2 Higher-order numerical schemes for heat, mass, and momentum transfer in fluid flow

2010 ◽  
pp. 19-60
Author(s):  
Mohsen M. M. Abou-Ellail ◽  
Yuan Li ◽  
Timothy W. Tong
Keyword(s):  
Fluid Flow ◽  
Momentum Transfer ◽  
Higher Order ◽  
Numerical Schemes

Pathwise convergent higher order numerical schemes for random ordinary differential equations

2007 ◽  
Vol 463 (2087) ◽  
pp. 2929-2944 ◽  
Author(s):  
Peter E Kloeden ◽  
Arnulf Jentzen
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
Vector Field ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Higher Order ◽  
Time Variable ◽  
Numerical Schemes ◽  
Hölder Continuous ◽  
Usual Order

Random ordinary differential equations (RODEs) are ordinary differential equations (ODEs) with a stochastic process in their vector field. They can be analysed pathwise using deterministic calculus, but since the driving stochastic process is usually only Hölder continuous in time, the vector field is not differentiable in the time variable, so traditional numerical schemes for ODEs do not achieve their usual order of convergence when applied to RODEs. Nevertheless deterministic calculus can still be used to derive higher order numerical schemes for RODEs via integral versions of implicit Taylor-like expansions. The theory is developed systematically here and applied to illustrative examples involving Brownian motion and fractional Brownian motion as the driving processes.

Higher Order Approximation of an Inelastic Fluid Flow

2003 ◽  
Vol 72 (4) ◽  
pp. 964-965
Author(s):  
Nirmal C. Sacheti ◽  
Pallath Chandran ◽  
Tayfour El-Bashir
Keyword(s):  
Fluid Flow ◽  
Order Approximation ◽  
Higher Order

Numerical schemes for unsteady fluid flow through collapsible tubes

1991 ◽  
Vol 13 (1) ◽  
pp. 10-18 ◽  
Author(s):  
D. Elad ◽  
D. Katz ◽  
E. Kimmel ◽  
S. Einav
Keyword(s):  
Fluid Flow ◽  
Numerical Schemes ◽  
Collapsible Tubes ◽  
Unsteady Fluid Flow ◽  
Flow Through ◽  
Unsteady Fluid

THE EFFECTS OF BOUNDARY CURVATURE ON HYDRODYNAMIC FLUID FLOW: CALCULATION OF SLIP LENGTHS

1992 ◽  
Vol 06 (20) ◽  
pp. 3251-3278 ◽  
Author(s):  
PETER PANZER ◽  
MARIO LIU ◽  
DIETRICH EINZEL
Keyword(s):  
Surface Roughness ◽  
Fluid Flow ◽  
Momentum Transfer ◽  
Free Path ◽  
Slip Length ◽  
Mean Free Path ◽  
Particle Scattering ◽  
Flow Calculation ◽  
Flow Past ◽  
Boundary Curvature

The slip description of fluid flow past solid boundaries is reconsidered. We find that the traditional picture of fluid slip as a mean free path correction to hydrodynamics has to be revised whenever the particle scattering becomes close to specular. Then the microscopic slip length may diverge and it is the boundary’s curvature which is decisive for the momentum transfer between fluid and wall. By explicitly considering surface roughness we can explain discrepancies between experimentally observed data and traditional slip theory.

A note on higher order numerical schemes for radioactivity migration

2012 ◽  
Vol 49 ◽  
pp. 227-231 ◽  
Author(s):  
Soubhadra Sen ◽  
N. Mohankumar
Keyword(s):  
Higher Order ◽  
Numerical Schemes

scholarly journals Convergence Analysis of a Numerical Method for a Fractional Model of Fluid Flow in Fractured Porous Media

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2179
Author(s):  
Dossan Baigereyev ◽  
Nurlana Alimbekova ◽  
Abdumauvlen Berdyshev ◽  
Muratkan Madiyarov
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Fractional Derivatives ◽  
Fractured Porous Media ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Numerical Schemes ◽  
Spatial Direction ◽  
Fully Discrete ◽  
Numerical Tests

The present paper is devoted to the construction and study of numerical methods for solving an initial boundary value problem for a differential equation containing several terms with fractional time derivatives in the sense of Caputo. This equation is suitable for describing the process of fluid flow in fractured porous media under some physical assumptions, and has an important applied significance in petroleum engineering. Two different approaches to constructing numerical schemes depending on orders of the fractional derivatives are proposed. The semi-discrete and fully discrete numerical schemes for solving the problem are analyzed. The construction of a fully discrete scheme is based on applying the finite difference approximation to time derivatives and the finite element method in the spatial direction. The approximation of the fractional derivatives in the sense of Caputo is carried out using the L1-method. The convergence of both numerical schemes is rigorously proved. The results of numerical tests conducted for model problems are provided to confirm the theoretical analysis. In addition, the proposed computational method is applied to study the flow of oil in a fractured porous medium within the framework of the considered model. Based on the results of the numerical tests, it was concluded that the model reproduces the characteristic features of the fluid flow process in the medium under consideration.

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