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77
A Tensorial Approach to Computational Continuum Mechanics using Object Orientated Techniques
, 1998
"... In this paper the principles of the FOAM C++ class library for continuum mechanics are outlined. The intention is to make it as easy as possible to develop reliable and efficient computational continuum mechanics (CCM) codes: this is achieved by making the top level syntax of the code as close as po ..."
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Cited by 60 (5 self)
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In this paper the principles of the FOAM C++ class library for continuum mechanics are outlined. The intention is to make it as easy as possible to develop reliable and efficient computational continuum mechanics (CCM) codes: this is achieved by making the top level syntax of the code as close as possible to conventional mathematical notation for tensors and partial differential equations. Object orientation techniques enable the creation of data types which closely mimic those of continuum mechanics, and the operator overloading possible in C++ allows normal mathematical symbols to be used for the basic operations. As an example, the implementation of various types of turbulence modelling in a FOAM computational uiddynamics (CFD) code is discussed, and calculations performed on a standard test case, that of flow around an square prism, are presented. To demonstrate the exibility of the FOAM library, codes for solving structures and magnetohydrodynamics are also presented w...
High Resolution NVD Differencing Scheme for Arbitrarily Unstructured Meshes
, 1998
"... The issue of boundedness in the discretisation of the convection term of transport equations has been widely discussed. A large number of local adjustment practices has been proposed, including the wellknown TVD and NVD families of differencing schemes. All of those use some sort of an "unboun ..."
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Cited by 21 (2 self)
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The issue of boundedness in the discretisation of the convection term of transport equations has been widely discussed. A large number of local adjustment practices has been proposed, including the wellknown TVD and NVD families of differencing schemes. All of those use some sort of an "unboundedness indicator" in order to determine the parts of the domain where intervention in the discretisation practice is needed. These, however, all use the "far upwind" value for each face under consideration, which is not appropriate for unstructured meshes. This paper proposes a modification of the NVD criterion which localises it and thus makes it applicable irrespective of the mesh structure, thus facilitating the implementation of "standard" bounded differencing schemes on unstructured meshes. Based on this strategy, a new bounded version of Central Differencing constructed on the compact computational molecule is proposed and its performance is compared with other popular differencing schemes...
Automatic Mesh Motion for the Unstructured Finite Volume Method
, 2004
"... Movingmesh unstructured Finite Volume Method (FVM) is a good candidate for tackling flow simulations where the shape of the domain changes during the simulation or represents a part of the solution. For efficient and userfriendly approach to the problem, it is necessary to automatically determine ..."
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Cited by 12 (4 self)
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Movingmesh unstructured Finite Volume Method (FVM) is a good candidate for tackling flow simulations where the shape of the domain changes during the simulation or represents a part of the solution. For efficient and userfriendly approach to the problem, it is necessary to automatically determine the point positions in the mesh, based on the prescribed boundary motion. In this paper, we present a vertexbased unstructured mesh motion solver designed to work with the movingmesh FVM. Motion is determined by solving the Laplace equation with variable diffusion on mesh points, using a tetrahedral decomposition of polyhedral cells. Cell decomposition and discretisation guarantees that an initially valid mesh remains geometrically valid for arbitrary boundary motion. Efficiency of the method is preserved by careful discretisation and the choice of iterative solvers, allowing the motion solver to efficiently couple with the FVM flow solver. This combination is tested on two free surface tracking flow simulations, including the simulation of freerising air bubbles in water.
Application of the Finite Volume Method and Unstructured Meshes to Linear Elasticity
, 1998
"... this paper the linear stress analysis problem is discretised using the practices usually associated with FVM in fluid flows. These include the secondorder accurate discretisation on Control Volumes of arbitrary polyhedral shape; segregated solution procedure, in which the displacement components ar ..."
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Cited by 10 (2 self)
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this paper the linear stress analysis problem is discretised using the practices usually associated with FVM in fluid flows. These include the secondorder accurate discretisation on Control Volumes of arbitrary polyhedral shape; segregated solution procedure, in which the displacement components are solved consecutively and iterative solvers for the systems of linear algebraic equations. Special attention is given to the optimisation of the discretisation practice in order to provide optimum convergence for the segregated solution procedure. The solver is set up to work efficiently on parallel distributed memory computer architectures, allowing a fast turnaround for the mesh sizes expected in an industrial environment. The methodology is validated on two test cases: stress concentration around a circular hole and transient wave propagation in a bar. Finally, the steady and transient stress analysis in a Diesel injector valve seat in 3D will be presented, together with the set of parallel speedup results.
Automatic Resolution Control for the Finite Volume Method. Part 1: Aposteriori Error Estimates
, 2000
"... Automatic Resolution Control for the Finite Volume Method (FVM) shows signs of rapid development in recent years. The objective of the procedure is to obtain a numerical solution of prescribed accuracy with minimum effort in terms of time and computational resources. It consists of two parts: an ap ..."
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Cited by 7 (3 self)
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Automatic Resolution Control for the Finite Volume Method (FVM) shows signs of rapid development in recent years. The objective of the procedure is to obtain a numerical solution of prescribed accuracy with minimum effort in terms of time and computational resources. It consists of two parts: an aposteriori error estimate and an appropriate modification of the spatial and temporal discretisation. In this paper, two new aposteriori error estimates concentrating on the absolute error levels are presented. The first, the Taylor Series Error Estimate, is based on Taylor series truncation error analysis and, unlike Richardson extrapolation, is capable of estimating the discretisation error from a single solution. In an attempt to overcome some deficiencies of the first method, the Moment Error Estimate is derived using the balance condition in the transport equation for the higher moments of the variable. It slightly overestimates the error, making it particularly useful in conjunction ...
OpenFOAM: A C++ Library for Complex Physics Simulations
 International Workshop on Coupled Methods in Numerical Dynamics, IUC
, 2007
"... Abstract. This paper describes the design of OpenFOAM, an objectoriented library for Computational Fluid Dynamics (CFD) and structural analysis. Efficient and flexible implementation of complex physical models in Continuum Mechanics is achieved by mimicking the form of partial differential equati ..."
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Cited by 7 (0 self)
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Abstract. This paper describes the design of OpenFOAM, an objectoriented library for Computational Fluid Dynamics (CFD) and structural analysis. Efficient and flexible implementation of complex physical models in Continuum Mechanics is achieved by mimicking the form of partial differential equation in software. The library provides Finite Volume and Finite Element discretisation in operator form and with polyhedral mesh support, with relevant auxiliary tools and support for massively parallel computing. Functionality of OpenFOAM is illustrated on three levels: improvements in linear solver technology with CGAMG solvers, LES data analysis using Proper Orthogonal Decomposition (POD) and a selfcontained fluidstructure interaction solver.
Residual Error Estimate for the Finite Volume Method
, 1999
"... Numerical simulation of fluid flows has received a wide acceptance in the industrial environment in recent years. If the results of simulations are to be used with confidence, it is necessary to provide a measure of their accuracy. The numerical accuracy of a simulation depends on the control of ..."
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Cited by 3 (0 self)
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Numerical simulation of fluid flows has received a wide acceptance in the industrial environment in recent years. If the results of simulations are to be used with confidence, it is necessary to provide a measure of their accuracy. The numerical accuracy of a simulation depends on the control of the discretisation error, introduced through the discretisation and numerical solution procedure. Our goal is to provide a measure of the discretisation error, which allows the user to control the overall quality of the simulation. In this paper, a novel aposteriori error estimate for the Finite Volume Method (FVM), measuring the absolute magnitude of the discretisation error, is presented. Unlike the more traditional truncation error estimates, the Residual Error Estimate is based on the cell residual, similar to the popular error estimates in the Finite Element community. An appropriate normalisation of the local residual creates the error estimate with the same dimensionality a...
ON THE RELEVANCE OF THE DAM BREAK PROBLEM IN THE CONTEXT OF NONLINEAR SHALLOW WATER EQUATIONS
, 2009
"... Abstract. The classical dam break problem has become the de facto standard in validating the nonlinear shallow water equations solvers. Moreover, the Nonlinear Shallow Water Equations (NSWE) are widely used for flooding simulations. While applied mathematics community is essentially focused on devel ..."
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Cited by 3 (2 self)
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Abstract. The classical dam break problem has become the de facto standard in validating the nonlinear shallow water equations solvers. Moreover, the Nonlinear Shallow Water Equations (NSWE) are widely used for flooding simulations. While applied mathematics community is essentially focused on developing new numerical schemes, we tried to examine the validity of the mathematical model under consideration. The main purpose of this study is to check the pertinence of the NSWE for flooding processes. From the mathematical point of view, the answer is not obvious since all derivation procedures assumes the total water depth positivity. We performed a comparison between the twofluid NavierStokes simulations and the NSWE solved analytically and numerically. Several conclusions are drawn out and perspectives for future research are outlined. 1. Introduction. During
Numerical Simulation of Local Scour with Free Surface and Automatic Mesh Deformation
"... A numerical model for local scour with free surface and automatic mesh deformation is constructed and numerical simulation is carried out to compare with experimental results. The k ɛ model is used to simulate the turbulent flow field. Two interfaces (water and air, water and sediment) in the domai ..."
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Cited by 2 (1 self)
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A numerical model for local scour with free surface and automatic mesh deformation is constructed and numerical simulation is carried out to compare with experimental results. The k ɛ model is used to simulate the turbulent flow field. Two interfaces (water and air, water and sediment) in the domain are captured with different approaches. The free surface of the flow is captured by Volume of Fluid (VOF) scheme which is a Eulerian approach. The watersediment interface (bed) is captured with moving mesh method which is a Lagrangian approach. The flow field is coupled with sediment transport using a quasisteady approach. Good results have been obtained using current model. The flow field is comparable with the experiment. Scour patterns are similar to the experimental data.
Numerical Models for Scour and Liquefaction Around Object Under Currents and Waves
, 2008
"... Local scour and liquefaction are two of the most important processes which affect the interactions between fluid, object and sediment when an object (such as bridge pier, offshore foundation, etc.) is exposed to currents and waves. In the present study, numerical models are developed to understand t ..."
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Cited by 1 (0 self)
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Local scour and liquefaction are two of the most important processes which affect the interactions between fluid, object and sediment when an object (such as bridge pier, offshore foundation, etc.) is exposed to currents and waves. In the present study, numerical models are developed to understand these complicated processes. For the local scour process, twodimensional and threedimensional models are developed respectively. In the twodimensional model, shallow water equations with finite volume method on unstructured mesh are used. The twodimensional model uses the Godunov scheme and approximate Riemann solvers. Hydrodynamics and sediment transport equations are coupled and solved simultaneously. Asymptotic analysis of the system eigenvalues is given and the approximation is compared with the numerical results. The model developed in this thesis can deal with wetting and drying automatically. Discontinuity of the flow, such as a hydraulic jump, can be captured. For the three dimensional model, free water surface and automatic mesh deformation for the bed are incorporated in the model. The Reynolds Averaged NavierStokes (RANS) turbulence model is used to simulate the turbulent flow field. The turbulence model used is k Model. Two interfaces