30 research outputs found

    An ELLAM Scheme for Multidimensional Advection-Reaction Equations and Its Optimal-Order Error Estimate

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    An Ellam Scheme for Advection-Diffusion Equations in Two Dimensions

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    We develop an Eulerian{Lagrangian localized adjoint method (ELLAM) to solve two-dimensional advection-diusion equations with all combinations of inflow and outflow Dirichlet, Neumann, and flux boundary conditions. The ELLAM formalism provides a systematic framework for implementation of general boundary conditions, leading to mass-conservative numerical schemes. The computational advantages of the ELLAM approximation have been demonstrated for a number of one-dimensional transport systems; practical implementations of ELLAM schemes in multiple spatial dimensions that require careful algorithm development are discussed in detail in this paper. Extensive numerical results are presented to compare the ELLAM scheme with many widely used numerical methods and to demonstrate the strength of the ELLAM scheme

    An ELLAM Scheme for Advection-Diffusion Equations in Two Dimensions

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    On the numerical solution of the three-dimensional advection-diffusion equation

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    A new approach is proposed for the numerical solution of three-dimensional advection-diffusion equations, which arise, among others, in air pollution modelling. The technique is based on directional operator splitting, which results in one-dimensional advection-diffusion equations. Then upstream-type difference approximations are applied for the first-order derivatives and non-standard difference approximations for the second-order derivatives. This approach leads to significant qualitative improvements in the behaviour of the numerical solutions

    Schnelle Löser für partielle Differentialgleichungen

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    The workshop Schnelle Löser für partielle Differentialgleichungen, organised by Randolph E. Bank (La Jolla), Wolfgang Hackbusch(Leipzig), Gabriel Wittum (Heidelberg) was held May 22nd - May 28th, 2005. This meeting was well attended by 47 participants with broad geographic representation from 9 countries and 3 continents. This workshop was a nice blend of researchers with various backgrounds

    An Explicit Characteristic-based Finite Volume-Element Method for Convection-Diffusion-Reaction Equation with Source Term

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    A second-order accurate characteristic-based finite volume method for analyzing time-dependent scalar convection-diffusion-reaction equation in two dimensions is presented. The concept of the characteristic-based scheme is applied to solve the convection-diffusion-reaction equation. The finite volume method is employed to establish the discretized equations for the spatial domain, while the weighted residuals finite element technique is used to estimate the gradient quantities at the cell faces and cell-centered of the control volume. Numerical test cases have shown that the method reduces spurious oscillations and does not require an explicit artificial diffusion for improving the solution stability. The efficiency, robustness and convergence order of the method are investigated by using available analytical and numerical solutions of pure convection, convection-diffusion and convection-diffusion-reaction problems
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