Multiscale Simulation Of Transport Research Articles

Hybrid [formula omitted] with Lagrange multiplier and upwinding for the multiscale transport capability in Rattlesnake

Two interface conditions, the Lagrange multiplier method and the upwinding method, for hybrid PN-SN calculations are proposed for the self-adjoint angular flux (SAAF) formulation of the transport equation using the continuous finite element method (FEM) for spatial discretization. These interface conditions are implemented in Rattlesnake, the radiation transport application built on MOOSE, for the on-going multiscale transport simulation effort at INL. For smoothing the solution at the interface for the Lagrange multiplier method, a SN Lagrange interpolation method on the unit sphere is proposed. The discrete PN interface condition with upwinding method for coupling the SN solution is desired. Numerical results indicate that the interface conditions give the expected convergence.

Influence of Binder Porosity on Gdl Gas Phase Transport

In polymer electrolyte fuels (PEFC) carbon fiber based gas diffusion layers (GDL) are used for fine distribution of reactant gases from the flow field channels to the catalyst layer (CL). It is a key component for PEFC as it serves also for water removal from the CL as well as heat and electricity transport between CL and the flow field plates. GDL materials can be classified as woven, felts, papers, where the later type requires a binder to mechanically stabilize the fiber arrangement. While most GDL binders are solid, the binder of SGL GDLs appears porous and it’s influence on gas phase transport is unclear [1]. In SEM surface images of SGL, GDL binder domains of appear as flake like fine-structure with particles of about 100 to 300 nm (see Fig. 1a). Here, we apply multi-dimensional X-ray imaging techniques and multi-scale numerical simulations to clarify possible contributions of the binder porosity to overall GDL gas transport. Absorption contrast X-ray tomographic microscopy measurements at the TOMCAT beamline of the Swiss Light Source (SLS) with voxel sizes of minimum 0.16 µm revealed a high porosity (59 %) of SGL 24 BA binder domains of (Fig. 1b). Computational transport simulations on the segmented binder structures showed, that the binder domains provide isotropic effective diffusivity of 0.30. In order to quantify the contribution of the porous binder to the overall fluid transport in the GDL, the obtained binder diffusivity values were used in multi-scale transport simulations of ternary segmented XTM data of representative GDL samples with 2.2 µm voxel size. If the binder was treated as solid, through-plane effective diffusivity of the GDL of 0.1 was obtained. If we applied a multi-scale simulation approach, that treats the binder domain as porous and uses the transport parameters of the binder domain as input values for the coarse scale simulations of the whole GDL domain, the through-plane effective diffusivity increased to 0.4 (+300 %). These numbers will be verified by X-ray ptychograptic computed tomography measurements of the binder fine structure at the cSAXS beamline of the SLS that proved resolutions of up to 16 nm [2].

High-precision synthetic computed tomography of reconstructed porous media

Multiscale simulation of transport in disordered and porous media requires microstructures covering several decades in length scale. X-ray and synchrotron computed tomography are presently unable to resolve more than one decade of geometric detail. Recent advances in pore scale modeling [Biswal, Held, Khanna, Wang, and Hilfer, Phys. Rev. E 80, 041301 (2009)] provide strongly correlated microstructures with several decades in microstructural detail. A carefully calibrated microstructure model for Fontainebleau sandstone has been discretized into a suite of three-dimensional microstructures with resolutions from roughly 128 μm down to roughly 500 nm. At the highest resolution the three-dimensional image consists of 32768^{3}=35184372088832 discrete cubic volume elements with gray values between 0 and 216. To the best of our knowledge, this synthetic image is the largest computed tomogram of a porous medium available at present.

Flow-based coarsening for multiscale simulation of transport in porous media

Geological models are becoming increasingly large and detailed to account for heterogeneous structures on different spatial scales. To obtain simulation models that are computationally tractable, it is common to remove spatial detail from the geological description by upscaling. Pressure and transport equations are different in nature and generally require different strategies for optimal upgridding. To optimize the accuracy of a transport calculation, the coarsened grid should generally be constructed based on a posteriori error estimates and adapt to the flow patterns predicted by the pressure equation. However, sharp and rigorous estimates are generally hard to obtain, and herein we therefore consider various ad hoc methods for generating flow-adapted grids. Common for all is that they start by solving a single-phase flow problem once and then continue to form a coarsened grid by amalgamating cells from an underlying fine-scale grid. We present several variations of the original method. First, we discuss how to include a priori information in the coarsening process, e.g. to adapt to special geological features or to obtain less irregular grids in regions where flow-adaption is not crucial. Second, we discuss the use of bi-directional versus net fluxes over the coarse blocks and show how the latter gives systems that better represent the causality in the flow equations, which can be exploited to develop very efficient nonlinear solvers. Finally, we demonstrate how to improve simulation accuracy by dynamically adding local resolution near strong saturation fronts.

Multi-scale Transport Simulation of Non-local Turbulent Effect on Internal Transport Barrier Collapse in Tokamak Plasma

Multi-scale Transport Simulation of Non-local Turbulent Effect on Internal Transport Barrier Collapse in Tokamak Plasma

Multi-scale transport simulation of toroidal momentum source profile effect on internal transport barrier collapse

The mechanism of internal transport barrier (ITB) collapse in the reversed magnetic shear configuration is investigated using a global ion temperature gradient (ITG) driven drift wave turbulence code. A heating source and a toroidal momentum source are introduced to follow the self-consistent evolution of the ion temperature and flow profiles. A scenario of transport barrier collapse driven by a meso-scale mode excited in the barrier region is suggested. The importance of the quasi-linear effect due to profile modification as well as three-wave coupling is clearly shown by means of energy transfer analysis. The effect of the toroidal flow shear (TFS) profile on the dynamics of ITB evolution is investigated. It is found that the decorrelation between meso-scale modes and ITG driven modes due to the TFS can prevent global relaxation.

Numerical analysis of a multiscale finite element scheme for the resolution of the stationary Schrödinger equation

A numerical method for the resolution of the one-dimensional Schrodinger equation with open boundary conditions was presented in N. Ben Abdallah and O. Pinaud (Multiscale simulation of transport in an open quantum system: resonances and WKB interpolation. J. Comp. Phys. 213(1), 288–310 (2006)). The main attribute of this method is a significant reduction of the computational cost for a desired accuracy. It is based particularly on the derivation of WKB basis functions, better suited for the approximation of highly oscillating wave functions than the standard polynomial interpolation functions. The present paper is concerned with the numerical analysis of this method. Consistency and stability results are presented. An error estimate in terms of the mesh size and independent on the wavelength λ is established. This property illustrates the importance of this method, as multiwavelength grids can be chosen to get accurate results, reducing by this manner the simulation time.

Multiscale simulation of transport in an open quantum system: Resonances and WKB interpolation

A numerical scheme for the one-dimensional stationary Schrödinger–Poisson model is described. The scheme is used to simulate a resonant tunneling diode and provides an important reduction of the simulation time. The improvement is twofold. First the grid spacing in the position variable is made coarser by using oscillating interpolation functions derived from the WKB asymptotics. Then the discretization of the energy variable, which is a parameter for the Schrödinger equation, is improved by approaching the wavefunctions in the double barrier region by its projection on the resonant states (following the work of Presilla–Sjöstrand and Jona-Lasinio [On Schrödinger equations with concentrated non-linearities, Ann. Phys. 240 (1995) 1–21]).