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Unstructured Grids (unstructured + grid)

Distribution by Scientific Domains

Engineering	96%

Kinds of Unstructured Grids

arbitrary unstructured grid

Selected Abstracts

Unstructured grid generation using LiDAR data for urban flood inundation modelling

HYDROLOGICAL PROCESSES, Issue 11 2010
Ryota Tsubaki
Abstract Inundation disasters, caused by sudden water level rise or rapid flow, occur frequently in various parts of the world. Such catastrophes strike not only in thinly populated flood plains or farmland but also in highly populated villages or urban areas. Inundation of the populated areas causes severe damage to the economy, injury, and loss of life; therefore, a proper management scheme for the disaster has to be developed. To predict and manage such adversity, an understanding of the dynamic processes of inundation flow is necessary because risk estimation is performed based on inundation flow information. In this study, we developed a comprehensive method to conduct detailed inundation flow simulations for a populated area with quite complex topographical features using LiDAR (Light Detection and Ranging) data. Detailed geospatial information including the location and shape of each building was extracted from the LiDAR data and used for the grid generation. The developed approach can distinguish buildings from vegetation and treat them differently in the flow model. With this method, a fine unstructured grid can be generated representing the complicated urban land features precisely without exhausting labour for data preparation. The accuracy of the generated grid with different grid spacing and grid type is discussed and the optimal range of grid spacing for direct representation of urban topography is investigated. The developed method is applied to the estimation of inundation flows, which occurred in the basin of the Shin-minato River. A detailed inundation flow structure is represented by the flow model, and the flow characteristics with respect to topographic features are discussed. Copyright © 2010 John Wiley & Sons, Ltd. [source]

Implicit enthalpy formulation of phase-change problems on unstructured grid

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2003
J. Caldwell
Abstract This paper presents an implicit finite-volume enthalpy formulation of the multidimensional phase-change problems involving a unique phase-change temperature. The derived formulation provides a simple method for local tracking of interface using the enthalpy variable on both structured as well as unstructured grids in a novel way. Results of economic computations of previously published problems are presented. Copyright © 2003 John Wiley & Sons, Ltd. [source]

PC cluster parallel finite element analysis of sloshing problem by earthquake using different network environments

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2002
Kazuo Kashiyama
Abstract This paper presents a parallel finite element method for the analysis of the sloshing problem caused by earthquakes. The incompressible Navier,Stokes equation based on Arbitrary Lagrangian,Eulerian description is used as the governing equation. The SUPG/PSPG formulation is employed to improve the numerical stability and the accuracy. Parallel implementation of the unstructured grid based formulation was carried out on a PC cluster. The present method was applied to analyse the sloshing problem of a rectangular tank and an actual reservoir. The effect of parallelization on the efficiency of the computations was examined using a number of different network environments. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Anisotropic mesh adaption by metric-driven optimization

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2004
Carlo L. Bottasso
Abstract We describe a Gauss,Seidel algorithm for optimizing a three-dimensional unstructured grid so as to conform to a given metric. The objective function for the optimization process is based on the maximum value of an elemental residual measuring the distance of any simplex in the grid to the local target metric. We analyse different possible choices for the objective function, and we highlight their relative merits and deficiencies. Alternative strategies for conducting the optimization are compared and contrasted in terms of resulting grid quality and computational costs. Numerical simulations are used for demonstrating the features of the proposed methodology, and for studying some of its characteristics. Copyright © 2004 John Wiley & Sons, Ltd. [source]

An accurate gradient and Hessian reconstruction method for cell-centered finite volume discretizations on general unstructured grids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2010
Lee J. Betchen
Abstract In this paper, a novel reconstruction of the gradient and Hessian tensors on an arbitrary unstructured grid, developed for implementation in a cell-centered finite volume framework, is presented. The reconstruction, based on the application of Gauss' theorem, provides a fully second-order accurate estimate of the gradient, along with a first-order estimate of the Hessian tensor. The reconstruction is implemented through the construction of coefficient matrices for the gradient components and independent components of the Hessian tensor, resulting in a linear system for the gradient and Hessian fields, which may be solved to an arbitrary precision by employing one of the many methods available for the efficient inversion of large sparse matrices. Numerical experiments are conducted to demonstrate the accuracy, robustness, and computational efficiency of the reconstruction by comparison with other common methods. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Multigrid convergence acceleration for implicit and explicit solution of Euler equations on unstructured grids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2010
Ali Ramezani
Abstract The multigrid method is one of the most efficient techniques for convergence acceleration of iterative methods. In this method, a grid coarsening algorithm is required. Here, an agglomeration scheme is introduced, which is applicable in both cell-center and cell-vertex 2 and 3D discretizations. A new implicit formulation is presented, which results in better computation efficiency, when added to the multigrid scheme. A few simple procedures are also proposed and applied to provide even higher convergence acceleration. The Euler equations are solved on an unstructured grid around standard transonic configurations to validate the algorithm and to assess its superiority to conventional explicit agglomeration schemes. The scheme is applied to 2 and 3D test cases using both cell-center and cell-vertex discretizations. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Finite element modelling of free-surface flows with non-hydrostatic pressure and k,, turbulence model

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2005
C. Leupi
Abstract Validation of 3D finite element model for free-surface flow is conducted using a high quality and high spatial resolution data set. The commonly numerical models with the conventional hydrostatic pressure still remain the most widely used approach for the solution of practical engineering problems. However, when a 3D description of the velocity field is required, it is useful to resort to a more accurate model in which the hydrostatic assumption is removed. The present research finds its motivation in the increasing need for efficient management of geophysical flows such as estuaries (multiphase fluid flow) or natural rivers with the presence of short waves and/or strong bathymetry gradient, and/or strong channel curvature. A numerical solution is based on the unsteady Reynolds-averaged Navier,Stokes equations on the unstructured grid. The eddy viscosity is calculated from the efficient k,, turbulence model. The model uses implicit fractional step time stepping, and the characteristics method is used to compute the convection terms in the multi-layers system (suitable for the vertical stratified fluid flow), in which the vertical grid is located at predefined heights and the number of elements in the water column depends on water depth. The bottommost and topmost elements of variable height allow a faithful representation of the bed and the time-varying free-surface, respectively. The model is applied to the 3D open channel flows of various complexity, for which experimental data are available for comparison. Computations with and without non-hydrostatic are compared for the same trench to test the validity of the conventional hydrostatic pressure assumption. Good agreement is found between numerical computations and experiments. Copyright © 2005 John Wiley & Sons, Ltd. [source]

The direct simulation Monte Carlo method using unstructured adaptive mesh and its application

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2002
J.-S. Wu
Abstract The implementation of an adaptive mesh-embedding (h-refinement) scheme using unstructured grid in two-dimensional direct simulation Monte Carlo (DSMC) method is reported. In this technique, local isotropic refinement is used to introduce new mesh where the local cell Knudsen number is less than some preset value. This simple scheme, however, has several severe consequences affecting the performance of the DSMC method. Thus, we have applied a technique to remove the hanging node, by introducing the an-isotropic refinement in the interfacial cells between refined and non-refined cells. Not only does this remedy increase a negligible amount of work, but it also removes all the difficulties presented in the originals scheme. We have tested the proposed scheme for argon gas in a high-speed driven cavity flow. The results show an improved flow resolution as compared with that of un-adaptive mesh. Finally, we have used triangular adaptive mesh to compute a near-continuum gas flow, a hypersonic flow over a cylinder. The results show fairly good agreement with previous studies. In summary, the proposed simple mesh adaptation is very useful in computing rarefied gas flows, which involve both complicated geometry and highly non-uniform density variations throughout the flow field. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Implicit enthalpy formulation of phase-change problems on unstructured grid

Comparison of three second-order accurate reconstruction schemes for 2D Euler and Navier,Stokes compressible flows on unstructured grids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2001
N. P. C. Marques
Abstract This paper reports an intercomparison of three second-order accurate reconstruction schemes to predict 2D steady-state compressible Euler and Navier,Stokes flows on unstructured meshes. The schemes comprise one monotone slope limiter (Barth and Jespersen, A1AA Paper 89-0366, 1989) and two approximately monotone methods: the slope limiter due to Venkatakrishnan and a data-dependent weighting least-squares procedure (Gooch, Journal of Computational Physics, 1997; 133:6,17). In addition to the 1D scalar wave problem, comparisons were performed under two inviscid test cases: a supersonic 10° ramp and a supersonic bump; and two viscous laminar compressible flow cases: the Blasius boundary layer and a double-throated nozzle. The data-dependent oscillatory behaviour is found to be dependent on a user-supplied constant. The three schemes are compared in terms of accuracy and computational efficiency. The results show that the data-dependent procedure always returns a numerical steady-state solution, more accurate than the ones returned by the slope limiters. Its use for Navier,Stokes flow calculations is recommended. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Quasi optimal finite difference method for Helmholtz problem on unstructured grids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010
Daniel T. Fernandes
Abstract A quasi optimal finite difference method (QOFD) is proposed for the Helmholtz problem. The stencils' coefficients are obtained numerically by minimizing a least-squares functional of the local truncation error for plane wave solutions in any direction. In one dimension this approach leads to a nodally exact scheme, with no truncation error, for uniform or non-uniform meshes. In two dimensions, when applied to a uniform cartesian grid, a 9-point sixth-order scheme is derived with the same truncation error of the quasi-stabilized finite element method (QSFEM) introduced by Babu,ka et al. (Comp. Meth. Appl. Mech. Eng. 1995; 128:325,359). Similarly, a 27-point sixth-order stencil is derived in three dimensions. The QOFD formulation, proposed here, is naturally applied on uniform, non-uniform and unstructured meshes in any dimension. Numerical results are presented showing optimal rates of convergence and reduced pollution effects for large values of the wave number. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Higher-resolution convection schemes for flow in porous media on highly distorted unstructured grids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2008
Sadok Lamine
Abstract Higher-resolution schemes are presented for convective flow approximation on highly distorted unstructured grids. The schemes are coupled with continuous full-tensor Darcy-flux approximations. A sequence of non-uniform and distorted grid formulations are developed and compared for a range of unstructured meshes with variable grid spacing. The higher-order schemes are constructed using non-uniform grid slope limiters such that they are stable with a local maximum principle, ensuring that solutions are free of spurious oscillations. Benefits of the resulting schemes are demonstrated for classical test problems in reservoir simulation including cases with full-tensor permeability fields. The test cases involve a range of unstructured grids with variations in grid spacing, orientation and permeability that lead to flow fields that are poorly resolved by standard simulation methods. The higher-order formulations are shown to effectively reduce numerical diffusion, leading to improved resolution of concentration and saturation fronts. Copyright © 2008 John Wiley & Sons, Ltd. [source]

On the computation of steady-state compressible flows using a discontinuous Galerkin method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2008
Hong Luo
Abstract Computation of compressible steady-state flows using a high-order discontinuous Galerkin finite element method is presented in this paper. An accurate representation of the boundary normals based on the definition of the geometries is used for imposing solid wall boundary conditions for curved geometries. Particular attention is given to the impact and importance of slope limiters on the solution accuracy for flows with strong discontinuities. A physics-based shock detector is introduced to effectively make a distinction between a smooth extremum and a shock wave. A recently developed, fast, low-storage p -multigrid method is used for solving the governing compressible Euler equations to obtain steady-state solutions. The method is applied to compute a variety of compressible flow problems on unstructured grids. Numerical experiments for a wide range of flow conditions in both 2D and 3D configurations are presented to demonstrate the accuracy of the developed discontinuous Galerkin method for computing compressible steady-state flows. Copyright © 2007 John Wiley & Sons, Ltd. [source]

An element-wise, locally conservative Galerkin (LCG) method for solving diffusion and convection,diffusion problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2008
C. G. Thomas
Abstract An element-wise locally conservative Galerkin (LCG) method is employed to solve the conservation equations of diffusion and convection,diffusion. This approach allows the system of simultaneous equations to be solved over each element. Thus, the traditional assembly of elemental contributions into a global matrix system is avoided. This simplifies the calculation procedure over the standard global (continuous) Galerkin method, in addition to explicitly establishing element-wise flux conservation. In the LCG method, elements are treated as sub-domains with weakly imposed Neumann boundary conditions. The LCG method obtains a continuous and unique nodal solution from the surrounding element contributions via averaging. It is also shown in this paper that the proposed LCG method is identical to the standard global Galerkin (GG) method, at both steady and unsteady states, for an inside node. Thus, the method, has all the advantages of the standard GG method while explicitly conserving fluxes over each element. Several problems of diffusion and convection,diffusion are solved on both structured and unstructured grids to demonstrate the accuracy and robustness of the LCG method. Both linear and quadratic elements are used in the calculations. For convection-dominated problems, Petrov,Galerkin weighting and high-order characteristic-based temporal schemes have been implemented into the LCG formulation. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Voronoi cell finite difference method for the diffusion operator on arbitrary unstructured grids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2003
N. SukumarArticle first published online: 11 MAR 200
Abstract Voronoi cells and the notion of natural neighbours are used to develop a finite difference method for the diffusion operator on arbitrary unstructured grids. Natural neighbours are based on the Voronoi diagram, which partitions space into closest-point regions. The Sibson and the Laplace (non-Sibsonian) interpolants which are based on natural neighbours have shown promise within a Galerkin framework for the solution of partial differential equations. In this paper, we focus on the Laplace interpolant with a two-fold objective: first, to unify the previous developments related to the Laplace interpolant and to indicate its ties to some well-known numerical methods; and secondly to propose a Voronoi cell finite difference scheme for the diffusion operator on arbitrary unstructured grids. A conservation law in integral form is discretized on Voronoi cells to derive a finite difference scheme for the diffusion operator on irregular grids. The proposed scheme can also be viewed as a point collocation technique. A detailed study on consistency is conducted, and the satisfaction of the discrete maximum principle (stability) is established. Owing to symmetry of the Laplace weight, a symmetric positive-definite stiffness matrix is realized which permits the use of efficient linear solvers. On a regular (rectangular or hexagonal) grid, the difference scheme reduces to the classical finite difference method. Numerical examples for the Poisson equation with Dirichlet boundary conditions are presented to demonstrate the accuracy and convergence of the finite difference scheme. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Simulations of flow through fluid/porous layers by a characteristic-based method on unstructured grids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2001
Baili Zhang
Abstract An upwind characteristic-based finite volume method on unstructured grids is employed for numerical simulation of incompressible laminar flow and forced convection heat transfer in 2D channels containing simultaneously fluid layers and fluid-saturated porous layers. Hydrodynamic and heat transfer results are reported for two configurations: the first one is a backward-facing step channel with a porous block inserted behind the step, and the second one is a partially porous channel with discrete heat sources on the bottom wall. The effects of Darcy numbers on heat transfer augmentation and pressure loss were investigated for low Reynolds laminar flows. The results demonstrate the accuracy and robustness of the numerical scheme proposed, and suggest that partially porous insertion in a channel can significantly improve heat transfer performance with affordable pressure loss. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Multi-material incompressible flow simulation using the moment-of-fluid method,

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2010
Samuel P. Schofield
Abstract This paper compares the numerical performance of the moment-of-fluid (MOF) interface reconstruction technique with Youngs, LVIRA, power diagram (PD), and Swartz interface reconstruction techniques in the context of a volume-of-fluid (VOF) based finite element projection method for the numerical simulation of variable-density incompressible viscous flows. In pure advection tests with multiple materials MOF shows dramatic improvements in accuracy compared with the other methods. In incompressible flows where density differences determine the flow evolution, all the methods perform similarly for two material flows on structured grids. On unstructured grids, the second-order MOF, LVIRA, and Swartz methods perform similarly and show improvement over the first-order Youngs' and PD methods. For flow simulations with more than two materials, MOF shows increased accuracy in interface positions on coarse meshes. In most cases, the convergence and accuracy of the computed flow solution was not strongly affected by interface reconstruction method. Published in 2009 by John Wiley & Sons, Ltd. [source]

An accurate gradient and Hessian reconstruction method for cell-centered finite volume discretizations on general unstructured grids

Multigrid convergence acceleration for implicit and explicit solution of Euler equations on unstructured grids

Numerical simulation of a single bubble by compressible two-phase fluids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2010
Siegfried Müller
Abstract The present work deals with the numerical investigation of a collapsing bubble in a liquid,gas fluid, which is modeled as a single compressible medium. The medium is characterized by the stiffened gas law using different material parameters for the two phases. For the discretization of the stiffened gas model, the approach of Saurel and Abgrall is employed where the flow equations, here the Euler equations, for the conserved quantities are approximated by a finite volume scheme, and an upwind discretization is used for the non-conservative transport equations of the pressure law coefficients. The original first-order discretization is extended to higher order applying second-order ENO reconstruction to the primitive variables. The derivation of the non-conservative upwind discretization for the phase indicator, here the gas fraction, is presented for arbitrary unstructured grids. The efficiency of the numerical scheme is significantly improved by employing local grid adaptation. For this purpose, multiscale-based grid adaptation is used in combination with a multilevel time stepping strategy to avoid small time steps for coarse cells. The resulting numerical scheme is then applied to the numerical investigation of the 2-D axisymmetric collapse of a gas bubble in a free flow field and near to a rigid wall. The numerical investigation predicts physical features such as bubble collapse, bubble splitting and the formation of a liquid jet that can be observed in experiments with laser-induced cavitation bubbles. Opposite to the experiments, the computations reveal insight to the state inside the bubble clearly indicating that these features are caused by the acceleration of the gas due to shock wave focusing and reflection as well as wave interaction processes. While incompressible models have been used to provide useful predictions on the change of the bubble shape of a collapsing bubble near a solid boundary, we wish to study the effects of shock wave emissions into the ambient liquid on the bubble collapse, a phenomenon that may not be captured using an incompressible fluid model. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Developing implicit pressure-weighted upwinding scheme to calculate steady and unsteady flows on unstructured grids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2008
M. Darbandi
Abstract The finite-volume methods normally utilize either simple or complicated mathematical expressions to interpolate the fluxes at the cell faces of their unstructured volumes. Alternatively, we benefit from the advantages of both finite-volume and finite-element methods and estimate the advection terms on the cell faces using an inclusive pressure-weighted upwinding scheme extended on unstructured grids. The present pressure-based method treats the steady and unsteady flows on a collocated grid arrangement. However, to avoid a non-physical spurious pressure field pattern, two mass flux per volume expressions are derived at the cell interfaces. The dual advantages of using an unstructured-based discretization and a pressure-weighted upwinding scheme result in obtaining high accurate solutions with noticeable progress in the performance of the primitive method extended on the structured grids. The accuracy and performance of the extended formulations are demonstrated by solving different standard and benchmark problems. The results show that there are excellent agreements with both benchmark and analytical solutions as well as experimental data. Copyright © 2007 John Wiley & Sons, Ltd. [source]

High-order ENO and WENO schemes for unstructured grids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2007
W. R. Wolf
Abstract This work describes the implementation and analysis of high-order accurate schemes applied to high-speed flows on unstructured grids. The class of essentially non-oscillatory schemes (ENO), that includes weighted ENO schemes (WENO), is discussed in the paper with regard to the implementation of third- and fourth-order accurate methods. The entire reconstruction process of ENO and WENO schemes is described with emphasis on the stencil selection algorithms. The stencils can be composed by control volumes with any number of edges, e.g. triangles, quadrilaterals and hybrid meshes. In the paper, ENO and WENO schemes are implemented for the solution of the dimensionless, 2-D Euler equations in a cell centred finite volume context. High-order flux integration is achieved using Gaussian quadratures. An approximate Riemann solver is used to evaluate the fluxes on the interfaces of the control volumes and a TVD Runge,Kutta scheme provides the time integration of the equations. Such a coupling of all these numerical tools, together with the high-order interpolation of primitive variables provided by ENO and WENO schemes, leads to the desired order of accuracy expected in the solutions. An adaptive mesh refinement technique provides better resolution in regions with strong flowfield gradients. Results for high-speed flow simulations are presented with the objective of assessing the implemented capability. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Solution of the 2-D shallow water equations with source terms in surface elevation splitting form

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2007
Dong-Jun Ma
Abstract A vertex-centred finite-volume/finite-element method (FV/FEM) is developed for solving 2-D shallow water equations (SWEs) with source terms written in a surface elevation splitting form, which balances the flux gradients and source terms. The method is implemented on unstructured grids and the numerical scheme is based on a second-order MUSCL-like upwind Godunov FV discretization for inviscid fluxes and a classical Galerkin FE discretization for the viscous gradients and source terms. The main advantages are: (1) the discretization of SWE written in surface elevation splitting form satisfies the exact conservation property (,,-Property) naturally; (2) the simple centred-type discretization can be used for the source terms; (3) the method is suitable for both steady and unsteady shallow water problems; and (4) complex topography can be handled based on unstructured grids. The accuracy of the method was verified for both steady and unsteady problems, including discontinuous cases. The results indicate that the new method is accurate, simple, and robust. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Comparison of GMRES and ORTHOMIN for the black oil model on unstructured grids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2006
Wenjun Li
Abstract This paper addresses an application of ORTHOMIN and GMRES to petroleum reservoir simulation using the black oil model on unstructured grids. Comparisons between these two algorithms are presented in terms of storage and total flops per restart step. Numerical results indicate that GMRES is faster than ORTHOMIN for all tested petroleum reservoir problems, particularly for large scale problems. The control volume function approximation method is utilized in the discretization of the governing equations of the black oil model. This method can accurately approximate both the pressure and velocity in the simulation of multiphase flow in porous media, effectively reduce grid orientation effects, and be easily applied to arbitrarily shaped control volumes. It is particularly suitable for hybrid grid reservoir simulation. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Simulation of shallow flows over variable topographies using unstructured grids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2006
A. Mohammadian
Abstract Simulation of shallow flows over variable topographies is a challenging case for most available shock-capturing schemes. This problem arises because the source terms and flux gradients are not balanced in the numerical computations. Treatments for this problem generally work well on structured grids, but they are usually too expensive, and most of them are not directly applicable to unstructured grids. In this paper we propose two efficient methods to treat the source terms without upwinding and to satisfy the compatibility condition on unstructured grids. In the first method, the calculation of the bed slope source term is performed by employing a compatible approximation of water depth at the cell interfaces. In the second one, different components of the bed slope term are considered separately and a compatible discretization of the components is proposed. The present treatments are applicable for most schemes including the Roe's method without changing the performance of the original scheme for smooth topographies. Copyright © 2006 John Wiley & Sons, Ltd. [source]

LES of the compressed Taylor vortex flow using a finite volume/finite element method on unstructured grids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2006
C. Le Ribault
Abstract Large-eddy simulations (LES) have been performed of a compressed vortex flow undergoing transition to turbulence. The numerical method is based on a finite volume/finite element discretization of the compressible Navier,Stokes equations on unstructured grids and a Roe second-order scheme with MUSCL extrapolation. A particular attention is paid to the dissipative character of the method, controlled by a coefficient related to the upwind part of the numerical scheme, and its interference with the subgrid model. The accuracy of the method is first checked in the case of decaying homogeneous isotropic turbulence. The investigation is then directed to a plane Taylor vortex flow submitted to compression, in a direction perpendicular to the vorticity vector. This flow is unstable with respect to three-dimensional perturbations and transition to turbulence is observed if the Reynolds number is large enough. The numerical method is used to simulate this vortex flow for two values of the Reynolds number. For the lower value, the flow is unstable but remains laminar and no subgrid model is used. For the higher one, the turbulence appears and the standard and the dynamic Smagorinsky models are tested. The LES results are compared to those obtained by direct numerical simulations (DNS) using a spectral Fourier method. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Flux and source term discretization in two-dimensional shallow water models with porosity on unstructured grids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2006
Vincent Guinot
Abstract Two-dimensional shallow water models with porosity appear as an interesting path for the large-scale modelling of floodplains with urbanized areas. The porosity accounts for the reduction in storage and in the exchange sections due to the presence of buildings and other structures in the floodplain. The introduction of a porosity into the two-dimensional shallow water equations leads to modified expressions for the fluxes and source terms. An extra source term appears in the momentum equation. This paper presents a discretization of the modified fluxes using a modified HLL Riemann solver on unstructured grids. The source term arising from the gradients in the topography and in the porosity is treated in an upwind fashion so as to enhance the stability of the solution. The Riemann solver is tested against new analytical solutions with variable porosity. A new formulation is proposed for the macroscopic head loss in urban areas. An application example is presented, where the large scale model with porosity is compared to a refined flow model containing obstacles that represent a schematic urban area. The quality of the results illustrates the potential usefulness of porosity-based shallow water models for large scale floodplain simulations. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Coupling between shallow water and solute flow equations: analysis and management of source terms in 2D

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2005
J. Murillo
Abstract A two-dimensional model for the simulation of solute transport by convection and diffusion into shallow water flow over variable bottom is presented. It is based on a finite volume method over triangular unstructured grids. A first order upwind technique is applied to solve the flux terms in both the flow and solute equations and the bed slope source terms and a centred discretization is applied to the diffusion and friction terms. The convenience of considering the fully coupled system of equations is indicated and the methodology is well explained. Three options are suggested and compared in order to deal with the diffusion terms. Some comparisons are carried out in order to show the performance in terms of accuracy and computational effort of the different options. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Progressive optimization on unstructured grids using multigrid-aided finite-difference sensitivities

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10-11 2005
L. A. Catalano
Abstract This paper proposes an efficient and robust progressive-optimization procedure, employing cheap, flexible and easy-to-program multigrid-aided finite-differences for the computation of the sensitivity derivatives. The entire approach is combined with an upwind finite-volume method for the Euler and the Navier,Stokes equations on cell-vertex unstructured (triangular) grids, and validated versus the inverse design of an airfoil, under inviscid (subsonic and transonic) and laminar flow conditions. The methodology turns out to be robust and highly efficient, the converged design optimization being obtained in a computational time equal to that required by 11,17 (depending on the application) multigrid flow analyses on the finest grid. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Internal wave computations using the ghost fluid method on unstructured grids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2005
Sangmook Shin
Abstract Two-layer incompressible flows are analysed using the ghost fluid method on unstructured grids. Discontinuities in dynamic pressure along interfaces are captured in one cell without oscillations. Because of data reconstructions based on gradients, the ghost fluid method can be adopted without additional storages for the ghost nodes at the expense of modification in gradient calculations due to the discontinuity. The code is validated through comparisons with experimental and other numerical results. Good agreements are achieved for internal waves generated by a body moving at transcritical speeds including a case where upstream solitary internal waves propagate. The developed code is applied to analyse internal waves generated by a NACA0012 section moving near interfaces. Variations of the lift acting on the body and configurations of the interfaces are compared for various distances between the wing and the interface. The effects of the interface are compared with the effects of a solid wall. Copyright © 2004 John Wiley & Sons, Ltd. [source]