Solution of the 2D Navier-Stokes equations on unstructured adaptive grids

Holmes, D. Graham; Connell, Stuart

doi:10.2514/6.1989-1932

Cited by 188 publications

(119 citation statements)

References 4 publications

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“…The merits of unstructured grids are that the lack of grid structure makes it possible to mesh arbitrary geometries with relative easiness, and offers capability to locally adapt the grid by simply adding extra grid points where they are needed, to improve the accuracy of the computation without incurring the penalties associated with global refinement (Anderson & Bonhaus, 1994;Holmes & Connell, 1989). The control volumes are formed by dividing the study region into a finite number of irregular elements such as triangles or quadrilaterals.…”

Section: Introductionmentioning

confidence: 99%

An Approach to Inundation Simulation in Large River Basins Using the Triangle Finite Difference Method

Zhang

2004

J ENV INFORM

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ABSTRACT. Disastrous flooding and inundation events have drawn much attention in regional sustainable development due to extensive life loss and property damage they have caused. To support river basin management practice, it is necessary to simulate flood inundation such that associated risks can be integrated into decision-making processes. Flood inundation is generally simulated by the 2-dimensional Saint Venant equations (2D SVEs), in which inertia terms are neglected in most cases, particularly in large floodplains. In this study, a diffusive wave model discretized by an implicit numerical scheme of the irregular triangle finite difference method (TFDM) was developed to examine the effect of arbitrary inner and outer boundaries within a floodplain. A case study has been conducted in the Fuefuki River basin in central Japan. Comparisons with simulation using complete 2D SVEs are made in this study. Results indicate that both the diffusive wave model and its TFDM numerical scheme are effective and accurate in the simulation of flood inundation.

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Section: Introductionmentioning

confidence: 99%

An Approach to Inundation Simulation in Large River Basins Using the Triangle Finite Difference Method

Zhang

2004

J ENV INFORM

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“…Further details about the discretization of the flow variables and different solution schemes used by the code can be found in the FLUENT documentation and also in the literature (e.g. Patankar, 1980;Issa, 1986;Berth and Jespersen, 1989;Holmes and Connell, 1989). The code is supplemented by a proprietary CAD based geometry construction and meshing engine, which allows users to build and mesh complex flow models to be used by the solver.…”

Section: Methodsmentioning

confidence: 99%

Characterization of in-Situ Stress and Permeability in Fractured Reservoirs

Burns¹,

Toksoz²

2004

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Expanded details and additional results are presented on two methods for estimating fracture orientation and density in subsurface reservoirs from scattered seismic wavefield signals. In the first, fracture density is estimated from the wavenumber spectra of the integrated amplitudes of the scattered waves as a function of offset in pre-stack data.Spectral peaks correctly identified the 50m, 35m, and 25m fracture spacings from numerical model data using a 40Hz source wavelet. The second method, referred to as the Transfer Function-Scattering Index Method, is based upon observations from 3D finite difference modeling that regularly spaced, discrete vertical fractures impart a ringing coda-type signature to any seismic energy that is transmitted through or reflected off of them. This coda energy is greatest when the acquisition direction is parallel to the fractures, the seismic wavelengths are tuned to the fracture spacing, and when the fractures have low stiffness. The method uses surface seismic reflection traces to derive a transfer function, which quantifies the change in an apparent source wavelet propagating through a fractured interval. The transfer function for an interval with low scattering will be more spike-like and temporally compact. The transfer function for an interval with high scattering will ring and be less temporally compact. A Scattering Index is developed based on a time lag weighting of the transfer function. When a 3D survey is acquired with a full range of azimuths, the Scattering Index allows the identification of subsurface areas with high fracturing and the orientation (or strike) of those fractures. The method was calibrated with model data and then applied to field data from a fractured reservoir giving results that agree with known field measurements.As an aid to understanding the scattered wavefield seen in finite difference models, a series of simple point scatterers was used to create synthetic seismic shot records collected over regular, discrete, vertical fracture systems. The model contains a series of point scatterers delineating the top tip and bottom tip of each vertical fracture. When the shot record is located in the middle of the fractured zone and oriented normal to the direction of fracturing, a complicated series of beating is observed in the back scattered MIT DOE DE-FC26-02NT15346 7/22/04 4 energy. When the shot record is oriented parallel to the fracturing, ringing wavetrains are observed with moveouts similar to reflections from many horizontal layers. These results are consistent with the full 3D elastic modeling results.An AVOA analysis method was refined and applied to a field data set. An iterative, nonlinear least squares inversion that uses the Gauss-Newton method and analyzes the full range of azimuths simultaneously was employed. Resulting fracture location and strike orientation estimates are consistent with other fracture information from the area.Two modeling approaches for estimating permeability values from seismically derived fracture parame...

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“…Equation (37) shows that the proposed source term treatment preserves the quiescent equilibrium perfectly. Equation (36) may seem similar to Equation (30) in [26], but is based on a different mathematical formulation and slope source flux computation through the interface. The proposed method of considering the reconstructed water depth at both sides of the interface in averaging water depths for source terms and convective flux serves to eliminate any chance for instabilities to arise due to a discontinuity of conserved variables at an interface caused by abrupt change in bed elevation.…”

Section: Slope Term Treatment and Preservation Of C-propertymentioning

confidence: 99%

“…A pseudo-Laplacian formula proposed Holmes and Connell in [30] is used to compute the values of conserved variables at vertices for gradient computation. The vertex values are given by the following equation:…”

Section: Variable Reconstruction and Limitingmentioning

confidence: 99%

Novel Slope Source Term Treatment for Preservation of Quiescent Steady States in Shallow Water Flows

Rehman

Cho

2016

Water

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This paper proposes a robust method for modeling shallow-water flows and near shore tsunami propagation, applicable for both simple and complex geometries with uneven beds. The novel aspect of the model includes the introduction of a new method for slope source terms treatment to preserve quiescent equilibrium over uneven topographies, applicable to both structured and unstructured mesh systems with equal accuracy. Our model is based on the Godunov-type finite volume numerical approximation. Second-order spatial and temporal accuracy is achieved through high resolution gradient reconstruction and the predictor-corrector method, respectively. The approximate Riemann solver of Harten, Lax, and van Leer with contact wave restoration (HLLC) is used to compute fluxes. Comparisons of the model's results with analytical, experimental, and published numerical solutions show that the proposed method is capable of accurately predicting experimental and real-time tsunami propagation/inundation, and dam-break flows over varying topographies.

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Solution of the 2D Navier-Stokes equations on unstructured adaptive grids

Cited by 188 publications

References 4 publications

An Approach to Inundation Simulation in Large River Basins Using the Triangle Finite Difference Method

An Approach to Inundation Simulation in Large River Basins Using the Triangle Finite Difference Method

Characterization of in-Situ Stress and Permeability in Fractured Reservoirs

Novel Slope Source Term Treatment for Preservation of Quiescent Steady States in Shallow Water Flows

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