Abstract The Poisson and Laplace equations arise in many engineering applications, such as the potential theory of hydrodynamics and electromagnetism. Also, in solving problems in incompressible flow, the pressure equation (Poisson equation) needs to be solved in updating the Navier–Stokes solver. In solid mechanics, the Poisson equation arises in the analysis of small transverse deflections of a tensed membrane subjected to a transverse load. If the membrane is replaced by a linearly elastic plate with bending stiffness, the transverse deflections must obey the inhomogeneous biharmonic equation. The biharmonic equation arises also in the analysis of two-dimensional elasticity problems formulated in terms of the Airy stress function. In the following sections, the solution of the above-mentioned equations by the lattice Boltzmann method (LBM) will be undertaken, and the results will be compared with available analytic solutions or with conventional numerical methods predictions.


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    Title :

    The Laplace, Poisson, and Biharmonic Equations


    Contributors:

    Published in:

    Edition :

    2nd ed. 2019


    Publication date :

    2019-01-01


    Size :

    6 pages




    Type of media :

    Article/Chapter (Book)


    Type of material :

    Electronic Resource


    Language :

    English