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Grid Refinement (grid + refinement)

Distribution by Scientific Domains
Engineering80%

Kinds of Grid Refinement

  • local grid refinement
    		•

    Selected Abstracts

    A practical grid-based method for tracking multiple refraction and reflection phases in three-dimensional heterogeneous media

    GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2006
    M. De Kool
    SUMMARY We present a practical grid-based method in 3-D spherical coordinates for computing multiple phases comprising any number of reflection and transmission branches in heterogeneous layered media. The new scheme is based on a multistage approach which treats each layer that the wave front enters as a separate computational domain. A finite-difference eikonal solver known as the fast-marching method (FMM) is reinitialized at each interface to track the evolving wave front as either a reflection back into the incident layer or a transmission through to the adjacent layer. Unlike the standard FMM, which only finds first arrivals, this multistage approach can track those later arriving phases explicitly caused by the presence of discontinuities. Notably, the method does not require an irregular mesh to be constructed in order to connect interface nodes to neighbouring velocity nodes which lie on a regular grid. To improve accuracy, local grid refinement is used in the neighbourhood of a source point where wave front curvature is high. The method also provides a way to trace reflections from an interface that are not the first arrival (e.g. the global PP phase). These are computed by initializing the multistage FMM from both the source and receiver, propagating the two wave fronts to the reflecting interface, and finding stationary points of the sum of the two traveltime fields on the reflecting interface. A series of examples are presented to test the efficiency, accuracy and robustness of the new scheme. As well as efficiently computing various global phases to an acceptable accuracy through the ak135 model, we also demonstrate the ability of the scheme to track complex crustal phases that may be encountered in coincident reflection, wide-angle reflection/refraction or local earthquake surveys. In one example, a variety of phases are computed in the presence of a realistic subduction zone, which includes several layer pinch-outs and a subducting slab. Our numerical tests show that the new scheme is a practical and robust alternative to conventional ray tracing for finding various phases in layered media at a variety of scales. [source]

    A Hybrid Finite-Difference and Analytic Element Groundwater Model

    GROUND WATER, Issue 4 2010
    H.M. Haitjema
    Regional finite-difference models tend to have large cell sizes, often on the order of 1,2 km on a side. Although the regional flow patterns in deeper formations may be adequately represented by such a model, the intricate surface water and groundwater interactions in the shallower layers are not. Several stream reaches and nearby wells may occur in a single cell, precluding any meaningful modeling of the surface water and groundwater interactions between the individual features. We propose to replace the upper MODFLOW layer or layers, in which the surface water and groundwater interactions occur, by an analytic element model (GFLOW) that does not employ a model grid; instead, it represents wells and surface waters directly by the use of point-sinks and line-sinks. For many practical cases it suffices to provide GFLOW with the vertical leakage rates calculated in the original coarse MODFLOW model in order to obtain a good representation of surface water and groundwater interactions. However, when the combined transmissivities in the deeper (MODFLOW) layers dominate, the accuracy of the GFLOW solution diminishes. For those cases, an iterative coupling procedure, whereby the leakages between the GFLOW and MODFLOW model are updated, appreciably improves the overall solution, albeit at considerable computational cost. The coupled GFLOW,MODFLOW model is applicable to relatively large areas, in many cases to the entire model domain, thus forming an attractive alternative to local grid refinement or inset models. [source]

    The identification of a Robin coefficient by a conjugate gradient method

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2009
    Fenglian Yang
    Abstract This paper investigates a non-linear inverse problem associated with the heat conduction problem of identifying a Robin coefficient from boundary temperature measurement. The variational formulation of the problem is given. The conjugate gradient method combining with the discrepancy principle for choosing the suitable stop step are proposed for solving the optimization problem, in which the finite difference method is used to solve the direct problems. The performance of the method is verified by simulating four examples. The convergence with respect to the grid refinement and the amount of noise in the data is also investigated. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    An adaptive multiresolution method for parabolic PDEs with time-step control

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2009
    M. O. Domingues
    Abstract We present an efficient adaptive numerical scheme for parabolic partial differential equations based on a finite volume (FV) discretization with explicit time discretization using embedded Runge,Kutta (RK) schemes. A multiresolution strategy allows local grid refinement while controlling the approximation error in space. The costly fluxes are evaluated on the adaptive grid only. Compact RK methods of second and third order are then used to choose automatically the new time step while controlling the approximation error in time. Non-admissible choices of the time step are avoided by limiting its variation. The implementation of the multiresolution representation uses a dynamic tree data structure, which allows memory compression and CPU time reduction. This new numerical scheme is validated using different classical test problems in one, two and three space dimensions. The gain in memory and CPU time with respect to the FV scheme on a regular grid is reported, which demonstrates the efficiency of the new method. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    A least square extrapolation method for the a posteriori error estimate of the incompressible Navier Stokes problem

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2005
    M. Garbey
    Abstract A posteriori error estimators are fundamental tools for providing confidence in the numerical computation of PDEs. To date, the main theories of a posteriori estimators have been developed largely in the finite element framework, for either linear elliptic operators or non-linear PDEs in the absence of disparate length scales. On the other hand, there is a strong interest in using grid refinement combined with Richardson extrapolation to produce CFD solutions with improved accuracy and, therefore, a posteriori error estimates. But in practice, the effective order of a numerical method often depends on space location and is not uniform, rendering the Richardson extrapolation method unreliable. We have recently introduced (Garbey, 13th International Conference on Domain Decomposition, Barcelona, 2002; 379,386; Garbey and Shyy, J. Comput. Phys. 2003; 186:1,23) a new method which estimates the order of convergence of a computation as the solution of a least square minimization problem on the residual. This method, called least square extrapolation, introduces a framework facilitating multi-level extrapolation, improves accuracy and provides a posteriori error estimate. This method can accommodate different grid arrangements. The goal of this paper is to investigate the power and limits of this method via incompressible Navier Stokes flow computations. Copyright © 2005 John Wiley & Sons, Ltd. [source]

    Patched grid and adaptive mesh refinement strategies for the calculation of the transport of vortices

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2002
    A. Benkenida
    Abstract This paper presents two techniques allowing local grid refinement to calculate the transport of vortices. one is the patched grid (PG) method which allows non-coincident interfaces between blocks. Treatment of the non-coincident interfaces is given in detail. The second one is the adaptive mesh refinement (AMR) method which has been developed in order to create embedded sub-grids. The efficiency of these two methods is demonstrated by some validating tests. Then the PG and AMR strategies are applied in the computation of the transport of vortices. We start with a simple vortex flow in a cubic box. Then, the flowfield around a complex aircraft configuration is calculated using the two refinement techniques. Results are compared with a fine, referenced grid calculation. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    A multi-block lattice Boltzmann method for viscous fluid flows

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2002
    Dazhi Yu
    Abstract Compared to the Navier,Stokes equation-based approach, the method of lattice Boltzmann Equation (LBE) offers an alternative treatment for fluid dynamics. The LBE method often employs uniform lattices to maintain a compact and efficient computational procedure, which makes it less efficient to perform flow simulations when there is a need for high resolution near the body and/or there is a far-field boundary. To resolve these difficulties, a multi-block method is developed. An accurate, conservative interface treatment between neighboring blocks is adopted, and demonstrated that it satisfies the continuity of mass, momentum, and stresses across the interface. Several test cases are employed to assess accuracy improvement with respect to grid refinement, the impact of the corner singularity, and the Reynolds number scaling. The present multi-block method can substantially improve the accuracy and computational efficiency of the LBE method for viscous flow computations. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    The shallow flow equations solved on adaptive quadtree grids

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2001
    A. G. L. Borthwick
    Abstract This paper describes an adaptive quadtree grid-based solver of the depth-averaged shallow water equations. The model is designed to approximate flows in complicated large-scale shallow domains while focusing on important smaller-scale localized flow features. Quadtree grids are created automatically by recursive subdivision of a rectangle about discretized boundary, bathymetric or flow-related seeding points. It can be fitted in a fractal-like sense by local grid refinement to any boundary, however distorted, provided absolute convergence to the boundary is not required and a low level of stepped boundary can be tolerated. Grid information is stored as a tree data structure, with a novel indexing system used to link information on the quadtree to a finite volume discretization of the governing equations. As the flow field develops, the grids may be adapted using a parameter based on vorticity and grid cell size. The numerical model is validated using standard benchmark tests, including seiches, Coriolis-induced set-up, jet-forced flow in a circular reservoir, and wetting and drying. Wind-induced flow in the Nichupté Lagoon, México, provides an illustrative example of an application to flow in extremely complicated multi-connected regions. Copyright © 2001 John Wiley & Sons, Ltd. [source]

    Finite volume multigrid method of the planar contraction flow of a viscoelastic fluid

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2001
    H. Al Moatssime
    Abstract This paper reports on a numerical algorithm for the steady flow of viscoelastic fluid. The conservative and constitutive equations are solved using the finite volume method (FVM) with a hybrid scheme for the velocities and first-order upwind approximation for the viscoelastic stress. A non-uniform staggered grid system is used. The iterative SIMPLE algorithm is employed to relax the coupled momentum and continuity equations. The non-linear algebraic equations over the flow domain are solved iteratively by the symmetrical coupled Gauss,Seidel (SCGS) method. In both, the full approximation storage (FAS) multigrid algorithm is used. An Oldroyd-B fluid model was selected for the calculation. Results are reported for planar 4:1 abrupt contraction at various Weissenberg numbers. The solutions are found to be stable and smooth. The solutions show that at high Weissenberg number the domain must be long enough. The convergence of the method has been verified with grid refinement. All the calculations have been performed on a PC equipped with a Pentium III processor at 550 MHz. Copyright © 2001 John Wiley & Sons, Ltd. [source]

    Progress in the Modelling of Air Flow Patterns in Softwood Timber Kilns

    ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING, Issue 3-4 2004
    T.A.G. Langrish
    Progress in modelling air flow patterns in timber kilns using computational fluid dynamics (CFD) is reviewed in this work. These simulations are intended to predict the distribution of the flow in the fillet spaces between boards in a hydraulic model of a timber kiln. Here, the flow regime between the boards is transitional between laminar and turbulent flow, with Reynolds numbers of the order of 5000. Running the simulation as a transient calculation has shown few problems with convergence issues, reaching a mass residual of 0.2% of the total inflow after 40 to 100 iterations per time step for time steps of 0.01 s. Grid sensitivity studies have shown that non-uniform grids are necessary because of the sudden changes in flow cross section, and the flow simulations are insensitive to grid refinement for non-uniform grids with more than 300,000 cells. The best agreement between the experimentally-measured flow distributions between fillet spaces and those predicted by the simulation have been achieved for (effective) bulk viscosities between the laminar viscosity for water and ten times that value. This change in viscosity is not very large (less than an order of magnitude), given that effective turbulent viscosities are typically several orders of magnitude greater than laminar ones. This result is consistent with the transitional flows here. The effect of weights above the stack can reduce the degree of non-uniformity in air velocities through the stack, especially when thick weights are used, because the stack may then be separated from the eddy at the top of the plenum chamber. [source]