scholarly journals A poro-viscoelastic substitute model of fine-scale poroelasticity obtained from homogenization and numerical model reduction

2020 ◽  
Vol 65 (4) ◽  
pp. 1063-1083 ◽  
Author(s):  
Ralf Jänicke ◽  
Fredrik Larsson ◽  
Kenneth Runesson
Keyword(s):  
Numerical Model ◽  
Model Reduction ◽  
Evolution Equations ◽  
Present Model ◽  
Scale Model ◽  
Reduced Basis ◽  
Pressure Fields ◽  
Linearly Independent ◽  
Macro Scale ◽  
Scale Fluctuation

AbstractNumerical model reduction is exploited for computational homogenization of the model problem of a poroelastic medium under transient conditions. It is assumed that the displacement and pore pressure fields possess macro-scale and sub-scale (fluctuation) parts. A linearly independent reduced basis is constructed for the sub-scale pressure field using POD. The corresponding reduced basis for the displacement field is constructed in the spirit of the NTFA strategy. Evolution equations that define an apparent poro-viscoelastic macro-scale model are obtained from the continuity equation pertinent to the RVE. The present model represents an extension of models available in literature in the sense that the pressure gradient is allowed to have a non-zero macro-scale component in the nested $$\hbox {FE}^2$$FE2 setting. The numerical results show excellent agreement between the results from numerical model reduction and direct numerical simulation. It was also shown that even 3D RVEs give tractable solution times for full-fledged $$\hbox {FE}^2$$FE2 computations.

scholarly journals Combining spectral and POD modes to improve error estimation of numerical model reduction for porous media

2021 ◽  
Author(s):  
Fredrik Ekre ◽  
Fredrik Larsson ◽  
Kenneth Runesson ◽  
Ralf Jänicke
Keyword(s):  
Porous Media ◽  
Numerical Model ◽  
Model Reduction ◽  
Error Control ◽  
Mode Selection ◽  
Selection Strategy ◽  
Error Estimator ◽  
Reduced Basis ◽  
The One ◽  
Estimated Error

AbstractNumerical model reduction (NMR) is used to solve the microscale problem that arises from computational homogenization of a model problem of porous media with displacement and pressure as unknown fields. The reduction technique and an associated error estimator for the NMR error have been presented in prior work, where both spectral decomposition (SD) and proper orthogonal decomposition (POD) were used to construct the reduced basis. It was shown that the POD basis performs better w.r.t. minimizing the residual, but the SD basis has some advantageous properties for the estimator. Since it is the estimated error that will govern the error control, the most efficient procedure is the one that results in the lowest error bound. The main contribution of this paper is further development of the previous work with a proposed combined basis constructed using both SD and POD modes together with an adaptive mode selection strategy. The performance of the combined basis is compared to (i) the pure SD basis and (ii) the pure POD basis via numerical examples. The examples show that it is possible to find a combination of SD/POD modes which is improved, i.e. it yields a smaller estimate, compared to the cases of pure SD or pure POD.

scholarly journals A Global Multimoment Constrained Finite-Volume Scheme for Advection Transport on the Hexagonal Geodesic Grid

2011 ◽  
Vol 140 (3) ◽  
pp. 941-955 ◽  
Author(s):  
Chungang Chen ◽  
Juzhong Bin ◽  
Feng Xiao
Keyword(s):  
Numerical Model ◽  
Finite Volume ◽  
Present Method ◽  
Evolution Equations ◽  
Present Model ◽  
Spherical Geometry ◽  
Finite Volume Scheme ◽  
Third Order ◽  
Order Accuracy ◽  
Volume Scheme

Abstract A third-order numerical model is developed for global advection transport computation. The multimoment constrained finite-volume scheme has been implemented to the hexagonal geodesic grid for spherical geometry. Two kinds of moments (i.e., point value and volume-integrated average) are used as the constraint conditions to derive the time evolution equations to update the computational variables, which are the values defined at the specified points over each mesh element in the present model. The numerical model has rigorous numerical conservation and third-order accuracy. One of the major merits of the present method is that it does not explicitly involve numerical quadrature, which leads to great convenience in accurately computing curved geometry and source terms. The present paper provides an accurate and practical formulation for advection calculation in the hexagonal-type geodesic grid.

Solidification of Phase Change Material Nanocomposite Inside a Finned Heat Sink: A Macro Scale Model of Nanoparticles Distribution

2019 ◽  
Vol 11 (4) ◽  
Author(s):  
Santosh Kumar Sahoo ◽  
Prasenjit Rath ◽  
Mihir Kumar Das
Keyword(s):  
Numerical Model ◽  
Phase Change ◽  
Phase Change Material ◽  
Finite Volume ◽  
Heat Sink ◽  
Numerical Models ◽  
Scale Model ◽  
Transfer Model ◽  
Macro Scale ◽  
Change Material

The present work aims at developing a heat transfer model for phase change material nanocomposite (PCMNC)-based finned heat sink to study its heat rejection potential. The proposed model is developed in line with the binary alloy formulation for smaller size nanoparticles. The present study gives a more insight into the nanoparticle distribution while the nanocomposite is undergoing phase change. The nanocomposite is placed in the gap between the fins in a finned heat sink where solidification occurs from the top and lateral sides of fins. The proposed numerical model is based on finite volume method. Fully implicit scheme is used to discretize the transient terms in the governing transport equations. Natural convection in the molten nanocomposite is simulated using the semi-implicit-pressure-linked–equations-revised (SIMPLER) algorithm. Nanoparticle transport is coupled with the energy equation via Brownian and thermophoretic diffusion. Enthalpy porosity approach is used to model the phase change of PCMNC. Scheil rule is used to compute the nanoparticle concentration in the mixture consisting of solid and liquid PCMNC. All the finite volume discrete algebraic equations are solved using the line-by-line tridiagonal-matrix-algorithm with multiple sweeping from all possible directions. The proposed numerical model is validated with the existing analytical and numerical models. A comparison in thermal performance is made between the heat sink with homogeneous nanocomposite and with nonhomogeneous nanocomposite. Finally, the effect of spherical nanoparticles and platelet nanoparticles to the solidification behavior is compared.

A Numerical Model of In-Channel Pebble Bed Thermal Storage for a Solar Chimney

2012 ◽  
Author(s):  
Brandon Schulte ◽  
O. A. Plumb
Keyword(s):  
Numerical Model ◽  
Present Model ◽  
Thermal Storage ◽  
Implicit Time ◽  
Heat Transfer Characteristics ◽  
Solar Chimney ◽  
Pebble Bed ◽  
One Dimensional ◽  
Time Stepping ◽  
Daily Energy

In this study, solar chimney performance is numerically modeled. Previously published models have considered water bags and natural earth as means to store daytime thermal energy for nighttime operation of the system. The present model considers in-channel pebble bed thermal storage. A one-dimensional, implicit time stepping numerical model is developed to predict solar chimney performance throughout a 24 hour period. The model is partially verified with available experimental data. The daily energy, daily efficiency and heat transfer characteristics of the solar chimney with pebble bed thermal storage are summarized. The numerical simulation showed that by introducing a pebble bed, nightly exit velocities reach 40% of the peak daytime velocity. However, the daily kinetic energy delivered by a solar chimney with pebble bed thermal storage is much less than a traditional solar chimney, suggesting pebble bed thermal storage is more practicable in building heating applications as opposed to power generation.

The Influence of Grain Size and Grain Size Distribution on Sliding Frictional Contact in Laterally Graded Materials

2012 ◽  
Vol 157-158 ◽  
pp. 964-969 ◽  
Author(s):  
Romik Khajehtourian ◽  
Saeed Adibnazari ◽  
Samaneh Tashi
Keyword(s):  
Grain Size ◽  
Half Plane ◽  
Frictional Contact ◽  
Crack Nucleation ◽  
Functionally Graded ◽  
Scale Model ◽  
Effective Parameters ◽  
Graded Materials ◽  
Macro Scale ◽  
Comparison Of The Results

The sliding frictional contact problem for a laterally graded half-plane has been considered. Two finite element (FE) models, in macro and micro scales have been developed to investigate the effective parameters in contact mechanics of laterally graded materials loaded by flat and triangular rigid stamps. In macro scale model, the laterally graded half-plane is discretized by piecewise homogeneous layers for which the material properties are specified at the centroids by Mori-Tanaka method. In micro scale model, functionally graded material (FGM) structure has been modeled as ideal solid quadrant particles which are spatially distributed in a homogeneous matrix. Boundary conditions and loading is the same in both models. The microstructure has modeled as rearrangement and sizes changing of particles are possible to provide the possibility of crack nucleation investigation in non-singular regions. Analyses and comparison of the results showed that micro and macro scale results are in very good agreement. Also, increasing the grains aspect ratio and using optimum distribution of grains decrease stress distribution roughness on the surface. Therefore, the possibility of surface cracking far from stamp’s edges decreased.

Wave Energy-Driven Resonant Sea-Water Pump

1997 ◽  
Vol 119 (3) ◽  
pp. 191-195 ◽  
Author(s):  
S. P. R. Czitrom
Keyword(s):  
Numerical Model ◽  
Sea Water ◽  
Scale Model ◽  
Water Pump ◽  
Incoming Wave ◽  
Frequency Wave ◽  
Variable Volume ◽  
Mass Spring ◽  
Air Compression ◽  
Compression Chamber

A wave-driven sea-water pump which operates by resonance is described. Oscillations in the resonant and exhaust ducts perform similar to two mass-spring systems coupled by a third spring acting for the compression chamber. Performance of the pump is optimized by means of a variable volume air compression chamber (patents pending) which tunes the system to the incoming wave frequency. Wave tank experiments with an instrumented, 1:20-scale model of the pump are described. Performance was studied under various wave and tuning conditions and compared to a numerical model which was found to describe the system accurately. Successful sea trials at an energetic coastline provide evidence of the system’s viability under demanding conditions.

scholarly journals THE USE OF ARRAY PROCESSORS FOR NUMERICAL MODELLING OF TIDAL ESTUARY DYNAMICS

1980 ◽  
Vol 1 (17) ◽  
pp. 142
Author(s):  
D. Prandle ◽  
E.R. Funke ◽  
N.L. Crookshank ◽  
R. Renner
Keyword(s):  
Numerical Model ◽  
Numerical Modelling ◽  
Hybrid Model ◽  
Numerical Models ◽  
Computer Time ◽  
Scale Model ◽  
Hybrid Modelling ◽  
Tidal Propagation ◽  
Physical Scale ◽  
Array Processors

The use of array processors for the numerical modelling of estuarine systems is discussed here in the context of "hybrid modelling", however, it is shown that array processors may be used to advantage in independent numerical simulations. Hybrid modelling of tidal estuaries was first introduced by fiolz (1977) and later by Funke and Crookshank (1978). In a hybrid model, tidal propagation in an estuary is simulated by dynamically linking an hydraulic (or physical) scale model of part of the estuary to a numerical model of the remaining part in a manner such that a free interchange of flow occurs at the interface(s). Typically, the elevation of the water surface at the boundary of the scale model is measured and transmitted to the numerical model. In return, the flow computed at the boundary of the numerical model is fed directly into the scale model. This approach enables the extent of the scale model to be limited to the area of immediate interest (or to that area where flow conditions are such that they can be most accurately simulated by a scale model). In addition, since the region simulated by the numerical model can be extended almost indefinitely, the problems of spurious reflections from downstream boundaries can be eliminated. In normal use, numerical models are evaluated on the basis of computing requirements, cost and accuracy. The computer time required to simulate one tide cycle is, in itself, seldom of interest except in so far as it affects the above criteria. However in hybrid modelling this parameter is often paramount since concurrent operation of the numerical and scale models requires that the former must keep pace with the latter. The earlier hybrid model of the St. Lawrence (Funke and Crookshank, 1978) involved a one-dimensional numerical model of the upstream regions of the river. However, future applications are likely to involve extensive two-dimensional numerical simulation.

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