 Home  About us  Contact  # Conservation Laws (conservation + law)

Distribution by Scientific Domains
Distribution within Engineering

Kinds of Conservation Laws

 hyperbolic conservation law scalar conservation law

## Selected Abstracts

### Flow simulation on moving boundary-fitted grids and application to fluid,structure interaction problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2006
Martin Engel
Abstract We present a method for the parallel numerical simulation of transient three-dimensional fluid,structure interaction problems. Here, we consider the interaction of incompressible flow in the fluid domain and linear elastic deformation in the solid domain. The coupled problem is tackled by an approach based on the classical alternating Schwarz method with non-overlapping subdomains, the subproblems are solved alternatingly and the coupling conditions are realized via the exchange of boundary conditions. The elasticity problem is solved by a standard linear finite element method. A main issue is that the flow solver has to be able to handle time-dependent domains. To this end, we present a technique to solve the incompressible Navier,Stokes equation in three-dimensional domains with moving boundaries. This numerical method is a generalization of a finite volume discretization using curvilinear coordinates to time-dependent coordinate transformations. It corresponds to a discretization of the arbitrary Lagrangian,Eulerian formulation of the Navier,Stokes equations. Here the grid velocity is treated in such a way that the so-called Geometric Conservation Law is implicitly satisfied. Altogether, our approach results in a scheme which is an extension of the well-known MAC-method to a staggered mesh in moving boundary-fitted coordinates which uses grid-dependent velocity components as the primary variables. To validate our method, we present some numerical results which show that second-order convergence in space is obtained on moving grids. Finally, we give the results of a fully coupled fluid,structure interaction problem. It turns out that already a simple explicit coupling with one iteration of the Schwarz method, i.e. one solution of the fluid problem and one solution of the elasticity problem per time step, yields a convergent, simple, yet efficient overall method for fluid,structure interaction problems. Copyright © 2005 John Wiley & Sons, Ltd. [source]

### Adaptive grid based on geometric conservation law level set method for time dependent PDE

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2009
Ali R. Soheili
Abstract A new method for mesh generation is formulated based on the level set functions, which are solutions of the standard level set evolution equation with the Cartesian coordinates as initial values (Liao et al. J Comput Phys 159 (2000), 103,122; Osher and Sethian J Comput Phys 79 (1988), 12; Sethian, Level set methods and fast marching methods, Cambridge University Press, 1999; Di et al. J Sci Comput 31 (2007), 75,98). The intersection of the level contours of the evolving functions form a new grid at each time. The velocity vector in the evolution equation is chosen according to the Geometric Conservation Law (GCL) method (Cao et al., SIAM J Sci Comput 24 (2002), 118,142.). This method has precise control over the Jacobian of transformation because of using the GCL method. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source]

### Die Novelle der Energieeinsparverordnung EnEV 2007 , Chancen für die bessere Bewertung von Nichtwohngebäuden und Einführung von Energieausweisen

BAUPHYSIK, Issue 6 2006
Hans-Dieter Hegner Baudirektor Dipl.-Ing.
Die EG-Richtlinie 2002/91/EG über die Gesamtenergieeffizienz von Gebäuden war bis zum Januar 2006 in nationales Recht umzusetzen . Dazu will die Bundesregierung das Energieeinsparrecht (Energieeinspargesetz, Energieeinsparverordnung) umfassend novellieren. Der folgende Beitrag stellt den Stand der Überlegungen, insbesondere zu den technischen Möglichkeiten der Bewertung von Nichtwohngebäuden, dar. Das Zweite Gesetz zur Änderung des Energieeinspargesetzes  ist am 08. 09. 2005 in Kraft getreten. Der Referentenentwurf zu einer neuen weiterentwickelten Energieeinsparverordnung (EnEV 2007) wurde am 16. 11. 2006 durch die Bundesregierung vorgelegt . Ein Inkrafttreten dieser Verordnung ist wegen der Befassung von Bundeskabinett und Bundesrat voraussichtlich erst Mitte 2007 zu erwarten. Der folgende Beitrag gibt eine Übersicht zu den vorgesehenen neuen Anforderungen beim energiesparenden Bauen. Amendment of the German Building Energy Conservation Ordinance (Energieeinsparverordnung , EnEV 2007) Opportunities for better assessment of non-domestic buildings and introduction of Energy Passports. EU member states were required to implement the Energy Performance of Buildings Directive (2002/91/EC) in their respective national law by January 2006 . In this context the German Government proposed comprehensive amendments of the existing energy saving legislation (,Energieeinspargesetz' or Energy Conservation Law, ,Energieeinsparverordnung' or Building Energy Conservation Ordinance). This article describes the current status of the considerations, in particular with regard to technical assessment options for non-domestic buildings. The second amendment to the German Energy Conservation Law  came into force on 8 September 2005. The draft amendment of the Building Energy Conservation Ordinance (EnEV 2007) was presented by the German Government on 16 November 2006 . However, due to the time required for consideration by the Federal Cabinet and the upper house of the German parliament it is not expected to come into force before mid 2007. This article provides an overview of the proposed new requirements for energy saving in buildings. [source]

### Mechanism of the formation of singularities for quasilinear hyperbolic systems with linearly degenerate characteristic fields

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 2 2008
Ta-Tsien Li
Abstract One often believes that there is no shock formation for the Cauchy problem of quasilinear hyperbolic systems (of conservation laws) with linearly degenerate characteristic fields. It has been a conjecture for a long time (see Arch. Rational Mech. Anal. 2004; 172:65,91; Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables. Springer: New York, 1984) and it is still an open problem in the general situation up to now. In this paper, a framework to justify this conjecture is proposed, and, by means of the concept such as the strict block hyperbolicity, the part richness and the successively block-closed system, some general kinds of quasilinear hyperbolic systems, which verify the conjecture, are given. Copyright © 2007 John Wiley & Sons, Ltd. [source]

### Conservation laws for Lotka,Volterra models

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 17 2003
Rainer Schimming
Abstract We derive necessary and sufficient conditions on a Lotka,Volterra model to admit a conservation law of Volterra's type. The result and the proof for the corresponding linear algebra problem are given in graph-theoretical terms; they refer to the directed graph which is defined by the coefficients of the differential equation system. Copyright © 2003 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]

### Composite high resolution localized relaxation scheme based on upwinding for hyperbolic conservation laws

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2009
Ritesh Kumar Dubey
Abstract In this work we present an upwind-based high resolution scheme using flux limiters. Based on the direction of flow we choose the smoothness parameter in such a way that it leads to a truly upwind scheme without losing total variation diminishing (TVD) property for hyperbolic linear systems where characteristic values can be of either sign. Here we present and justify the choice of smoothness parameters. The numerical flux function of a high resolution scheme is constructed using wave speed splitting so that it results into a scheme that truly respects the physical hyperbolicity property. Bounds are given for limiter functions to satisfy TVD property. The proposed scheme is extended for non-linear problems by using the framework of relaxation system that converts a non-linear conservation law into a system of linear convection equations with a non-linear source term. The characteristic speed of relaxation system is chosen locally on three point stencil of grid. This obtained relaxation system is solved using composite scheme technique, i.e. using a combination of proposed scheme with the conservative non-standard finite difference scheme. Presented numerical results show higher resolution near discontinuity without introducing spurious oscillations. Copyright © 2008 John Wiley & Sons, Ltd. [source]

### On the geometric conservation law in transient flow calculations on deforming domains

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2006
Ch. Förster
Abstract This note revisits the derivation of the ALE form of the incompressible Navier,Stokes equations in order to retain insight into the nature of geometric conservation. It is shown that the flow equations can be written such that time derivatives of integrals over moving domains are avoided prior to discretization. The geometric conservation law is introduced into the equations and the resulting formulation is discretized in time and space without loss of stability and accuracy compared to the fixed grid version. There is no need for temporal averaging remaining. The formulation applies equally to different time integration schemes within a finite element context. Copyright © 2005 John Wiley & Sons, Ltd. [source]

### Generation of Arbitrary Lagrangian,Eulerian (ALE) velocities, based on monitor functions, for the solution of compressible fluid equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10-11 2005
B. V. Wells
Abstract A moving mesh method is outlined based on the use of monitor functions. The method is developed from a weak conservation principle. From this principle a conservation law for the mesh position is derived. Using the Helmholtz decomposition theorem, this conservation law can be converted into an elliptic equation for a mesh velocity potential. The moving mesh method is discretized using standard finite elements. Once the mesh velocities are obtained an arbitrary Lagrangian,Eulerian (ALE) (Journal of Computational Physics 1974; 14:227) fluid solver is used to update the solution on the adaptive mesh. Results are shown for the compressible Euler equations of gas dynamics in one and two spatial dimensions. Two monitor functions are used, the fluid density (which corresponds to a Lagrangian description), and a function which includes the density gradient. A variety of test problems are considered. Copyright © 2005 John Wiley & Sons, Ltd. [source]

### Weak formulation of boundary conditions for scalar conservation laws: an application to highway traffic modelling

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 16 2006
Issam S. Strub
Abstract This article proves the existence and uniqueness of a weak solution to a scalar conservation law on a bounded domain. A weak formulation of the boundary conditions is needed for the problem to be well posed. The existence of the solution results from the convergence of the Godunov scheme. This weak formulation is written explicitly in the context of a strictly concave flux function (relevant for highway traffic). The numerical scheme is then applied to a highway scenario with data from highway Interstate-80 obtained from the Berkeley Highway Laboratory. Finally, the existence of a minimiser of travel time is obtained, with the corresponding optimal boundary control. Copyright © 2006 John Wiley & Sons, Ltd. [source]

### Linear instability of ideal flows on a sphere

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 3 2009
Yuri N. Skiba
Abstract A unified approach to the normal mode instability study of steady solutions to the vorticity equation governing the motion of an ideal incompressible fluid on a rotating sphere is considered. The four types of well-known solutions are considered, namely, the Legendre-polynomial (LP) flows, Rossby,Haurwitz (RH) waves, Wu,Verkley (WV) waves and modons. A conservation law for disturbances to each solution is derived and used to obtain a necessary condition for its exponential instability. By these conditions, Fjörtoft's (Tellus 1953; 5:225,230) average spectral number of the amplitude of an unstable mode must be equal to a special value. In the case of LP flows or RH waves, this value is related only with the basic flow degree. For the WV waves and modons, it depends both on the basic flow degree and on the spectral distribution of the mode energy in the inner and outer regions of the flow. Peculiarities of the instability conditions for different types of modons are discussed. The new instability conditions specify the spectral structure of growing disturbances localizing them in the phase space. For the LP flows, this condition complements the well-known Rayleigh,Kuo and Fjörtoft conditions related to the zonal flow profile. Some analytical and numerical examples are considered. The maximum growth rate of unstable modes is also estimated, and the orthogonality of any unstable, decaying and non-stationary mode to the basic flow is shown in the energy inner product. The analytical instability results obtained here can also be applied for testing the accuracy of computational programs and algorithms used for the numerical stability study. It should be stressed that Fjörtoft's spectral number appearing both in the instability conditions and in the maximum growth rate estimates is the parameter of paramount importance in the linear instability problem of ideal flows on a sphere. Copyright © 2008 John Wiley & Sons, Ltd. [source]

### Conservation laws for Lotka,Volterra models

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 17 2003
Rainer Schimming
Abstract We derive necessary and sufficient conditions on a Lotka,Volterra model to admit a conservation law of Volterra's type. The result and the proof for the corresponding linear algebra problem are given in graph-theoretical terms; they refer to the directed graph which is defined by the coefficients of the differential equation system. Copyright © 2003 John Wiley & Sons, Ltd. [source]

### Conformal transformations and conformal invariance in gravitation

ANNALEN DER PHYSIK, Issue 1 2009
M.P. Da, browski
Abstract Conformal transformations are frequently used tools in order to study relations between various theories of gravity and Einstein's general relativity theory. In this paper we discuss the rules of these transformations for geometric quantities as well as for the matter energy-momentum tensor. We show the subtlety of the matter energy-momentum conservation law which refers to the fact that the conformal transformation "creates" an extra matter term composed of the conformal factor which enters the conservation law. In an extreme case of the flat original spacetime the matter is "created" due to work done by the conformal transformation to bend the spacetime which was originally flat. We discuss how to construct the conformally invariant gravity theories and also find the conformal transformation rules for the curvature invariants R2, RabRab, RabcdRabcd and the Gauss-Bonnet invariant in a spacetime of an arbitrary dimension. Finally, we present the conformal transformation rules in the fashion of the duality transformations of the superstring theory. In such a case the transitions between conformal frames reduce to a simple change of the sign of a redefined conformal factor. [source]

### A quantitative compactness estimate for scalar conservation laws

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 7 2005
Camillo de Lellis
In the case of a scalar conservation law with convex flux in space dimension one, P. D. Lax proved [Comm. Pure and Appl. Math.7 (1954)] that the semigroup defining the entropy solution is compact in L for each positive time. The present note gives an estimate of the ,-entropy in L of the set of entropy solutions at time t > 0 whose initial data run through a bounded set in L1. © 2005 Wiley Periodicals, Inc. [source]

### Numerical simulation of DNA sample preconcentration in microdevice electrophoresis

ELECTROPHORESIS, Issue 6 2005
Alok Srivastava
Abstract A numerical model is presented for the accurate and efficient prediction of preconcentration and transport of DNA during sample introduction and injection in microcapillary electrophoresis. The model incorporates conservation laws for the different buffer ions, salt ions, and DNA sample, coupled through a Gaussian electric field to account for the field modifications that cause electromigration. The accuracy and efficiency required to capture the physics associated with such a complex transient problem are realized by the use of the finite element-flux corrected transport (FE-FCT) algorithm in two dimensions. The model has been employed for the prediction of DNA sample preconcentration and transport during electrophoresis in a double-T injector microdevice. To test its validity, the numerical results have been compared with the corresponding experimental data under similar conditions, and excellent agreement has been found. Finally, detailed results from a simulation of DNA sample preconcentration in electrophoretic microdevices are presented using as parameters the electric field strength and the other species concentrations. The effect of the Tris concentration on sample stacking is also investigated. These results demonstrate the great potential offered by the model for future optimization of such microchip devices with respect to significantly enhanced speed and resolution of sample separation. [source]

### Computational physiology and the physiome project

EXPERIMENTAL PHYSIOLOGY, Issue 1 2004
Edmund J. Crampin
Bioengineering analyses of physiological systems use the computational solution of physical conservation laws on anatomically detailed geometric models to understand the physiological function of intact organs in terms of the properties and behaviour of the cells and tissues within the organ. By linking behaviour in a quantitative, mathematically defined sense across multiple scales of biological organization , from proteins to cells, tissues, organs and organ systems , these methods have the potential to link patient-specific knowledge at the two ends of these spatial scales. A genetic profile linked to cardiac ion channel mutations, for example, can be interpreted in relation to body surface ECG measurements via a mathematical model of the heart and torso, which includes the spatial distribution of cardiac ion channels throughout the myocardium and the individual kinetics for each of the approximately 50 types of ion channel, exchanger or pump known to be present in the heart. Similarly, linking molecular defects such as mutations of chloride ion channels in lung epithelial cells to the integrated function of the intact lung requires models that include the detailed anatomy of the lungs, the physics of air flow, blood flow and gas exchange, together with the large deformation mechanics of breathing. Organizing this large body of knowledge into a coherent framework for modelling requires the development of ontologies, markup languages for encoding models, and web-accessible distributed databases. In this article we review the state of the field at all the relevant levels, and the tools that are being developed to tackle such complexity. Integrative physiology is central to the interpretation of genomic and proteomic data, and is becoming a highly quantitative, computer-intensive discipline. [source]

### Conserving Galerkin weak formulations for computational fracture mechanics

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2002
Shaofan Li
Abstract In this paper, a notion of invariant Galerkin-variational weak forms is proposed. Two specific invariant variational weak forms, the J-invariant and the L-invariant, are constructed based on the corresponding conservation laws in elasticity, one of which is the conservation of Eshelby's energy-momentum (Eshelby. Philos. Trans. Roy. Soc. 1951; 87: 12; In Solid State Physics, Setitz F, Turnbull D (eds). Academic Press: New York, 1956; 331; Rice, J. Appl. Mech. 1968; 35: 379). It is shown that the finite element solution obtained from the invariant Galerkin weak formulations proposed here can conserve the value of J-integral, or L-integral exactly. In other words, the J and L integrals of the Galerkin finite element solutions are path independent in the discrete sense. It is argued that by using the J-invariant Galerkin weak form to compute near crack-tip field in an elastic solid, one may accurately calculate the crack extension energy release rate and subsequently the stress intensity factors in numerical computations, because the flux of the energy-momentum is conserved in discrete computations. This may provide an alternative means to accurately simulate crack growth and propagation. Copyright © 2002 John Wiley & Sons, Ltd. [source]

### Arbitrary discontinuities in space,time finite elements by level sets and X-FEM

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2004
Jack Chessa
Abstract An enriched finite element method with arbitrary discontinuities in space,time is presented. The discontinuities are treated by the extended finite element method (X-FEM), which uses a local partition of unity enrichment to introduce discontinuities along a moving hyper-surface which is described by level sets. A space,time weak form for conservation laws is developed where the Rankine,Hugoniot jump conditions are natural conditions of the weak form. The method is illustrated in the solution of first order hyperbolic equations and applied to linear first order wave and non-linear Burgers' equations. By capturing the discontinuity in time as well as space, results are improved over capturing the discontinuity in space alone and the method is remarkably accurate. Implications to standard semi-discretization X-FEM formulations are also discussed. Copyright © 2004 John Wiley & Sons, Ltd. [source]

### An objective finite element approximation of the kinematics of geometrically exact rods and its use in the formulation of an energy,momentum conserving scheme in dynamics

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2002
I. Romero
Abstract We present in this paper a new finite element formulation of geometrically exact rod models in the three-dimensional dynamic elastic range. The proposed formulation leads to an objective (or frame-indifferent under superposed rigid body motions) approximation of the strain measures of the rod involving finite rotations of the director frame, in contrast with some existing formulations. This goal is accomplished through a direct finite element interpolation of the director fields defining the motion of the rod's cross-section. Furthermore, the proposed framework allows the development of time-stepping algorithms that preserve the conservation laws of the underlying continuum Hamiltonian system. The conservation laws of linear and angular momenta are inherited by construction, leading to an improved approximation of the rod's dynamics. Several numerical simulations are presented illustrating these properties. Copyright © 2002 John Wiley & Sons, Ltd. [source]

### Shoreline tracking and implicit source terms for a well balanced inundation model

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2010
Giovanni FranchelloArticle first published online: 31 JUL 200
Abstract The HyFlux2 model has been developed to simulate severe inundation scenario due to dam break, flash flood and tsunami-wave run-up. The model solves the conservative form of the two-dimensional shallow water equations using the finite volume method. The interface flux is computed by a Flux Vector Splitting method for shallow water equations based on a Godunov-type approach. A second-order scheme is applied to the water surface level and velocity, providing results with high accuracy and assuring the balance between fluxes and sources also for complex bathymetry and topography. Physical models are included to deal with bottom steps and shorelines. The second-order scheme together with the shoreline-tracking method and the implicit source term treatment makes the model well balanced in respect to mass and momentum conservation laws, providing reliable and robust results. The developed model is validated in this paper with a 2D numerical test case and with the Okushiri tsunami run up problem. It is shown that the HyFlux2 model is able to model inundation problems, with a satisfactory prediction of the major flow characteristics such as water depth, water velocity, flood extent, and flood-wave arrival time. The results provided by the model are of great importance for the risk assessment and management. Copyright © 2009 John Wiley & Sons, Ltd. [source]

### An approximate-state Riemann solver for the two-dimensional shallow water equations with porosity

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2010
P. Finaud-Guyot
Abstract PorAS, a new approximate-state Riemann solver, is proposed for hyperbolic systems of conservation laws with source terms and porosity. The use of porosity enables a simple representation of urban floodplains by taking into account the global reduction in the exchange sections and storage. The introduction of the porosity coefficient induces modified expressions for the fluxes and source terms in the continuity and momentum equations. The solution is considered to be made of rarefaction waves and is determined using the Riemann invariants. To allow a direct computation of the flux through the computational cells interfaces, the Riemann invariants are expressed as functions of the flux vector. The application of the PorAS solver to the shallow water equations is presented and several computational examples are given for a comparison with the HLLC solver. Copyright © 2009 John Wiley & Sons, Ltd. [source]

### 1-D numerical modelling of shallow flows with variable horizontal density

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2010
Feifei Zhang Leighton
Abstract A1-D numerical model is presented for vertically homogeneous shallow flows with variable horizontal density. The governing equations represent depth-averaged mass and momentum conservation of a liquid,species mixture, and mass conservation of the species in the horizontal direction. Here, the term ,species' refers to material transported with the liquid flow. For example, when the species is taken to be suspended sediment, the model provides an idealized simulation of hyper-concentrated sediment-laden flows. The volumetric species concentration acts as an active scalar, allowing the species dynamics to modify the flow structure. A Godunov-type finite volume scheme is implemented to solve the conservation laws written in a deviatoric, hyperbolic form. The model is verified for variable-density flows, where analytical steady-state solutions are derived. The agreement between the numerical predictions and benchmark test solutions illustrates the ability of the model to capture rapidly varying flow features over uniform and non-uniform bed topography. A parameter study examines the effects of varying the initial density and depth in different regions. Copyright © 2009 John Wiley & Sons, Ltd. [source]

### Composite high resolution localized relaxation scheme based on upwinding for hyperbolic conservation laws

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2009
Ritesh Kumar Dubey
Abstract In this work we present an upwind-based high resolution scheme using flux limiters. Based on the direction of flow we choose the smoothness parameter in such a way that it leads to a truly upwind scheme without losing total variation diminishing (TVD) property for hyperbolic linear systems where characteristic values can be of either sign. Here we present and justify the choice of smoothness parameters. The numerical flux function of a high resolution scheme is constructed using wave speed splitting so that it results into a scheme that truly respects the physical hyperbolicity property. Bounds are given for limiter functions to satisfy TVD property. The proposed scheme is extended for non-linear problems by using the framework of relaxation system that converts a non-linear conservation law into a system of linear convection equations with a non-linear source term. The characteristic speed of relaxation system is chosen locally on three point stencil of grid. This obtained relaxation system is solved using composite scheme technique, i.e. using a combination of proposed scheme with the conservative non-standard finite difference scheme. Presented numerical results show higher resolution near discontinuity without introducing spurious oscillations. Copyright © 2008 John Wiley & Sons, Ltd. [source]

### A finite-volume particle method for conservation laws on moving domains

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2008
D. Teleaga
Abstract The paper deals with the finite-volume particle method (FVPM), a relatively new method for solving hyperbolic systems of conservation laws. A general formulation of the method for bounded and moving domains is presented. Furthermore, an approximation property of the reconstruction formula is proved. Then, based on a two-dimensional test problem posed on a moving domain, a special Ansatz for the movement of the particles is proposed. The obtained numerical results indicate that this method is well suited for such problems, and thus a first step to apply the FVPM to real industrial problems involving free boundaries or fluid,structure interaction is taken. Finally, we perform a numerical convergence study for a shock tube problem and a simple linear advection equation. Copyright © 2008 John Wiley & Sons, Ltd. [source]

### A further work on multi-phase two-fluid approach for compressible multi-phase flows

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2008
Yang-Yao Niu
Abstract This paper is to continue our previous work Niu (Int. J. Numer. Meth. Fluids 2001; 36:351,371) on solving a two-fluid model for compressible liquid,gas flows using the AUSMDV scheme. We first propose a pressure,velocity-based diffusion term originally derived from AUSMDV scheme Wada and Liou (SIAM J. Sci. Comput. 1997; 18(3):633,657) to enhance its robustness. The scheme can be applied to gas and liquid fluids universally. We then employ the stratified flow model Chang and Liou (J. Comput. Physics 2007; 225:240,873) for spatial discretization. By defining the fluids in different regions and introducing inter-phasic force on cell boundary, the stratified flow model allows the conservation laws to be applied on each phase, and therefore, it is able to capture fluid discontinuities, such as the fluid interfaces and shock waves, accurately. Several benchmark tests are studied, including the Ransom's Faucet problem, 1D air,water shock tube problems, 2D shock-water column and 2D shock-bubble interaction problems. The results indicate that the incorporation of the new dissipation into AUSM+ -up scheme and the stratified flow model is simple, accurate and robust enough for the compressible multi-phase flows. Copyright © 2008 John Wiley & Sons, Ltd. [source]

### A method of coupling non-linear hyperbolic systems: examples in CFD and plasma physics

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10-11 2005
E. Godlewski
Abstract This paper analyses a method of coupling systems of conservation laws with examples in two fluid flows. Copyright © 2005 John Wiley & Sons, Ltd. [source]

### Chebyshev super spectral viscosity solution of a two-dimensional fluidized-bed model

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2003
Scott A. SarraArticle first published online: 13 MAY 200
Abstract The numerical solution of a model describing a two-dimensional fluidized bed by a Chebyshev super spectral viscosity (SSV) method is considered. The model is in the form of a hyperbolic system of conservation laws with a source term, coupled with an elliptic equation for determining a stream function. The coupled elliptic equation is solved by a finite-difference method. The mixed SSV/finite-difference method produces physically shaped bubbles, on a very coarse grid. Fine scale details, which were not present in previous finite-difference solutions, are present in the solution. Copyright © 2003 John Wiley & Sons, Ltd. [source]

### Finite-element simulation of incompressible fluid flow in an elastic vessel

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2003
Harry Y. H. Chen
Abstract Finite-element simulation was performed to predict the incompressible Navier,Stokes flow in a domain, partly bounded by an elastic vessel, which is allowed to vary with time. Besides satisfying the physical conservation laws, both surface and the volume conservation laws are satisfied at the discrete level for ensuring the balance between physical and geometrical variables. Several problems which are amenable to analytical solutions were tested for validating the method. The simulated results are observed to agree favourably with analytical solutions. Having verified the applicability of the finite-element code to problems involving moving grids, we consider an incompressible fluid flow bounded by rigid and elastic vessel walls. Our emphasis was placed on the validation of the formulation developed within the moving-grid framework. Copyright © 2003 John Wiley & Sons, Ltd. [source]

### Simulation of shockwave propagation with a thermal lattice Boltzmann model

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2003
ShiDe Feng
Abstract A two-dimensional 19-velocity (D2Q19) lattice Boltzmann model which satisfies the conservation laws governing the macroscopic and microscopic mass, momentum and energy with local equilibrium distribution order O(u4) rather than the usual O(u3) has been developed. This model is applied to simulate the reflection of shockwaves on the surface of a triangular obstacle. Good qualitative agreement between the numerical predictions and experimental measurements is obtained. As the model contains the higher-order terms in the local equilibrium distribution, it performs much better in terms of numerical accuracy and stability than the earlier 13-velocity models with the local equilibrium distribution accurate only up to the second order in the velocity u. Copyright © 2003 John Wiley & Sons, Ltd. [source]

### Moving meshes, conservation laws and least squares equidistribution

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1-2 2002
M. J. Baines
Abstract In this paper a least squares measure of a residual is minimized to move an unstructured triangular mesh into an optimal position, both for the solution of steady systems of conservation laws and for functional approximation. The result minimizes a least squares measure of an equidistribution norm, which is a norm measuring the uniformity of a fluctuation monitor. The minimization is carried out using a steepest descent approach. Shocks are treated using a mesh with degenerate triangles. Results are shown for a steady-scalar advection problem and two flows governed by the Euler equations of gasdynamics. Copyright © 2002 John Wiley & Sons, Ltd. [source]