calculate the mass of water in the aqueous phase during reaction and transport calculations; to keep track of the moles of minerals present in the solid phases and determine antomaticaHy the thermodynamically stable phase assemblage; to simulate advective transport in combination with PHREEQC's reaction-modeling capability; and to make inverse modeling calculations that allow for uncertainties in the analytical data. The user interface is improved through the use of a simplified approach to redox reactions, which includes explicit mole-balance equations for hydrogen and oxygen; the use of a revised input that is modular and completely free format; and the use of mineral names and standard chemical symbolism rather than index numbers. The use of (2 eliminates nearly all limitations on army sizes, including numbers of elements, aqueous species, solutions, phases, and lengths of character
Anderman, Evan R.; Hill, Mary Catherine
2001-01-01
Observations of the advective component of contaminant transport in steady-state flow fields can provide important information for the calibration of ground-water flow models. This report documents the Advective-Transport Observation (ADV2) Package, version 2, which allows advective-transport observations to be used in the three-dimensional ground-water flow parameter-estimation model MODFLOW-2000. The ADV2 Package is compatible with some of the features in the Layer-Property Flow and Hydrogeologic-Unit Flow Packages, but is not compatible with the Block-Centered Flow or Generalized Finite-Difference Packages. The particle-tracking routine used in the ADV2 Package duplicates the semi-analytical method of MODPATH, as shown in a sample problem. Particles can be tracked in a forward or backward direction, and effects such as retardation can be simulated through manipulation of the effective-porosity value used to calculate velocity. Particles can be discharged at cells that are considered to be weak sinks, in which the sink applied does not capture all the water flowing into the cell, using one of two criteria: (1) if there is any outflow to a boundary condition such as a well or surface-water feature, or (2) if the outflow exceeds a user specified fraction of the cell budget. Although effective porosity could be included as a parameter in the regression, this capability is not included in this package. The weighted sum-of-squares objective function, which is minimized in the Parameter-Estimation Process, was augmented to include the square of the weighted x-, y-, and z-components of the differences between the simulated and observed advective-front locations at defined times, thereby including the direction of travel as well as the overall travel distance in the calibration process. The sensitivities of the particle movement to the parameters needed to minimize the objective function are calculated for any particle location using the exact sensitivity-equation
Parameterization and Monte Carlo solutions to PDF evolution equations
NASA Astrophysics Data System (ADS)
Suciu, Nicolae; Schüler, Lennart; Attinger, Sabine; Knabner, Peter
2015-04-01
The probability density function (PDF) of the chemical species concentrations transported in random environments is governed by unclosed evolution equations. The PDF is transported in the physical space by drift and diffusion processes described by coefficients derived by standard upscaling procedures. Its transport in the concentration space is described by a drift determined by reaction rates, in a closed form, as well as a term accounting for the sub-grid mixing process due to molecular diffusion and local scale hydrodynamic dispersion. Sub-grid mixing processes are usually described by models of the conditionally averaged diffusion flux or models of the conditional dissipation rate. We show that in certain situations mixing terms can also be derived, in the form of an Itô process, from simulated or measured concentration time series. Monte Carlo solutions to PDF evolution equations are usually constructed with systems of computational particles, which are well suited for highly dimensional advection-dominated problems. Such solutions require the fulfillment of specific consistency conditions relating the statistics of the random concentration field, function of both space and time, to that of the time random function describing an Itô process in physical and concentration spaces which governs the evolution of the system of particles. We show that the solution of the Fokker-Planck equation for the concentration-position PDF of the Itô process coincides with the solution of the PDF equation only for constant density flows in spatially statistically homogeneous systems. We also find that the solution of the Fokker-Planck equation is still equivalent to the solution of the PDF equation weighted by the variable density or by other conserved scalars. We illustrate the parameterization of the sub-grid mixing by time series and the Monte Carlo solution for a problem of contaminant transport in groundwater. The evolution of the system of computational particles whose
Advection and evolution of river basins in mountain ranges.
NASA Astrophysics Data System (ADS)
Castelltort, S.; Simpson, G.; Willett, S.
2009-04-01
Simpson (2006) have proposed a mechanism which involves (1) the idea that river networks in the lowland plains are incorporated in the orogen as it widens, and (2) that they do not change after their incorporation, thus "importing" a geometry acquired outside of the range independently of the tectonic and climatic influences acting inside the uplifting zone. This mechanisms implies rather a "static" view of river networks which serves as an alternative to models in which river networks continuously reorganize inside uplifting topography in such a way as to maintain a statistical geometry dictated solely by geomorphic processes. In the present work our approach to this problem is to measure and compare the form of river basins in the lowlands and in the uplands of the Himalayas, New-Zealand, Taiwan, the European Alps, the Pyrenees and the Apennines. We first present the method we employ to measure the shape of river basins and the data used. Second, we analyse and discuss our results which show a correlation between the shape of networks developed in the pro-lowlands of active orogens and their upland counterparts whereas such a correlation does not exist on the retro-side of the considered orogens. Our results thus support (1) the horizontal advection of river basins from the pro-lowlands to the pro-uplands, (2) a certain amount of reorganization by widening of basin boundaries, and (3) the existence of a different mechanism of drainage network evolution in the retro-side of the orogens. Castelltort, S., and Simpson, G., 2006, Basin Research, 18: 267-276. Hallet, B. and Molnar, P., 2001. J. Geophys. Res, 106: 13697-13709. Hovius, N., 1996, Basin Research, 8: 29-44.
Advective transport observations with MODPATH-OBS--documentation of the MODPATH observation process
Hanson, R.T.; Kauffman, L.K.; Hill, M.C.; Dickinson, J.E.; Mehl, S.W.
2013-01-01
The MODPATH-OBS computer program described in this report is designed to calculate simulated equivalents for observations related to advective groundwater transport that can be represented in a quantitative way by using simulated particle-tracking data. The simulated equivalents supported by MODPATH-OBS are (1) distance from a source location at a defined time, or proximity to an observed location; (2) time of travel from an initial location to defined locations, areas, or volumes of the simulated system; (3) concentrations used to simulate groundwater age; and (4) percentages of water derived from contributing source areas. Although particle tracking only simulates the advective component of conservative transport, effects of non-conservative processes such as retardation can be approximated through manipulation of the effective-porosity value used to calculate velocity based on the properties of selected conservative tracers. This program can also account for simple decay or production, but it cannot account for diffusion. Dispersion can be represented through direct simulation of subsurface heterogeneity and the use of many particles. MODPATH-OBS acts as a postprocessor to MODPATH, so that the sequence of model runs generally required is MODFLOW, MODPATH, and MODPATH-OBS. The version of MODFLOW and MODPATH that support the version of MODPATH-OBS presented in this report are MODFLOW-2005 or MODFLOW-LGR, and MODPATH-LGR. MODFLOW-LGR is derived from MODFLOW-2005, MODPATH 5, and MODPATH 6 and supports local grid refinement. MODPATH-LGR is derived from MODPATH 5. It supports the forward and backward tracking of particles through locally refined grids and provides the output needed for MODPATH_OBS. For a single grid and no observations, MODPATH-LGR results are equivalent to MODPATH 5. MODPATH-LGR and MODPATH-OBS simulations can use nearly all of the capabilities of MODFLOW-2005 and MODFLOW-LGR; for example, simulations may be steady-state, transient, or a combination
NASA Astrophysics Data System (ADS)
Liu, Chongxuan; Szecsody, Jim E.; Zachara, John M.; Ball, William P.
The generalized integral transform technique (GITT) is applied to solve the one-dimensional advection-dispersion equation (ADE) in heterogeneous porous media coupled with either linear or nonlinear sorption and decay. When both sorption and decay are linear, analytical solutions are obtained using the GITT for one-dimensional ADEs with spatially and temporally variable flow and dispersion coefficient and arbitrary initial and boundary conditions. When either sorption or decay is nonlinear the solutions to ADEs with the GITT are hybrid analytical-numerical. In both linear and nonlinear cases, the forward and inverse integral transforms for the problems described in the paper are apparent and straightforward. Some illustrative examples with linear sorption and decay are presented to demonstrate the application and check the accuracy of the derived analytical solutions. The derived hybrid analytical-numerical solutions are checked against a numerical approach and demonstratively applied to a nonlinear transport example, which simulates a simplified system of iron oxide bioreduction with nonlinear sorption and nonlinear reaction kinetics.
Dispersive properties of multisymplectic integrators
NASA Astrophysics Data System (ADS)
Schober, C. M.; Wlodarczyk, T. H.
2008-05-01
Multisymplectic (MS) integrators, i.e. numerical schemes which exactly preserve a discrete space-time symplectic structure, are a new class of structure preserving algorithms for solving Hamiltonian PDEs. In this paper we examine the dispersive properties of MS integrators for the linear wave and sine-Gordon equations. In particular a leapfrog in space and time scheme (a member of the Lobatto Runge-Kutta family of methods) and the Preissman box scheme are considered. We find the numerical dispersion relations are monotonic and that the sign of the group velocity is preserved. The group velocity dispersion (GVD) is found to provide significant information and succinctly explain the qualitative differences in the numerical solutions obtained with the different schemes. Further, the numerical dispersion relations for the linearized sine-Gordon equation provides information on the ability of the MS integrators to capture the sine-Gordon dynamics. We are able to link the numerical dispersion relations to the total energy of the various methods, thus providing information on the coarse grid behavior of MS integrators in the nonlinear regime.
Dispersive solitons in magneto-optic waveguides
NASA Astrophysics Data System (ADS)
Vega-Guzman, Jose; Ullah, Malik Zaka; Asma, Mir; Zhou, Qin; Biswas, Anjan
2017-03-01
This paper obtains bright, dark and singular dispersive optical soliton solutions with magneto-optic waveguides. The governing equation is the coupled Schrödinger-Hirota equation. The existence criteria of these solitons are also presented. Both Kerr law and power law of nonlinearity are considered.
Soliton trapping of dispersive waves in photonic crystal fiber with two zero dispersive wavelengths.
Wang, Weibin; Yang, Hua; Tang, Pinghua; Zhao, Chujun; Gao, Jing
2013-05-06
Based on the generalized nonlinear Schrödinger equation, we present a numerical study of trapping of dispersive waves by solitons during supercontinuum generation in photonic crystal fibers pumped with femtosecond pulses in the anomalous dispersion region. Numerical simulation results show that the generated supercontinuum is bounded by two branches of dispersive waves, namely blue-shifted dispersive waves (B-DWs) and red-shifted dispersive waves (R-DWs). We find a novel phenomenon that not only B-DWs but also R-DWs can be trapped by solitons across the zero-dispersion wavelength when the group-velocity matching between the soliton and the dispersive wave is satisfied, which may led to the generation of new spectral components via mixing of solitons and dispersive waves. Mixing of solitons with dispersive waves has been shown to play an important role in shaping not only the edge of the supercontinuum, but also its central part around the higher zero-dispersion wavelength. Further, we show that the phenomenon of soliton trapping of dispersive waves in photonic crystal fibers with two zero-dispersion wavelengths has a very close relationship with pumping power and the interval between two zero-dispersion wavelengths. In order to clearly display the evolution of soliton trapping of dispersive waves, the spectrogram of output pulses is observed using cross-correlation frequency-resolved optical gating technique (XFROG).
NASA Technical Reports Server (NTRS)
Lang, Steve; Tao, W.-K.; Simpson, J.; Ferrier, B.; Einaudi, Franco (Technical Monitor)
2001-01-01
Six different convective-stratiform separation techniques, including a new technique that utilizes the ratio of vertical and terminal velocities, are compared and evaluated using two-dimensional numerical simulations of a tropical [Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE)] and midlatitude continental [Preliminary Regional Experiment for STORM-Central (PRESTORM)] squall line. The simulations are made using two different numerical advection schemes: 4th order and positive definite advection. Comparisons are made in terms of rainfall, cloud coverage, mass fluxes, apparent heating and moistening, mean hydrometeor profiles, CFADs (Contoured Frequency with Altitude Diagrams), microphysics, and latent heating retrieval. Overall, it was found that the different separation techniques produced results that qualitatively agreed. However, the quantitative differences were significant. Observational comparisons were unable to conclusively evaluate the performance of the techniques. Latent heating retrieval was shown to be sensitive to the use of separation technique mainly due to the stratiform region for methods that found very little stratiform rain. The midlatitude PRESTORM simulation was found to be nearly invariant with respect to advection type for most quantities while for TOGA COARE fourth order advection produced numerous shallow convective cores and positive definite advection fewer cells that were both broader and deeper penetrating above the freezing level.
Advection of Microphysical Scalars in Terminal Area Simulation System (TASS)
NASA Technical Reports Server (NTRS)
Ahmad, Nashat N.; Proctor, Fred H.
2011-01-01
The Terminal Area Simulation System (TASS) is a large eddy scale atmospheric flow model with extensive turbulence and microphysics packages. It has been applied successfully in the past to a diverse set of problems ranging from prediction of severe convective events (Proctor et al. 2002), tracking storms and for simulating weapons effects such as the dispersion and fallout of fission debris (Bacon and Sarma 1991), etc. More recently, TASS has been used for predicting the transport and decay of wake vortices behind aircraft (Proctor 2009). An essential part of the TASS model is its comprehensive microphysics package, which relies on the accurate computation of microphysical scalar transport. This paper describes an evaluation of the Leonard scheme implemented in the TASS model for transporting microphysical scalars. The scheme is validated against benchmark cases with exact solutions and compared with two other schemes - a Monotone Upstream-centered Scheme for Conservation Laws (MUSCL)-type scheme after van Leer and LeVeque's high-resolution wave propagation method. Finally, a comparison between the schemes is made against an incident of severe tornadic super-cell convection near Del City, Oklahoma.
Liu, Gaisheng; Lu, Zhiming; Zhang, Dongxiao
2007-01-01
A new approach has been developed for solving solute transport problems in randomly heterogeneous media using the Karhunen-Loève-based moment equation (KLME) technique proposed by Zhang and Lu (2004). The KLME approach combines the Karhunen-Loève decomposition of the underlying random conductivity field and the perturbative and polynomial expansions of dependent variables including the hydraulic head, flow velocity, dispersion coefficient, and solute concentration. The equations obtained in this approach are sequential, and their structure is formulated in the same form as the original governing equations such that any existing simulator, such as Modular Three-Dimensional Multispecies Transport Model for Simulation of Advection, Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems (MT3DMS), can be directly applied as the solver. Through a series of two-dimensional examples, the validity of the KLME approach is evaluated against the classical Monte Carlo simulations. Results indicate that under the flow and transport conditions examined in this work, the KLME approach provides an accurate representation of the mean concentration. For the concentration variance, the accuracy of the KLME approach is good when the conductivity variance is 0.5. As the conductivity variance increases up to 1.0, the mismatch on the concentration variance becomes large, although the mean concentration can still be accurately reproduced by the KLME approach. Our results also indicate that when the conductivity variance is relatively large, neglecting the effects of the cross terms between velocity fluctuations and local dispersivities, as done in some previous studies, can produce noticeable errors, and a rigorous treatment of the dispersion terms becomes more appropriate.
Siebert, Julien; Alonso, Sergio; Bär, Markus; Schöll, Eckehard
2014-05-01
A one-component bistable reaction-diffusion system with asymmetric nonlocal coupling is derived as a limiting case of a two-component activator-inhibitor reaction-diffusion model with differential advection. The effects of asymmetric nonlocal couplings in such a bistable reaction-diffusion system are then compared to the previously studied case of a system with symmetric nonlocal coupling. We carry out a linear stability analysis of the spatially homogeneous steady states of the model and numerical simulations of the model to show how the asymmetric nonlocal coupling controls and alters the steady states and the front dynamics in the system. In a second step, a third fast reaction-diffusion equation is included which induces the formation of more complex patterns. A linear stability analysis predicts traveling waves for asymmetric nonlocal coupling, in contrast to a stationary Turing patterns for a system with symmetric nonlocal coupling. These findings are verified by direct numerical integration of the full equations with nonlocal coupling.
Existence of Traveling Waves for the Generalized F-KPP Equation.
Kollár, Richard; Novak, Sebastian
2017-03-01
Variation in genotypes may be responsible for differences in dispersal rates, directional biases, and growth rates of individuals. These traits may favor certain genotypes and enhance their spatiotemporal spreading into areas occupied by the less advantageous genotypes. We study how these factors influence the speed of spreading in the case of two competing genotypes under the assumption that spatial variation of the total population is small compared to the spatial variation of the frequencies of the genotypes in the population. In that case, the dynamics of the frequency of one of the genotypes is approximately described by a generalized Fisher-Kolmogorov-Petrovskii-Piskunov (F-KPP) equation. This generalized F-KPP equation with (nonlinear) frequency-dependent diffusion and advection terms admits traveling wave solutions that characterize the invasion of the dominant genotype. Our existence results generalize the classical theory for traveling waves for the F-KPP with constant coefficients. Moreover, in the particular case of the quadratic (monostable) nonlinear growth-decay rate in the generalized F-KPP we study in detail the influence of the variance in diffusion and mean displacement rates of the two genotypes on the minimal wave propagation speed.
Flow and axial dispersion in a sinusoidal-walled tube: Effects of inertial and unsteady flows
NASA Astrophysics Data System (ADS)
Richmond, Marshall C.; Perkins, William A.; Scheibe, Timothy D.; Lambert, Adam; Wood, Brian D.
2013-12-01
In this work, we consider a sinusoidal-walled tube (a three-dimensional tube with sinusoidally-varying diameter) as a simplified conceptualization of flow in porous media. Direct numerical simulation using computational fluid dynamics (CFD) methods was used to compute velocity fields by solving the Navier-Stokes equations, and also to numerically solve the volume averaging closure problem, for a range of Reynolds numbers (Re) spanning the low-Re to inertial flow regimes, including one simulation at Re=449 for which unsteady flow was observed. The longitudinal dispersion observed for the flow was computed using a random walk particle tracking method, and this was compared to the longitudinal dispersion predicted from a volume-averaged macroscopic mass balance using the method of volume averaging; the results of the two methods were consistent. Our results are compared to experimental measurements of dispersion in porous media and to previous theoretical results for both the low-Re, Stokes flow regime and for values of Re representing the steady inertial regime. In the steady inertial regime, a power-law increase in the effective longitudinal dispersion (DL) with Re was found, and this is consistent with previous results. This rapid rate of increase is caused by trapping of solute in expansions due to flow separation (eddies). One unsteady (but non-turbulent) flow case (Re=449) was also examined. For this case, the rate of increase of DL with Re was smaller than that observed at lower Re. Velocity fluctuations in this regime lead to increased rates of solute mass transfer between the core flow and separated flow regions, thus diminishing the amount of tailing caused by solute trapping in eddies and thereby reducing longitudinal dispersion. The observed tailing was further explored through analysis of concentration skewness (third moment) and its assymptotic convergence to conventional advection-dispersion behavior (skewness = 0). The method of volume averaging was
Dense-Gas Dispersion in Complex Terrain (PREPRINT)
1993-05-01
public release; distribution unlimited. A dense-gas version of the ADPIC Lagrangian particle, advection-diffusion model has been developed to...of momentum principles along with the ideal gas law equation of state for a mixture of gases. ADPIC , which is generally run in conjunction with a...versatility of coupling the new dense-gas ADPIC with alternative wind flow models. The new dense-gas ADPIC has been used to simulate the atmospheric
Tomography-based monitoring of isothermal snow metamorphism under advective conditions
NASA Astrophysics Data System (ADS)
Ebner, P. P.; Schneebeli, M.; Steinfeld, A.
2015-07-01
Time-lapse X-ray microtomography was used to investigate the structural dynamics of isothermal snow metamorphism exposed to an advective airflow. The effect of diffusion and advection across the snow pores on the snow microstructure were analysed in controlled laboratory experiments and possible effects on natural snowpacks discussed. The 3-D digital geometry obtained by tomographic scans was used in direct pore-level numerical simulations to determine the effective permeability. The results showed that isothermal advection with saturated air have no influence on the coarsening rate that is typical for isothermal snow metamorphism. Isothermal snow metamorphism is driven by sublimation deposition caused by the Kelvin effect and is the limiting factor independently of the transport regime in the pores.
NASA Technical Reports Server (NTRS)
Mcfarland, M. J.
1975-01-01
Horizontal wind components, potential temperature, and mixing ratio fields associated with a severe storm environment in the south central U.S. were analyzed from synoptic upper air observations with a nonhomogeneous, anisotropic weighting function. Each data field was filtered with variational optimization analysis techniques. Variational optimization analysis was also performed on the vertical motion field and was used to produce advective forecasts of the potential temperature and mixing ratio fields. Results show that the dry intrusion is characterized by warm air, the advection of which produces a well-defined upward motion pattern. A corresponding downward motion pattern comprising a deep vertical circulation in the warm air sector of the low pressure system was detected. The axes alignment of maximum dry and warm advection with the axis of the tornado-producing squall line also resulted.
Small-scale particle advection, manipulation and mixing: beyond the hydrodynamic scale.
Straube, Arthur V
2011-05-11
In this paper we discuss the problems of particle advection, manipulation and mixing at small scales. We start by considering reaction-advection-diffusion systems with the focus on mixing. We show how mixing advection affects the processes of reaction-diffusion and discuss mixing-induced instabilities. Further, we consider the problem of particle manipulation and discuss collective effects in systems comprising solid and compressible particles. We particularly discuss mechanisms of particle entrapment, the role of compressibility in the dynamics of bubbly liquids and nonequilibrium colloidal explosion. Finally, we address two issues related to the problem of wetting. First, we study the role of contact line motion for a sessile droplet (or a bubble) on an oscillating substrate. Second, we discuss an instability of a thin film leading to the formation of a fractal structure of droplets.
Large-eddy Advection in Evapotranspiration Estimates from an Array of Eddy Covariance Towers
NASA Astrophysics Data System (ADS)
Lin, X.; Evett, S. R.; Gowda, P. H.; Colaizzi, P. D.; Aiken, R.
2014-12-01
Evapotranspiration was continuously measured by an array of eddy covariance systems and large weighting lysimeter in a sorghum in Bushland, Texas in 2014. The advective divergence from both horizontal and vertical directions were measured through profile measurements above canopy. All storage terms were integrated from the depth of soil heat flux plate to the height of eddy covariance measurement. Therefore, a comparison between the eddy covariance system and large weighing lysimeter was conducted on hourly and daily basis. The results for the discrepancy between eddy covariance towers and the lysimeter will be discussed in terms of advection and storage contributions in time domain and frequency domain.
An extension of Prandtl-Batchelor theory and consequences for chaotic advection
NASA Astrophysics Data System (ADS)
Mezic, Igor
2002-09-01
We extend the Prandtl-Batchelor theory of steady laminar motion at large Reynolds number to derive conditions that steady three-dimensional Navier-Stokes flows have to satisfy. We combine these results with ergodic theory to show that flows with strong Beltrami property (e.g., ABC flows) cannot be a paradigm for chaotic advection in inertia-dominated boundary-driven three-dimensional flows. Our results indicate that viscous forces are responsible for chaotic advection in steady, three-dimensional boundary-driven Navier-Stokes flows at large Reynolds numbers.
The impact of air mass advection on aerosol optical properties over Gotland (Baltic Sea)
NASA Astrophysics Data System (ADS)
Zdun, Agnieszka; Rozwadowska, Anna; Kratzer, Susanne
2016-12-01
In the present paper, measurements of aerosol optical properties from the Gotland station of the AERONET network, combined with a two-stage cluster analysis of back trajectories of air masses moving over Gotland, were used to identify the main paths of air mass advection to the Baltic Sea and to relate them to aerosol optical properties, i.e. the aerosol optical thickness at the wavelength λ = 500 nm, AOT (500) and the Ångström exponent for the spectral range from 440 to 870 nm, α(440,870). One- to six-day long back trajectories ending at 300, 500 and 3000 m above the station were computed using the HYSPLIT model. The study shows that in the Gotland region, variability in aerosol optical thickness AOT(500) is more strongly related to advections in the boundary layer than to those in the free troposphere. The observed variability in AOT(500) was best explained by the advection speeds and directions given by clustering of 4-day backward trajectories of air arriving in the boundary layer at 500 m above the station. 17 clusters of 4-day trajectories arriving at altitude 500 m above the Gotland station (sea level) derived using two-stage cluster analysis differ from each other with respect to trajectory length, the speed of air mass movement and the direction of advection. They also show different cluster means of AOT(500) and α(440,870). The cluster mean AOT(500) ranges from 0.342 ± 0.012 for the continental clusters M2 (east-southeast advection with moderate speed) and 0.294 ± 0.025 for S5 (slow south-southeast advection) to 0.064 ± 0.002 and 0.069 ± 0.002 for the respective marine clusters L3 (fast west-northwest advection) and M3 (north-northwest advection with moderate speed). The cluster mean α(440,870) varies from 1.65-1.70 for the short-trajectory clusters to 0.98 ± 0.03 and 1.06 ± 0.03 for the Arctic marine cluster L4 (fast inflow from the north) and marine cluster L5 (fast inflow from the west) respectively.
Anninos, P
2002-02-11
Several advection algorithms are presented within the remap framework for unstructured mesh ALE codes. The methods discussed include a generic advection scheme based on a finite volume approach, and three groups of algorithms for the treatment of material boundary interfaces. The interface capturing algorithms belong to the Volume of Fluid (VoF) class of methods to approximate material interfaces from the local fractional volume of fluid distribution in arbitrary unstructured polyhedral meshes appropriate for the Kull code. Also presented are several schemes for extending single material radiation diffusion solvers to account for multi-material interfaces.
Variational integrators for nonvariational partial differential equations
NASA Astrophysics Data System (ADS)
Kraus, Michael; Maj, Omar
2015-08-01
Variational integrators for Lagrangian dynamical systems provide a systematic way to derive geometric numerical methods. These methods preserve a discrete multisymplectic form as well as momenta associated to symmetries of the Lagrangian via Noether's theorem. An inevitable prerequisite for the derivation of variational integrators is the existence of a variational formulation for the considered problem. Even though for a large class of systems this requirement is fulfilled, there are many interesting examples which do not belong to this class, e.g., equations of advection-diffusion type frequently encountered in fluid dynamics or plasma physics. On the other hand, it is always possible to embed an arbitrary dynamical system into a larger Lagrangian system using the method of formal (or adjoint) Lagrangians. We investigate the application of the variational integrator method to formal Lagrangians, and thereby extend the application domain of variational integrators to include potentially all dynamical systems. The theory is supported by physically relevant examples, such as the advection equation and the vorticity equation, and numerically verified. Remarkably, the integrator for the vorticity equation combines Arakawa's discretisation of the Poisson brackets with a symplectic time stepping scheme in a fully covariant way such that the discrete energy is exactly preserved. In the presentation of the results, we try to make the geometric framework of variational integrators accessible to non specialists.
Assessment of nitrate transport parameters using the advection-diffusion cell.
Aljazzar, Taiseer; Al-Qinna, Mohammed
2016-11-01
This study aimed to better understand nitrate transport in the soil system in a part of the state of North Rhine-Westphalia, in Germany, and to aid in the development of groundwater protection plans. An advection-diffusion (AD) cell was used in a miscible displacement experiment setup to characterize nitrate transport in 12 different soil samples from the study area. The three nitrate sorption isotherms were tested to define the exact nitrate interaction with the soil matrix. Soils varied in their properties which in its turn explain the variations in nitrate transport rates. Soil texture and organic matter content showed to have the most important effect on nitrate recovery and retardation. The miscible displacement experiment indicated a decrease in retardation by increasing sand fraction, and an increase in retardation by increasing soil organic matter content. Soil samples with high sand fractions (up to 94 %) exhibited low nitrate sorption capacity of less than 10 %, while soils with high organic matter content showed higher sorption of about 30 %. Based on parameterization for nitrate transport equation, the pore water velocity for both sandy and loamy soils were significantly different (P < 0.001). Pore water velocity in sandy soil (about 4 × 10(-3) m/s) was about 100 to 1000 larger than in loamy soils (8.7 × 10(-5) m/s). On the other hand, the reduction in nitrate transport in soils associated with high organic matter was due to fine pore pathways clogged by fine organic colloids. It is expected that the existing micro-phobicity increased the nitrate recovery from 9 to 32 % resulting in maximum diffusion rates of about 3.5 × 10(-5) m/s(2) in sandy soils (sample number CS-04) and about 1.4 × 10(-7) m/s(2) in silt loam soils (sample number FS-02).
NASA Astrophysics Data System (ADS)
Shotwell, S. Kalei; Hanselman, Dana H.; Belkin, Igor M.
2014-09-01
In fisheries stock assessment, reliable estimation of year-class strength is often hindered by lack of data on early life history stages and limited knowledge of the underlying environmental processes influencing survival through these stages. One solution to improving these estimates of year-class strength or recruitment is to first develop regional indices representing the spatial and temporal extent of a hypothesized feature influencing a species' recruitment. These covariates should then be integrated within a population model where a variety of model selection techniques may be conducted to test for a reduction in recruitment uncertainty. The best selected model(s) may provide insight for developing hypotheses of mechanisms influencing recruitment. Here we consider the influence of a large-scale oceanographic feature, the North Pacific Polar Front, on recruitment of Alaska sablefish (Anoplopoma fimbria). Our working hypothesis is that advection of oceanic properties along the Polar Front and associated currents plays a key role in shaping the oceanographic climate of Alaskan waters and, hence, the environment that sablefish encounter during their early life history. As a first step in this investigation, we developed time series of sea surface temperature along the Polar Front mean path. We then integrated this data into the recruitment equations of the sablefish assessment base model. Model selection was based on a multistage hypothesis testing procedure combined with cross-validation and a retrospective analysis of prediction error. The impact of the best model was expressed in terms of increased precision of recruitment estimates and proportional changes in female spawning biomass for both current estimates and in future projections. The best model suggested that colder than average wintertime sea surface temperatures in the central North Pacific represent oceanic conditions that create positive recruitment events for sablefish. The incorporation of this
Transport of nanoparticles with dispersant through biofilm coated drinking water sand filters.
Li, Zhen; Aly Hassan, Ashraf; Sahle-Demessie, Endalkachew; Sorial, George A
2013-11-01
This article characterizes, experimentally and theoretically, the transport and retention of engineered nanoparticles (NP) through sand filters at drinking water treatment plants (DWTPs) under realistic conditions. The transport of four commonly used NPs (ZnO, CeO2, TiO2, and Ag, with bare surfaces and coating agents) through filter beds filled with sands from either acid washed and calcined, freshly acquired filter media, and used filter media from active filter media, were investigated. The study was conducted using water obtained upstream of the sand filter at DWTP. The results have shown that capping agents have a determinant importance in the colloidal stability and transport of NPs through the different filter media. The presence of the biofilm in used filter media increased adsorption of NPs but its effects in retaining capped NPs was less significant. The data was used to build a mathematical model based on the advection-dispersion equation. The model was used to simulate the performance of a scale-up sand filter and the effects on filtration cycle of traditional sand filtration system used in DWTPs.
NASA Astrophysics Data System (ADS)
Jensen, Andrew D.; Lupo, Anthony R.
2014-06-01
In this note, equations for enstrophy and enstrophy advection are derived in terms of well-known quantities, assuming horizontal frictionless flow on a beta-plane. Specifically, enstrophy can be written in terms of the geopotential (or pressure), relative vorticity, zonal wind, and resultant deformation. Enstrophy advection is shown to be related to the time evolution of deformation and ageostrophic relative vorticity. Based on previous research, these terms may contribute to instability associated with atmospheric blocking development and decay.
Spatial Moment Equations for a Groundwater Plume with Degradation and Rate-Limited Sorption
In this note, we analytically derive the solution for the spatial moments of groundwater solute concentration distributions simulated by a one-dimensional model that assumes advective-dispersive transport with first-order degradation and rate-limited sorption. Sorption kinetics...
NASA Astrophysics Data System (ADS)
Leitch, A. S.; Nesic, Z.; Christen, A.; Black, T. A.
2010-12-01
opposing gradient in manual chamber-measured soil CO2 effluxes. The additional CO2 difference measurement period at the 2.6-m height (with IRGAs measuring at 2 Hz) also included 5 CSAT3 sonic anemometers measuring at the same locations at 10 Hz. The setup permits back-of-the-envelope calculation of horizontal turbulent CO2 flux divergence along the 73.5-m transect, a term in the scalar conservation equation which has received much interest but little quantification in the literature. The IRGAs also measured high frequency water vapour concentrations, permitting the calculation of (horizontal) turbulent and (horizontal and vertical) advective H2O fluxes. H2O fluxes other than the vertical turbulent flux are not routinely calculated, but may have the potential to shed light on the energy-balance closure problem in the same manner as advective CO2 fluxes comment on the friction velocity correction procedure. Horizontal turbulent carbon dioxide flux divergence and energy balance closure will be discussed, along with final conclusions for advective carbon dioxide fluxes at DF49.
NASA Astrophysics Data System (ADS)
Maiti, Soumyabrata; Chaudhury, Kaustav; DasGupta, Debabrata; Chakraborty, Suman
2013-01-01
Spatial distributions of particles carried by blood exhibit complex filamentary pattern under the combined effects of geometrical irregularities of the blood vessels and pulsating pumping by the heart. This signifies the existence of so called chaotic advection. In the present article, we argue that the understanding of such pathologically triggered chaotic advection is incomplete without giving due consideration to a major constituent of blood: abundant presence of red blood cells quantified by the hematocrit (HCT) concentration. We show that the hematocrit concentration in blood cells can alter the filamentary structures of the spatial distribution of advected particles in an intriguing manner. Our results reveal that there primarily are two major impacts of HCT concentrations towards dictating the chaotic dynamics of blood flow: changing the zone of influence of chaotic mixing and determining the enhancement of residence time of the advected particles away from the wall. This, in turn, may alter the extent of activation of platelets or other reactive biological entities, bearing immense consequence towards dictating the biophysical mechanisms behind possible life-threatening diseases originating in the circulatory system.
MECHANISM OF OUTFLOWS IN ACCRETION SYSTEM: ADVECTIVE COOLING CANNOT BALANCE VISCOUS HEATING?
Gu, Wei-Min
2015-01-20
Based on the no-outflow assumption, we investigate steady-state, axisymmetric, optically thin accretion flows in spherical coordinates. By comparing the vertically integrated advective cooling rate with the viscous heating rate, we find that the former is generally less than 30% of the latter, which indicates that the advective cooling itself cannot balance the viscous heating. As a consequence, for radiatively inefficient flows with low accretion rates such as M-dot ≲10{sup −3} M-dot {sub Edd}, where M-dot {sub Edd} is the Eddington accretion rate, the viscous heating rate will be larger than the sum of the advective cooling rate and the radiative cooling one. Thus, no thermal equilibrium can be established under the no-outflow assumption. We therefore argue that in such cases outflows ought to occur and take away more than 70% of the thermal energy generated by viscous dissipation. Similarly, for optically thick flows with extremely large accretion rates such as M-dot ≳10 M-dot {sub Edd}, outflows should also occur owing to the limited advection and the low efficiency of radiative cooling. Our results may help to understand the mechanism of outflows found in observations and numerical simulations.
NASA Astrophysics Data System (ADS)
Rogers, M. A.
2015-12-01
Using satellite observations from GOES-E and GOES-W platforms in concert with GFS-derived cloud-level winds and a standalone radiative transfer model, an advection-derived forecast for surface GHI over the continental United States, with intercomparison between forecasts for four zones over the CONUS and Central Pacific with SURFRAD results. Primary sources for error in advection-based forecasts, primarily driven by false- or mistimed ramp events are discussed, with identification of error sources quantified along with techniques used to improve advection-based forecasts to approximately 10% MAE for designated surface locations. Development of a blended steering wind product utilizing NWP output combined with satellite-derived winds from AMV techniques to improve 0-1 hour advection forecasts will be discussed. Additionally, the use of two years' of solar forecast observations in the development of a prototype probablistic forecast for ramp events will be shown, with the intent of increasing the use of satellite-derived forecasts for grid operators and optimizing integration of renewable resources into the power grid. Elements of the work were developed under the 'Public-Private-Academic Partnership to Advance Solar Power Forecasting' project spearheaded by the National Center for Atmospheric Research.
DEVELOPMENT AND DEMONSTRATION OF A BIDIRECTIONAL ADVECTIVE FLUX METER FOR SEDIMENT-WATER INTERFACE
A bidirectional advective flux meter for measuring water transport across the sediment-water interface has been successfully developed and field tested. The flow sensor employs a heat-pulse technique combined with a flow collection funnel for the flow measurement. Because the dir...
A Study of the Physical Processes of an Advection Fog Boundary Layer
NASA Astrophysics Data System (ADS)
Liu, Duan Yang; Yan, Wen Lian; Yang, Jun; Pu, Mei Juan; Niu, Sheng Jie; Li, Zi Hua
2016-01-01
A large quantity of advection fog appeared in the Yangtze River delta region between 1 and 2 December 2009. Here, we detail the fog formation and dissipation processes and the background weather conditions. The fog boundary layer and its formation and dissipation mechanisms have also been analyzed using field data recorded in a northern suburb of Nanjing. The results showed the following: (1) This advection fog was generated by interaction between advection of a north-east cold ground layer and a south-east warm upper layer. The double-inversion structure generated by this interaction between the cold and warm advections and steady south-east vapour transport was the main cause of this long-lasting fog. The double-inversion structure provided good thermal conditions for the thick fog, and the south-east vapour transport was not only conducive to maintaining the thickness of the fog but also sustained its long duration. (2) The fog-top altitude was over 600 m for most of the time, and the fog reduced visibility to less than 100 m for approximately 12 h. (3) The low-level jet near the lower inversion layer also played a role in maintaining the thick fog system by promoting heat, momentum and south-east vapour transport.
Differential operator multiplication method for fractional differential equations
NASA Astrophysics Data System (ADS)
Tang, Shaoqiang; Ying, Yuping; Lian, Yanping; Lin, Stephen; Yang, Yibo; Wagner, Gregory J.; Liu, Wing Kam
2016-11-01
Fractional derivatives play a very important role in modeling physical phenomena involving long-range correlation effects. However, they raise challenges of computational cost and memory storage requirements when solved using current well developed numerical methods. In this paper, the differential operator multiplication method is proposed to address the issues by considering a reaction-advection-diffusion equation with a fractional derivative in time. The linear fractional differential equation is transformed into an integer order differential equation by the proposed method, which can fundamentally fix the aforementioned issues for select fractional differential equations. In such a transform, special attention should be paid to the initial conditions for the resulting differential equation of higher integer order. Through numerical experiments, we verify the proposed method for both fractional ordinary differential equations and partial differential equations.
Global Regularity Results of the 2D Boussinesq Equations with Fractional Laplacian Dissipation
NASA Astrophysics Data System (ADS)
Ye, Zhuan; Xu, Xiaojing
2016-06-01
In this paper, we study the 2D Boussinesq equations with fractional Laplacian dissipation. In particular, we prove the global regularity of the smooth solutions of the 2D Boussinesq equations with a new range of fractional powers of the Laplacian. The main ingredient of the proof is the utilization of the Hölder estimates for advection fractional-diffusion equations as well as Littlewood-Paley technique.
Truncation effect on Taylor-Aris dispersion in lattice Boltzmann schemes: Accuracy towards stability
NASA Astrophysics Data System (ADS)
Ginzburg, Irina; Roux, Laetitia
2015-10-01
The Taylor dispersion in parabolic velocity field provides a well-known benchmark for advection-diffusion (ADE) schemes and serves as a first step towards accurate modeling of the high-order non-Gaussian effects in heterogeneous flow. While applying the Lattice Boltzmann ADE two-relaxation-times (TRT) scheme for a transport with given Péclet number (Pe) one should select six free-tunable parameters, namely, (i) molecular-diffusion-scale, equilibrium parameter; (ii) three families of equilibrium weights, assigned to the terms of mass, velocity and numerical-diffusion-correction, and (iii) two relaxation rates. We analytically and numerically investigate the respective roles of all these degrees of freedom in the accuracy and stability in the evolution of a Gaussian plume. For this purpose, the third- and fourth-order transient multi-dimensional analysis of the recurrence equations of the TRT ADE scheme is extended for a spatially-variable velocity field. The key point is in the coupling of the truncation and Taylor dispersion analysis which allows us to identify the second-order numerical correction δkT to Taylor dispersivity coefficient kT. The procedure is exemplified for a straight Poiseuille flow where δkT is given in a closed analytical form in equilibrium and relaxation parameter spaces. The predicted longitudinal dispersivity is in excellent agreement with the numerical experiments over a wide parameter range. In relatively small Pe-range, the relative dispersion error increases with Péclet number. This deficiency reduces in the intermediate and high Pe-range where it becomes Pe-independent and velocity-amplitude independent. Eliminating δkT by a proper parameter choice and employing specular reflection for zero flux condition on solid boundaries, the d2Q9 TRT ADE scheme may reproduce the Taylor-Aris result quasi-exactly, from very coarse to fine grids, and from very small to arbitrarily high Péclet numbers. Since free-tunable product of two
NASA Astrophysics Data System (ADS)
Prentis, Jeffrey J.
1996-05-01
One of the most challenging goals of a physics teacher is to help students see that the equations of physics are connected to each other, and that they logically unfold from a small number of basic ideas. Derivations contain the vital information on this connective structure. In a traditional physics course, there are many problem-solving exercises, but few, if any, derivation exercises. Creating an equation poem is an exercise to help students see the unity of the equations of physics, rather than their diversity. An equation poem is a highly refined and eloquent set of symbolic statements that captures the essence of the derivation of an equation. Such a poetic derivation is uncluttered by the extraneous details that tend to distract a student from understanding the essential physics of the long, formal derivation.
Young, C.W.
1997-10-01
In 1967, Sandia National Laboratories published empirical equations to predict penetration into natural earth materials and concrete. Since that time there have been several small changes to the basic equations, and several more additions to the overall technique for predicting penetration into soil, rock, concrete, ice, and frozen soil. The most recent update to the equations was published in 1988, and since that time there have been changes in the equations to better match the expanding data base, especially in concrete penetration. This is a standalone report documenting the latest version of the Young/Sandia penetration equations and related analytical techniques to predict penetration into natural earth materials and concrete. 11 refs., 6 tabs.
NASA Astrophysics Data System (ADS)
Peleg, Nadav; Fatichi, Simone; Burlando, Paolo
2015-04-01
A new stochastic approach to generate wind advection, cloud cover and precipitation fields is presented with the aim of formulating a space-time weather generator characterized by fields with high spatial and temporal resolution (e.g., 1 km x 1 km and 5 min). Its use is suitable for stochastic downscaling of climate scenarios in the context of hydrological, ecological and geomorphological applications. The approach is based on concepts from the Advanced WEather GENerator (AWE-GEN) presented by Fatichi et al. (2011, Adv. Water Resour.), the Space-Time Realizations of Areal Precipitation model (STREAP) introduced by Paschalis et al. (2013, Water Resour. Res.), and the High-Resolution Synoptically conditioned Weather Generator (HiReS-WG) presented by Peleg and Morin (2014, Water Resour. Res.). Advection fields are generated on the basis of the 500 hPa u and v wind direction variables derived from global or regional climate models. The advection velocity and direction are parameterized using Kappa and von Mises distributions respectively. A random Gaussian fields is generated using a fast Fourier transform to preserve the spatial correlation of advection. The cloud cover area, total precipitation area and mean advection of the field are coupled using a multi-autoregressive model. The approach is relatively parsimonious in terms of computational demand and, in the context of climate change, allows generating many stochastic realizations of current and projected climate in a fast and efficient way. A preliminary test of the approach is presented with reference to a case study in a complex orography terrain in the Swiss Alps.
Advective removal of intraparticle uranium from contaminated vadose zone sediments, Hanford, U.S.
Ilton, Eugene S; Qafoku, Nikolla P; Liu, Chongxuan; Moore, Dean A; Zachara, John M
2008-03-01
A column study on U(VI)-contaminated vadose zone sediments from the Hanford Site, WA, was performed to investigate U(VI) release kinetics with water advection and variable geochemical conditions. The sediments were collected from an area adjacent to and below tank BX-102 that was contaminated as a result of a radioactive tank waste overfill event. The primary reservoir for U(VI) in the sediments are micrometer-size precipitates composed of nanocrystallite aggregates of a Na-U-Silicate phase, most likely Na-boltwoodite, that nucleated and grew within microfractures of the plagioclase component of sand-sized granitic clasts. Two sediment samples, with different U(VI) concentrations and intraparticle mass transfer properties, were leached with advective flows of three different solutions. The influent solutions were all calcite-saturated and in equilibrium with atmospheric CO2. One solution was prepared from DI water, the second was a synthetic groundwater (SGW) with elevated Na that mimicked groundwater at the Hanford site, and the third was the same SGW but with both elevated Na and Si. The latter two solutions were employed, in part, to test the effect of saturation state on U(VI) release. For both sediments, and all three electrolytes, there was an initial rapid release of U(VI) to the advecting solution followed by slower near steady-state release. U(VI)aq concentrations increased during subsequent stop-flow events. The electrolytes with elevated Na and Si depressed U(VL)aq concentrations in effluent solutions. Effluent U(VI)aq concentrations for both sediments and all three electrolytes were simulated reasonably well by a three domain model (the advecting fluid, fractures, and matrix) that coupled U(VI) dissolution, intraparticle U(VI)aq diffusion, and interparticle advection, where diffusion and dissolution properties were parameterized in a previous batch study.
Continuous time series of dissolved oxygen (DO) have been used to compute estimates of metabolism in aquatic ecosystems. Central to this open water or "Odum" method is the assumption that the DO time is not strongly affected by advection and that effects due to advection or mixin...
Electromagnetic energy momentum in dispersive media
Philbin, T. G.
2011-01-15
The standard derivations of electromagnetic energy and momentum in media take Maxwell's equations as the starting point. It is well known that for dispersive media this approach does not directly yield exact expressions for the energy and momentum densities. Although Maxwell's equations fully describe electromagnetic fields, the general approach to conserved quantities in field theory is not based on the field equations, but rather on the action. Here an action principle for macroscopic electromagnetism in dispersive, lossless media is used to derive the exact conserved energy-momentum tensor. The time-averaged energy density reduces to Brillouin's simple formula when the fields are monochromatic. The time-averaged momentum density for monochromatic fields corresponds to the familiar Minkowski expression DxB, but for general fields in dispersive media the momentum density does not have the Minkowski value. The results are unaffected by the debate over momentum balance in light-matter interactions.
Numerical Study of Fractional Ensemble Average Transport Equations
NASA Astrophysics Data System (ADS)
Kim, S.; Park, Y.; Gyeong, C. B.; Lee, O.
2014-12-01
In this presentation, a newly developed theory is applied to the case of stationary and non-stationary stochastic advective flow field, and a numerical solution method is presented for the resulting fractional Fokker-Planck equation (fFPE), which describes the evolution of the probability density function (PDF) of contaminant concentration. The derived fFPE is evaluated for three different form: 1) purely advective form, 2) second-order moment form and 3) second-order cumulant form. The Monte Carlo analysis of the fractional governing equation is then performed in a stochastic flow field, generated by a fractional Brownian motion for the stationary and non-stationary stochastic advection, in order to provide a benchmark for the results obtained from the fFPEs. When compared to the Monte Carlo simulation based PDFs and their ensemble average, the second-order cumulant form gives a good fit in terms of the shape and mode of the PDF of the contaminant concentration. Therefore, it is quite promising that the non-Fickian transport behavior can be modeled by the derived fractional ensemble average transport equations either by means of the long memory in the underlying stochastic flow, or by means of the time-space non-stationarity of the underlying stochastic flow, or by means of the time and space fractional derivatives of the transport equations.
Integrability test for discrete equations via generalized symmetries
Levi, D.; Yamilov, R. I.
2010-12-23
In this article we present some integrability conditions for partial difference equations obtained using the formal symmetries approach. We apply them to find integrable partial difference equations contained in a class of equations obtained by the multiple scale analysis of the general multilinear dispersive difference equation defined on the square.
NASA Astrophysics Data System (ADS)
Mazaheri, Alireza; Nishikawa, Hiroaki
2016-09-01
We propose arbitrary high-order discontinuous Galerkin (DG) schemes that are designed based on a first-order hyperbolic advection-diffusion formulation of the target governing equations. We present, in details, the efficient construction of the proposed high-order schemes (called DG-H), and show that these schemes have the same number of global degrees-of-freedom as comparable conventional high-order DG schemes, produce the same or higher order of accuracy solutions and solution gradients, are exact for exact polynomial functions, and do not need a second-derivative diffusion operator. We demonstrate that the constructed high-order schemes give excellent quality solution and solution gradients on irregular triangular elements. We also construct a Weighted Essentially Non-Oscillatory (WENO) limiter for the proposed DG-H schemes and apply it to discontinuous problems. We also make some accuracy comparisons with conventional DG and interior penalty schemes. A relative qualitative cost analysis is also reported, which indicates that the high-order schemes produce orders of magnitude more accurate results than the low-order schemes for a given CPU time. Furthermore, we show that the proposed DG-H schemes are nearly as efficient as the DG and Interior-Penalty (IP) schemes as these schemes produce results that are relatively at the same error level for approximately a similar CPU time.
TWO-LEVEL TIME MARCHING SCHEME USING SPLINES FOR SOLVING THE ADVECTION EQUATION. (R826371C004)
A new numerical algorithm using quintic splines is developed and analyzed: quintic spline Taylor-series expansion (QSTSE). QSTSE is an Eulerian flux-based scheme that uses quintic splines to compute space derivatives and Taylor series expansion to march in time. The new scheme...
Atmospheric dispersion of natural carbon dioxide emissions on Vulcano Island, Italy
NASA Astrophysics Data System (ADS)
Granieri, D.; Carapezza, M. L.; Barberi, F.; Ranaldi, M.; Ricci, T.; Tarchini, L.
2014-07-01
La Fossa quiescent volcano and its surrounding area on the Island of Vulcano (Italy) are characterized by intensive, persistent degassing through both fumaroles and diffuse soil emissions. Periodic degassing crises occur, with marked increase in temperature and steam and gas output (mostly CO2) from crater fumaroles and in CO2 soil diffuse emission from the crater area as well as from the volcano flanks and base. The gas hazard of the most inhabited part of the island, Vulcano Porto, was investigated by simulating the CO2 dispersion in the atmosphere under different wind conditions. The DISGAS (DISpersion of GAS) code, an Eulerian model based on advection-diffusion equations, was used together with the mass-consistent Diagnostic Wind Model. Numerical simulations were validated by measurements of air CO2 concentration inside the village and along the crater's rim by means of a Soil CO2 Automatic Station and a Tunable Diode Laser device. The results show that in the village of Vulcano Porto, the CO2 air concentration is mostly due to local soil degassing, while the contribution from the crater gas emission is negligible at the breathing height for humans and always remains well below the lowest indoor CO2 concentration threshold recommended by the health authorities (1000 ppm). Outdoor excess CO2 maxima up to 200 ppm above local background CO2 air concentration are estimated in the center of the village and up to 100 ppm in other zones. However, in some ground excavations or in basements the health code threshold can be exceeded. In the crater area, because of the combined effect of fumaroles and diffuse soil emissions, CO2 air concentrations can reach 5000-7000 ppm in low-wind conditions and pose a health hazard for visitors.
Numerical Experiments on Advective Transport in Large Three-Dimensional Discrete Fracture Networks
NASA Astrophysics Data System (ADS)
Makedonska, N.; Painter, S. L.; Karra, S.; Gable, C. W.
2013-12-01
Modeling of flow and solute transport in discrete fracture networks is an important approach for understanding the migration of contaminants in impermeable hard rocks such as granite, where fractures provide dominant flow and transport pathways. The discrete fracture network (DFN) model attempts to mimic discrete pathways for fluid flow through a fractured low-permeable rock mass, and may be combined with particle tracking simulations to address solute transport. However, experience has shown that it is challenging to obtain accurate transport results in three-dimensional DFNs because of the high computational burden and difficulty in constructing a high-quality unstructured computational mesh on simulated fractures. An integrated DFN meshing [1], flow, and particle tracking [2] simulation capability that enables accurate flow and particle tracking simulation on large DFNs has recently been developed. The new capability has been used in numerical experiments on advective transport in large DFNs with tens of thousands of fractures and millions of computational cells. The modeling procedure starts from the fracture network generation using a stochastic model derived from site data. A high-quality computational mesh is then generated [1]. Flow is then solved using the highly parallel PFLOTRAN [3] code. PFLOTRAN uses the finite volume approach, which is locally mass conserving and thus eliminates mass balance problems during particle tracking. The flow solver provides the scalar fluxes on each control volume face. From the obtained fluxes the Darcy velocity is reconstructed for each node in the network [4]. Velocities can then be continuously interpolated to any point in the domain of interest, thus enabling random walk particle tracking. In order to describe the flow field on fractures intersections, the control volume cells on intersections are split into four planar polygons, where each polygon corresponds to a piece of a fracture near the intersection line. Thus
Perko, Janez; Patel, Ravi A
2014-05-01
The paper presents an approach that extends the flexibility of the standard lattice Boltzmann single relaxation time scheme in terms of spatial variation of dissipative terms (e.g., diffusion coefficient) and stability for high Péclet mass transfer problems. Spatial variability of diffusion coefficient in SRT is typically accommodated through the variation of relaxation time during the collision step. This method is effective but cannot deal with large diffusion coefficient variations, which can span over several orders of magnitude in some natural systems. The approach explores an alternative way of dealing with large diffusion coefficient variations in advection-diffusion transport systems by introducing so-called diffusion velocity. The diffusion velocity is essentially an additional convective term that replaces variations in diffusion coefficients vis-à-vis a chosen reference diffusion coefficient which defines the simulation time step. Special attention is paid to the main idea behind the diffusion velocity formulation and its implementation into the lattice Boltzmann framework. Finally, the performance, stability, and accuracy of the diffusion velocity formulation are discussed via several advection-diffusion transport benchmark examples. These examples demonstrate improved stability and flexibility of the proposed scheme with marginal consequences on the numerical performance.
Plasma Dispersion Function for the Kappa Distribution
NASA Technical Reports Server (NTRS)
Podesta, John J.
2004-01-01
The plasma dispersion function is computed for a homogeneous isotropic plasma in which the particle velocities are distributed according to a Kappa distribution. An ordinary differential equation is derived for the plasma dispersion function and it is shown that the solution can be written in terms of Gauss' hypergeometric function. Using the extensive theory of the hypergeometric function, various mathematical properties of the plasma dispersion function are derived including symmetry relations, series expansions, integral representations, and closed form expressions for integer and half-integer values of K.
Particulate export vs lateral advection in the Antarctic Polar Front (Southern Pacific Ocean)
NASA Astrophysics Data System (ADS)
Tesi, T.; Langone, L.; Ravaioli, M.; Capotondi, L.; Giglio, F.
2012-04-01
The overarching goal of our study was to describe and quantify the influence of lateral advection relative to the vertical export in the Antarctic Polar Front (Southern Pacific Ocean). In areas where lateral advection of particulate material is significant, budgets of bioactive elements can be inaccurate if fluxes through the water column and to the seabed are exclusively interpreted as passive sinking of particles. However, detailed information on the influence of lateral advection in the water column in the southern ocean is lacking. With this in mind, our study focused between the twilight zone (i.e. mesopelagic) and the benthic nepheloid layer to understand the relative importance of lateral flux with increasing water depth. Measurements were performed south of the Antarctic Polar Front for 1 year (January 10th 1999-January 3rd 2000) at 900, 1300, 2400, and 3700 m from the sea surface. The study was carried out using a 3.5 km long mooring line instrumented with sediment traps, current meters and sensors of temperature and conductivity. Sediment trap samples were characterized via several parameters including total mass flux, elemental composition (organic carbon, total nitrogen, biogenic silica, and calcium carbonate), concentration of metals (aluminum, iron, barium, and manganese), 210Pb activity, and foraminifera taxonomy. High fluxes of biogenic particles were observed in both summer 1999 and 2000 as a result of seasonal algal blooms associated with sea ice retreat and water column stratification. During no-productive periods, several high energy events occurred and resulted in advecting resuspended biogenic particles from flat-topped summits of the Pacific Antarctic Ridge. Whereas the distance between seabed and uppermost sediment traps was sufficient to avoid lateral advection processes, resuspension was significant in the lowermost sediment traps accounting for ~60 and ~90% of the material caught at 2400 and 3700 m, respectively. Samples collected during
Factorizable Schemes for the Equations of Fluid Flow
NASA Technical Reports Server (NTRS)
Sidilkover, David
1999-01-01
We present an upwind high-resolution factorizable (UHF) discrete scheme for the compressible Euler equations that allows to distinguish between full-potential and advection factors at the discrete level. The scheme approximates equations in their general conservative form and is related to the family of genuinely multidimensional upwind schemes developed previously and demonstrated to have good shock-capturing capabilities. A unique property of this scheme is that in addition to the aforementioned features it is also factorizable, i.e., it allows to distinguish between full-potential and advection factors at the discrete level. The latter property facilitates the construction of optimally efficient multigrid solvers. This is done through a relaxation procedure that utilizes the factorizability property.
Smelling home can prevent dispersal of reef fish larvae
Gerlach, Gabriele; Atema, Jelle; Kingsford, Michael J.; Black, Kerry P.; Miller-Sims, Vanessa
2007-01-01
Many marine fish and invertebrates show a dual life history where settled adults produce dispersing larvae. The planktonic nature of the early larval stages suggests a passive dispersal model where ocean currents would quickly cause panmixis over large spatial scales and prevent isolation of populations, a prerequisite for speciation. However, high biodiversity and species abundance in coral reefs contradict this panmixis hypothesis. Although ocean currents are a major force in larval dispersal, recent studies show far greater retention than predicted by advection models. We investigated the role of animal behavior in retention and homing of coral reef fish larvae resulting in two important discoveries: (i) Settling larvae are capable of olfactory discrimination and prefer the odor of their home reef, thereby demonstrating to us that nearby reefs smell different. (ii) Whereas one species showed panmixis as predicted from our advection model, another species showed significant genetic population substructure suggestive of strong homing. Thus, the smell of reefs could allow larvae to choose currents that return them to reefs in general and natal reefs in particular. As a consequence, reef populations can develop genetic differences that might lead to reproductive isolation. PMID:17213323
Applying Dispersive Changes to Lagrangian Particles in Groundwater Transport Models
Konikow, L.F.
2010-01-01
Method-of-characteristics groundwater transport models require that changes in concentrations computed within an Eulerian framework to account for dispersion be transferred to moving particles used to simulate advective transport. A new algorithm was developed to accomplish this transfer between nodal values and advecting particles more precisely and realistically compared to currently used methods. The new method scales the changes and adjustments of particle concentrations relative to limiting bounds of concentration values determined from the population of adjacent nodal values. The method precludes unrealistic undershoot or overshoot for concentrations of individual particles. In the new method, if dispersion causes cell concentrations to decrease during a time step, those particles in the cell having the highest concentration will decrease the most, and those with the lowest concentration will decrease the least. The converse is true if dispersion is causing concentrations to increase. Furthermore, if the initial concentration on a particle is outside the range of the adjacent nodal values, it will automatically be adjusted in the direction of the acceptable range of values. The new method is inherently mass conservative. ?? US Government 2010.
Applying dispersive changes to Lagrangian particles in groundwater transport models
Konikow, Leonard F.
2010-01-01
Method-of-characteristics groundwater transport models require that changes in concentrations computed within an Eulerian framework to account for dispersion be transferred to moving particles used to simulate advective transport. A new algorithm was developed to accomplish this transfer between nodal values and advecting particles more precisely and realistically compared to currently used methods. The new method scales the changes and adjustments of particle concentrations relative to limiting bounds of concentration values determined from the population of adjacent nodal values. The method precludes unrealistic undershoot or overshoot for concentrations of individual particles. In the new method, if dispersion causes cell concentrations to decrease during a time step, those particles in the cell having the highest concentration will decrease the most, and those with the lowest concentration will decrease the least. The converse is true if dispersion is causing concentrations to increase. Furthermore, if the initial concentration on a particle is outside the range of the adjacent nodal values, it will automatically be adjusted in the direction of the acceptable range of values. The new method is inherently mass conservative.
Kinetic equation for nonlinear resonant wave-particle interaction
NASA Astrophysics Data System (ADS)
Artemyev, A. V.; Neishtadt, A. I.; Vasiliev, A. A.; Mourenas, D.
2016-09-01
We investigate the nonlinear resonant wave-particle interactions including the effects of particle (phase) trapping, detrapping, and scattering by high-amplitude coherent waves. After deriving the relationship between probability of trapping and velocity of particle drift induced by nonlinear scattering (phase bunching), we substitute this relation and other characteristic equations of wave-particle interaction into a kinetic equation for the particle distribution function. The final equation has the form of a Fokker-Planck equation with peculiar advection and collision terms. This equation fully describes the evolution of particle momentum distribution due to particle diffusion, nonlinear drift, and fast transport in phase-space via trapping. Solutions of the obtained kinetic equation are compared with results of test particle simulations.
Nonlinear acoustic wave equations with fractional loss operators.
Prieur, Fabrice; Holm, Sverre
2011-09-01
Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlinear wave equation which describes attenuation and dispersion laws that match observations. This wave equation is a generalization of the Westervelt equation, and also leads to a fractional version of the Khokhlov-Zabolotskaya-Kuznetsov and Burgers' equations.
Relativistic radiation transport in dispersive media
Kichenassamy, S.; Krikorian, R.A.
1985-10-15
A general-relativistic radiative transfer equation in an isotropic, weakly absorbing, nonmagnetized dispersive medium is derived using the kinetic-theoretical approach and the relativistic Hamiltonian theory of geometrical optics in those media. It yields the generally accepted classical equation in the special-relativistic approximation and in stationary conditions. The influence of the gravitational field and of space-time variations of the refractive index n on the radiation distribution is made explicit in the case of spherical symmetry.
NASA Technical Reports Server (NTRS)
Gal-Chen, T.
1981-01-01
The laws of fluid motion are invariant under a Gallilean transformation. For a perfect observing system, the data analysis should, therefore, also be invariant under a Gallilean transformation. This invariance is often not preserved in practical observing systems. In this connection, it is often advisable to perform mesoscale analysis in a frame moving with respect to the earth's surface. In the present investigation the velocity of such a frame is referred to as an advection velocity. The investigation is concerned with remaining problems regarding the Gallilean transformation. The establishment of a frame of reference for the achievement of maximum coherence is considered, taking into account the case of given nonsimultaneous observations of scalars or Cartesian vectors. It is found that advection speed can be estimated objectively if a scalar or Cartesian vector can be observed directly and if, in addition, the time and position of each observation is approximately known.
The effect of advection on the nutrient reservoir in the North Atlantic subtropical gyre.
Palter, Jaime B; Lozier, M Susan; Barber, Richard T
2005-09-29
Though critically important in sustaining the ocean's biological pump, the cycling of nutrients in the subtropical gyres is poorly understood. The supply of nutrients to the sunlit surface layer of the ocean has traditionally been attributed solely to vertical processes. However, horizontal advection may also be important in establishing the availability of nutrients. Here we show that the production and advection of North Atlantic Subtropical Mode Water introduces spatial and temporal variability in the subsurface nutrient reservoir beneath the North Atlantic subtropical gyre. As the mode water is formed, its nutrients are depleted by biological utilization. When the depleted water mass is exported to the gyre, it injects a wedge of low-nutrient water into the upper layers of the ocean. Contrary to intuition, cold winters that promote deep convective mixing and vigorous mode water formation may diminish downstream primary productivity by altering the subsurface delivery of nutrients.
Scalar variance decay in chaotic advection and Batchelor-regime turbulence
NASA Astrophysics Data System (ADS)
Fereday, D. R.; Haynes, P. H.; Wonhas, A.; Vassilicos, J. C.
2002-03-01
The decay of the variance of a diffusive scalar in chaotic advection flow (or equivalently Batchelor-regime turbulence) is analyzed using a model in which the advection is represented by an inhomogeneous baker's map on the unit square. The variance decays exponentially at large times, with a rate that has a finite limit as the diffusivity κ tends to zero and is determined by the action of the inhomogeneous map on the gravest Fourier modes in the scalar field. The decay rate predicted by recent theoretical work that follows scalar evolution in linear flow and then averages over all stretching histories is shown to be incorrect. The exponentially decaying scalar field is shown to have a spatial power spectrum of the form P(k)~k-σ at wave numbers small enough for diffusion to be neglected, with σ<1.
Analytic radiative-advective equilibrium as a model for high-latitude climate
NASA Astrophysics Data System (ADS)
Cronin, Timothy W.; Jansen, Malte F.
2016-01-01
We propose radiative-advective equilibrium as a basic-state model for the high-latitude atmosphere. Temperature profiles are determined by a competition between stabilization by atmospheric shortwave absorption and advective heat flux convergence, and destabilization by surface shortwave absorption. We derive analytic expressions for temperature profiles, assuming power law atmospheric heating profiles as a function of pressure and two-stream windowed-gray longwave radiative transfer. We discuss example profiles with and without an atmospheric window and show that the sensitivity of surface temperature to forcing depends on the nature of the forcing, with greatest sensitivity to radiative forcing by increased optical thickness and least sensitivity to increased atmospheric heat transport. These differences in sensitivity of surface temperature to forcing can be explained in terms of a forcing-dependent lapse-rate feedback.
Advective-diffusive motion on large scales from small-scale dynamics with an internal symmetry
NASA Astrophysics Data System (ADS)
Marino, Raffaele; Aurell, Erik
2016-06-01
We consider coupled diffusions in n -dimensional space and on a compact manifold and the resulting effective advective-diffusive motion on large scales in space. The effective drift (advection) and effective diffusion are determined as a solvability conditions in a multiscale analysis. As an example, we consider coupled diffusions in three-dimensional space and on the group manifold SO(3) of proper rotations, generalizing results obtained by H. Brenner [J. Colloid Interface Sci. 80, 548 (1981), 10.1016/0021-9797(81)90214-9]. We show in detail how the analysis can be conveniently carried out using local charts and invariance arguments. As a further example, we consider coupled diffusions in two-dimensional complex space and on the group manifold SU(2). We show that although the local operators may be the same as for SO(3), due to the global nature of the solvability conditions the resulting diffusion will differ and generally be more isotropic.
NASA Technical Reports Server (NTRS)
Shia, Run-Lie; Ha, Yuk Lung; Wen, Jun-Shan; Yung, Yuk L.
1990-01-01
Extensive testing of the advective scheme proposed by Prather (1986) has been carried out in support of the California Institute of Technology-Jet Propulsion Laboratory two-dimensional model of the middle atmosphere. The original scheme is generalized to include higher-order moments. In addition, it is shown how well the scheme works in the presence of chemistry as well as eddy diffusion. Six types of numerical experiments including simple clock motion and pure advection in two dimensions have been investigated in detail. By comparison with analytic solutions, it is shown that the new algorithm can faithfully preserve concentration profiles, has essentially no numerical diffusion, and is superior to a typical fourth-order finite difference scheme.
Advection and the Efficiency of Spectral Energy Transfer in Two-Dimensional Turbulence.
Fang, Lei; Ouellette, Nicholas T
2016-09-02
We report measurements of the geometric alignment of the small-scale turbulent stress and the large-scale rate of strain that together lead to the net flux of energy from small scales to large scales in two-dimensional turbulence. We find that the instantaneous alignment between these two tensors is weak and, thus, that the spectral transport of energy is inefficient. We show, however, that the strain rate is much better aligned with the stress at times in the past, suggesting that the differential advection of the two is responsible for the inefficient spectral transfer. We provide evidence for this conjecture by measuring the alignment statistics conditioned on weakly changing stress history. Our results give new insight into the relationship between scale-to-scale energy transfer, geometric alignment, and advection in turbulent flows.
NASA Astrophysics Data System (ADS)
Yochelis, Arik; Bar-On, Tomer; Gov, Nir S.
2016-04-01
Unconventional myosins belong to a class of molecular motors that walk processively inside cellular protrusions towards the tips, on top of actin filament. Surprisingly, in addition, they also form retrograde moving self-organized aggregates. The qualitative properties of these aggregates are recapitulated by a mass conserving reaction-diffusion-advection model and admit two distinct families of modes: traveling waves and pulse trains. Unlike the traveling waves that are generated by a linear instability, pulses are nonlinear structures that propagate on top of linearly stable uniform backgrounds. Asymptotic analysis of isolated pulses via a simplified reaction-diffusion-advection variant on large periodic domains, allows to draw qualitative trends for pulse properties, such as the amplitude, width, and propagation speed. The results agree well with numerical integrations and are related to available empirical observations.
Optical dispersive shock waves in defocusing colloidal media
NASA Astrophysics Data System (ADS)
An, X.; Marchant, T. R.; Smyth, N. F.
2017-03-01
The propagation of an optical dispersive shock wave, generated from a jump discontinuity in light intensity, in a defocusing colloidal medium is analysed. The equations governing nonlinear light propagation in a colloidal medium consist of a nonlinear Schrödinger equation for the beam and an algebraic equation for the medium response. In the limit of low light intensity, these equations reduce to a perturbed higher order nonlinear Schrödinger equation. Solutions for the leading and trailing edges of the colloidal dispersive shock wave are found using modulation theory. This is done for both the perturbed nonlinear Schrödinger equation and the full colloid equations for arbitrary light intensity. These results are compared with numerical solutions of the colloid equations.
Estimating Advective Near-surface Currents from Ocean Color Satellite Images
2015-01-01
RESPONSIBLE PERSON 19b. TELEPHONE NUMBER (Include area code) 01/23/2015 Journal Article Estimating advective near-surface currents from ocean color ...currents from the sequential ocean color imagery provided by multiple newer generations of satellite sensors on hourly scales in the Yellow Sea and the...optical properties are discussed regarding the performances of various color products on the retrieval of currents. Similarities of velocity
A family of compact high order coupled time-space unconditionally stable vertical advection schemes
NASA Astrophysics Data System (ADS)
Lemarié, Florian; Debreu, Laurent
2016-04-01
Recent papers by Shchepetkin (2015) and Lemarié et al. (2015) have emphasized that the time-step of an oceanic model with an Eulerian vertical coordinate and an explicit time-stepping scheme is very often restricted by vertical advection in a few hot spots (i.e. most of the grid points are integrated with small Courant numbers, compared to the Courant-Friedrichs-Lewy (CFL) condition, except just few spots where numerical instability of the explicit scheme occurs first). The consequence is that the numerics for vertical advection must have good stability properties while being robust to changes in Courant number in terms of accuracy. An other constraint for oceanic models is the strict control of numerical mixing imposed by the highly adiabatic nature of the oceanic interior (i.e. mixing must be very small in the vertical direction below the boundary layer). We examine in this talk the possibility of mitigating vertical Courant-Friedrichs-Lewy (CFL) restriction, while avoiding numerical inaccuracies associated with standard implicit advection schemes (i.e. large sensitivity of the solution on Courant number, large phase delay, and possibly excess of numerical damping with unphysical orientation). Most regional oceanic models have been successfully using fourth order compact schemes for vertical advection. In this talk we present a new general framework to derive generic expressions for (one-step) coupled time and space high order compact schemes (see Daru & Tenaud (2004) for a thorough description of coupled time and space schemes). Among other properties, we show that those schemes are unconditionally stable and have very good accuracy properties even for large Courant numbers while having a very reasonable computational cost.
Statistical evaluation of thermal advection and stratification effects in scatterometer observations
NASA Technical Reports Server (NTRS)
Levy, Gad; Tiu, F. S.
1991-01-01
The effects of thermal advection and atmospheric stratification are statistically evaluated using Seasat scatterometer observations as a data base. The results indicate that, whenever the surface winds or wind stress are related to the atmospheric pressure field, the appropriate stratification and baroclinic corrections should be applied. Without such corrections, errors of 15-25 percent are likely to arise in the surface fluxes computed from model low-level winds or pressure measurements.
Multiphase Advection and Radiation Diffusion with Material Interfaces on Unstructured Meshes
Anninos, P
2002-10-03
A collection of numerical methods are presented for the advection or remapping of material properties on unstructured and staggered polyhedral meshes in arbitrary Lagrange-Eulerian calculations. The methods include several new procedures to track and capture sharp interface boundaries, and to partition radiation energy into multi-material thermal states. The latter is useful for extending and applying consistently single material radiation diffusion solvers to multi-material problems.
A computational Lagrangian-Eulerian advection remap for free surface flows
NASA Astrophysics Data System (ADS)
Ashgriz, Nasser; Barbat, Tiberiu; Wang, Gang
2004-01-01
A VOF-based algorithm for advecting free surfaces and interfaces across a 2-D unstructured grid is presented. This algorithm is based on a combination of a Computational Lagrangian-Eulerian Advection Remap and the Volume of the Fluid method (CLEAR-VOF). A set of geometric tools are used to remap the advected shape of the volume fraction from one cell onto the Eulerian fixed unstructured grid. The geometric remapping is used to compute the fluxes onto a group of neighbouring cells of the mesh. These fluxes are then redistributed and corrected to satisfy the conservation of mass. Here, we present methods for developing identification algorithms for surface cells and incorporating them with CLEAR-VOF. The CLEAR-VOF algorithm is then tested for translation of several geometries. It is also incorporated in a finite element based flow solver and tested in a laminar flow over a broad-crested weir and a turbulent flow over a semi-circular obstacle.
NASA Astrophysics Data System (ADS)
Chauhan, R. P.; Kumar, Amit
The present work is aimed that out of diffusive and advective transport which is dominant process for indoor radon entry under normal room conditions. For this purpose the radon diffusion coefficient and permeability of concrete were measured by specially designed experimental set up. The radon diffusion coefficient of concrete was measured by continuous radon monitor. The measured value was (3.78 ± 0.39)×10-8 m2/s and found independent of the radon gas concentration in source chamber. The radon permeability of concrete varied between 1.85×10-17 to 1.36×10-15 m2 for the bulk pressure difference fewer than 20 Pa to 73.3 kPa. From the measured diffusion coefficient and absolute permeability, the radon flux from the concrete surface having concentrations gradient 12-40 kBq/m3 and typical floor thickness 0.1 m was calculated by the application of Fick and Darcy laws. Using the measured flux attributable to diffusive and advective transport, the indoor radon concentration for a typical Indian model room having dimension (5×6×7) m3 was calculated under average room ventilation (0.63 h-1). The results showed that the contribution of diffusive transport through intact concrete is dominant over the advective transport, as expected from the low values of concrete permeability.
NASA Technical Reports Server (NTRS)
Levy, Gad; Tiu, Felice S.
1990-01-01
Statistical tests are performed on the Seasat scatterometer observations to examine if and to what degree thermal advection and stratification effects manifest themselves in these remotely sensed measurements of mean wind and wind stress over the ocean. On the basis of a two layer baroclinic boundary layer model which is presented, it is shown that the thermal advection and stratification of the entire boundary layer as well as the geostrophic forcing influence the modeled near surface wind and wind stress profiles. Evidence of diurnal variation in the stratification under barotropic conditions is found in the data, with the daytime marine boundary layer being more convective than its nighttime counterpart. The temporal and spacial sampling pattern of the satellite makes it impossible to recover the full diurnal cycle, however. The observed effects of the thermal advection are shown to be statistically significant during the day (and presumed more convective) hours, causing a systematic increase in the poleward transport of mass and heat. The statistical results are in a qualitative agreement with the model simulations and cannot be reproduced in randomized control tests.
An improved lattice Boltzmann method for simulating advective-diffusive processes in fluids
NASA Astrophysics Data System (ADS)
Aursjø, Olav; Jettestuen, Espen; Vinningland, Jan Ludvig; Hiorth, Aksel
2017-03-01
Lattice Boltzmann methods are widely used to simulate advective-diffusive processes in fluids. Lattice Bhatnagar-Gross-Krook methods presented in the literature mostly just exhibit first order spatial accuracy and introduce errors proportional to the velocity squared. Formulations proposed to alleviate this have only been partly successful and are valid only in certain specific situations. We present and demonstrate here a formulation that produces no such second order errors. This formulation suggests that a subtle, but important, adjustment is all it takes to improve the accuracy of the method. The key to the improved accuracy of this new model is the non-standard definition of the concentration that relates to the distribution function describing the advection-diffusion in lattice Boltzmann. The main advantage of the algorithm comes to view when simulating situations where fluid density variations appear. The present formulation of the advection-diffusion algorithm will, by taking into account these fluid density variations, drastically reduce the errors produced compared to the standard formulations. We also show how a source term is included in this new formulation without it losing its second order spatial accuracy.
Yao, Yijun; Wu, Yun; Wang, Yue; Verginelli, Iason; Zeng, Tian; Suuberg, Eric M; Jiang, Lin; Wen, Yuezhong; Ma, Jie
2015-10-06
At petroleum vapor intrusion (PVI) sites at which there is significant methane generation, upward advective soil gas transport may be observed. To evaluate the health and explosion risks that may exist under such scenarios, a one-dimensional analytical model describing these processes is introduced in this study. This new model accounts for both advective and diffusive transport in soil gas and couples this with a piecewise first-order aerobic biodegradation model, limited by oxygen availability. The predicted results from the new model are shown to be in good agreement with the simulation results obtained from a three-dimensional numerical model. These results suggest that this analytical model is suitable for describing cases involving open ground surface beyond the foundation edge, serving as the primary oxygen source. This new analytical model indicates that the major contribution of upward advection to indoor air concentration could be limited to the increase of soil gas entry rate, since the oxygen in soil might already be depleted owing to the associated high methane source vapor concentration.
Gu Weimin
2012-07-10
By taking into account the local energy balance per unit volume between the viscous heating and the advective cooling plus the radiative cooling, we investigate the vertical structure of radiation pressure-supported accretion disks in spherical coordinates. Our solutions show that the photosphere of the disk is close to the polar axis and therefore the disk seems to be extremely thick. However, the density profile implies that most of the accreted matter exists in a moderate range around the equatorial plane. We show that the well-known polytropic relation between the pressure and the density is unsuitable for describing the vertical structure of radiation pressure-supported disks. More importantly, we find that the energy advection is significant even for slightly sub-Eddington accretion disks. We argue that the non-negligible advection may help us understand why the standard thin disk model is likely to be inaccurate above {approx}0.3 Eddington luminosity, which was found by some works on black hole spin measurement. Furthermore, the solutions satisfy the Solberg-Hoiland conditions, which indicate the disk to be convectively stable. In addition, we discuss the possible link between our disk model and ultraluminous X-ray sources.
Advection-Dominant MHD Computation for External Kinks and Edge-Localized Modes
NASA Astrophysics Data System (ADS)
Sovinec, C. R.
2016-10-01
Separation of temporal and spatial scales is the primary consideration for computation of macroscopic dynamics in magnetically confined plasma. Dynamic shock capturing is not needed, but nonlinear external kinks and ELMs advect large gradients near the plasma surface. Using an implicit time-advance with Galerkin projection can be problematic in these applications when advection is stronger than dissipation on the spatial scale of the mesh. The applied math community has investigated many approaches to stabilizing numerical advection. One approach is the least-squares finite element method, which has previously been applied to MHD and plasma-fluid models. Here, we adapt this technique for MHD computation with the NIMROD code, starting with the scalar dependent fields that need to have definite sign: density and temperature. Time-splitting physical diffusion maintains the original size of the algebraic systems that are solved at each time-step. Upwinding explicit terms where derivatives are discontinuous avoids overshoot error while minimizing numerical dissipation. Work supported by U.S. DOE Grant DE-FC02-08ER54975.
NASA Astrophysics Data System (ADS)
Chaynikov, S.; Porta, G.; Riva, M.; Guadagnini, A.
2012-04-01
We focus on a theoretical analysis of nonreactive solute transport in porous media through the volume averaging technique. Darcy-scale transport models based on continuum formulations typically include large scale dispersive processes which are embedded in a pore-scale advection diffusion equation through a Fickian analogy. This formulation has been extensively questioned in the literature due to its inability to depict observed solute breakthrough curves in diverse settings, ranging from the laboratory to the field scales. The heterogeneity of the pore-scale velocity field is one of the key sources of uncertainties giving rise to anomalous (non-Fickian) dispersion in macro-scale porous systems. Some of the models which are employed to interpret observed non-Fickian solute behavior make use of a continuum formulation of the porous system which assumes a two-region description and includes a bimodal velocity distribution. A first class of these models comprises the so-called ''mobile-immobile'' conceptualization, where convective and dispersive transport mechanisms are considered to dominate within a high velocity region (mobile zone), while convective effects are neglected in a low velocity region (immobile zone). The mass exchange between these two regions is assumed to be controlled by a diffusive process and is macroscopically described by a first-order kinetic. An extension of these ideas is the two equation ''mobile-mobile'' model, where both transport mechanisms are taken into account in each region and a first-order mass exchange between regions is employed. Here, we provide an analytical derivation of two region "mobile-mobile" meso-scale models through a rigorous upscaling of the pore-scale advection diffusion equation. Among the available upscaling methodologies, we employ the Volume Averaging technique. In this approach, the heterogeneous porous medium is supposed to be pseudo-periodic, and can be represented through a (spatially) periodic unit cell
Highly dispersive slot waveguides.
Zhang, Lin; Yue, Yang; Xiao-Li, Yinying; Beausoleil, Raymond G; Willner, Alan E
2009-04-27
We propose a slot-waveguide with high dispersion, in which a slot waveguide is coupled to a strip waveguide. A negative dispersion of up to -181520 ps/nm/km is obtained due to a strong interaction of the slot and strip modes. A flat and large dispersion is achievable by cascading the dispersive slot-waveguides with varied waveguide thickness or width for dispersion compensation and signal processing applications. We show - 31300 ps/nm/km dispersion over 147-nm bandwidth with <1% variance.
Transport Equation Based Wall Distance Computations Aimed at Flows With Time-Dependent Geometry
NASA Technical Reports Server (NTRS)
Tucker, Paul G.; Rumsey, Christopher L.; Bartels, Robert E.; Biedron, Robert T.
2003-01-01
Eikonal, Hamilton-Jacobi and Poisson equations can be used for economical nearest wall distance computation and modification. Economical computations may be especially useful for aeroelastic and adaptive grid problems for which the grid deforms, and the nearest wall distance needs to be repeatedly computed. Modifications are directed at remedying turbulence model defects. For complex grid structures, implementation of the Eikonal and Hamilton-Jacobi approaches is not straightforward. This prohibits their use in industrial CFD solvers. However, both the Eikonal and Hamilton-Jacobi equations can be written in advection and advection-diffusion forms, respectively. These, like the Poisson's Laplacian, are commonly occurring industrial CFD solver elements. Use of the NASA CFL3D code to solve the Eikonal and Hamilton-Jacobi equations in advective-based forms is explored. The advection-based distance equations are found to have robust convergence. Geometries studied include single and two element airfoils, wing body and double delta configurations along with a complex electronics system. It is shown that for Eikonal accuracy, upwind metric differences are required. The Poisson approach is found effective and, since it does not require offset metric evaluations, easiest to implement. The sensitivity of flow solutions to wall distance assumptions is explored. Generally, results are not greatly affected by wall distance traits.
Transport Equation Based Wall Distance Computations Aimed at Flows With Time-Dependent Geometry
NASA Technical Reports Server (NTRS)
Tucker, Paul G.; Rumsey, Christopher L.; Bartels, Robert E.; Biedron, Robert T.
2003-01-01
Eikonal, Hamilton-Jacobi and Poisson equations can be used for economical nearest wall distance computation and modification. Economical computations may be especially useful for aeroelastic and adaptive grid problems for which the grid deforms, and the nearest wall distance needs to be repeatedly computed. Modifications are directed at remedying turbulence model defects. For complex grid structures, implementation of the Eikonal and Hamilton-Jacobi approaches is not straightforward. This prohibits their use in industrial CFD solvers. However, both the Eikonal and Hamilton-Jacobi equations can be written in advection and advection-diffusion forms, respectively. These, like the Poisson s Laplacian, are commonly occurring industrial CFD solver elements. Use of the NASA CFL3D code to solve the Eikonal and Hamilton-Jacobi equations in advective-based forms is explored. The advection-based distance equations are found to have robust convergence. Geometries studied include single and two element airfoils, wing body and double delta configurations along with a complex electronics system. It is shown that for Eikonal accuracy, upwind metric differences are required. The Poisson approach is found effective and, since it does not require offset metric evaluations, easiest to implement. The sensitivity of flow solutions to wall distance assumptions is explored. Generally, results are not greatly affected by wall distance traits.
NASA Astrophysics Data System (ADS)
de Lorenzo, Salvatore; Loddo, Mariano
2010-01-01
Laboratory experiments on simulated faults in rocks clearly show the temperature dependence of dynamic rock friction. Since rocks surrounding faults are permeable, we have developed a numerical method to describe the thermo-mechanical evolution of the pre-seismic sliding phase which takes into account both the rate-, state- and temperature-dependent friction law and the heat advection term in the energy equation. We consider a laminar fluid motion perpendicular to a vertical fault plane and assume that fluids move away from the fault plane. A semi-analytical temperature solution which accounts for the variability of slip velocity and stress on the fault has been found. This solution has been generalized to the case of a time varying fluid velocity and then was used to include the thermal pressurization effect. After discretizing the temperature solution, the evolution of the system is obtained by the solution of a system of first order differential equations which allows us to determine the evolution of slip, slip rate, friction coefficient, effective normal stress, temperature and fluid velocity. The numerical solutions are found using a Runge-Kutta method with an adaptative stepsize control in time. When the thermal pressurization effects can be neglected, the heat advection effect gives rise to a delay, with respect to the purely conductive case, of the earthquake occurrence time. This delay increases with increasing permeability H of the system. When the thermal pressurization effects are taken into account the situation is opposite, i.e. the onset of instability tends to precede that of the purely conductive case. The advance in the time of occurrence of instability increases with increasing coefficient of thermal pressurization. In the small permeability range ( H ≤ 10 -18 m 2), the seismic moment and nucleation length of the pre-seismic phase are significantly smaller than those predicted by the purely conductive model.
Angular radiation transfer in inhomogeneous dispersive media
NASA Astrophysics Data System (ADS)
Saad, E. A.; El Ghazaly, A. A.; Krim, M. S. Abdel
1988-10-01
The equation of radiative transfer for an inhomogeneous dispersive finite medium subject to general boundary conditions is solved. The Padé approximation technique is used to calculate the angular distribution of radiation. Numerical results for the [0/1] Padé approximant lead to numerical results that compare with the exact results.
NASA Astrophysics Data System (ADS)
Viljamaa, Panu; Jacobs, J. Richard; Chris; JamesHyman; Halma, Matthew; EricNolan; Coxon, Paul
2014-07-01
In reply to a Physics World infographic (part of which is given above) about a study showing that Euler's equation was deemed most beautiful by a group of mathematicians who had been hooked up to a functional magnetic-resonance image (fMRI) machine while viewing mathematical expressions (14 May, http://ow.ly/xHUFi).
DOE R&D Accomplishments Database
Salam, A.
1956-04-01
Lectures with mathematical analysis are given on Dispersion Theory and Causality and Dispersion Relations for Pion-nucleon Scattering. The appendix includes the S-matrix in terms of Heisenberg Operators. (F. S.)
Dispersive shock waves and modulation theory
NASA Astrophysics Data System (ADS)
El, G. A.; Hoefer, M. A.
2016-10-01
There is growing physical and mathematical interest in the hydrodynamics of dissipationless/dispersive media. Since G.B. Whitham's seminal publication fifty years ago that ushered in the mathematical study of dispersive hydrodynamics, there has been a significant body of work in this area. However, there has been no comprehensive survey of the field of dispersive hydrodynamics. Utilizing Whitham's averaging theory as the primary mathematical tool, we review the rich mathematical developments over the past fifty years with an emphasis on physical applications. The fundamental, large scale, coherent excitation in dispersive hydrodynamic systems is an expanding, oscillatory dispersive shock wave or DSW. Both the macroscopic and microscopic properties of DSWs are analyzed in detail within the context of the universal, integrable, and foundational models for uni-directional (Korteweg-de Vries equation) and bi-directional (Nonlinear Schrödinger equation) dispersive hydrodynamics. A DSW fitting procedure that does not rely upon integrable structure yet reveals important macroscopic DSW properties is described. DSW theory is then applied to a number of physical applications: superfluids, nonlinear optics, geophysics, and fluid dynamics. Finally, we survey some of the more recent developments including non-classical DSWs, DSW interactions, DSWs in perturbed and inhomogeneous environments, and two-dimensional, oblique DSWs.
NASA Astrophysics Data System (ADS)
Jeschke, Anja; Behrens, Jörn
2015-04-01
In tsunami modeling, two different systems of dispersive long wave equations are common: The nonhydrostatic pressure correction for the shallow water equations derived out of the depth-integrated 3D Reynolds-averaged Navier-Stokes equations, and the category of Boussinesq-type equations obtained by an expansion in the nondimensional parameters for nonlinearity and dispersion in the Euler equations. The first system uses as an assumption a linear vertical interpolation of the nonhydrostatic pressure, whereas the second system's derivation includes an quadratic vertical interpolation for the nonhydrostatic pressure. In this case the analytical dispersion relations do not coincide. We show that the nonhydrostatic correction with a quadratic vertical interpolation yields an equation set equivalent to the Serre equations, which are 1D Boussinesq-type equations for the case of a horizontal bottom. Now, both systems yield the same analytical dispersion relation according up to the first order with the reference dispersion relation of the linear wave theory. The adjusted model is also compared to other Boussinesq-type equations. The numerical model with the nonhydrostatic correction for the shallow water equations uses Leapfrog timestepping stabilized with the Asselin filter and the P1-PNC1 finite element space discretization. The numerical dispersion relations are computed and compared by employing a testcase of a standing wave in a closed basin. All numerical values match their theoretical expectations. This work is funded by project ASTARTE - Assessment, Strategy And Risk Reduction for Tsunamis in Europe - FP7-ENV2013 6.4-3, Grant 603839. We acknowledge the support given by Geir K. Petersen from the University of Oslo.
Development of the DUSTRAN GIS-Based Complex Terrain Model for Atmospheric Dust Dispersion
2007-05-10
scenario and run the underlying models. Through the process of data layering, the model domain, sources, and results—including the calculated wind-vector...advection, diffusion, and deposition calculations . Figure 4.2 shows the linkages of these dust-dispersion models within DUSTRAN. CALMET...interface CALMET, CALPUFF, and CALGRID to routinely available terrain elevation and land-use datasets for use in model calculations . A post-processing
Upscaling of Solute Transport in Heterogeneous Media with Non-uniform Flow and Dispersion Fields
Xu, Zhijie; Meakin, Paul
2013-10-01
An analytical and computational model for non-reactive solute transport in periodic heterogeneous media with arbitrary non-uniform flow and dispersion fields within the unit cell of length ε is described. The model lumps the effect of non-uniform flow and dispersion into an effective advection velocity Ve and an effective dispersion coefficient De. It is shown that both Ve and De are scale-dependent (dependent on the length scale of the microscopic heterogeneity, ε), dependent on the Péclet number Pe, and on a dimensionless parameter α that represents the effects of microscopic heterogeneity. The parameter α, confined to the range of [-0.5, 0.5] for the numerical example presented, depends on the flow direction and non-uniform flow and dispersion fields. Effective advection velocity Ve and dispersion coefficient De can be derived for any given flow and dispersion fields, and . Homogenized solutions describing the macroscopic variations can be obtained from the effective model. Solutions with sub-unit-cell accuracy can be constructed by homogenized solutions and its spatial derivatives. A numerical implementation of the model compared with direct numerical solutions using a fine grid, demonstrated that the new method was in good agreement with direct solutions, but with significant computational savings.
Consistent lattice Boltzmann equations for phase transitions
NASA Astrophysics Data System (ADS)
Siebert, D. N.; Philippi, P. C.; Mattila, K. K.
2014-11-01
Unlike conventional computational fluid dynamics methods, the lattice Boltzmann method (LBM) describes the dynamic behavior of fluids in a mesoscopic scale based on discrete forms of kinetic equations. In this scale, complex macroscopic phenomena like the formation and collapse of interfaces can be naturally described as related to source terms incorporated into the kinetic equations. In this context, a novel athermal lattice Boltzmann scheme for the simulation of phase transition is proposed. The continuous kinetic model obtained from the Liouville equation using the mean-field interaction force approach is shown to be consistent with diffuse interface model using the Helmholtz free energy. Density profiles, interface thickness, and surface tension are analytically derived for a plane liquid-vapor interface. A discrete form of the kinetic equation is then obtained by applying the quadrature method based on prescribed abscissas together with a third-order scheme for the discretization of the streaming or advection term in the Boltzmann equation. Spatial derivatives in the source terms are approximated with high-order schemes. The numerical validation of the method is performed by measuring the speed of sound as well as by retrieving the coexistence curve and the interface density profiles. The appearance of spurious currents near the interface is investigated. The simulations are performed with the equations of state of Van der Waals, Redlich-Kwong, Redlich-Kwong-Soave, Peng-Robinson, and Carnahan-Starling.
Dispersion y dinamica poblacional
Technology Transfer Automated Retrieval System (TEKTRAN)
Dispersal behavior of fruit flies is appetitive. Measures of dispersion involve two different parameter: the maximum distance and the standard distance. Standard distance is a parameter that describes the probalility of dispersion and is mathematically equivalent to the standard deviation around ...
Dispersive internal long wave models
Camassa, R.; Choi, W.; Holm, D.D.; Levermore, C.D.; Lvov, Y.
1998-11-01
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). This work is a joint analytical and numerical study of internal dispersive water wave propagation in a stratified two-layer fluid, a problem that has important geophysical fluid dynamics applications. Two-layer models can capture the main density-dependent effects because they can support, unlike homogeneous fluid models, the observed large amplitude internal wave motion at the interface between layers. The authors have derived new model equations using multiscale asymptotics in combination with the method they have developed for vertically averaging velocity and vorticity fields across fluid layers within the original Euler equations. The authors have found new exact conservation laws for layer-mean vorticity that have exact counterparts in the models. With this approach, they have derived a class of equations that retain the full nonlinearity of the original Euler equations while preserving the simplicity of known weakly nonlinear models, thus providing the theoretical foundation for experimental results so far unexplained.
Dispersion-relation-preserving schemes for computational aeroacoustics
NASA Technical Reports Server (NTRS)
Tam, Christopher K. W.; Webb, Jay C.
1992-01-01
Finite difference schemes that have the same dispersion relations as the original partial differential equations are referred to as dispersion-relation-preserving (DRP) schemes. A method to construct time marching DRP schemes by optimizing the finite difference approximations of the space and time derivatives in the wave number and frequency space is presented. A sequence of numerical simulations is then performed.
NASA Astrophysics Data System (ADS)
Dakova, D.; Dakova, A.; Slavchev, V.; Staykov, P.; Kovachev, L.
2016-01-01
In last two decades the phenomena resulting from the evolution of ultra-short laser pulses in nonlinear dispersive medium actively are being studied. The most commonly used equation for describing the dynamics of optical pulses in one-dimensional and planar waveguides is the standard nonlinear Schrodinger equation (NSE). It works very well for nanosecond and picosecond laser pulses, but in the frames of femtosecond optics, it is necessary two additional terms to be included. They are responsible for higher order of linear dispersion and dispersion of nonlinearity. These effects are significant in the range of ultra-short light pulses. In the present paper, it is presented a theoretical model of the propagation of optical solitons. We found an exact analytical soliton solution of the modified NSE, including third order of linear dispersion and dispersion of nonlinearity. It is possible to observe a soliton as a result of the dynamic balance between effects of higher order of dispersion and nonlinearity.
DOE R&D Accomplishments Database
1998-09-21
In the late 1950s to early 1960s Rudolph A. Marcus developed a theory for treating the rates of outer-sphere electron-transfer reactions. Outer-sphere reactions are reactions in which an electron is transferred from a donor to an acceptor without any chemical bonds being made or broken. (Electron-transfer reactions in which bonds are made or broken are referred to as inner-sphere reactions.) Marcus derived several very useful expressions, one of which has come to be known as the Marcus cross-relation or, more simply, as the Marcus equation. It is widely used for correlating and predicting electron-transfer rates. For his contributions to the understanding of electron-transfer reactions, Marcus received the 1992 Nobel Prize in Chemistry. This paper discusses the development and use of the Marcus equation. Topics include self-exchange reactions; net electron-transfer reactions; Marcus cross-relation; and proton, hydride, atom and group transfers.
Theory of dispersive microlenses
NASA Technical Reports Server (NTRS)
Herman, B.; Gal, George
1993-01-01
A dispersive microlens is a miniature optical element which simultaneously focuses and disperses light. Arrays of dispersive mircolenses have potential applications in multicolor focal planes. They have a 100 percent optical fill factor and can focus light down to detectors of diffraction spot size, freeing up areas on the focal plane for on-chip analog signal processing. Use of dispersive microlenses allows inband color separation within a pixel and perfect scene registration. A dual-color separation has the potential for temperature discrimination. We discuss the design of dispersive microlenses and present sample results for efficient designs.
Five-wave classical scattering matrix and integrable equations
NASA Astrophysics Data System (ADS)
Zakharov, V. E.; Odesskii, A. V.; Cisternino, M.; Onorato, M.
2014-07-01
We study the five-wave classical scattering matrix for nonlinear and dispersive Hamiltonian equations with a nonlinearity of the type u∂u/∂x. Our aim is to find the most general nontrivial form of the dispersion relation ω(k) for which the five-wave interaction scattering matrix is identically zero on the resonance manifold. As could be expected, the matrix in one dimension is zero for the Korteweg-de Vries equation, the Benjamin-Ono equation, and the intermediate long-wave equation. In two dimensions, we find a new equation that satisfies our requirement.
A tracer-based inversion method for diagnosing eddy-induced diffusivity and advection
NASA Astrophysics Data System (ADS)
Bachman, S. D.; Fox-Kemper, B.; Bryan, F. O.
2015-02-01
A diagnosis method is presented which inverts a set of tracer flux statistics into an eddy-induced transport intended to apply for all tracers. The underlying assumption is that a linear flux-gradient relationship describes eddy-induced tracer transport, but a full tensor coefficient is assumed rather than a scalar coefficient which allows for down-gradient and skew transports. Thus, Lagrangian advection and anisotropic diffusion not necessarily aligned with the tracer gradient can be diagnosed. In this method, multiple passive tracers are initialized in an eddy-resolving flow simulation. Their spatially-averaged gradients form a matrix, where the gradient of each tracer is assumed to satisfy an identical flux-gradient relationship. The resulting linear system, which is overdetermined when using more than three tracers, is then solved to obtain an eddy transport tensor R which describes the eddy advection (antisymmetric part of R) and potentially anisotropic diffusion (symmetric part of R) in terms of coarse-grained variables. The mathematical basis for this inversion method is presented here, along with practical guidelines for its implementation. We present recommendations for initialization of the passive tracers, maintaining the required misalignment of the tracer gradients, correcting for nonconservative effects, and quantifying the error in the diagnosed transport tensor. A method is proposed to find unique, tracer-independent, distinct rotational and divergent Lagrangian transport operators, but the results indicate that these operators are not meaningfully relatable to tracer-independent eddy advection or diffusion. With the optimal method of diagnosis, the diagnosed transport tensor is capable of predicting the fluxes of other tracers that are withheld from the diagnosis, including even active tracers such as buoyancy, such that relative errors of 14% or less are found.