The local microscale problem in the multiscale modeling of strongly heterogeneous media: Effects of boundary conditions and cell size

2007 ◽  
Vol 222 (2) ◽  
pp. 556-572 ◽  
Author(s):  
Xingye Yue ◽  
Weinan E
Keyword(s):  
Boundary Conditions ◽  
Cell Size ◽  
Multiscale Modeling ◽  
Media Effects ◽  
Heterogeneous Media

Comparison of Various Pressure Based Boundary Conditions for Three-Dimensional Subsonic DSMC Simulation

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Niraj Shah ◽  
Abhimanyu Gavasane ◽  
Amit Agrawal ◽  
Upendra Bhandarkar
Keyword(s):  
Boundary Conditions ◽  
Cell Size ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Direct Simulation Monte Carlo ◽  
Statistical Error ◽  
Nonequilibrium Effect ◽  
Time Required ◽  
Characteristic Scheme ◽  
Simulation Time

Three-dimensional (3D) direct simulation Monte Carlo (DSMC) has been used to simulate flow in a straight microchannel using an in-house parallelized code. In the present work, a comparative study of seven boundary conditions is carried out with respect to time required for achieving steady-state, accuracy in predicting the specified pressure at the boundaries, and the total simulation time required for attaining a statistical error within one percent. The effect of changing the Knudsen number, pressure ratio (PR), and cross aspect ratio (CAR) on these parameters is also studied. The presence of a boundary is seen to affect the simulated pressure in a cell when compared to the specified pressure, the difference being highest for corner cells and least for cells away from walls. All boundary conditions tested work well at the inlet boundary; however, similar results are not obtained at the outlet boundary. For the same cell size, the schemes that employ first- and second-order corrections lead to a smaller pressure difference compared to schemes applying no corrections. The best predictions can be obtained by using first-order corrections with finer cell size close to the boundary. For most of the simulated cases, the boundary condition employing the characteristic scheme with nonequilibrium effect leads to the minimum simulation time. Considering the nonequilibrium effect, prediction of inlet and outlet pressures and the speed of simulation, the characteristic scheme with nonequilibrium effect performs better than all the other schemes, at least over the range of parameters investigated herein.

Multiscale Modeling of Random Lattices: Critical Issues on Continuum Approximation

2011 ◽  
Author(s):  
Haifeng Zhao ◽  
Gregory J. Rodin
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Multiscale Modeling ◽  
Trigonometric Fourier Series ◽  
Continuum Approximation ◽  
Various Boundary Conditions ◽  
Random Lattices ◽  
Critical Issues

In this work, we are concerned that transmission of various boundary conditions through irregular lattices. The boundary conditions are parameterized using trigonometric Fourier series, and it is shown that, under certain conditions, transmission through irregular lattices can be well approximated by that through classical continuum. It is determined that such transmission must involve the wavelength of at least 12 lattice spacings; for smaller wavelength classical continuum approximations become increasingly inaccurate.

3D finite-difference dynamic-rupture modeling along nonplanar faults

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. SM123-SM137 ◽  
Author(s):  
Víctor M. Cruz-Atienza ◽  
Jean Virieux ◽  
Hideo Aochi
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Heterogeneous Media ◽  
Slip Rate ◽  
Quantitative Agreement ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Weight Functions ◽  
Dynamic Rupture ◽  
Fault Surface

Proper understanding of seismic emissions associated with the growth of complexly shaped microearthquake networks and larger-scale nonplanar fault ruptures, both in arbitrarily heterogeneous media, requires accurate modeling of the underlying dynamic processes. We present a new 3D dynamic-rupture, finite-difference model called the finite-difference, fault-element (FDFE) method; it simulates the dynamic rupture of nonplanar faults subjected to regional loads in complex media. FDFE is based on a 3D methodology for applying dynamic-rupture boundary conditions along the fault surface. The fault is discretized by a set of parallelepiped fault elements in which specific boundary conditions are applied. These conditions are applied to the stress tensor, once transformed into a local fault referenceframe. Numerically determined weight functions multiplying particle velocities around each element allow accurate estimates of fault kinematic parameters (i.e., slip and slip rate) independent of faulting mechanism. Assuming a Coulomb-like slip-weakening friction law, a parametric study suggests that the FDFE method converges toward a unique solution, provided that the cohesive zone behind the rupture front is well resolved (i.e., four or more elements inside this zone). Solutions are free of relevant numerical artifacts for grid sizes smaller than approximately [Formula: see text]. Results yielded by the FDFE approach are in good quantitative agreement with those obtained by a semianalytical boundary integral method along planar and nonplanar parabola-shaped faults. The FDFE method thus provides quantitative, accurate results for spontaneous-rupture simulations on intricate fault geometries.

Permeation of ions through a model biological channel: effect of periodic boundary conditions and cell size

2002 ◽  
Vol 100 (18) ◽  
pp. 3011-3019 ◽  
Author(s):  
YAN YANG ◽  
DAVID D. BUSATH ◽  
DOUGLAS HENDERSON ◽  
PAUL CROZIER ◽  
RICHARD L. ROWLEY
Keyword(s):  
Boundary Conditions ◽  
Cell Size ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Channel Effect

3D layer-to-layer orthogonal interlock woven composites under monotonic loading: Multiscale modeling

2017 ◽  
Vol 36 (17) ◽  
pp. 1263-1285 ◽  
Author(s):  
M Muthukumar ◽  
J Prasath ◽  
S Sathish ◽  
G Ravikumar ◽  
YM Desai ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Multiscale Modeling ◽  
Cross Section ◽  
Composite Structure ◽  
Volume Fraction ◽  
Woven Composites ◽  
Woven Composite ◽  
Fiber Volume ◽  
Element Analysis ◽  
Unit Cells

Multiscale modeling of 3D layer-to-layer orthogonal interlock woven composite structure for elastic and strength behavior is presented. Due to the inherent nature of weaving, 3D woven composites can be represented by repetitive unit cells at the meso level. The present study focuses on identifying different types of repetitive unit cells considering both the geometry and the boundary conditions. For a typical 3D layer-to-layer orthogonal interlock woven composite, there are eight types of meso repetitive unit cells taking into account both the geometry and the boundary conditions. Additionally, for a practical situation, fiber volume fraction (Vf) in the impregnated strand is not uniform throughout the cross-section. In other words, Vf would be different for different micro repetitive unit cells. The properties of the macro structure, i.e. the 3D woven composite structure has been determined by applying periodic boundary conditions at micro and meso levels and iso-strain conditions at the macro level using finite element analysis. The continuity between the blocks is provided by merging the nodes in the intersection regions. The effect of different Vf at different locations in the transverse cross-section of the strand on the elastic and the strength properties of 3D layer-to-layer woven composite structure is presented.

Multiscale Modeling of Heterogeneous Media Applying AEH to 3D Bodies

2012 ◽  
pp. 675-690
Author(s):  
Bárbara de Melo Quintela ◽  
Daniel Mendes Caldas ◽  
Michèle Cristina Resende Farage ◽  
Marcelo Lobosco
Keyword(s):  
Multiscale Modeling ◽  
Heterogeneous Media
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