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Applications of operator-splitting methods to the direct numerical simulation of particulate and free-surface flows and to the numerical solution of the two-dimensional elliptic Monge-Ampère equation

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Abstract

The main goal of this article is to review some recent applications of operator-splitting methods. We will show that these methods are well-suited to the numerical solution of outstanding problems from various areas in Mechanics, Physics and Differential Geometry, such as the direct numerical simulation of particulate flow, free boundary problems with surface tension for incompressible viscous fluids, and the elliptic real Monge-Ampère equation. The results of numerical experiments will illustrate the capabilities of these methods.

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Authors and Affiliations

  1. Department of Mathematics, University of Houston, 77204, Houston, Texas, USA

    R. Glowinski, E. J. Dean, G. Guidoboni & T. -W. Pan

  2. Laboratoire Jacques-Louis Lions, University of Pierre et Marie Curie, Paris, France

    R. Glowinski

  3. Departamento de Matematicas, Universidad Autónoma Metropolitana-Iztapalapa, D.F. 09340, Iztapalapa, Mexico

    L. H. Juárez

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  1. R. Glowinski
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  2. E. J. Dean
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  3. G. Guidoboni
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  4. L. H. Juárez
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  5. T. -W. Pan
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Correspondence to R. Glowinski.

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Dedicated to J. Douglas, G.I. Marchuk, D.H. Peaceman and H.H. Rachford

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Glowinski, R., Dean, E.J., Guidoboni, G. et al. Applications of operator-splitting methods to the direct numerical simulation of particulate and free-surface flows and to the numerical solution of the two-dimensional elliptic Monge-Ampère equation. Japan J. Indust. Appl. Math. 25, 1 (2008). https://doi.org/10.1007/BF03167512

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  • DOI: https://doi.org/10.1007/BF03167512

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