Summary.
Particle methods are numerical methods designed to solve problems in fluid mechanics and related problems in continuum mechanics. A general approach to the construction of such particle methods is presented in this article. The particles are no mass points but possess a finite extension. They can rotate in space and have a spin. The conservation of mass is automatically guaranteed by the ansatz. The forces of interaction between the particles are derived in a canonical way from the force laws of continuum mechanics and are directly based on a regularized stress tensor. In the absence of external forces and of heat sources and sinks, momentum, angular momentum, and energy are conserved as in the continuum case.
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Received February 17, 1995 / Revised version received December 28, 1995
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Yserentant, H. A new class of particle methods . Numer. Math. 76, 87–109 (1997). https://doi.org/10.1007/s002110050255
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DOI: https://doi.org/10.1007/s002110050255