Wyniki wyszukiwania - Biblioteka Nauki

1

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

100%

Hejazi H. , Moroney T. , Liu F.

Open Physics

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2013

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tom 11

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nr 10

1275-1283

EN

We present a finite volume method to solve the time-space two-sided fractional advection-dispersion equation on a one-dimensional domain. The spatial discretisation employs fractionally-shifted Grünwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes. We demonstrate how the finite volume formulation provides a natural, convenient and accurate means of discretising this equation in conservative form, compared to using a conventional finite difference approach. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

2

Numerical simulations of the humid atmosphere above a mountain

86%

Bousquet A. , Chekroun M. D. , Hong Y. , Temam R. M. , Tribbia J.

Mathematics of Climate and Weather Forecasting

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2015

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tom 1

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nr 1

EN

New avenues are explored for the numerical study of the two dimensional inviscid hydrostatic primitive equations of the atmosphere with humidity and saturation, in presence of topography and subject to physically plausible boundary conditions for the system of equations. Flows above a mountain are classically treated by the so-called method of terrain following coordinate system. We avoid this discretization method which induces errors in the discretization of tangential derivatives near the topography. Instead we implement a first order finite volume method for the spatial discretization using the initial coordinates x and p. A compatibility condition similar to that related to the condition of incompressibility for the Navier- Stokes equations, is introduced. In that respect, a version of the projection method is considered to enforce the compatibility condition on the horizontal velocity field, which comes from the boundary conditions. For the spatial discretization, a modified Godunov type method that exploits the discrete finite-volume derivatives by using the so-called Taylor Series Expansion Scheme (TSES), is then designed to solve the equations. We report on numerical experiments using realistic parameters. Finally, the effects of a random small-scale forcing on the velocity equation is numerically investigated.

3

Numerical simulations of the humid atmosphere above a mountain

86%

Bousquet A. , Chekroun M. D. , Hong Y. , Temam R. M. , Tribbia J.

Mathematics of Climate and Weather Forecasting

|

2015

|

tom 1

|

nr 1

EN

New avenues are explored for the numerical study of the two dimensional inviscid hydrostatic primitive equations of the atmosphere with humidity and saturation, in presence of topography and subject to physically plausible boundary conditions for the system of equations. Flows above a mountain are classically treated by the so-called method of terrain following coordinate system. We avoid this discretization method which induces errors in the discretization of tangential derivatives near the topography. Instead we implement a first order finite volume method for the spatial discretization using the initial coordinates x and p. A compatibility condition similar to that related to the condition of incompressibility for the Navier- Stokes equations, is introduced. In that respect, a version of the projection method is considered to enforce the compatibility condition on the horizontal velocity field, which comes from the boundary conditions. For the spatial discretization, a modified Godunov type method that exploits the discrete finite-volume derivatives by using the so-called Taylor Series Expansion Scheme (TSES), is then designed to solve the equations. We report on numerical experiments using realistic parameters. Finally, the effects of a random small-scale forcing on the velocity equation is numerically investigated.

4

Transformation kinetic for instantaneous nucleation in the finite volume - application of statistical theory of shielding

86%

Burbelko A. A.

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2009

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tom Vol. 54, iss. 2

358-367

EN

The framework of the Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory is applied usually for the study of transition kinetics when the processes are ruled by nucleation and growth. This theory accurately describes only the transitions with the identical convex shape of new nuclei with the identical growth velocity distribution at an interface of the growing grains. The infinite initial volume of the mother phase is one of the indispensable conditions for the above theory. The proposed earlier extension of KJMA theory (statistical theory of the shielding growth) enlarges the scope of its application and eliminates the above limitation. The model of the transformation kinetics in the space of finite volume has been analyzed and discussed.

PL

W badaniach kinetyki procesów kontrolowanych zarodkowaniem i wzrostem skutecznie wykorzystuje się statystyczną teorię krystalizacji, podwaliny której zostały założone przez Kołmogorova, Jonhsona, Mehla i Avramiego (teoria KJMA). Powyższa teoria opisuje badane zjawiska precyzyjnie w przypadku, gdy wszystkie nowopowstające obiekty mają identyczny rozkład prędkości wzrostu na powierzchni (podobny kształt geometryczny), są wypukłe, a w przypadku anizotropii kształtu są identycznie zorientowane w przestrzeni. Jednym z założeń powyższej teorii jest nieskonczona objetość zanikającego materiału. Zaproponowane wczesniej rozszerzenie teorii KJMA (statystyczna teoria ekranowanego wzrostu) zwiększa zakres zastosowania klasycznych równań, pokonując niektóre ograniczenia. W artykule przedstawiono badania kinetyki wzrostu ziaren nowej fazy w przypadku małej objętosci fazy macierzystej.