scholarly journals Assessment of Hydrometeor Collection Rates from Exact and Approximate Equations. Part II: Numerical Bounding

2007 ◽  
Vol 46 (1) ◽  
pp. 82-96
Author(s):  
Brian J. Gaudet ◽  
Jerome M. Schmidt
Keyword(s):  
Mass Transfer ◽  
Exact Solution ◽  
Splitting Method ◽  
Time Discretization ◽  
Large Mass ◽  
Time Step ◽  
Transfer Rates ◽  
Mass Moment ◽  
Time Splitting ◽  
Approximate Equations

Abstract Past microphysical investigations, including Part I of this study, have noted that the collection equation, when applied to the interaction between different hydrometeor species, can predict large mass transfer rates, even when an exact solution is used. The fractional depletion in a time step can even exceed unity for the collected species with plausible microphysical conditions and time steps, requiring “normalization” by a microphysical scheme. Although some of this problem can be alleviated through the use of more moment predictions and hydrometeor categories, the question as to why such “overdepletion” can be predicted in the first place remains insufficiently addressed. It is shown through both physical and conceptual arguments that the explicit time discretization of the bulk collection equation for any moment is not consistent with a quasi-stochastic view of collection. The result, under certain reasonable conditions, is a systematic overprediction of collection, which can become a serious error in the prediction of higher-order moments in a bulk scheme. The term numerical bounding is used to refer to the use of a quasi-stochastically consistent formula that prevents fractional collections exceeding unity for any moments. Through examples and analysis it is found that numerical bounding is typically important in mass moment prediction for time steps exceeding approximately 10 s. The Poisson-based numerical bounding scheme is shown to be simple in application and conceptualization; within a straightforward idealization it completely corrects overdepletion while even being immune to the rediagnosis error of the time-splitting method. The scheme’s range of applicability and utility are discussed.

scholarly journals Efficient time-splitting Hermite-Galerkin spectral method for the coupled nonlinear Schrödinger equations

2020 ◽  
Vol 14 ◽  
pp. 174830262097353
Author(s):  
Qingqu Zhuang ◽  
Yi Yang
Keyword(s):  
Splitting Method ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Coupled Nonlinear Schrödinger Equations ◽  
Time Step ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Time Splitting ◽  
Coupled Nonlinear Schrodinger Equations

The paper focuses on efficient time-splitting Hermite-Galerkin spectral approximation of the coupled nonlinear Schrödinger equations on the whole line. The original problem is decomposed into one nonlinear subproblem and one linear subproblem by time-splitting method. At each time step, the nonlinear subproblem is solved exactly. While the linear subproblem is efficiently solved by choosing suitable Hermite basis functions with matrix decomposition technique. Numerical experiments are carried out to demonstrate the effectiveness and efficiency of the proposed method.

scholarly journals Stability Analysis of Decoupled Time-stepping Schemes for the Specialized Conduction System/myocardium Coupled Problem in Cardiology

2017 ◽  
Vol 12 (5) ◽  
pp. 208-239 ◽  
Author(s):  
S. Mani Aouadi ◽  
W. Mbarki ◽  
N. Zemzemi
Keyword(s):  
Time Discretization ◽  
Conduction System ◽  
Splitting Schemes ◽  
Time Step ◽  
Time Stepping ◽  
Time Splitting ◽  
Coupling Terms ◽  
The Stability ◽  
Fully Coupled ◽  
Purkinje Network

The Purkinje network is the rapid conduction system in the heart. It ensures the physiological spread of the electrical wave in the ventricles. In this work, we consider a problem that models the coupling between the Purkinje network and the myocardium. We first prove the stability of the space semi-discretized problem. Then we present four different strategies for solving the Purkinje/ myocardium coupling. The strategies are based on different time discretization of the coupling terms. The first scheme is fully coupled, where the coupling terms are considered implicit. The second and the third schemes are based on Gauss-Seidel time-splitting schemes where one coupling term is considered explicit and the other is implicit. The last is a Jacobi-like time-splitting scheme where both coupling terms are considered explicit. Our main result is the proof of the stability of the three considered schemes under the same restriction on the time step. Moreover, we show that the energy of the problem is slightly affected by the time-splitting schemes. We illustrate the theoretical result by different numerical simulations in 2D. We also conduct 3D simulations using physiologically detailed ionic models.

scholarly journals Influence of radiation pressure and wind momentum on mass transfer in massive binaries

2003 ◽  
Vol 212 ◽  
pp. 408-409
Author(s):  
Luc Dessart ◽  
Jelena Petrovic ◽  
Norbert Langer
Keyword(s):  
Mass Transfer ◽  
Radiation Pressure ◽  
Binary Systems ◽  
Large Mass ◽  
Roche Lobe ◽  
Radiation Hydrodynamics ◽  
Dense Gas ◽  
Transfer Rates ◽  
Massive Binary Systems ◽  
The Impact

We perform radiation hydrodynamics simulations of mass transfer in close and massive binary systems, focusing especially on the impact of radiation pressure and wind momentum from the two luminous stars that compose the system. We find that for the large mass transfer rates important for the evolution of such binary systems (of the order of 10–3M⊙yr–1), the light and wind momenta are too low to affect the behaviour of the dense gas stream ejected by the Roche Lobe filling component. In particular, the presence of a wind-wind collision between the two stars has no effect on the gas stream dynamics.

Solution of heat and mass transfer problems with non-linear coefficients

2019 ◽  
Vol 5 (4) ◽  
pp. 10-20
Author(s):  
Boris G. Aksenov ◽  
Yuri E. Karyakin ◽  
Svetlana V. Karyakina
Keyword(s):  
Mass Transfer ◽  
Exact Solution ◽  
Numerical Methods ◽  
Heat And Mass Transfer ◽  
Unknown Function ◽  
Comparison Theorems ◽  
Upper And Lower Bounds ◽  
Maximum Deviation ◽  
Approximate Methods ◽  
Nonmonotonic Dependence

Equations, which have nonlinear nonmonotonic dependence of one of the coefficients on an unknown function, can describe processes of heat and mass transfer. As a rule, existing approximate methods do not provide solutions with acceptable accuracy. Numerical methods do not involve obtaining an analytical expression for the unknown function and require studying the convergence of the algorithm used. The value of absolute error is uncertain. The authors propose an approximate method for solving such problems based on Westphal comparison theorems. The comparison theorems allow finding upper and lower bounds of the unknown exact solution. A special procedure developed for the stepwise improvement of these bounds provide solutions with a given accuracy. There are only a few problems for equations with nonlinear nonmonotonic coefficients for which the exact solution has been obtained. One of such problems, presented in this article, shows the efficiency of the proposed method. The results prove that the proposed method for obtaining bounds of the solution of a nonlinear nonmonotonic equation of parabolic type can be considered as a new method of the approximate analytical solution having guaranteed accuracy. In addition, the proposed here method allows calculating the maximum deviation from the unknown exact solution of the results of other approximate and numerical methods.

Generalized Transient Leveque Problem

1996 ◽  
Vol 61 (9) ◽  
pp. 1267-1284
Author(s):  
Ondřej Wein
Keyword(s):  
Mass Transfer ◽  
Exact Solution ◽  
Shear Rate ◽  
Transfer Problem ◽  
Numerical Data ◽  
Wall Shear Rate ◽  
Response Operator ◽  
Mass Transfer Problem ◽  
Finite Step ◽  
General Response

Response of an electrodiffusion friction sensor to a finite step of the wall shear rate is studied by numerically solving the relevant mass-transfer problem. The resulting numerical data on transient currents are treated further to provide reasonably accurate analytical representations. Existing approximations to the general response operator are checked by using the obtained exact solution.

scholarly journals Effects of Variable Transport Properties on Heat and Mass Transfer in MHD Bioconvective Nanofluid Rheology with Gyrotactic Microorganisms: Numerical Approach

Coatings ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 231
Author(s):  
Muhammad Awais ◽  
Saeed Ehsan Awan ◽  
Muhammad Asif Zahoor Raja ◽  
Nabeela Parveen ◽  
Wasim Ullah Khan ◽  
...  
Keyword(s):  
Mass Transfer ◽  
Transport Properties ◽  
Heat And Mass Transfer ◽  
Group Analysis ◽  
Numerical Approach ◽  
Validity Of Results ◽  
Gyrotactic Microorganisms ◽  
Transfer Rates ◽  
Buongiorno’S Model ◽  
Density Distributions

Rheology of MHD bioconvective nanofluid containing motile microorganisms is inspected numerically in order to analyze heat and mass transfer characteristics. Bioconvection is implemented by combined effects of magnetic field and buoyancy force. Gyrotactic microorganisms enhance the heat and transfer as well as perk up the nanomaterials’ stability. Variable transport properties along with assisting and opposing flow situations are taken into account. The significant influences of thermophoresis and Brownian motion have also been taken by employing Buongiorno’s model of nanofluid. Lie group analysis approach is utilized in order to compute the absolute invariants for the system of differential equations, which are solved numerically using Adams-Bashforth technique. Validity of results is confirmed by performing error analysis. Graphical and numerical illustrations are prepared in order to get the physical insight of the considered analysis. It is observed that for controlling parameters corresponding to variable transport properties c2, c4, c6, and c8, the velocity, temperature, concentration, and bioconvection density distributions accelerates, respectively. While heat and mass transfer rates increases for convection parameter and bioconvection Rayleigh number, respectively.

scholarly journals A First-Order Explicit-Implicit Splitting Method for a Convection-Diffusion Problem

2020 ◽  
Vol 20 (4) ◽  
pp. 769-782
Author(s):  
Amiya K. Pani ◽  
Vidar Thomée ◽  
A. S. Vasudeva Murthy
Keyword(s):  
Splitting Method ◽  
Diffusion Problem ◽  
Euler Method ◽  
Second Order ◽  
Time Step ◽  
Convection Diffusion ◽  
First Order ◽  
Backward Euler ◽  
Strang Splitting ◽  
Spatially Periodic

AbstractWe analyze a second-order in space, first-order in time accurate finite difference method for a spatially periodic convection-diffusion problem. This method is a time stepping method based on the first-order Lie splitting of the spatially semidiscrete solution. In each time step, on an interval of length k, of this solution, the method uses the backward Euler method for the diffusion part, and then applies a stabilized explicit forward Euler approximation on {m\geq 1} intervals of length {\frac{k}{m}} for the convection part. With h the mesh width in space, this results in an error bound of the form {C_{0}h^{2}+C_{m}k} for appropriately smooth solutions, where {C_{m}\leq C^{\prime}+\frac{C^{\prime\prime}}{m}}. This work complements the earlier study [V. Thomée and A. S. Vasudeva Murthy, An explicit-implicit splitting method for a convection-diffusion problem, Comput. Methods Appl. Math. 19 2019, 2, 283–293] based on the second-order Strang splitting.

Prediction of Growth Parameters of Frost Deposits in Forced Convection

1981 ◽  
Vol 103 (1) ◽  
pp. 3-6 ◽  
Author(s):  
J. E. White ◽  
C. J. Cremers
Keyword(s):  
Mass Transfer ◽  
Forced Convection ◽  
Growth Parameters ◽  
Experimental Investigations ◽  
Experimental Conditions ◽  
Transfer Rates ◽  
Air Stream ◽  
Transient Period ◽  
Approximate Expressions ◽  
Frost Layer

Experimental investigations of frost deposition under forced convection conditions have shown that in most cases heat and mass transfer rates become constant after an initial transient period. It is shown that, in such cases, approximately half of the mass transfer from a humid air stream to a frost layer diffuses inward, condenses and increases the density of the frost. The other half is deposited at the surface and increases the thickness of the layer. Approximate expressions for density and thickness of the frost layer are derived and compared with data from the literature and also with experimental work reported in this paper. The correlations are shown to work well for a broad range of experimental conditions.

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