Chapter 14 Arbitrary Lagrangian-Eulerian Methods

The numerical simulation of multidimensional problems in fluid dynamics and nonlinear solid mechanics often requires coping with strong distortions of the continuum under consideration while allowing for a clear delineation of free surfaces and fluid–fluid, solid–solid, or fluid–structure interfaces. A fundamentally important consideration when developing a computer code for simulating problems in this class is the choice of an appropriate kinematical description of the continuum. In fact, such a choice determines the relationship between the deforming continuum and the finite grid or mesh of computing zones, and thus conditions the ability of the numerical method to deal with large distortions and provide an accurate resolution of material interfaces and mobile boundaries.

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