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Advection Problem (advection + problem)

Distribution by Scientific Domains

Engineering	75%

Selected Abstracts

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]

Short fibers suspension in steady recirculating flows

THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 3 2002
Francisco Chinesta
Abstract Numerical modeling of short fiber suspensions flows involves the coupling between motion equations, which definean elliptic problem, and the fluid constitutive equation, which introduces a non-linear advection problem related to the fiber orientation (induced anisotropy). In a previous work these authors have proposed a numerical procedure to determine a steady solution of the fibers orientation in steady recirculating flows, taking into account that neither initial nor boundary conditions are given. This procedure may be used in the numerical simulation of SFRT flows involving recirculating parts as encountered in the simulationof industrial processes, as well as in inverse rheological identification using, for example, rotative rheometric devices. La modélisation numérique des suspensions de fibres courtes implique le couplage entre les équations de mouvement (qui définissent un problème élliptique) et l'equation constitutive qui introduit un problème de transport non linéaire asocié à l'orientation des fibres. Les auteurs ont proposé, dans des travaux précédents, une technique numérique pour le calcul de l'orientation des fibres dans un écoulement stationnaire recirculant pour lequel les conditions aux limites et les conditions initiates ne sont pas connues. Cette technique peut être utilisée dans la simulation d'écoulements de fibres courtes présentant des recirculations, comme c'est le cas dans les écoulements industrielles en contraction ainsi que dans les instruments rhéométriques rotatifs. [source]

Exponential finite elements for diffusion,advection problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2005
Abbas El-Zein
Abstract A new finite element method for the solution of the diffusion,advection equation is proposed. The method uses non-isoparametric exponentially-varying interpolation functions, based on exact, one- and two-dimensional solutions of the Laplace-transformed differential equation. Two eight-noded elements are developed and tested for convergence, stability, Peclet number limit, anisotropy, material heterogeneity, Dirichlet and Neumann boundary conditions and tolerance for mesh distortions. Their performance is compared to that of conventional, eight- and 12-noded polynomial elements. The exponential element based on two-dimensional analytical solutions fails basic tests of convergence. The one based on one-dimensional solutions performs particularly well. It reduces by about 75% the number of elements and degrees of freedom required for convergence, yielding an error that is one order of magnitude smaller than that of the eight-noded polynomial element. The exponential element is stable and robust under relatively high degrees of heterogeneity, anisotropy and mesh distortions. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Numerical simulation of three-dimensional free surface flows

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2003
V. Maronnier
Abstract A numerical model is presented for the simulation of complex fluid flows with free surfaces in three space dimensions. The model described in Maronnier et al. (J. Comput. Phys. 1999; 155(2) : 439) is extended to three dimensional situations. The mathematical formulation of the model is similar to that of the volume of fluid (VOF) method, but the numerical procedures are different. A splitting method is used for the time discretization. At each time step, two advection problems,one for the predicted velocity field and the other for the volume fraction of liquid,are to be solved. Then, a generalized Stokes problem is solved and the velocity field is corrected. Two different grids are used for the space discretization. The two advection problems are solved on a fixed, structured grid made out of small cubic cells, using a forward characteristic method. The generalized Stokes problem is solved using continuous, piecewise linear stabilized finite elements on a fixed, unstructured mesh of tetrahedrons. The three-dimensional implementation is discussed. Efficient postprocessing algorithms enhance the quality of the numerical solution. A hierarchical data structure reduces memory requirements. Numerical results are presented for complex geometries arising in mold filling. Copyright © 2003 John Wiley & Sons, Ltd. [source]